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Autonomic and metabolic effects of obstructive sleep apnea in childhood obesity
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Autonomic and metabolic effects of obstructive sleep apnea in childhood obesity
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Content
AUTONOMIC AND METABOLIC EFFECTS OF OBSTRUCTIVE SLEEP APNEA IN
CHILDHOOD OBESITY
by
Flavia Maria Guerra de Sousa Aranha Oliveira
____________________________________________
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHYLOSOPHY
(BIOMEDICAL ENGINEERING)
August 2011
Copyright 2011 Flavia Maria Guerra de Sousa Aranha Oliveira
ii
Dedication
I would like to dedicate this dissertation to my husband, Marcio. His willingness to
accompany me during my PhD studies at USC, his encouragement from the moment it
was just a distant dream to the final preparation of this dissertation, his never ending
support, motivation, love, and patience, and his passion for and dedication to knowledge
and research, were crucial for the success of this journey. Thank you with all my heart. I
wouldn't have made it without you.
I would also like to dedicate this work to my mother and father, Ivan and Fatima, whose
example of having pursued the same dream over 30 years ago, when they both completed
their own PhD studies at Ohio State University, and their own dedication to science and
research, certainly motivated me since childhood to study hard and love what you do.
Thank you for everything.
iii
Acknowledgements
This work would not have been possible without the help and support from many
wonderful and dedicated people. I would first like to deeply thank my advisor and
mentor, Dr. Michael C. K. Khoo. When I first typed in “Physiological Control Systems”
on google, while still in Brazil and starting to get to know the exciting field of biomedical
engineering, I discovered a book with these exact words in the title from this author
named Michael Khoo. When I bought the book and started going through its content, I
was hooked. This first contact with the biomedical engineering field, and with
physiological control systems modeling in particular, led me to look for financing
opportunities to US universities. After a long and tiring selection process, I was rewarded
with a Fulbright/CAPES scholarship to pursue my goal of a PhD in Biomedical
Engineering at the University of Southern California, at the Cardiorespiratory Sleep Lab,
under the guidance of Prof. Dr. Michael C. K. Khoo. From my first email contact during
the Fulbright/CAPES scholarship process, culminating with the development of this
dissertation, I am deeply indebted to Dr. Khoo for his constant guidance and support
through all the phases of research, for his vast experience and knowledge in the field of
biomedical engineering, for his passion for research and teaching, for the friendly and
enriching atmosphere at the Cardiorespiratory Sleep Lab at USC, and also for the
financial support during this period, without which I would not have been able to come to
USC. His dedication to his students and advisees is a lesson I will take with me
throughout my academic career.I hope this to be the beginning of a fruitful academic
cooperation for years to come, upon my return to the University of Brasilia.
iv
I would also like to thank our research group at Children’s Hospital Los Angeles
(CHLA). In particular, I would like to thank both Dr. Daniel Lesser and Dr. Rajeev
Bhatia, who were directly involved in patient recruiting and consenting and who also
participated in the execution of the research studies in each patient. Thank you for your
experience and friendship. I’m also grateful to Dr. Thomas Keens, Dr. Sally Ward, and
Dr. Steven Mittelman for their invaluable experience as senior research doctors in our
study and for the exciting knowledge exchange and valuable advices during our many
research meetings at CHLA. I would also like to thank the whole team at the General
Clinical Research Center (GCRC) at CHLA, for their expertise in performing the
FSIVGTT studies, as well as for their always great spirits and patience dealing with even
the most complicated situations during the studies. Thank you Zanmei Lopez, Regina
Olivas-Ho, Karen Reed, Susana Rivera, and Montre Koh.Great thanks to Ricardo Ortega,
Venita Polonio, and Wendy Haugen, our previous study coordinators, and Vanessa
Vasco, our current study coordinator. Great job in all the patient recruiting, consenting,
confirmation, rescheduling, etc.
A special thanks goes to Dr. Toke Hoppenbrouwers, with whom I initially worked with,
during my lab rotation periods at USC, studying data from Torajan babies she collected
herself. Her passion for SIDS research was inspiring. Working with her and her data in
my first couple of years at USC was a great experience for me.
I would also like to thank all of my professors at the Biomedical Engineering Department
at USC. Thank you for your classes and your time. Special thanks to Prof. Christopher
v
Walker, from the Department of Electrical Engineering, for your help in demystifying
Random Processes; Prof. Melissa Wilson, from the Department of Preventive Medicine,
for making me finally understand why, when, and how to apply statistical tests to analyze
biomedical data; and Prof. Vasilis Marmarelis, from the Department of Biomedical
Engineering, for all of your invaluable comments and suggestions to help me understand
the basis functions expansions modeling approach and how it can help in interpreting and
better understand the information contained in my dataset.
Thank you also Mischalgrace Diasanta, our Graduate Advisor, for all the permits to
register, signed forms, friendly reminders, and all kinds of advices along the way. Thank
you Mischal and Diana Sabogal for your experience and invaluable help organizing the
Grodins Graduate Research Symposium every year, as well as for your friendship. Thank
you also Marcos Briano, Sandra Johns, and Nareen Tamanaha, for all your aid and
support when I needed help dealing with administrative matters.
Thank you also to all the friends I made during classes, at the annual Grodins
symposiums, and BME get togethers. To avoid forgetting to list any one in particular, my
thanks goes to all of you for your friendship and encouragement. A special thanks to
Gabriela Mallen-Ornelas and Eric Persson. Since the day Gabriela came to say hello
during Viterbi’s international graduate student orientation, your friendship and great
company has made our time here even more unforgettable. Thank you for all your advice,
great restaurant choices, our opera and concert dates, as well as your love and support.
vi
Sorry for being so busy all the time, but I’m glad I could make it most of the time. I hope
this friendship will last a lifetime.
I would also like to thank Dr. David D'Argenio, Dr. Thomas Keens, and Dr. Sally Ward
for your time, instruction, and advice as members of my dissertation committee.
A very special thanks goes to all of my lab mates at the Cardiorespiratory Sleep Lab, at
the University of Southern California. Much thanks to Winton Tran, who preceded me in
this study and helped me get acquainted with all the equipment for the autonomic studies,
and also analyzed all the raw data from the IVGTT studies using Minmod. Thank you
also to Patjanaporn (Sang) Chalacheva, my “next door (cubical) neighbor” at the lab, for
your competent analysis of the raw autonomic data, as well as your tennis lessons! Thank
you Nestor as well for your tennis advice, great conversation, and always good humor.
Welcome to the lab! Thank you also Limei, Ming, and Wenli, my more “experienced’ lab
mates, for all of your great advice, patience, and understanding when I needed help with
either a computer problem, a statistical test, or a Matlab doubt. Thank you all for all our
lunch hours and great talks! I would also like to thank Adam and Jasmine for their
friendship. Welcome to the lab and I hope you enjoy your time there as much as I did.
Finally, this acknowledgment would not be complete if I didn’t mention my dear
brothers, Sergio and Ivan Junior, and their wives, Sandra and Anelise. Thank you for
your ever-present encouragement, motivation, and support.
vii
This work would not have been possible without the financial support from Fulbright,
from the CAPES scholarship program, from the Viterbi School of Engineering Graduate
Top-Off Fellowship, andfrom NIH Grants HL090451, EB001978, RR00047 and the USC
Center for Transdisciplinary Research on Energetics and Cancer (TREC U54 CA
116848).
viii
Table of Contents
Dedication..... ...................................................................................................................... ii
Acknowledgements ............................................................................................................ iii
List of Tables ..................................................................................................................... xi
List of Figures ................................................................................................................ xviii
Abbreviations .................................................................................................................. xxii
Abstract.......... .................................................................................................................. xxv
Chapter 1: Introduction ................................................................................................... 1
1.1. Motivation ............................................................................................................ 1
1.2. Specific aims ........................................................................................................ 2
1.3. Dissertation organization...................................................................................... 3
Chapter 2: Sleep parameters ........................................................................................... 6
2.1. Obstructive Sleep Apnea Syndrome .................................................................... 7
2.1.1. Sleep parameters ........................................................................................... 8
2.2. Obesity and sleep apnea ....................................................................................... 9
2.3. OSA, autonomic dysfunction, and cardiovascular disease ................................ 10
2.4. OSA and metabolic dysfunctions ....................................................................... 12
Chapter 3: Metabolic parameters .................................................................................. 16
3.1. Impaired glucose regulation, insulin resistance, and the metabolic
syndrome ....................................................................................................................... 17
3.1.1. Impaired fasting glucose (IFG) and impaired glucose tolerance
(IGT)...... .................................................................................................................... 17
3.1.2. Insulin resistance and the metabolic syndrome .......................................... 19
3.2. Insulin resistance and diabetes ........................................................................... 24
3.3. Measurement of insulin resistance ..................................................................... 25
3.3.1. Hyperinsulinemic euglycemic clamp .......................................................... 25
3.3.2. The HOMA index ....................................................................................... 26
3.3.3. OGTT test ................................................................................................... 28
3.3.4. Bergman’s minimal model of glucose kinetics (Minmod) and
metabolic parameters ................................................................................................ 29
3.4. Metabolic syndrome and autonomic nervous system dysfunction..................... 36
3.5. Sleep apnea, obesity, metabolic dysfunctions, autonomic imbalance, and
hypertension .................................................................................................................. 38
3.5.1. Hyperinsulinemia, increased sympathetic activation, baroreflex
impairment, and hypertension ................................................................................... 41
ix
Chapter 4: Cardiac autonomic nervous system: overview and measurement of
autonomic function ........................................................................................................... 44
4.1. Systemic hypertension, baroreflex sensitivity, and cardiovascular risks ........... 46
4.2. Autonomic nervous system ................................................................................ 48
4.2.1. Overview ..................................................................................................... 49
4.2.2. Autonomic testing ....................................................................................... 50
4.3. Frequency response ............................................................................................ 51
4.4. Transfer function analysis of heart rate variability ............................................ 56
4.5. Baroreflex sensitivity as a measurement of autonomic function ....................... 57
4.5.1. Assessment of baroreceptor sensitivity ....................................................... 60
4.6. Respiratory sinus arrhythmia as a measure of cardiac autonomic control ......... 62
4.6.1. Assessment of respiratory sinus arrhythmia ............................................... 63
4.7. The autonomic nervous system and metabolic and sleep disorders ................... 64
Chapter 5: Minimal cardiorespiratory model ............................................................... 66
5.1. Control systems approach to the analysis of cardiovascular variables .............. 67
5.2. The minimal model of cardiorespiratory control ............................................... 70
5.2.1. Autonomic parameters G
ABR
and G
RCC
....................................................... 74
5.3. Study protocol and instrumentation ................................................................... 76
5.3.1. Study protocol ............................................................................................. 76
5.3.2. Instrumentation ........................................................................................... 83
5.4. Autonomic compact descriptors ......................................................................... 87
5.5. Pulse transit time, PTT ....................................................................................... 89
Chapter 6: Identification of physiological systems ...................................................... 93
6.1. Mathematical dynamic equations of the minimal model of
cardiorespiratory control and impulse response estimation .......................................... 94
6.1.1. Impulse response estimation ....................................................................... 97
6.2. Mathematical modeling of dynamic systems ................................................... 102
6.2.1. Orthonormal basis functions (OBF).......................................................... 109
6.2.2. FIR model and Laguerre expansion of kernels ......................................... 112
6.3. Laguerre network derivation from state space representation ......................... 114
6.3.1. Laguerre Networks as a network of cascaded all-pass filters ................... 117
6.4. Model evaluation .............................................................................................. 120
Chapter 7: Volterra models and the Meixner expansion of kernels ........................... 122
7.1. Volterra models ................................................................................................ 123
7.1.1. Volterra kernels ......................................................................................... 124
7.2. Discrete-time Volterra models ......................................................................... 125
7.2.1. Kernel memory length M and system bandwidth B
s
................................. 126
7.2.2. Sampling time T ........................................................................................ 128
7.2.3. Model error and model complexity........................................................... 128
7.2.4. System order r ........................................................................................... 129
7.2.5. Model evaluation: use of information criteria .......................................... 130
x
7.2.6. Cross-correlation between residuals and input sequence .......................... 130
7.2.7. Estimation of Volterra kernels .................................................................. 131
7.3. Wiener kernels.................................................................................................. 132
7.4. Volterra kernel expansion approach ................................................................. 134
7.4.1. The Laguerre basis expansion ................................................................... 135
7.4.2. The Meixner basis expansion.................................................................... 136
Chapter 8: Statistical analysis ..................................................................................... 143
8.1. Multiple linear regression................................................................................. 143
8.2. Standardized regression coefficients ................................................................ 145
8.3. Partial correlations for autonomic and metabolic parameters, controlling
for adiposity and age ................................................................................................... 147
8.4. Significant F-test in the multiple linear regression .......................................... 151
Chapter 9: Results and discussion .............................................................................. 153
9.1. SBP vs. PTT as input to the ABR transfer function in the minimal model
of cardiorespiratory control ........................................................................................ 155
9.2. Autonomic reactivity to posture change: supine to standing ........................... 159
9.3. Correlations between sleep apnea and metabolic parameters .......................... 162
9.4. Correlations between sleep apnea and autonomic parameters ......................... 178
9.5. Correlations between autonomic and metabolic parameters ............................ 190
9.6. Multiple linear regression analysis ................................................................... 195
9.6.1. Baseline autonomic parameters, OSA, and metabolic function ............... 199
9.6.2. Autonomic parameters in the standing posture, OSA, and metabolic
function. .................................................................................................................. 204
9.6.3. Standing/supine ratio, sleep indices, and metabolic parameters ............... 218
9.7. Metabolic parameters as the dependent variable .............................................. 228
9.7.1. Baseline autonomic parameters, metabolic function, and OSA ............... 231
9.7.2. Autonomic parameters in the standing posture, metabolic function,
and OSA .................................................................................................................. 239
9.7.3. Stand/supine ratios, metabolic parameters, and OSA ............................... 247
9.8. Discussion ........................................................................................................ 258
9.8.1. SBP as input .............................................................................................. 258
9.8.2. Controlling for age and adiposity: summary ............................................ 260
9.8.3. Multiple linear regression model: summary ............................................. 265
9.8.4. PTT as input .............................................................................................. 270
9.9. Conclusion ........................................................................................................ 272
9.10. Future directions ............................................................................................... 275
Bibliography. .................................................................................................................. 277
xi
List of Tables
Table 1: Descriptive statistics of male subjects in study ................................................ 154
Table 2: Pearson’s correlation coefficient (r) and corresponding p-value between
the ABR and RCC autonomic parameters, determined in the supine posture, with
either SBP or PTT as input to the ABR transfer function............................................... 158
Table 3: Pearson’s correlation coefficient (r) and corresponding p-value between
the ABR and RCC autonomic parameters, determined in the standing posture,
with either SBP or PTT as input to the ABR transfer function. ..................................... 158
Table 4: Pearson’s correlation coefficient (r) and corresponding p-value between
the ABR and RCC autonomic parameters, determined as the ratio of the gain in
the standing posture to the gain in the supine posture, with either SBP or PTT as
input to the ABR transfer function.................................................................................. 158
Table 5: Pearson’s correlation coefficient (and corresponding p-value) between
the obesity measures considered in this study. ............................................................... 163
Table 6: Metabolic parameters for the subjects analyzed in this study .......................... 164
Table 7: Sleep parameters for the subjects analyzed in this study .................................. 165
Table 8: Studies for each subject .................................................................................... 166
Table 9: Partial correlation between key polysomnographic and metabolic
parameters (after adjustment for age and adiposity) ....................................................... 167
Table 10: Pearson’s product moment correlation between measures of insulin
resistance and sensitivity (HOMA, QUICKI, FGIR, S
I
), as well as IVGTT
parameters such as acute insulin response to glucose (AIRg), disposition index
(DI), and glucose effectiveness (Sg), and fasting glucose and insulin. .......................... 172
Table 11: Partial correlation between log(ABR
_HF_sup_PTT
) and log(Desat) (after
adjustment for age and adiposity) ................................................................................... 182
Table 12: Partial correlation between log(ABR
_HF_stand_PTT
)and total sleep time (in
minutes)(after adjustment for age and adiposity) ........................................................... 184
Table 13: Partial correlation coefficients and corresponding p-values for
correlations between log(G
RCC_stand/supine_SBP
) and log(TAI) as well as
log(G
RCC_stand/supine_SBP
) and TST, both controlling for age and adiposity. ...................... 186
xii
Table 14: Partial correlation coefficients and corresponding p-values for
correlations between log(G
RCC_stand/supine_SBP
) and log(TAI) as well as
log(G
RCC_stand/supine_SBP
) and TST, both controlling for age and adiposity. ...................... 189
Table 15: Results for the correlations log(G
ABR_stand_SBP
) and fasting glucose,
correcting for age and adiposity. ..................................................................................... 191
Table 16: Results for the correlations between sleep and the ratios standing/supine
of the autonomic parameters, controlling for age and adiposity. .................................... 192
Table 17: Multiple linear regression analysis (dependent variable Y =
G
ABR_sup_SBP
; independent variables: X
met
= fasting insulin, X
sleep
= REM (%TST),
X
age
, X
adip
) for the supine posture, showing that G
ABR_sup_SBP
is significantly
correlated with the sleep parameter for 3 of the 6 adiposity parameters considered
when also controlling for fasting insulin levels, age, and adiposity. .............................. 200
Table 18: Standardized and corresponding p-values for the multiple linear
regression analysis (dependent variable Y = G
ABR_sup_SBP
; independent variables:
X
met
= fasting insulin, X
sleep
= REM (%TST), X
age
, X
adip
) for the supine posture,
showing that G
ABR_sup_SBP
is significantly correlated with X
sleep
= REM (%TST) for
3 of the 6 adiposity parameters considered when also controlling for fasting
insulin levels, besides age and adiposity. The power of this multiple linear
regression is > 0.63 all adiposity measures related to a significant correlation. ............. 200
Table 19: Multiple linear regression analysis (dependent variable Y =
G
ABR_sup_SBP
; independent variables: X
met
= HOMA, X
sleep
= REM (%TST), X
age
,
X
adip
) for the supine posture, showing that G
ABR_sup_SBP
is significantly correlated
with the sleep parameter for 3 of the 6 adiposity parameters considered when also
controlling for HOMA levels, age, and adiposity. .......................................................... 201
Table 20: Standardized and corresponding p-values for the multiple linear
regression analysis (dependent variable Y = G
ABR_sup_SBP
; independent variables:
X
met
= HOMA, X
sleep
= REM (%TST), X
age
, X
adip
) for the supine posture, showing
that G
ABR_sup_SBP
is significantly correlated with X
sleep
= REM (%TST) for 3 of the
6 adiposity parameters considered when also controlling for HOMA levels,
besides age and adiposity. The power of this regression is > 0.68 and R
2
> 0.27 for
the significant correlations. ............................................................................................. 201
Table 21: Multiple linear regression analysis (dependent variable Y =
log(ABR
_HF_sup_PTT
); independent variables: X
met
= log(DI), X
sleep
= Efficiency (%),
X
age
, X
adip
) for the supine posture, showing that log(ABR
_HF_sup_PTT
) is significantly
correlated with the sleep parameter (except for total % body fat and trunk % fat),
when also controlling for log(DI) levels, age, and adiposity. The R
2
of this
multiple linear regression is > 0.29 for the significant correlations. .............................. 203
xiii
Table 22: Standardized and corresponding p-values for the multiple linear
regression analysis (dependent variable Y = log(ABR
_HF_sup_PTT
); independent
variables: X
met
= log(DI), X
sleep
= Efficiency (%), X
age
, X
adip
) for the supine
posture, showing that log(ABR
_HF_sup_PTT
) is significantly correlated with X
sleep
=
Efficiency (%) for 4 of the 6 adiposity parameters considered, when also
controlling for log(DI) levels, besides age and adiposity. .............................................. 204
Table 23: Standardized and associated p-values for the multiple linear
regressionfor log(G
ABR_stand_SBP
) and fasting glucose, considering the autonomic
parameter as the dependent variable (Y) and IVGTT, sleep, age, and adiposity as
the independent, or explanatory, variables (X
met
, X
sleep
, X
age
, and X
adip
),
respectively. The power of any of these tests is greater than 0.80, and R
2
> 0.42. ......... 206
Table 24: Multiple linear regression analysis for Y = log(G
RCC_stand_SBP
) as the
dependent variable and age, total sleep time, adiposity, and the listed metabolic
parameters as the independent variables. This shows that log(G
RCC_stand_SBP
) is
significantly correlated with total sleep time when the listed metabolic parameters
are added as independent variables, along with age and adiposity. ................................ 208
Table 25: Multiple linear regression analysis (dependent variable Y =
log(ABR
_HF_stand_PTT
); independent variables: X
met
= log(DI), X
sleep
= log(OAHI),
X
age
, X
adip
) for the supine posture, showing that log(ABR
_HF_stand_PTT
) is
significantly correlated with both the sleep parameter and the metabolic
parameter, for all adiposity measures. The power of this multiple linear regression
is > 0.90 and R
2
> 0.45 for any adiposity measure. ........................................................ 210
Table 26: Multiple linear regression analysis (dependent variable Y =
log(ABR
_HF_stand_PTT
); independent variables: X
met
= log(DI),X
sleep
=
log(OAHI),X
age
, X
adip
) for the supine posture, showing that log(ABR
_HF_stand_PTT
) is
significantly correlated with both the sleep parameter, log(OAHI), and the
metabolic parameter, log(DI), for all adiposity measures. The power of this
multiple linear regression is > 0.90 and R
2
> 0.45 for any adiposity measure. .............. 210
Table 27: Standardized and associated p-values for the multiple linear
regression for Y = log(ABR
_HF_stand_PTT
) as the dependent variable and age, X
sleep
= log(OAHI), adiposity, and the listed metabolic parameters X
met
as the
independent variables. Interpreted from a partial correlation perspective, this
appears to show that log(ABR
_HF_stand_PTT
) is significantly correlated with
log(OAHI) when controlling for age, adiposity, and all listed metabolic
parameters. ...................................................................................................................... 213
Table 27: Multiple linear regression analysis for Y = log(ABR
_HF_stand_PTT
) as the
dependent variable and age, X
sleep
= total sleep time (TST), adiposity, and the
listed metabolic parameters X
met
as independent variables. This shows that
xiv
log(ABR
_HF_stand_PTT
) is significantly correlated with TST even when the listed
metabolic parameters are added as independent variables, along with age and
adiposity, an indication that these X
met
are uncorrelated with X
sleep
= TST. ................... 217
Table 29: Multiple linear regression analysis (dependent variable Y =
log(G
ABR_stand/supine_SBP
); independent variables: X
met
= fasting glucose, X
sleep
=
sleep efficiency (%), X
age
, X
adip
) for the stand/supine ratio, showing that
log(G
ABR_stand/supine_SBP
) is significantly correlated with the sleep efficiency, when
also controlling for fasting glucose levels, age, and adiposity. The power of this
multiple linear regression is > 0.75 and R
2
> 0.30 for all adiposity measures. ............... 219
Table 30: Multiple linear regression analysis (dependent variable Y =
log(G
ABR_stand/supine_SBP
); independent variables: X
met
= fasting glucose, X
sleep
=
sleep efficiency (%), X
age
, X
adip
) for the G
ABR
stand/supine ratio, showing that
log(G
ABR_stand/supine_SBP
) is significantly correlated with X
met
= fasting glucose only
after considering X
sleep
= sleep efficiency (%), besides age and adiposity. .................... 219
Table 31: Multiple linear regression analysis (dependent variable Y
=log(G
RCC_stand/supine_SBP
); independent variables: X
met
= HOMA, X
sleep
=
log(OAHI), X
age
, X
adip
) for the G
RCC
stand/supine ratio, showing that
log(G
RCC_stand/supine_SBP
) is significantly correlated with the HOMA index, when
also controlling for age, adiposity, and OSA severity. measured by log(OAHI).
The power of this multiple linear regression is > 0.73 and R
2
> 0.28 all adiposity
measures related to a significant Y vs. X
met
correlation. ................................................. 221
Table 32: Multiple linear regression analysis (dependent variable Y =
log(G
RCC_stand/supine_SBP
);independent variables: X
met
= HOMA, X
sleep
=
log(OAHI),X
age
, X
adip
) for the stand/supine ratio, showing that
log(G
RCC_stand/supine_SBP
)is significantly correlated with X
met
= HOMA only after
considering OSA severity, measured by log(OAHI), besides age and adiposity.
The power of this multiple linear regression is > 0.73 and R
2
> 0.28 all adiposity
measures related to a significant Y vs. X
met
correlation. ................................................. 222
Table 33: Multiple linear regression analysis (dependent variable Y =
log(G
RCC_stand/supine_SBP
); independent variables: X
met
= HOMA, X
sleep
= REM (%
TST), X
age
, X
adip
) for the G
RCC
stand/supine ratio, showing that
log(G
RCC_stand/supine_SBP
) is significantly correlated with the HOMA, when also
controlling for age, adiposity, and REM (% TST). The power of this multiple
linear regression is > 0.72 and R
2
> 0.29 for all adiposity measures related to a
significant Y vs. X
met
correlation. .................................................................................... 223
Table 34: Multiple linear regression analysis (dependent variable Y =
log(G
RCC_stand/supine_SBP
); independent variables: X
met
= fasting insulin, X
sleep
= REM
( % TST), X
age
, X
adip
) for the G
RCC
stand/supine ratio, showing that
log(G
RCC_stand/supine_SBP
) is significantly correlated with fasting insulin, when also
xv
controlling for age, adiposity, and REM (% TST). The power of this multiple
linear regression is > 0.72 and R
2
> 0.29 for all adiposity measures related to a
significant Y vs. X
met
correlation. .................................................................................... 223
Table 35: Multiple linear regression analysis for Y = log(G
RCC_stand/supine_SBP
) as
the dependent variable and age, adiposity, X
sleep
= REM (% of total sleep time),
and X
met
= HOMA or fasting insulin as the independent variables. Interpreted
from a partial correlation perspective, this shows that log(G
RCC_stand/supine_SBP
) is
significantly correlated with both HOMA and fasting insulin levels (the latter only
for trunk fat and trunk % fat), when REM (% of total sleep time) is added as an
additional explanatory variable, along with age and adiposity (except for BMI and
BMI z-score). .................................................................................................................. 224
Table 36: Multiple linear regression analysis (dependent variable Y =
log(ABR
_HF_stand/supine_PTT
); independent variables: X
met
= log(DI), X
sleep
= Sleep
efficiency (%), X
age
, X
adip
) for the G
ABR
stand/supine ratio (PTT input), showing
that log(ABR
_HF_stand/supine_PTT
) is significantly correlated with X
met
= log(DI), when
also controlling for age, adiposity, and X
sleep
= Sleep efficiency (%). The power of
this multiple linear regression is > 0.71 and R
2
> 0.29 for all adiposity measures
related to a significant correlation................................................................................... 226
Table 37: Multiple linear regression analysis (dependent variable Y =
G
RCC_stand/supine_PTT
; independent variables: X
met
= log(DI), X
sleep
= TST, X
age
, X
adip
)
for the G
RCC
stand/supine ratio (PTT input), showing that G
RCC_stand/supine_PTT
is
significantly correlated with X
sleep
= TST, when also controlling for age, adiposity,
and X
met
. The results are similar for any metabolic parameter X
met
. The power of
this multiple linear regression is > 0.87 and R
2
> 0.36 for all adiposity measures
related to a significant correlation................................................................................... 228
Table 37: Multiple linear regression analysis (dependent variable Y
met
= fasting
insulin; independent variables: X
aut
= G
ABR_sup_SBP
, X
sleep
= REM (%TST), X
age
,
X
adip
) for the supine posture, showing that Y
met
= fasting insulin is not significantly
correlated with either X
sleep
or X
aut
. ................................................................................. 232
Table 38: Multiple linear regression analysis (dependent variable Y
met
= HOMA;
independent variables: X
aut
= G
ABR_sup_SBP
, X
sleep
= REM (%TST), X
age
, X
adip
) for
the supine posture, showing that HOMA is not significantly correlated with either
X
sleep
or X
aut
. .................................................................................................................... 233
Table 40: Multiple linear regression analysis (dependent variable Y
met
= log(DI);
independent variables: X
aut
= log(ABR
_HF_sup_PTT
), X
sleep
= Efficiency (%), X
age
,
X
adip
) for the supine posture. These results show that none of the explanatory
variables are significant for determining log(DI) for the multiple linear regression
equation above. ............................................................................................................... 234
xvi
Table 41: Multiple linear regression analysis (dependent variable Y
met
=
log(AIRg); independent variables: X
aut
= log(G
RCC_stand_SBP
), X
sleep
= TST, X
age
,
X
adip
). ............................................................................................................................... 241
Table 42: Multiple linear regression analysis (dependent variable Y
met
= log(DI);
independent variables: X
aut
= log(G
RCC_stand_SBP
), X
sleep
= TST, X
age
, X
adip
). ................... 241
Table 43: Multiple linear regression analysis (dependent variable Y
met
= Sg;
independent variables: X
aut
= log(G
RCC_stand_SBP
), X
sleep
= TST, X
age
, X
adip
). ................... 242
Table 44: Multiple linear regression analysis (dependent variable Y
met
= log(S
I
);
independent variables: X
aut
= log(ABR
_HF_stand_PTT
), X
sleep
= log(OAHI), X
age
, X
adip
).
......................................................................................................................................... 244
Table 45: Multiple linear regression analysis (dependent variable Y
met
= Sg;
independent variables: X
aut
= log(ABR
_HF_stand_PTT
), X
sleep
= log(OAHI), X
age
, X
adip
).
......................................................................................................................................... 244
Table 46: Multiple linear regression analysis (dependent variable Y
met
= fasting
insulin; independent variables: X
aut
= log(ABR
_HF_stand_PTT
), X
sleep
= log(OAHI),
X
age
, X
adip
). ....................................................................................................................... 244
Table 47: Multiple linear regression analysis (dependent variable Y
met
= HOMA;
independent variables: X
aut
= log(ABR
_HF_stand_PTT
), X
sleep
= log(OAHI), X
age
, X
adip
).
......................................................................................................................................... 245
Table 48: Multiple linear regression analysis (dependent variable Y
met
=
log(QUICKI); independent variables: X
aut
= log(ABR
_HF_stand_PTT
), X
sleep
=
log(OAHI), X
age
, X
adip
). ................................................................................................... 245
Table 49: Multiple linear regression analysis (dependent variable Y
met
=
log(FGIR); independent variables: X
aut
= log(ABR
_HF_stand_PTT
), X
sleep
=
log(OAHI), X
age
, X
adip
). ................................................................................................... 245
Table 50: Multiple linear regression analysis (dependent variable Y
met
= Fasting
Glucose; independent variables: X
aut
= log(G
ABR_stand/supine_SBP
), X
sleep
= Efficiency
(%), X
age
, X
adip
). The power of this multiple linear regression is > 0.79 and R
2
>
0.33 for all adiposity measures related to a significant Y vs. X
aut
correlation. ............... 248
Table 51: p-values for the multiple linear regression analysis (dependent variable
Y
met
= HOMA; independent variables: X
aut
= log(G
RCC_stand/supine_SBP
), X
sleep
=
log(OAHI), X
age
, X
adip
). The associated standardized -values for X
sleep
are also
displayed. The power of this multiple linear regression is > 0.87 and R
2
> 0.42 all
adiposity measures related to a significant correlation. .................................................. 251
xvii
Table 52: Multiple linear regression analysis (dependent variable Y
met
= HOMA;
independent variables: X
aut
= log(G
RCC_stand/supine_SBP
), X
sleep
= REM (% TST), X
age
,
X
adip
). The power of this multiple linear regression is > 0.81 and R
2
> 0.34 for all
adiposity measures related to a significant correlation. .................................................. 251
Table 53: Multiple linear regression analysis (dependent variable Y
met
= Fasting
Insulin; independent variables: X
aut
= log(G
RCC_stand/supine_SBP
), X
sleep
= log(OAHI),
X
age
, X
adip
). The associated standardized -values for X
sleep
are also displayed. The
power of this multiple linear regression is > 0.88 and R
2
> 0.39 for all adiposity
measures related to a significant correlation. .................................................................. 251
Table 54: Multiple linear regression analysis (dependent variable Y
met
= Fasting
Insulin; independent variables: X
aut
= log(G
RCC_stand/supine_SBP
), X
sleep
= REM (%
TST), X
age
, X
adip
). The power of this multiple linear regression is > 0.82 and R
2
>
0.34 for all adiposity measures related to a significant correlation. ............................... 252
Table 55: Multiple linear regression analysis (dependent variable Y
met
= log(DI);
independent variables: X
aut
= G
RCC_stand/supine_PTT
, X
sleep
= TST, X
age
, X
adip
). The
power of this multiple linear regression is > 0.75 and R
2
> 0.31 all adiposity
measures related to a significant correlation. .................................................................. 255
Table 56: Multiple linear regression analysis (dependent variable Y
met
= log(DI);
independent variables: X
aut
= log(ABR
HF_stand/supine_PTT
), X
sleep
= Sleep efficiency
(%), X
age
, X
adip
). The power of this multiple linear regression is > 0.75 and R
2
>
0.31 for all adiposity measures related to a significant correlation. ............................... 256
Table 57: Multiple linear regression analysis (dependent variable Y
met
= log(S
I
);
independent variables: X
aut
= log(ABR
_HF_stand/supine_PTT
), X
sleep
= log(Desat), X
age
,
X
adip
). ............................................................................................................................... 258
Table 58: Pearson’s correlation coefficient (and corresponding p-value) between
the sleep architecture and OSA measures considered in this study. ............................... 262
xviii
List of Figures
Figure 1: Mean and standard error for insulin-mediated glucose uptake (Rd)
(glucose-clamp method) in subjects with normal glucose tolerance, the control
group, and in those with impaired glucose tolerance (IGT) and non-insulin
dependent diabetes mellitus (NIDDM). The latter two groups differed
significantly from the control group (p < 0.001). From (Golay, et al., 1986). ................. 20
Figure 2: Insulin-mediated glucose uptake (Rd) - glucose clamp method vs.
fasting plasma glucose in subjects with normal glucose tolerance ( ), IGT (o), or
NIDDM (*). These data are from the same subjects as in Figure 1. From (Golay,
et al., 1986). ...................................................................................................................... 20
Figure 3: Mean and standard error values for glucose uptake (M) during glucose
clamp studies in 100 non-obese subjects with normal oral glucose tolerance.
From: (Hollenbeck, et al., 1987) ....................................................................................... 21
Figure 4: Plasma glucose and insulin responses to OGTT in the four quartiles seen
in Figure 3 (1
st
, ; 2
nd
,; 3
rd
,Δ; 4
th
, o). From: (Hollenbeck, et al., 1987) ....................... 22
Figure 5: Glucose (blue dots) and insulin (green dots) data from the FSIVGTT
protocol and the Minmod fit (red line) for glucose dynamics. The time course of
the glucose and insulin measurements is used by the model to estimate the
aforementioned metabolic parameters. ............................................................................. 32
Figure 6: Hypothesis to explain mechanism relating obesity to hypertension,
proposed by Landsberg (adapted from (Landsberg, 1986)).............................................. 40
Figure 7: Baroreceptor control loops, adapted from (Batzel, et al., 2006).P
ra
: right
arterial pressure. ................................................................................................................ 59
Figure 8: Schematic representation of the principal physiological mechanisms
contributing to heart rate variability and blood pressure variability (Khoo, 2008). ......... 70
Figure 9: Closed-loop minimal model of cardiorespiratory control (from
Belozeroff et al., 2002). .................................................................................................... 71
Figure 10: Subset (2-input 1-output) of the minimal cardiorespiratory model. ................ 73
Figure 11: Closed loop minimal model of cardiorespiratory control. The subset
indicated by the dashed line corresponds to the subset of the model considered in
the current study.The dynamics of respiratory cardiac-coupling are represented by
the impulse response function h
RCC
(t), while the arterial baroreflex dynamics are
represented by the impulse response function h
ABR
(t). ...................................................... 75
xix
Figure 12: Experimental setup for autonomic study ......................................................... 77
Figure 13: FIR filter representation ................................................................................ 113
Figure 14: A more general OBF function ....................................................................... 114
Figure 15: Cascade all-pass filter network. The H
i
(z) form orthonormal basis
functions. ......................................................................................................................... 118
Figure 16: The cascaded filter network to generate the Laguerre (dashed box) and
Meixner basis functions. ................................................................................................. 119
Figure 17: First 5 Laguerre basis functions (order i = 0 to order i = 4) for a
2
=
0.25, 0.5, and 0.7, respectively. ...................................................................................... 136
Figure 18: First 5 Meixner basis functions (order i = 0 to order i = 4) for decay
parameter a
2
= 0.25 and order of generalization n = 2, 4, and 8, respectively. .............. 137
Figure 19: G
RCC
supine vs. standing, determined using either (a) SBP or (b) PTT. ....... 160
Figure 20: G
ABR
supine vs. standing, determined using either (a) SBP or (b) PTT
as input. ........................................................................................................................... 162
Figure 21: Linear regression between log10(SI) and log10(desaturation index),
controlling for age and adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.21,
partial correlation coefficient = 0.46, partial p-value = 0.043, = 0.59, =
0.23, standardized
sleep
= 0.50, standardized
adiposity
= 0.099, standardized
age
= 0.022. .................................................................................................................. 168
Figure 22: Linear regression between Glucose Effectiveness (Sg) and Sleep
Efficiency (%), controlling for age and adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.21, partial correlation coefficient = 0.45, partial p-value = 0.044, =-
0.013, = 0.00040, standardized
sleep
= 0.46, standardized
adiposity
= -0.089,
standardized
age
= -0.071. .............................................................................................. 170
Figure 23: Linear regression between Fasting Insulin and Total Arousal Index
(TAI), controlling for age and adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
)=
0.28, partial correlation coefficient = 0.53, partial p-value = 0.016, = 0.31, =
0.73, standardized
sleep
= 0.55, standardized
adiposity
= 0.0066, standardized
age
=
0.044................................................................................................................................ 171
Figure 24: Linear regression between HOMA and Total Arousal Index (TAI),
controlling for age and adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.27,
partial correlation coefficient = 0.52, partial p-value = 0.019, = -0.39, = 0.75,
xx
standardized
sleep
= 0.53, standardized
adiposity
= 0.0049, standardized
age
=
0.058................................................................................................................................ 173
Figure 25: Linear regression between QUICKI and Total Arousal Index (TAI),
controlling for age and adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.28,
partial correlation coefficient = 0.53, partial p-value = 0.012, = -0.72, = -0.12,
standardized
sleep
= -0.53, standardized
adiposity
= 0.00069, standardized
age
=
0.084................................................................................................................................ 174
Figure 26: Linear regression between FGIR and Total Arousal Index (TAI),
controlling for age and adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.30,
partial correlation coefficient = -0.54, partial p-value = 0.013, = 1.59, = -0.70,
standardized
sleep
= -0.56, standardized
adiposity
= -0.0085, standardized
age
= -
0.027................................................................................................................................ 174
Figure 27: A high stand/supine ratio (e.g. a high G
ABR
and/or G
RCC
ratios) means a
smaller autonomic reactivity to postural change, an indication of autonomic
impairment, while a low stand/supine ratio is an indication of a higher autonomic
reactivity to postural change. .......................................................................................... 180
Figure 28: Linear regression between log(ABR
_HF_sup_PTT
) and log(Desat),
controlling for age and adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.16,
partial correlation coefficient = -0.40, partial p-value = 0.046, = -0.25, = -
0.32, standardized
sleep
= -0.43, standardized
adiposity
= 0.10, standardized
age
=
0.0034.............................................................................................................................. 182
Figure 29: Linear regression between log(ABR
_HF_stand_PTT
) and total sleep time
(in minutes), controlling for age and adiposity (total percent body fat). R
2
(Y
adj
vs.
X
adj
) = 0.21, partial correlation coefficient = 0.46, partial p-value = 0.017, = -
1.18, = 0.0019, standardized
sleep
= 0.45, standardized
adiposity
= -0.21,
standardized
age
= -0.22. ................................................................................................ 184
Figure 30: Linear regression between log(G
RCC_stand/supine_SBP
) and total arousal
index (TAI), controlling for age and adiposity (total percent body fat). R
2
(Y
adj
vs.
X
adj
)= 0.21, partial correlation coefficient = 0.46, partial p-value = 0.017, = -
1.09, = 0.61, standardized
sleep
= 0.45, standardized
adiposity
= -0.31,
standardized
age
= -0.36. ................................................................................................ 187
Figure 31: Linear regression between log(G
RCC_stand/supine_SBP
) and total sleep time
(TST), controlling for age and adiposity (total percent body fat). R
2
(Y
adj
vs.
X
adj
)= 0.20, partial correlation coefficient = -0.45, partial p-value = 0.021, =
0.16, = 0.0021, standardized
sleep
= -0.44, standardized
adiposity
= -0.16,
standardized
age
= -0.29. ................................................................................................ 187
xxi
Figure 32: Linear regression between log(G
RCC_stand/supine_PTT
) and total arousal
index (TAI), controlling for age and adiposity (total % body fat). R
2
(Yadj vs.
Xadj) = 0.14, partial correlation coefficient = 0.38, partial p-value = 0.055, = -
0.90, = 0.40, standardized
sleep
= 0.38, standardized
adiposity
= -0.29,
standardized
age
= -0.29. ................................................................................................ 189
Figure 33: Linear regression between log(G
RCC_stand/supine_PTT
) and total sleep time
(TST), controlling for age and adiposity (total % body fat). R
2
(Yadj vs. Xadj) =
0.15, partial correlation coefficient = -0.39, partial p-value = 0.050, = -0.053,
= -0.0014, standardized
sleep
= -0.38, standardized
adiposity
= -0.16, standardized
age
= -0.24. ..................................................................................................................... 190
Figure 34: Linear regression between log(G
RCC_stand/supine_SBP
) and HOMA,
controlling for age and adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
) = 0.14,
partial correlation coefficient = 0.37, partial p-value = 0.11, = -0.71, = 0.074,
standardized
metab
= 0.37, standardized
adiposity
= -0.21, standardized
age
= -0.25. ..... 193
Figure 35: Linear regression between log(G
ABR_stand/supine_SBP
) and fasting glucose,
controlling for age and adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
) = 0.19,
partial correlation coefficient = 0.43, partial p-value = 0.056, = -1.72, = 0.021,
standardized
metab
= 0.44, standardized
adiposity
= -0.17, standardized
age
= -0.39. ..... 194
Figure 36: Hypotheses for different pathways that could be involved in the
association among sleep apnea, autonomic dysfunction, and metabolic imbalance. ...... 229
Figure 37: Diagram showing the associations found in the present group of
subjects ............................................................................................................................ 259
Figure 38: Diagram showing the associations found in our present group of
subjects ............................................................................................................................ 270
xxii
Abbreviations
ABR Arterial baroreflex
AIRg Acute insulin response to glucose
BMI Body mass index
CHD Coronary heart disease
CID Circulatory dynamics
DER Direct effects of respiration transfer function
DEXA scan Dual energy X-ray absorptiometry scan
DI Disposition index
FSIVGTT Frequently sampled intravenous glucose tolerance test
G
ABR
Baroreflex gain
G
ABR_std
Baroreflex gain determined in the standing posture
G
ABR_std/sup_PTT
G
ABR_std_PTT
/ G
ABR_sup_PTT
G
ABR_std/sup_SBP
G
ABR_std_SBP
/ G
ABR_sup_SBP
G
ABR_std_PTT
Standing baroreflex gain determined using PTT as input to the ABR transfer
function
G
ABR_std_SBP
Standing baroreflex gain determined using PTT as input to the ABR transfer
function
G
ABR_sup
Baroreflex gain determined in the supine posture
G
ABR_sup_PTT
Supine baroreflex gain determined using PTT as input to the ABR transfer
function
G
ABR_sup_SBP
Supine baroreflex gain determined using SBP as input to the ABR transfer
function
G
RCC
Respiratory cardiac coupling gain
G
RCC_std
Respiratory cardiac coupling gain determined in the standing posture
xxiii
G
RCC_std/sup_PTT
G
RCC_std_PTT
/ G
RCC_sup_PTT
G
RCC_std/sup_SBP
G
RCC_std_SBP
/ G
RCC_sup_SBP
G
RCC_std_PTT
Standing respiratory cardiac coupling gain determined using PTT as input to the
ABR transfer function
G
RCC_std_SBP
Standing respiratory cardiac coupling gain determined using SBP as input to the
ABR transfer function
G
RCC_sup
Respiratory cardiac coupling gain determined in the supine posture
G
RCC_sup_PTT
Supine respiratory cardiac coupling gain determined using PTT as input to the
ABR transfer function
G
RCC_sup_SBP
Supine respiratory cardiac coupling gain determined using SBP as input to the
ABR transfer function
H
ABR
Arterial baroreflex transfer function
h
ABR
Arterial baroreflex impulse response
H
CID
Circulatory dynamics transfer function
H
DER
Direct effects of respiration transfer function
HF High frequency
HOMA Homeostasis model assessment of insulin resistance
H
RCC
Respiratory cardiac coupling transfer function
h
RCC
Respiratory cardiac coupling impulse response
HRV Heart rate variability
IGT Impaired glucose tolerance
IVGTT Intra-venous glucose tolerance test
LF Low frequency
NIDDM Non-insulin-dependent diabetes mellitus
NREM Non-rapid eye movement
OAHI Obstructive apnea-hypopnea index
xxiv
OGTT Oral glucose tolerance test
OSA Obstructive sleep apnea
OSAS Obstructive sleep apnea syndrome
PEP Pre-ejection period
PTT Pulse transit time
RCC Respiratory cardiac coupling
REM Rapid eye movement
RRI R-to-R interval
SBP Systolic blood pressure
SD Standard deviation
SDB Sleep disordered breathing
Sg Glucose effectiveness
SI Insulin sensitivity
TAI Total arousal index
TST Total sleep time
xxv
Abstract
The current evidence in adults suggests that, independent of obesity, obstructive sleep
apnea (OSA) can lead to both autonomic dysfunction and impaired glucose metabolism.
These relationships have been less well studied in children. Since sleep-disordered
breathing occurs in over 13% of the obese pediatric population, knowledge about the
autonomic and metabolic effects of OSA is crucial in determining the importance of OSA
as an independent factor in promoting the development of childhood metabolic
syndrome. The hypothesis in this study is that OSA severity in overweight/obese children
is associated with both autonomic abnormality and insulin resistance. This study will also
investigate if there is a direct association between autonomic dysfunction and insulin
resistance.
To evaluate this hypothesis, overnight polysomnographic studies and tests of metabolic
and autonomic function were conducted in 22 obese male subjects (age: 13.4 ± 2.1 years
(mean ± SD), BMI>95% for age) with varying degrees of OSA severity (obstructive
apnea-hypopnea index (OAHI): 1-14.1 events/h; desaturation index: 0.1-40.1). Exclusion
criteria included diabetes and treatment for OSA.
Each subject participated in a series of procedures that included: (1) polysomnography;
(2) morning fasting blood samples, followed by a frequently-sampled intravenous
glucose tolerance test (FSIVGTT); (3) dual energy X-ray absorptiometry for assessing
adiposity; and (4) measurement of respiration, heart rate and noninvasive continuous
blood pressure during supine and standing postures. Insulin sensitivity, disposition index
xxvi
(a measure of pancreatic beta cell function) and other Bergman minimal model
parameters were derived from the FSIVGTT data. Baroreflex gain and respiratory cardiac
coupling gain, computed using a minimal model of cardiorespiratory control, were taken
to represent indices of autonomic function.
For this sample of patients, insulin sensitivity was found to decrease with desaturation
index. Insulin resistance (as measured by the HOMA index) and fasting insulin levels
were correlated positively with sleep fragmentation, as represented by the total arousal
index (TAI). The HOMA index (p = 0.025) and fasting insulin levels (p = 0.017), but not
fasting glucose, were found to be significantly correlated to insulin sensitivity. Baseline
autonomic function was found to be uncorrelated with all indices of OSA severity.
However, autonomic reactivity to orthostatic stress (supine to standing) decreased with
increasing TAI.
Baseline autonomic function and autonomic reactivity to orthostatic stress were not
correlated to insulin sensitivity or any other measure of insulin resistance, contrary to
initial expectations. However, autonomic reactivity was found to be correlated with
insulin resistance when OSA severity is also considered in the multiple regression model.
In this case, both autonomic reactivity and OSA severity were correlated with insulin
resistance.
Elevated fasting glucose levels were found to be correlated with smaller autonomic
adjustments to postural change (as measured by the baroreceptor reflex reactivity) when
xxvii
controlling for age, adiposity, and sleep efficiency, indicating impaired autonomic
reactivity.
These combined results suggest that insulin resistance is related not only to intermittent
hypoxia (high desaturation index) and sleep fragmentation (high TAI) that accompanies
OSA, but also to increased OSA severity through autonomic dysfunction. An additional
speculation is that increased levels of baseline sympathetic modulation related to
decreased sleep efficiency further contribute to metabolic dysfunction by increased
fasting glucose levels, through sympathetically induced glycogen breakdown and
gluconeogenesis.
1
Chapter 1: Introduction
1.1. Motivation
Epidemiological studies show that sleep apnea, obesity, cardiovascular disease, diabetes,
dyslipidemia, and hypertension seem to interact with each other, increasing the risk for
cardiovascular disease (Jean-Louis, et al., 2008). Obstructive sleep apnea (OSA) refers to
the presence of intermittent, repetitive interruptions or reduction of airflow during sleep
due to obstructions of the upper airway. Pediatric obstructive sleep apnea syndrome is
characterized by episodic hypoxia, intermittent hypercapnia, snoring, and sleep
fragmentation, affecting 2 to 3% of middle-school children (Franks, et al., 2010).
Obesity increases the risk for sleep disordered breathing in children and adolescents
(Ievers-Landis, et al., 2007). Obesity in children is also associated with the risk of
premature death from endogenous causes during early adulthood (Franks, et al., 2010).
There is a strong association between OSA and cardiovascular disease (e.g.
hypertension)(Franks, et al., 2010). It has also been found that sleep apnea is associated
with insulin resistance independent of obesity (Vgontzas, et al., 2008).
Apneic and hypopneic events are associated with sympathetic activation,
vasoconstriction, increases in blood pressure and heart rate, as well as reduced
oxyhemoglobin saturation (Caples, et al., 2005). Studies in adults show that elevated
muscle sympathetic nerve activity is higher in patients with OSA than in normal controls
even during wakefulness, suggesting that sympathetic overactivity plays an important
role in subsequent cardiovascular disease (Somers, et al., 1995).
2
Sleep apnea in adults has also been found to be associated with glucose intolerance,
independently of age, gender, body mass index, and waist circumference (Punjabi, et al.,
2004). Moreover, in adults it has been found that sleep apnea is associated with a
decrease in insulin sensitivity, glucose effectiveness, and pancreatic -cell function,
independent of adiposity (percent body fat), age, sex, and race (Punjabi, et al., 2009).
The underlying mechanisms explaining the associations among sleep apnea,
cardiovascular disease, and the metabolic system are not entirely delineated (Jean-Louis,
et al., 2008). Moreover, these relationships in children are less studied and not clearly
understood. In this study, we hypothesize that the autonomic nervous system (ANS) and
glucose metabolism are adversely affected by OSA in children. We also wish to
investigate if autonomic abnormalities are linked to alterations in glucose metabolism.
1.2. Specific aims
The specific aims to the research proposed in this work are to:
Update the minimal model of cardiorespiratory control and apply it to determine
quantitative descriptors of the autonomic function for each individual subject, in both
baseline conditions (supine posture) andduring standing (steady-state orthostatic
stress). These autonomic descriptors are a means to assess each patient's
cardiovascular autonomic control either at baseline or due to a response to some
autonomic stimulus (e.g. change in posture).
3
Investigate the relationships among sleep apnea, metabolic function, and autonomic
control in our study population, controlling for age and adiposity.
Determine if the parameters that characterize the autonomic state using either systolic
blood pressure (SBP) or pulse transit time (PTT) as one of the inputs to the minimal
model of cardiorespiratory control are correlated.
1.3. Dissertation organization
This dissertation is structured in the following manner.
Chapter 2 presents an overview of obstructive sleep apnea, explains the sleep parameters
used in this study, and describes the results of different studies relating sleep apnea to
obesity, autonomic dysfunction, cardiovascular disease, and metabolic imbalances.
Chapter 3 presents parameters and procedures used in the literature to describe metabolic
dysfunctions and includes a description of the indexes used to quantify metabolic
function adopted in the present work. It also discusses the associations found in different
studies among the metabolic dysfunctions, autonomic nervous system impairments, sleep
apnea severity, obesity, and hypertension.
An overview of the cardiac autonomic system, as well as the different methods used in
the literature to measure autonomic function, is presented in chapter 4. This chapter also
reviews the time and frequency (power spectrum and transfer function) analysis of
cardiovascular variables and describes the use of baroreflex sensitivity and respiratory
sinus arrhythmia as measures of cardiac autonomic control.
4
The minimal model of cardiovascular control used in this study is described in chapter 5.
This chapter also details the systems approach to the study of beat-to-beat oscillations of
cardiovascular variables and describes the autonomic parameters obtained from the
model, including their physiological interpretation. Chapter 5 also details the autonomic
study protocol and describes the instrumentation used. Details on obtaining the
autonomic compact descriptors from the autonomic study are presented, followed by a
discussion of the use of the pulse transit time as a surrogate measure of systolic blood
pressure.
Chapter 6 reviews the methodology adopted in this text for the identification of
physiological systems. In particular, it reviews the use of orthonormal basis functions for
the impulse response representation of systems, in particular the use of Laguerre and
Meixner basis functions. It also justifies the choice for the use of this representation in
physiological systems in general, and in our minimal cardiovascular model in particular.
Chapter 7 contextualizes the Laguerre and Meixner basis functions in the general
framework of Volterra models, for completeness. The Volterra models are a
nonparametric modeling technique based on the Volterra series, which can be interpreted
as a mapping of the input-output relation of continuous and stable nonlinear dynamic
systems with finite memory. The discrete-time Volterra models are also presented, where
the choice of important parameters such as kernel memory length, system bandwidth,
sampling time, and system order are discussed. The Laguerre and Meixner orthogonal
5
basis function expansions are then presented as a compact representation of the Volterra
kernels.
Chapter 8 discusses the statistical analysis used to investigate the relationships between
the autonomic, metabolic, and sleep parameters obtained, accounting for differences in
age and adiposity between the subjects.
The results obtained are presented and discussed in chapter 9, while the principle
bibliographical references used are presented in the last chapter.
6
Chapter 2: Sleep parameters
Obstructive sleep apnea (OSA) is characterized by repetitive interruption of ventilation
during sleep caused by increased upper airway resistance due to collapse of the
pharyngeal airway (Somers, et al., 2008), resulting in intermittent partial (hypopnea) or
complete (apnea) airway closure, intermittent respiratory efforts, sleep fragmentation,
and/or gas exchange abnormalities. Apneic and hypopneic events may lead to arousal
from sleep, which normally terminates the events, opens the airway, and normalizes gas
exchange abnormalities and oxygen saturation levels.
Obstructive sleep apnea syndrome (OSAS) occurs in children of all ages, from neonates
to adolescents (American Academy of Pediatrics, 2002). An increased prevalence of
OSAS in children seems to be associated with the increasing prevalence of obesity in the
pediatric population (Arens, et al., 2010). Childhood obesity is estimated to affect around
18% of children, its prevalence having tripled in the last 25 years (Katz, et al., 2010).
About 36% of obese children are estimated to suffer from the obstructive sleep apnea
syndrome (OSAS). The risk of having moderate OSAS increases 12% for each 1kg/m
2
of
body mass index (BMI) above the mean. Nevertheless, fat distribution, not BMI, is
considered to have a stronger relationship with OSAS severity (Katz, et al., 2010).
Adiposity influences the dimension and collapsibility of the upper airway, thus directly
influencing upper airway resistance.
Obesity in children is also associated with insulin resistance, dyslipidemia, and
hypertension, which is related with adverse cardiovascular outcomes in adulthood
7
(Sinaiko, et al., 2006). OSAS has been independently associated with insulin resistance,
dyslipidemia, and blood pressure dysregulation in obese (Redline, et al., 2007), but not
lean (Tauman, et al., 2005) or morbidly obese, children (Katz, et al., 2010).
Children with OSAS have also been found to present altered sympathovagal balance,
oxidative stress, and endothelial cell dysfunction, among other cardiovascular
abnormalities. As in adults, it has also been observed that children with OSAS have an
increased sympathetic drive both during sleep and wakefulness, as measured by heart rate
variability, peripheral arterial tonometry, pulse transit time, and beat-to-beat blood
pressure, suggesting autonomic dysfunction (Katz, et al., 2010). OSAS children have also
been reported to present reduced baroreflex sensitivity (McConnell, et al., 2009).
This chapter begins with an overview of obstructive sleep apnea, including the pediatric
sleep apnea markers or parameters used in this study. The association of sleep apnea with
obesity, autonomic imbalance, cardiovascular disease, and metabolic dysfunctions is then
discussed. Results from the comparison of the different parameters obtained for each
patient from the different studies performed (autonomic, metabolic, and sleep) will be
presented and discussed in chapter 9.
2.1. Obstructive Sleep Apnea Syndrome
Obstructive sleep apnea syndrome (OSAS), also called obstructive sleep apnea-hypopnea
syndrome (OSAHS), involves upper-airway collapse that partially or totally occludes
airflow (referred to as hypopnea or apnea, respectively) despite ongoing respiratory
efforts, resulting in oxygen desaturation and arousal from sleep. It is characterized by
8
repetitive episodes of apnea and/or hypopnea episodes, oxyhemoglobin desaturation, and
sleep fragmentation (The Report of an American Academy of Sleep Medicine Task
Force, 1999).
Sleep data is obtained via an overnight sleep study (polysomnography). The sleep studies
were conducted in the sleep laboratory at Children’s Hospital Los Angeles (CHLA).
2.1.1. Sleep parameters
From the overnight sleep study, measurements such as electroencephalography (EEG),
electrooculography (EOG), electromyography (EMG), electrocardiography (ECG),
breathing, respiratory efforts, snoring, body position, and oxygen saturation (SaO
2
) were
obtained. With these measurements, the sleep parameters determined included: (a)
obstructive apnea-hypopnea index (OAHI), which measures the average number of
apneas (greater than 90% decrease in airflow from baseline value) and hypopnea
(between 50% and 90% decrease in airflow from baseline value) episodes per hour of
sleep, commonly used as a measure of OSA severity (The Report of an American
Academy of Sleep Medicine Task Force, 1999); (b) desaturation index, a measure of the
severity of exposure to intermittent hypoxia in OSA, defined as the number of events per
hour of sleep where oxygen saturation decreased by 3% or more from baseline; (c) total
arousal index (TAI), the average number of arousals per hour, which may be a superior
marker of sleep fragmentation and better explain daytime sleepiness when compared with
the apnea-hypopnea index (Hosselet, et al., 2001); (d) SpO
2
_nadir, which is the lowest
value of oxygen saturation of the blood, measured via pulse oxymetry, that occurred
9
during sleep; (e) sleep efficiency (%), a measure of sleep duration as a percentage of
total time in bed; (f) total sleep time (TST), the total of all REM and NREM sleep in a
sleep episode; (g) rapid eye movement (REM) sleep as a percent of total sleep time
(REM (% TST) ) (Kakkar, et al., 2007; Wagner, et al., 2007). REM sleep normally
accounts for 20% to 25% of sleep time (Lee-Chiong, 2006). While NREM sleep is
characterized by parasympathetic predominance, REM sleep is characterized by
sympathetic surges with variable states of parasympathetic tone (Caples, et al., 2009).
In children, mild obstructive sleep apnea syndrome (OSAS) is characterized by an
obstructive apnea-hypopnea index (OAHI) between 1.5 and 5 events per hour, moderate
OSAS between 5 and 10 events per hour, while severe OSAS is characterized by OAHI
greater than 10 events per hour.
2.2. Obesity and sleep apnea
In the past 30 years, the prevalence of obesity in children between 2 and 5 years of age
increased from 5.0% to 12.4%, children between 6 and 11 yr increased from 6.5% to
17.0%, and children between 12 and 19 yr increased from 5.0% to 17.6 % (Arens, et al.,
2010). A study by Redline and colleagues (Redline, et al., 1999) involving 399 children
between 2 and 18 years of age found that obesity was the most significant risk factor for
OSAS, with an odds ratio of 4.5.The metabolic syndrome has been shown to be an
important manifestation of obesity in children and may play an independent role in the
development of pediatric OSAS, especially in obese children (Gozal, et al.,
10
2008).Overnight hypoxemia may be a central mediator of metabolic disturbances in
obese children with OSA (Redline, et al., 2007).
In the present study we are using body mass index (BMI), BMI z-score (BMI normalized
for age and gender, which measures the deviation of the value for an individual from the
mean value of the reference population divided by the standard deviation for the
reference population (Kuczmarski, et al., 2002)), and the following adiposity measures
obtained from a dual-energy X-ray absorptiometry (DEXA) scan: total body fat (g), trunk
fat (g), total % body fat, and total % trunk fat. In this particular sample of subjects, the
correlation between body mass index (BMI) and total percent body fat was not found to
be statistically significant, even after correcting for age and height. Since BMI does not
distinguish between lean body mass and fat, the relationship between BMI and body
fatness varies according to body composition and proportions (Garn, et al., 1986). In this
sample we found that BMI was significantly correlated with measures of total body fat
and trunk body fat in grams, while total percent body fat was significantly correlated with
trunk percent body fat as well as with total and trunk body fat in grams.
2.3. OSA, autonomic dysfunction, and cardiovascular disease
The prevalence OSA in cardiovascular patients seems to be 2 to 3 times higher than in
populations without cardiovascular disease. Studies with OSA populations have shown a
higher prevalence of hypertension, type II diabetes, cardiovascular disease, and stroke in
these populations when compared to those without OSA. It has also been suggested that
11
younger people with OSA may be more likely to have hypertension and atrial fibrillation
and to suffer greater all-cause mortality (Somers, et al., 2008).
Studies in adults have shown that intermittent apnea, in particular intermittent hypoxia, is
a major factor in the physiological changes leading to increased risk of hypertension, and
the link appears to be sustained sympathetic activation (Weiss, et al., 2007). Patients with
severe sleep apnea present elevated sympathetic nerve activity not only during sleep,
associated with apneic events, but also during wakefulness (Somers, et al., 1995;
Prabhakar, et al., 2007; Narkiewicz, et al., 2001). This effect seems to be independent of
adiposity. Narkiewicz and colleagues (Narkiewicz, et al., 1998) compared obese adult
subjects with and without sleep apnea and showed that obesity alone, in the absence of
OSA, is not accompanied by increased sympathetic activity to muscle blood vessels.
They also mention that unrecognized OSA may contribute, in part, to the metabolic and
cardiovascular derangements that are thought to be linked to obesity and to the
association between obesity and cardiovascular risk.
The mechanism relating cyclic intermittent hypoxia to sustained sympathetic activation,
that outlasts the hypoxic stimulus, may be associated with augmentation of peripheral
chemoreflex sensitivity and direct effects on sites of central sympathetic regulation
(Weiss, et al., 2007). Baroreflex impairment in OSA patients has also been proposed as a
possible explanation of altered vasoconstrictor function and systemic hypertension
(Cortelli, et al., 1994; Lai, et al., 2006). Narkiewicz and colleagues have reported that
adult patients with sleep apnea show an impairment of baroreflex sympathetic
12
modulation, which is not accompanied by any impairment of baroreflex control of heart
rate (Narkiewicz, et al., 1998). Intermittent hypoxia is also linked to endothelial
dysfunction and impaired vascular control (Foster, et al., 2007).
Reduction in blood pressure and sympathetic activity during sleep after treatment with
continuous positive airway pressure (CPAP) (Narkiewicz, et al., 1997) may provide
evidence of a causative role of sleep apnea in hypertension.Treatment with CPAP also
seems to improve vagal heart rate control in patients with OSA, the degree of
improvement varying directly with compliance level (Khoo, et al., 2001). CPAP therapy
has also been associated with significant benefits to cardiovascular morbidity and
mortality (Otay, et al., 2009). Nevertheless, further studies are needed to elucidate
whether abnormalities evident in the sleep apnea patient with cardiovascular disease are
secondary to the sleep apnea, the cardiovascular condition, or both (Somers, et al., 2008).
2.4. OSA and metabolic dysfunctions
Insulin resistance and compensatory hyperinsulinemia are associated with glucose
intolerance, fasting hyperglycemia, increased triglyceride concentration, low high-density
lipoprotein cholesterol concentration, and essential hypertension, and these aggregated
states associated with insulin resistance characterize the metabolic or insulin resistance
syndrome, presenting an increased risk for coronary artery disease (Reaven, 1988). Sleep
disturbances such as obstructive sleep apnea and sleep deprivation may independently
lead to the development of both insulin resistance and individual components of the
metabolic syndrome, while the converse may also be true (Wolk, et al., 2007).
13
Sleep apnea has been linked to obesity, insulin resistance, diabetes, lipid dysfunction,
inflammatory disorders, and hypertension (Wolk, et al., 2007), all components of the
metabolic syndrome. OSAS has also been independently associated with an increased
prevalence of the metabolic syndrome (Coughlin, et al., 2004). Wilcox and colleagues
(Wilcox, et al., 1998) have proposed that OSA is indeed another component of the
metabolic syndrome.
Punjabi and Beamer (Punjabi, et al., 2009), in a study of 118 nondiabetic subjects,
reported that, independent of adiposity, patients with sleep disordered breathing exhibited
impairments in insulin sensitivity, glucose disposal independent of insulin action, and
pancreatic insulin secretion, as measured by the parameters SI, S
G
, and DI, respectively,
obtained from the FSIVGTT data using Minmod (Bergman, 2005).
Some reports suggest that CPAP treatment in OSA patients can reverse insulin resistance
and glucose intolerance observed in these subjects. Harsch and colleagues (Harsch, et al.,
2004), in a study with 40 adult non-diabetic patients with insulin responsiveness
measured by a hyperinsulinemic euglycemic clamp, found that short term use of CPAP
treatment (from 2 days to 3 months) improved insulin sensitivity in as early as 2 days
after beginning of treatment, remaining stable after 3 months of treatment, especially in
patients with body mass index less than 30 kg/m
2
. Also, their AHI and daytime sleepiness
were normalized. These patients used the CPAP devices on average for 5.2 hours/night
and for 38.1 nights.
14
Babu and colleagues (Babu, et al., 2005)studied the effects of CPAP treatment of sleep
disordered breathing (SDB) on glycemic control in a group of 25 obese adult patients
with type II diabetes. Using a 72-hour continuous glucose monitoring system to measure
interstitial glucose levels, they found that for patients who used CPAP for more than
4h/day there was a correlation between days of CPAP use and reduction in hemoglobin
A
1C
level. Hemoglobin A
1C
is a measure used to identify long-term serum glucose
regulation and is directly correlated with average levels of blood glucose concentration
over the previous four weeks to three months (Nathan, et al., 2008).Steiropoulos and
colleagues (Steiropoulos, et al., 2009) have also reported a correlation between adherence
to CPAP treatment (more than 4 h/night for 6 months) and reduction in hemoglobin A
1C
levels in adult non-diabetic OSAS patients, but found no effect of CPAP on markers of
insulin resistance (HOMA index). They also found a negative correlation of average
sleep oxygen desaturation with fasting insulin levels and HOMA.
Proposed mechanisms linking OSA to insulin resistance in humans include pro-
inflammatory state and elevated cytokine levels observed in OSA patients (Vgontzas, et
al., 1997; Ciftci, et al., 2004), oxidative stress due to recurrent episodes of intermittent
hypoxia (Rudich, et al., 1998), increased lipolysis and fatty acid availability as a result of
the observed increase in sympathetic activation, itself also associated with intermittent
hypoxia (Kjeldsen, et al., 1992), among others.
Sleep deprivation may also play a role in the association of sleep apnea and insulin
resistance. There may be an indirect pathway between lack of sleep and the metabolic
15
syndrome through its relation with obesity, the latter being a known risk factor for the
metabolic syndrome. Gangwisch and colleagues (Gangwisch, et al., 2005)studied
longitudinal data of the 1982-1984, 1987, and 1992 NHANES I Follow-up Studies and
cross-sectional analysis of the 1982-1982 study in adults and found a nearly inverse
linear relationship between weight and sleep time.
Sleep deprivation may also be directly implicated as a risk factor for metabolic syndrome.
In a study by Spiegel and colleagues (Spiegel, et al., 1999), healthy young adult subjects
sleep deprived for six consecutive days showed reduced glucose tolerance and a blunted
insulin response to glucose, as well as an increase in sympathetic nervous system activity.
Shigeta and colleagues (Shigeta, et al., 2001) have shown that sustained sleep debt is
associated with obesity and a decrease in insulin sensitivity (as determined from HOMA).
In this present study, data obtained from the sleep studies, metabolic (IVGTT) test, and
autonomic tests will be analyzed in order to evaluate the influence of severity of sleep
apnea (as assessed by the parameters OAHI, TAI, and desaturation index) on the
autonomic (baroreflex and respiratory cardiac coupling gains) and metabolic (as
measured by the IVGTT parameters AIRg, SI, DI, S
G
as well as fasting glucose, fasting
insulin, and HOMA index) systems. These results are presented in chapter 9.
16
Chapter 3: Metabolic parameters
Epidemiological studies in adults suggest that sleep apnea, obesity, cardiovascular
disease, diabetes, dyslipidemia, and hypertension interact with one another, increasing the
risk for cardiovascular disease (Jean-Louis, et al., 2008). Franks and colleagues (Franks,
et al., 2010), in a longitudinal study of diabetes and related disorders, with a median
follow-up period of 23.9 years, have shown that obesity, glucose intolerance, and
hypertension in childhood were strongly associated with increased rates of death from
endogenous causes during early adulthood.
Recently different studies have shown that sleep disordered breathing increases the risk
for insulin resistance, glucose intolerance, and overt diabetes (Punjabi, et al., 2004;
Aurora, et al., 2007; Ip, et al., 2002). Sleep apnea and its associated sleep fragmentation,
decreased sleep duration, and exposure to intermittent hypoxia have been found to
increase the propensity for metabolic dysfunction (Spiegel, et al., 2005; Foster, et al.,
2009).
This chapter begins with a brief summary of the terminology used to describe metabolic
dysfunctions, including insulin resistance, metabolic syndrome, and diabetes. This will be
followed by an overview of glucose and insulin dynamics in humans. The protocol used
for the frequently-sampled intravenous glucose tolerance test (FSIVGTT) adopted in this
study is then presented, together with Dr. Bergman’s minimal model parameters
(Bergman, et al., 1979). These parameters characterize the dynamics of glucose
homeostasis and provide a means to quantify the body’s ability to dispose of glucose and
17
its sensitivity to insulin mediated glucose disposal. The chapter concludes with results
from different studies showing relationships found among sleep apnea, metabolic
imbalance, and autonomic dysfunctions.
The objective of this study is to analyze the information obtained from the FSIVGTT
study with the information obtained from the autonomic and sleep studies, in order to
obtain a better understanding of the underlying mechanisms that characterize the
interrelationships between metabolic dysfunction, autonomic imbalance, and sleep apnea
severity.
3.1. Impaired glucose regulation, insulin resistance, and the metabolic
syndrome
3.1.1. Impaired fasting glucose (IFG) and impaired glucose tolerance (IGT)
The 1999 report from the World Health Organization on the diagnosis and classification
of diabetes mellitus (World Health Organization, 1999) defined impaired glucose
regulation as a metabolic state between glucose homeostasis and diabetes, characterized
by the presence of impaired fasting glucose (IFG) and/or impaired glucose tolerance
(IGT). Subjects with impaired fasting glucose and those with impaired glucose tolerance
have an increased risk of diabetes and cardiovascular diseases.
A state of impaired fasting glucose refers to fasting glucose concentrations higher than
the reference range considered normal, but still lower than that required for the diagnosis
of diabetes. In particular, that refers to fasting plasma glucose concentration between 110
mg/dl (6.1 mmol/l) and 126 mg/dl (7.0 mmol/l) (World Health Organization, 1999;
18
World Health Organization and International Diabetes Federation, 2006). While impaired
fasting glucose represents abnormalities of glucose regulation in the fasting state,
impaired glucose tolerance refers to post-prandial disorder of glucose regulation, and is
measured by response to an oral glucose load challenge.
The following protocol for the oral glucose tolerance test (OGTT) is recommended by the
WHO (World Health Organization, 1999). After an overnight fast of 8 to 14 hours, a
fasting blood sample should be drawn, followed by the ingestion of 75 g of anhydrous
glucose or 82.5 g of glucose monohydrate in 250 to 300 ml of water over the course of 5
minutes. For children, the report recommends a test load of 1.75 g of glucose per kg body
weight, up to a total of 75 g of glucose. Blood samples should then be collected after 2
hours from the glucose load ingestion.
The World Health Organization andthe International Diabetes Federation, in their 2006
report (World Health Organization and International Diabetes Federation, 2006),
recommend that an OGTT should be used in subjects with fasting plasma glucose
between 110 and 125 mg/dl (6.1 to 6.9 mmol/l) in order to determine their glucose
tolerance status. In the same report, impaired glucose tolerance (IGT) is defined as a
sustained fasting plasma glucose of less than 126 mg/dl (7.0 mmol/l) and a 2 hour plasma
glucose greater or equal to 140 mg/dl (7.8 mmol/l) and less than 200 mg/dl (11.1
mmol/l).
Impaired fasting glucose and impaired glucose tolerance are also associated with
increased risk of cardiovascular disease. The Paris Prospective Study (Fontbonne, et al.,
19
1991), that followed 6557 healthy men for 23 years, showed that the relative risk for
death from coronary heart disease for subjects with fasting glucose varied from 1.32 for
subjects with a fasting glucose less than 5.8 mmol/l to almost double, or 2.63, for subjects
with values greater than 6.9 mmol/l. Ceriello (Ceriello, 2004) has shown that the
glycemia level after 2 hours of the oral glucose tolerance test is a direct and independent
risk factor of cardiovascular disease.
3.1.2. Insulin resistance and the metabolic syndrome
Sensitivity to insulin-mediated glucose disposal can vary significantly either when
considering individuals with normal glucose tolerance or when comparing normal
subjects with those that have impaired glucose tolerance (IGT) or non-insulin-dependent
diabetes mellitus (NIDDM). Golay and colleagues (Golay, et al., 1986) have shown that
measurements of insulin-mediated glucose uptake (Rd), as measured by the glucose
clamp method, is lower in subjects with either IGT or NIDDM when compared to
individuals with normal glucose tolerance, as illustrated in Figure 1. This figure also
shows that glucose uptake in patients with IGT or NIDDM is reduced to practically the
same degree.
20
Figure 1: Mean and standard error for insulin-mediated glucose uptake (Rd) (glucose-clamp method) in subjects
with normal glucose tolerance, the control group, and in those with impaired glucose tolerance (IGT) and non-
insulin dependent diabetes mellitus (NIDDM). The latter two groups differed significantly from the control
group (p < 0.001). From (Golay, et al., 1986).
The same study also showed that in subjects with IGT or NIDDM there is no significant
relationship between fasting plasma glucose concentration and resistance to insulin-
stimulated glucose uptake, as can be seen in Figure 2. This same figure also shows that
for subjects with normal glucose tolerance insulin-mediated glucose uptake can vary
almost threefold.
Figure 2: Insulin-mediated glucose uptake (Rd) - glucose clamp method vs. fasting plasma glucose in subjects
with normal glucose tolerance ( ), IGT (o), or NIDDM (*). These data are from the same subjects as in Figure 1.
From (Golay, et al., 1986).
This threefold variation in insulin sensitivity in individuals with normal oral glucose
tolerance was also found by Hollenbeck and Reaven (Hollenbeck, et al., 1987). The
results of a glucose-clamp study in 100 non-obese subjects with normal oral glucose
21
tolerance showed that glucose uptake in the first quartile (subjects with higher insulin
resistance) was about 33% of the value in the fourth quartile (subjects with lower insulin
resistance, or equivalently, higher insulin sensitivity), as shown in Figure 3.
Figure 3: Mean and standard error values for glucose uptake (M) during glucose clamp studies in 100 non-obese
subjects with normal oral glucose tolerance. From: (Hollenbeck, et al., 1987)
The plasma glucose and insulin response curves to a 75g oral glucose tolerance test for
these same patients showed that, while the plasma glucose response of the four groups
were similar, the insulin response was significantly different. The subjects in the first
quartile (highest insulin resistance) in Figure 3 had the highest insulin response, while
those in the fourth quartile (lowest insulin resistance) had the lowest insulin response, as
shown in Figure 4. Overall, there was a significant correlation between the degree of
insulin resistance and insulin response (r = 0.65, p < 0.001).
22
Figure 4: Plasma glucose and insulin responses to OGTT in the four quartiles seen in Figure 3 (1
st
, ; 2
nd
, ;
3
rd
, Δ; 4
th
, o). From: (Hollenbeck, et al., 1987)
These results suggest that insulin resistant subjects with normal glucose tolerance have an
increased insulin secretion as a compensatory mechanism. Thus, the similar degrees of
glucose tolerance seen in subjects with varying degrees of insulin sensitivity can be
explained by the ability of the pancreatic -cells to increase insulin secretion. When the
compensatory hyperinsulinemic state cannot be sustained in individuals who are insulin
resistant, severe hyperglycemia develops (Reaven, 1988).
The study by Reaven in 1988 (Reaven, 1988) also showed that insulin resistance and
compensatory hyperinsulinemia in non-diabetic individuals were associated with glucose
intolerance, high plasma triglycerides, low high-density lipoprotein cholesterol
concentration, and essential hypertension, among others. This cluster of abnormalities
usually associated with insulin resistance and the resulting compensatory
hyperinsulinemia is today commonly known as the metabolic syndrome (Grundy, et al.,
2005) or the insulin resistance syndrome (Reaven, 2003). These different nomenclatures
reflect differences in interpretation of the role of insulin resistance in this cluster of
abnormalities and clinical syndromes (either as playing a central role in the syndrome,
23
thus requiring evidence of insulin resistance for diagnosis, or as simply an additional
factor that may or may not be present for diagnosis of the syndrome).
In a joint scientific statement (Grundy, et al., 2005), the American Heart Association
(AHA) and the National Heart, Lung, and Blood Institute (NHLBI) have defined the
metabolic syndrome as a “constellation of interrelated risk factors of metabolic origin –
metabolic risk factors – that appear to directly promote the development of
atherosclerotic cardiovascular disease”. In particular, the criteria for diagnosis of the
metabolic syndrome recommended by the AHA/NHLBI is the presence of any three of
five measures in a subject: (1) elevated waist circumference ( 102 cm in men, 88 cm
in women); (2) elevated triglycerides ( 150 mg/dL, or 1.7 mmol/L) or on drug treatment
for elevated triglycerides; (3) reduced high-density lipoprotein cholesterol, HDL-C (< 40
mg/dL or 1.03 mmol/L in men, < 50 mg/dL or 1.3 mmol/L in women) or on drug
treatment for reduced HDL-C; (4) elevated blood pressure, 130 mm Hg systolic blood
pressure or 85 mm Hg diastolic blood pressure, or on antihypertensive drug treatment
in a patient with a history of hypertension; (5) elevated fasting glucose ( 100 mg/dL) or
on drug treatment for elevated glucose.
Insulin resistance and the compensatory hyperinsulinemia are associated with endothelial
dysfunction (Steinberg, et al., 1996), impaired fasting glucose, impaired glucose
tolerance, increased triglycerides, decreased high-density lipoprotein cholesterol,
increased sympathetic nervous system activity, increased renal sodium retention,
increased c-reactive protein, increased plasma uric acid concentration, and sleep apnea,
24
among other physiological abnormalities (Reaven, 2005). Insulin resistant individuals are
at increased risk of developing type 2 diabetes, cardiovascular disease, essential
hypertension, nonalcoholic fatty liver disease, among others (Reaven, 2003).
3.2. Insulin resistance and diabetes
The American Diabetes Association defines diabetes mellitus as a group of metabolic
diseases characterized by hyperglycemia resulting from defects in insulin secretion,
insulin action, or both (American Diabetes Association, 2010). The long term effect of
chronic hyperglycemia of diabetes is associated with damage in different organs,
especially the eyes, kidneys, nerves, heart, and blood vessels.
Different from type I diabetes, which is characterized by an autoimmune destruction of
the beta-cells of the pancreas, the cause of type II diabetes is a combination of tissue
resistance to insulin mediated glucose uptake and inadequate compensatory insulin
secretion. Impaired fasting glucose (IFG) and/or impaired glucose tolerance (IGT) may
be present before the criteria for the diagnosis of diabetes is met. The degree of
hyperglycemia reflects the severity of the underlying metabolic process. Type I, or
immune-mediated diabetes, accounts for only 5 to 10% of the diabetic patients, while
type II diabetes accounts for approximately 90 to 95% of subjects with diabetes
(American Diabetes Association, 2010).
The 2003 Expert Committee report (Expert Committee on the Diagnosis and
Classification of Diabetes Mellitus, 2003) considered individuals having impaired fasting
glucose (IFG), defined as fasting plasma glucose levels between 100 mg/dl (5.6 mmol/l)
25
to 125 mg/dl (6.9 mmol/l), or impaired glucose tolerance (IGT), defined as 2-hour values
in the oral glucose tolerance test (IGT) of 140 mg/dl (7.8 mmol/l) to 199 mg/dl (11.0
mmol/dl), to be at increased risk for the future development of diabetes as well as
cardiovascular risk, and are frequently referred to as being pre-diabetic.
According to the 2007 National Diabetes Statistics (NIDDK/NIH), in 1988 to 1994,
33.8% of U.S. adults aged 40 to 74 years old had IFG, 15.4% of this population presented
IGT, and 40.1% had pre-diabetes IGT or IFG or both. In 1999 to 2000, among U.S.
adolescents 12 to 19 years old, 7.0% had IFG. In terms of diabetes, the prevalence of both
diagnosed and undiagnosed diabetes in the United States in 2007, considering subjects of
all ages, was estimated at 23.6 million people, or 7.8 % of the population. In terms of age
group, the estimated prevalence of diagnosed and undiagnosed diabetes is 2.6% of all
people 20 to 39 years old, 10.8% of all people 40 to 59 years old, and 23.1% of all people
60 or older (National Institute of Diabetes and Digestive and Kidney Diseases
(NNIDDK), National Institute of Health (NIH), 2008).
3.3. Measurement of insulin resistance
3.3.1. Hyperinsulinemic euglycemic clamp
Different methods have been proposed for measurement of the degree of insulin
resistance of an individual. The hyperinsulinemic euglycemic clamp (DeFronzo, et al.,
1979) has been usually regarded as the standard to quantify the degree of insulin
resistance. In this procedure, plasma glucose concentration is infused and held constant at
the basal arterial plasma glucose concentration level, by periodically adjusting the
26
glucose infusion, based on the negative feedback principle. In other words, if the actual
glucose concentration is higher than the desired set point, the infusion is decreased, and
vice-versa. Since this test maintains the basal glucose level after insulin administration, it
avoids the physiological responses to hypoglycemia and thus provides a reliable estimate
of tissue sensitivity to insulin.
This test measures the total amount of glucose needed to compensate for an increased
insulin level. Under steady-state plasma glucose conditions, the infused glucose must
equal the metabolized glucose, M, or whole body insulin-mediated glucose disposal. The
use of the variable M as a measure of total body glucose metabolism is based on the
assumption that basal hepatic glucose production is suppressed by the infusion of glucose
and insulin (DeFronzo, et al., 1979). Steady-state glucose infusion rate is usually
calculated over the last 30 minutes of the clamp (i.e. between 90 and 120 minutes).
Whole body insulin sensitivity during the clamp is measured as M/SSPI, where SSPI is
the steady-state plasma insulin concentration (Matsuda, et al., 1999).
The steady-state level of plasma insulin concentration makes it possible to determine the
metabolic clearance rate of insulin. Since the rate of glucose metabolism is determined at
5-min intervals, the curve reflecting how tissue sensitivity to insulin changes with time
can be obtained.
3.3.2. The HOMA index
Another commonly used surrogate measure for insulin sensitivity is the Homeostasis
Model Assessment of Insulin Resistance, or HOMA-IR index. Since this score requires
27
the use of only fasting plasma glucose and insulin, it is a more simple and inexpensive
alternative to the determination of insulin resistance. The HOMA method derives an
estimate of insulin sensitivity from the mathematical modeling of fasting plasma glucose
and insulin concentrations.
The HOMA index was proposed by Matthew and colleagues (Matthews, et al., 1985).
They used a model of insulin-glucose interactions to determine an array of fasting plasma
insulin and glucose concentrations that would be expected for varying degrees of -cell
deficiency and insulin resistance. From this array, the insulin resistance and deficient -
cell function which might have been expected to give the fasting plasma glucose and
insulin concentrations observed in a patient can be estimated.
A simple equation that approximates the HOMA indexes obtained by use of themodel has
been proposed by (Galvin, et al., 1992) and is given by
k
I G
HOMA
b b
where G
b
and I
b
are basal glucose and insulin concentrations (in mmol/l and U/ml,
respectively) and k is a constant to scale the HOMA insulin resistance index so that it has
a value of 1 (or 100%) with mean normal basal glucose and insulin. For the given units of
glucose and insulin, k = 22.5 (Pacini, et al., 2003). If the fasting glucose values in the
HOMA equation are in mg/dL, k = 405 (Chavez, et al., 2006).
28
High HOMA scores denote low insulin sensitivity (or high insulin resistance). Since the
HOMA score estimates the spontaneous homeostatic characteristics by inferring what
degree of insulin sensitivity is compatible with the homeostatic characteristics of the
metabolic system in each individual, it is less accurate than the clamp method for
assessing insulin sensitivity. Even so, Bonora and colleagues (Bonora, et al., 2000) have
shown that the HOMA score could account for 65% of the variability in insulin
sensitivity assessed by the glucose clamp technique (p < 0.0001).
According to these same authors, the results they obtained support the use of the HOMA
index as a surrogate index of insulin sensitivity in humans, especially for large-scale or
epidemiological studies, ranking the individuals similarly to the glucose clamp technique.
The authors do mention, however, that comparing HOMA scores obtained in different
studies cannot be done unless the insulin assay is standardized. They also mention that
standardization of the insulin assay is also a prerequisite for introducing the HOMA in
clinical practice.
3.3.3. OGTT test
The oral glucose tolerance test is a dynamic test from which surrogate indexes of insulin
sensitivity can be obtained. The protocol for the OGTT test has been described in section
3.1.1. This test stimulates both glucose disposal and insulin secretion. Different
approaches are available for a measure of insulin sensitivity from the OGTT protocol,
including purely empirical, e.g. ISIcomp
1
(Matsuda, et al., 1999) and MCRest
2
(Stumvoll,
1
Insulin sensitivity index
2
Metabolic clearance rate of glucose
29
et al., 2000), and model based with empirical assumptions, e.g. OGIS
3
(Mari, et al.,
2001). The OGTT is a relatively simple test that activates the insulin-glucose homeostatic
process. However, the interpretation of the OGTT data is more uncertain among other
reasons due to the difficulty in distinguishing direct metabolic actions of insulin
following oral ingestion of glucose (Muniyappa, et al., 2008).
3.3.4. Bergman’s minimal model of glucose kinetics (Minmod) and metabolic
parameters
The minimal model of glucose regulation, or Minmod, estimates metabolic indexes of
insulin sensitivity and glucose effectiveness after a single frequently sampled intravenous
glucose tolerance test (FSIVGTT). Like OGTT, this is a dynamic test to assess glucose
metabolism. Steady-state measures obtained from studies based on fasting values only are
unable to characterize the dynamic relation between insulin sensitivity and insulin
secretion (Punjabi, et al., 2009).
Minmod is defined by two coupled differential equations, one describing plasma glucose
dynamics in a single compartment and the other insulin dynamics in a “remote
compartment”. From these equations and using experimental data points of plasma
glucose and insulin, model parameters corresponding to a best fit to glucose
disappearance are estimated. In this test, information about insulin sensitivity, glucose
effectiveness, and beta-cell function are derived from a single dynamic test. Since this is
the test used in this study, it will be reviewed in more detail.
3
Oral glucose insulin sensitivity model
30
The original intravenous glucose tolerance test protocol (standard IVGTT) (Bergman, et
al., 1979) based on a single injection (glucose only) was modified (insulin-modified
FSIVGTT) (Bergman, et al., 1987) to include an infusion of insulin between 20 and 25
minutes from the glucose injection, in order to improve the estimates of glucose
effectiveness (S
G
) and insulin sensitivity (SI) (Pacini, et al., 1998). This modified
protocol is the one used in the present study. Other modifications (e.g. the use of
population analysis (Vicini, et al., 2001) and the introduction of a second compartment
for glucose (Vicini, et al., 1997; Caumo, et al., 1999)) have been proposed in the
literature. However, these have not yet become as well established as the modified
FSIVGTT.
The protocol adopted in this study is the modified FSIVGTT, consisting of timed blood
samples after an overnight fast (12 hours). In particular, after two baseline samples
(which are averaged) 10 minutes apart for measurement of fasting glucose, fasting
insulin, and triglyceride levels, glucose (300 mg/kg of body weight) is administered at
time zero and infused over 2 minutes, followed by six timed blood samples within 19
minutes from glucose administration (in particular, at times 2, 4, 8, 12, 16, and 19
minutes), in order to follow the body’s own dynamic response to the glucose injection.
After 20 minutes from the glucose injection, insulin (0.02 units per kilogram body
weight) is administered, followed by subsequent timed blood samples (in particular, at
times 22, 24, 26, 30, 35, 40, 50, 70, 100, 140, 180 minutes after glucose injection). A
total of 19 samples were drawn for the measurement of glucose and insulin over the
duration of 3 hours following the glucose injection.
31
These data are then analyzed using the program Minmod (Bergman, 2005) to generate
parameters that characterize the dynamics of glucose and insulin during testing. The
“minmod” model predicts the time course of plasma glucose in response to the insulin
injection, using a pharmacodynamic model that describes the dependence of glucose
dynamics on plasma insulin and glucose levels.
The model assumes instantaneous distribution of the glucose bolus in a
monocompartmental space. Glucose is assumed to leave or enter this “glucose space” at a
rate proportional to insulin levels in the “remote insulin compartment”. The model
assumes insulin acts from a remote or extravascular compartment to promote glucose
disappearance. Moreover, glucose disappearance in response to glucose and/or insulin is
assumed to occur at a monoexponential rate. In addition, it is assumed that the glucose
concentration at the end of the FSIVGTT is identical to the initial concentration (Nittala,
et al., 2006).
The metabolic parameters, estimated by Minmod, considered in this study are insulin
sensitivity (SI), the acute insulin response to glucose (AIRg), disposition index (DI), and
glucose effectiveness (S
G
). The model has been designed such that glucose
disappearance, described by SI and S
G
, includes peripheral uptake and net hepatic
glucose balance (Bergman, 1979; Bergman, et al., 1987).
Figure 5 shows the glucose (blue dots) and insulin (green dots) data points, obtained from
the FSIVGTT protocol described. The glucose injection was administered at time 0 min
(observe the delayed peak in plasma glucose shown by the blue data points). The
32
exogenous insulin injection occurred at time 20 min. The model estimates the metabolic
parameters from the time course of the measured plasma glucose and insulin (Bergman,
1979; Bergman, et al., 1987). The red line in the figure corresponds to the model’s
estimate for glucose dynamics, based on the model’s equations and assumptions.
Figure 5: Glucose (blue dots) and insulin (green dots) data from the FSIVGTT protocol and the Minmod fit (red
line) for glucose dynamics. The time course of the glucose and insulin measurements is used by the model to
estimate the aforementioned metabolic parameters.
Insulin sensitivity, SI
Insulin sensitivity, SI (× 10
4
ml/min/ U), is defined as fractional glucose disappearance
per insulin concentration unit and is a measure of the capability of insulin-stimulated
glucose uptake. In other words, it measures the ability of insulin to enhance glucose
uptake and to inhibit liver glucose production (Boston, et al., 2003), and is of
fundamental importance in the pathology of type II diabetes (Reaven, 1988).
This minimal model-based insulin sensitivity (SI) has been shown to be equivalent to that
obtained by using the euglycemic hyperinsulinemic clamp (Bergman, et al., 1987). It has
also been shown to function well as a surrogate measure of cardiovascular disease risk in
normal subjects (Howard, et al., 1998) and in type 2 diabetics (Haffner, et al., 1999).
33
Normal average SI levels in adultshave been reported to be 2.62 ± 2.21, IGT levels to be
1.27 ± 1.20, and type II diabetes levels to be 0.57 ± 0.82 (Bergman, 2007). In a study
with nondiabetic overweight Hispanic young adolescents these levels have been reported
as 2.17 0.14 for boys and 1.88 0.15 for girls (Koebnick, et al., 2008).
Glucose effectiveness, S
G
Glucose effectiveness, S
G
(min
-1
), is a measure of the ability of glucose per se to promote
its own disposal as well as inhibit hepatic glucose production with insulin at basal
levels(Bergman, 1979). S
G
quantifies the actions of glucose per se, independent of
increased insulin, to normalize glucose concentration through actions on glucose
production and utilization (Pacini, et al., 1998). Since S
G
represents basal fractional
glucose clearance (i.e. clearance/volume), which depends on basal insulin concentration,
it is not completely independent of insulin. Therefore, it is not as robust as SI to different
insulin levels, but is still a significant measure (Pacini, et al., 2003).
In normal individuals, glucose effectiveness accounts for approximately 50% of the
glucose disposal during an oral glucose tolerance test, which makes S
G
at least as
important to determining glucose tolerance as insulin itself (Nishida, et al., 2001).
(Bergman, 2007) states that normal average Sg levelsin adults are 0.021 ± 0.008 (mean ±
standard deviation), IGT levels are 0.016 ± 0.007, and type II diabetes are 0.015 ± 0.011.
Acute insulin response to glucose (AIRg)
The acute insulin response to glucose AIRg ( U/ml × min) is a measure of first phase
pancreatic responsiveness, corresponding to the total insulin released during first phase
34
(before the injection of exogenous insulin). It is measured as the mean insulin
concentration above basal of the insulin values measured during the first peak, from times
2 to 10 min after a maximally stimulating (300 mg/kg) intravenous glucose bolus (Pacini,
et al., 2003; Ahrén, et al., 2004; Kahn, et al., 1993). According to (Bergman, 2007),
normal average AIRg levels in adults are 59.6±54.8(mean ± standard deviation), IGT
levels are 42.4±42.6, and type II diabetes levels are 6.7 ± 18.5. In a study with
nondiabetic overweight Hispanic young adolescents these levels have been reported as
1,806 124 for boys and 1,681 129 for girls (Koebnick, et al., 2008).
The relationship between insulin secretion measures and insulin sensitivity has been
shown to be hyperbolic (Kahn, et al., 1993). As a consequence of the hyperbolic
relationship between AIRg and SI, the magnitude of the change in the beta-function
response measured by AIRg accompanying a change in SI depends on the initial degree
of insulin sensitivity. Therefore, in subjects with high insulin resistance (or low insulin
sensitivity), small changes in insulin sensitivity would produce large changes in insulin
levels, while in subjects with low insulin resistance (high insulin sensitivity) large
changes in SI would be associated with small changes in insulin concentrations (Kahn, et
al., 1993; Bergman, 1989).
In terms of AIRg, an extremely low first phase insulin response to glucose would be
expected in highly insulin-sensitive individuals, indicating normal -cell function.
However, in individuals with low insulin sensitivity, a low AIRg would indicate impaired
-cell function (Kahn, et al., 1993).
35
Disposition index (DI)
The disposition index DI (× 10
4
/ min) is defined by the product of SI and AIRg and
represents the ability of the pancreatic -cells to compensate for insulin resistance by
increasing insulin production (Bergman, 2007). It is a measure of pancreatic -cell
functionality, accounting for the influence of both endogenous insulin secretion (AIRg)
and insulin sensitivity (SI). -cell function as measured by first phase insulin response to
glucose (AIRg) is inversely related to insulin sensitivity such that an increased insulin
resistance (decreased insulin sensitivity) is related to an increase in -cell function
(increased insulin production) in normal glucose homeostasis. Since the product AIRg ×
SI is nearly constant for a particular individual, the disposition index DI can be
interpreted as an index of normalized -cell function (Pacini, et al., 2003). Bergman
states that normal average DI levels are 1,249 ± 1,559, IGT levels are 430 ± 594, and
type II diabetes levels are 30 ± 95. In overweight nondiabetic young Hispanic adolescents
these levels have been reported as 2,873 118 for boys and 2,246 116 for girls
(Koebnick, et al., 2008).
Weyer and colleagues (Weyer, et al., 2000), in a longitudinal study with the Gila River
Indian Community population of American Indians, found that DI was the strongest
predictor of conversion from normal glucose tolerance to type 2 diabetes in at-risk
populations.The Insulin Resistance Atherosclerosis (IRAS) Family Study group
performed a genome scan for glucose homeostasis traits in African Americans and found
that DI is linked to chromosome 11q and further speculate of an independent AIRg loci in
36
the same region (Palmer, et al., 2006). These and further studies may validate the
assumption that the combination of insulin resistance and -cell failure are strongly
involved in the etiology of type II diabetes mellitus.
Other metabolic parameters considered in this study
Besides these parameters determined from the FSIVGTT data, we also looked at the
fasting glucose and insulin levels, as well as the HOMA index (homeostasis model
assessment), a quantitative estimate of the contributions of insulin resistance and
deficient -cell function to the fasting hyperglycemia, which is proportional to the
product of the subject’s fasting plasma insulin and glucose measures (Matthews, et al.,
2002).
3.4. Metabolic syndrome and autonomic nervous system dysfunction
Subjects with metabolic syndrome present autonomic nervous system dysfunction, with
increased sympathetic activity, detected as increased heart rate and blood pressure and
decreased heart rate variability and baroreceptor sensitivity, among other characteristics
(Tentolouris, et al., 2008). Grassi and colleagues have found that patients diagnosed with
the metabolic syndrome, either normotensive or hypertensive, have increased muscle
sympathetic nerve activity, as measured by the microneurography technique. They also
found that this elevation in sympathetic activity is related to insulin resistance ,as
measured by the HOMA index (Matthews, et al., 1985), and is associated with a decrease
in baroreflex sensitivity (measured by the pharmacological approach) (Grassi, et al.,
2005).
37
Insulin resistance has also been related to increased cardiovascular risk. Ducimetiere and
colleagues(Ducimetiere, et al., 1980), studying 7246 middle-aged non diabetic men,
found that the fasting plasma insulin level and the fasting insulin-glucose ratio are
positively associated with risk of coronary heart disease (CHD) independent of other
factors. The corresponding values two hours after a glucose load, although also positively
associated with risk of CHD, were not found to be significant when considering
multivariate analysis.In a longitudinal 5-year study involving 2103 Canadian men who
did not have ischemic heart disease, Després and colleagues found that high fasting
insulin concentrations were independently associated with risk of ischemic heart disease
(Després, et al., 1996).
Results from the San Antonio Heart study involving 2390 subjects showed that, in the
same patient, a combination of three or more risk factors for coronary artery disease
(CAD) was more prevalent than either the presence of each risk factor in isolation or in
combination with just one another. This study also found that subjects who developed
multiple metabolic disorders had higher insulin concentrations than those who developed
only a single disorder (Haffner, et al., 1997).
The ARIC (Atherosclerosis Risk in Communities) study (Liese, et al., 1999), involving
5221 middle-aged subjects free of component disorders of the multiple metabolic
syndrome at baseline, examined the predictive associations of fasting insulin with
incident hypertension, occurring either alone or as part of the metabolic syndrome.
Results from this study showed that elevated fasting insulin was more strongly predictive
38
of hypertension occurring as a component of the multiple metabolic syndrome than of
hypertension occurring alone, adjusting for age, gender, study center, BMI, and
abdominal girth (at the umbilical level). The authors further speculate that the stronger
association found between increased fasting insulin and hypertension occurring in
combination with dyslipidemia or diabetes would indicate a causal role of insulin
resistance for each of these metabolic disorders.
3.5. Sleep apnea, obesity, metabolic dysfunctions, autonomic imbalance,
and hypertension
The associations among obesity, insulin resistance, sympathetic nervous system
stimulation, and hypertension in both animals and humans have been shown by different
studies. Studies by different groups seem to agree on the relationships among obesity,
insulin resistance, and sympathetic nervous system activity. However, the association
between these variables and hypertension are not a consensus.
When comparing normal weight with obese children, Freedman and colleagues
(Freedman, et al., 1999) have shown that the latter have an odds ratio greater than 12 for
hyperinsulinemia when compared to normal weight children. Redlineand colleagues
reported that, in an obese pediatric population aged 2 to 18 years, the odds ratio for sleep-
disordered breathing of moderate severity (OAHI ≥ 10) was 4.59 times that of the non-
obese population (Redline, et al., 1999).In adults, insulin resistance has been shown to be
independently correlated with OSA after controlling for BMI (Ip, et al., 2002). Pediatric
OSA has also been correlated with hyperinsulinemia after controlling for BMI (Redline,
39
et al., 2007). OSA therefore may be an independent contributor to metabolic dysfunctions
seen in childhood obesity (Fennoy, 2010).
In terms of the relationships of hyperinsulinemia and increased sympathetic activity with
blood pressure, some studies show that these variables are related to an increase in blood
pressure (Landsberg, 2001), while others show a decrease in blood pressure.
Nevertheless, when considering obese subjects with a high level of insulin secretion as a
response to an elevated insulin resistance state, there seems to be a tendency of these
individuals to present hypertension.
In his 1986 article (Landsberg, 1986), Landsberg proposed a hypothesis to explain the
association of obesity and hypertension, described by the relations shown in Figure 6.
40
Figure 6: Hypothesis to explain mechanism relating obesity to hypertension, proposed by Landsberg (adapted
from (Landsberg, 1986)).
In sum, obesity is shown to be the result of excessive dietary intake or a low metabolic
rate, or both (pathway (1) in Figure 6). Obesity is known to be related to an increase in
insulin resistance (pathway (2) in Figure 6) (Westphal, 2008). An increased insulin
resistance is compensated by an increase in insulin production (3), in order to maintain
glucose homeostasis. A hyperinsulinemic state stimulates the sympathetic nervous system
(SNS) activity (4), which in turn produces a stimulating effect on the body's
thermogenesis (5). An increase in thermogenic mechanisms in response to the increased
SNS activity would tend to limit further weight gain by elevating the body's metabolic
rate (6). An increased SNS activity may also be the direct result of an increase in dietary
intake (7), unrelated to hyperinsulinemia. Elevation in sympathetic nerve activity has a
stimulating effect (8) on blood vessels, heart rate, and sodium retention by the kidneys.
Diet Thermogenesis Insulin resistance
Hyperinsulinemia SNS activity
Blood vessels
Vasoconstriction Cardiac output Na
+
Reabsorption
Kidneys Heart
Blood pressure
Obesity
(+)
(+)
(+)
(+)
(+)
(+)
(+)
(+)
(+)
(+)
(-)
(+)
(+)
(+)
(+)
(+)
(2)
(3)
(4)
(5)
(6)
(1)
(8)
(9)
(10)
(7)
41
Insulin is also known to produce an inhibitory effect on sodium excretion and to stimulate
renal sodium reabsorption (9). These aggregated factors have a pro-hypertensive effect
(10), and this could be one of the mechanisms responsible for the relation between obesity
and hypertension. In other words, according to this hypothesis, hypertension that occurs
in association with obesity is the undesirable result of a compensatory mechanism in
obese individuals to restore energy balance and limit further weight gain.
3.5.1. Hyperinsulinemia, increased sympathetic activation, baroreflex impairment,
and hypertension
Acute physiological elevation in plasma insulin has been shown to cause prolonged
increases in muscle sympathetic nerve activity and vasodilation (Anderson, et al., 1991).
Studies in both normotensive (Anderson, et al., 1991) and borderline hypertensive
(Anderson, et al., 1992) young adults have shown that acute increases in plasma insulin
within the physiological postprandial range, while maintaining constant blood glucose
levels, cause an elevation in sympathetic nerve activity (measured by increases in
postganglionic muscle sympathetic nerve activity, MSNA, using microneurography) but
not arterial pressure, probably due to skeletal muscle vasodilation. These studies do
mention, however, that subjects with insulin resistance may have an exaggerated
sympathetic activation response to hyperinsulinemia or impaired vasodilation, which
could then result in an increase in arterial pressure.
Grassi and colleagues (Grassi, et al., 1995), comparing normotensive obese and control
subjects, report that basal values of plasma norepinephrine were not statistically
significantly different between the two groups, while muscle sympathetic nerve activity
42
(MSNA), measured using the microneurographic technique and expressed as either bursts
per minute or bursts per 100 heartbeats, was about twice as high in obese subjects when
compared to the control group. They also found that plasma norepinephrine and MSNA
were positively correlated in control subjects (r = 0.76, p < 0.05) but not in obese ones (r
= 0.35, p > 0.05). In the same study, when evaluating baroreflex sensitivity using
vasoactive drug infusions, they found that the average baroreflex sensitivities during
baroreceptor stimulation and deactivation were significantly reduced in obese subjects
when compared to the lean control subjects. Both changes in heart rate and MSNA
induced by the drugs were significantly smaller in obese subjects than in controls.
Grassi et al (1995) concluded that human obesity is associated with a significant
sympathetic activation, occurring in the absence of any blood pressure elevation, as well
as with an impairment of the baroreceptor reflex. They also mention that the
enhancement of sympathetic activity may be due to the baroreflex impairment as well as
to the increase in levels of circulating insulin and/or angiotensin II. The authors speculate
that the significant increase in sympathetic activity observed in obese normotensive
subjects may be one of the factors responsible for, in the long term, the development of
hypertension in this group of patients.
The study of (Laakso, et al., 1990) in obese subjects indicates that obese subjects with
decreased insulin sensitivity (or, equivalently, with increased insulin resistance) showed
impairment in limb vasodilator response to insulin. Insulin mediated glucose uptake
(IMGU) in insulin sensitive tissues is believed to be determined by two major
43
components, glucose extraction in insulin sensitive tissues (arteriovenous glucose
difference, AVGd, across the muscle) and blood flow into the muscle, according to Fick's
principle (Zierler, 1961). Laakso and colleagues (Laakso, et al., 1990) have found that, in
obese men, the decrease in rates of whole body IMGU is due to both a reduction in
skeletal muscle glucose uptake and an impairment in insulin's physiological effect to
increase blood flow to skeletal muscle. They conclude that this observed reduction in
blood flow to insulin-sensitive tissues in obese subjects may be an important component
in the increased insulin resistance observed in these subjects.
In another study, (Laakso, et al., 1992) have shown that impaired insulin-mediated
augmentation of skeletal muscle blood flow in obese non-insulin dependent diabetes
mellitus (NIDDM) patients is not related to the obesity status of these patients, but to the
diabetic state per se.
The mechanism by which insulin promotes vasodilation is not yet clear. Aggregated
results from different studies so far suggest that insulin regulates nitric oxide (NO)
mediated vasodilation (Vischer, 1998). Impairment in insulin-mediated NO production
may, thus, be the link relating insulin resistance and an increased risk of vascular diseases
(Steinberg, et al., 1996). Whether there is a direct effect of insulin on endothelial cells or
whether insulin exerts an indirect effect via a metabolic intermediate is still an open
question.
A recent study by Koulouridis and colleagues (Koulouridis, et al., 2008) in children and
adolescents relating hyperinsulinemia and hypertension showed that, for subjects with
44
insulin levels lower than the 75th percentile, an increase in insulin level was related to an
increase in both systolic and diastolic blood pressure, while insulin levels greater than the
75th percentile were negatively related to blood pressure (BP), especially to diastolic BP.
The authors defend the vasodilation effect of insulin in these subjects, since they mention
that diastolic BP is primarily regulated by peripheral vascular resistance. They also note
that the vasodilating action of insulin upon skeletal muscle vasculature was abolished
among obese subjects in their study.
Chapter 4: Cardiac autonomic nervous system: overview and
measurement of autonomic function
A person’s instantaneous heart rate at rest, as well as arterial blood pressure and other
hemodynamic parameters, fluctuates on a beat-to-beat basis (Akselrod, et al., 1981).
Heart rate variability (HRV) has been used to refer to the beat-to-beat oscillations
between consecutive instantaneous heart rates as well as those between consecutive heart
beats or RR intervals (Task Force, 1996). HRV, in individuals with no sinus node
disease, relates to the state of the autonomic nervous system (Davey, 2004). It has been
shown that a person with a high HRV post myocardial infarction has a lower risk of
presenting ventricular arrhythmias and, thus, of sudden cardiac death. Likewise, reduced
HRV appears to be a marker of ventricular arrhythmia (Davey, 2004).
The autonomic nervous system has also been shown to be closely related to sudden
cardiac death. In particular, sympathetic hyperactivity has been related to ventricular
tachyarrhythmias, while an increase in vagal tone is believed have a protective and
antifibrillatory effect (Hohnloser, et al., 1994). It is usually considered that the
45
sympathetic and parasympathetic nervous systems are the principal systems involved in
short-term cardiovascular control (seconds to minutes) (Akselrod, et al., 1981). Spectral
analysis of heart rate variability (HRV) is a widely used simple quantitative non-invasive
assessment of autonomic function (Task Force, 1996).
In order to better characterize the underlying dynamics and relationships between the
cardiovascular variables involved in the cardiac autonomic control, not only variations
observed at the output variable as is the case of HRV, this study proposes the use of the
minimal model of cardiorespiratory control (detailed in chapter 5) as a means to obtain
quantitative measures of the autonomic function of individual subjects using noninvasive
measurements of respiration, blood pressure, and heart rate. Other authors have shown
that multivariate models, which allow the interactions between changes in cardiovascular
variables (e.g. blood pressure, heart rate, respiration) to be evaluated, offer a more
comprehensive approach to the assessment of autonomic cardiovascular regulation than
that represented by the separate analysis of fluctuations in blood pressure or heart rate
only (Parati, et al., 1995).
Based on our accumulated experience from previous studies using the minimal model of
cardiorespiratory control, the respiratory cardiac coupling gain G
RCC
obtained from the
model quantifies cardiac vagal modulation, while the baroreflex gain G
ABR
, which reflects
baroreflex sensitivity, is a measure of sympathetic and vagal balance (Khoo, 2010;
Chaicharn, et al., 2009). The G
RCC
gain reflects vagal modulation such that a decrease in
G
RCC
is related to a decrease in vagal modulation. In terms of the baroreflex gain, a
46
reduction in G
ABR
is related to a decrease in vagal modulation, an increase in sympathetic
modulation, or both. These parameters will be presented in more detail in chapter 5.
This chapter begins by presenting previous studies investigating the relationships among
autonomic imbalance and cardiovascular dysfunctions, such as hypertension. This is
followed by a discussion of the frequency domain and transfer function analysis of the
cardiac autonomic system. The chapter is finalized by an overview of the use of
baroreflex sensitivity and respiratory sinus arrhythmia as measures of cardiac autonomic
control.
4.1. Systemic hypertension, baroreflex sensitivity, and cardiovascular risks
Rademacher and colleagues have shown that childhood blood pressure, independent of
BMI, is related to the development of cardiovascular risk factors in early adulthood, and
that the combination of hypertension and obesity in childhood predicts the highest levels
of cardiovascular risk factors in the young adult (Rademacher, et al., 2009).
Obstructive sleep apnea has been linked to cardiovascular complications. In particular,
studies indicate that long-term exposure to repetitive episodes of apnea and arousals
constitutes an independent risk factor for systemic hypertension, heart failure, myocardial
infarction, and stroke (Brooks, et al., 1997; Butt, et al., 2010; Roux, et al., 2000).
Different studies have shown that the use of continuous positive airway pressure (CPAP)
by patients with OSA both reduces the risk of developing cardiovascular disorders and
reduces disease severity (Butt, et al., 2010; Khan, et al., 2010; Doherty, et al., 2005).
47
Among the pathophysiological pathways suggested for the development of
cardiovascular disease in OSA are endothelial dysfunction, overactive sympathetic
system, oxidative and inflammatory stress, metabolic dysregulation, and reduced
baroreflex sensitivity (Baguet, et al., 2009; Khan, et al., 2010; Lavie, et al., 2009).
Baroreceptor sensitivity and cardiovascular mortality
An increase in baroreceptor sensitivity is associated with a greater decrease in heart rate
with baroreceptor activation. Osterziel and colleagues (Osterziel, et al., 1995)have shown
that patients with myocardial infarction who did not have congestive heart failure but
who presented a decreased baroreflex sensitivity had an increased risk for sudden death.
They showed diminished baroreflex sensitivity, related to low vagal tone and/or increased
sympathetic tone, to be a prognostic indicator in patients with congestive heart failure.
The ATRAMI
4
study(La Rovere, et al., 1998), provided clinical evidence that after
myocardial infarction the baroreflex sensitivity (BRS) has significant prognostic value
independently of the established clinical predictors low left-ventricular ejection fraction
(LVEF) and ventricular arrhythmias (frequent ventricular premature complexes, VPC).
In a comprehensive review paper, (Vaseghi, et al., 2008) discuss the role of alterations in
autonomic function in several interrelated cardiac conditions including sudden cardiac
death, congestive heart failure, diabetic neuropathy, and myocardial ischemia. They show
that sympathetic activation has been linked with ventricular arrhythmias and sudden
cardiac death, whereas vagal activity may exert a protective effect. They discuss the
4
Autonomic Tone and Reflexes After Myocardial Infarction
48
association between loss of protective vagal reflexes with ventricular tachyarrhythmias in
heart failure and myocardial infarction. They also mention that depressed baroreflex
sensitivity and decreasedheart rate variability have been associated with greater
susceptibility to ventricular fibrillation during and after ischemic episodes.
Metabolic and autonomic dysfunctions
Patients with diabetes have also been shown to present autonomic abnormalities even in
the absence of clinical symptoms. Most frequently, these patients have been reported to
show a slight increase in heart rate and a reduction in heart rate variability, which has
been linked to vagal damage. Diabetic subjects have also been reported to present a
reduction in measures of cardiac baroreflex gain or sensitivity (Bernardi, 2000).
Experimental diabetic neuropathy in animal models have shown that induced diabetes
resulted in a reduction in respiratory sinus arrhythmia, increased resting heart rate, and
decreased gain of the baroreflex-mediated bradycardia in response to transient
hypertension (Low, 2007). Chapter 3 presented in greater details the relationships
between metabolic and autonomic dysfunctions.
4.2. Autonomic nervous system
The visceral or autonomic nervous system can be defined in broad terms as “the neuronal
groups and fiber connections that control the activity of visceral organs, vessels, and
glands” (Brodal, 2003). The heart muscle, smooth muscle of visceral organs, and
exocrine glands are thus controlled by the autonomic nervous system (Kandel, et al.,
49
2000). As its name implies, its activity does not depend on voluntary or conscious
control.
An anatomical and functional division normally used divides the autonomic nervous
system into the sympathetic, the parasympathetic, and the enteric nervous system. The
latter, comprising sensory and motor neurons in the gastrointestinal tract that mediate
digestive reflexes (Kandel, et al., 2000), will not be addressed in this study.
For the body to function properly, its internal milieu should be regulated to maintain an
optimal environment for the function of cells, tissues and organs, even in the presence of
varying internal and external demands. This control is achieved by means of the
autonomic nervous system, where the autonomic regulation is usually fast, occurring
within seconds, and the neuroendocrine system, where the neuroendocrine regulation is
relatively slower, occurring over tens of minutes, hours or days (Jänig, et al., 1999;
Sparks, et al., 1987). Since this study is focused on the effects of the autonomic nervous
system on cardiorespiratory regulation, the latter will not be discussed.
4.2.1. Overview
The sympathetic and parasympathetic divisions of the autonomic nervous system
typically function in a complementary fashion. For instance, arterial blood pressure
depends on the cardiac output and blood flow resistance. The heart is innervated by both
sympathetic and parasympathetic nerves that usually function reciprocally to regulate
heart rate, contractility, and conduction velocity. The sympathetic system increases blood
pressure by increasing heart rate, heart contractility and inducing vasoconstriction, thus
50
increasing peripheral resistance, while the parasympathetic system decreases heart rate
and has some effect on vasodilation (Kandel, et al., 2000; Constanzo, 2006). The
inhibition of one system and the concomitant activation of the other are the basis for the
arterial baroreceptor reflex or baroreflex, a negative feedback system for short-term
regulation (time scale of seconds to minutes) of mean arterial blood pressure (Pinna,
2007; Wallin, et al., 1988).
However, some stimuli may be such that vagal and sympathetic responses are both
activated. For instance, the cold face test, a modification of the diving reflex that occurs
with, for instance, immersion of the face in water, activates both the peripheral
sympathetic and the cardiac parasympathetic nervous system. This combined activation
induces peripheral vasoconstriction and consequent blood pressure increase as well as a
decrease of heart rate induced by the cold stimulation of the face via reflex centers
located in the brainstem region (Hilz, et al., 1999; Hilz, et al., 2006). Subjects presenting
a disturbance in the integrity of the trigeminal-brainstem-vagal reflex arc yield a cold
face test response with absent or diminished bradycardia (Hilz, et al., 2006; Khurana, et
al., 1980). Patients with diabetes mellitus, brainstem stroke, or Shy-Drager syndrome
present an attenuated cardiovagal response or even a slight increase in heart rate in
response to cold face stimulation (Khurana, et al., 1980).
4.2.2. Autonomic testing
Autonomic testing gives an indication of the overall integrity and the function of afferent
pathways, central processing systems, and efferent pathways of autonomic reflexes. One
51
method of testing an autonomic reflex is by recording efferent neural activity directly
from the nerves (Jänig, 1990). Indirect noninvasive methods, such as heart rate variability
based methods, record responses from end organs which are part of the efferent pathway
(Loewy, et al., 1990).
Autonomic cardiovascular reflexes are commonly used as tests of the autonomic
function, since heart rate and blood pressure measurements are relatively easy to obtain
and abnormal findings usually indicate diffuse autonomic damage (Appenzeller, et al.,
1997).
A tool to quantitatively measure the functioning of the autonomic nervous system is not
only useful but an important aid in evaluating a person's health. This study is interested in
quantifying the contributions of the sympathetic and parasympathetic systems in heart
rate and blood pressure regulations, as these are an indication of a subject’s overall
autonomic function. The minimal model of cardiorespiratory control, presented in the
next chapter, is used in this study to characterize both baseline autonomic activity (supine
posture) and the response of the autonomic system to prolonged orthostatic stress (steady-
state standing posture) from noninvasive measurements of respiration, blood pressure,
and heart rate.
4.3. Frequency response
Vagal activity slows conduction of the sinoatrial (SA) and atrioventricular (AV) node,
slowing the heart rate (or, equivalently, increasing the R-R interval). The latency of the
response of the sinus node is very short. It has been reported that vagal stimulation results
52
in a peak response in either the first or second heart beat (1 to 2 secs for a heart rate of 60
beats per minute, bpm) after its onset, and that after cessation of the stimulus the heart
rate returns to its previous level a little slower, but in less than 5 seconds. An increase in
cardiac sympathetic nerve activity increases both the heart rate and the force of
contraction. The latency period after the onset of sympathetic stimulation is longer than
that of the onset of vagal simulation, around 5 seconds, after which a progressive increase
in heart rate is observed, achieving a steady level in 20 to 30 seconds (Hainsworth, 1995).
Usually both divisions of the autonomic nervous system are observed, and the net effect
on heart rate reflects the balance between the two effects. At rest, for instance, the vagal
effect is dominant. A reflex increase in heart rate may be the result of a decrease in vagal
tone, an increase in sympathetic tone, or both.
In terms of frequency response, the parasympathetic system has been shown to respond
over a wide frequency range, effectively up to 1.0 Hz (corresponding to an oscillation
period of 1 second) (Parati, et al., 1995), while the sympathetic system can only respond
at relatively lower frequencies below roughly 0.1 Hz (Akselrod, et al., 1985). Thus, heart
rate fluctuations below 0.1 Hz (corresponding to oscillation periods above 10 seconds)
can be mediated by both the sympathetic and parasympathetic systems, while faster
fluctuations can only be mediated by the latter. Consequently, heart rate response to
sympathetic stimulation acts as a low-pass filter system (Mokrane, et al., 1998) with a
low cutoff frequency of about 0.1 Hz, while response to vagal cardiac control, while also
53
having a low-pass filter characteristic, has a relatively much higher cutoff frequency, at
approximately 1.0 Hz (Parati, et al., 1995).
Studies in humans with pharmacological agents have shown evidence for these
considerations. For instance, it has been shown that administration of atropine, a
muscarinic receptor antagonist used to inhibit vagal activation on heart, eliminates most
of the HR oscillations above 0.15 Hz while still leaving variabilities below 0.15 Hz partly
unaffected. On the other hand, the administration of propranolol, a beta-blocker that
binds to beta-adrenoceptors, thus blocking the binding of norepinephrine and epinephrine
to these receptors, inhibiting sympathetic activity, has been found to reduce HR
fluctuations below 0.15 Hz, while those above this mark remain relatively unaffected
(Parati, et al., 1995).
In order to disentangle the contributions of different systems which respond within
different time periods or, equivalently, with different oscillation frequencies, spectral
analysis is commonly used. By this approach, different contributions in the form of
different oscillation frequency components can be analyzed.
For instance, various studies have shown that fluctuations in blood pressure (BP) and
heart rate (HR) with frequencies ranging between 0.025 and 0.50 Hz (corresponding to
periods from 2 to 40 seconds) are at least in part mediated by neural autonomic influence
(Parati, et al., 1995). For this reason, spectral or frequency domain analysis of the
variabilities observed in heart rate and blood pressure is normally focused on the
frequency components within this frequency range. There are a large number of studies
54
that have analyzed HR and BP fluctuations in order to obtain information about the
neural regulations believed to cause these variations. However, the physiological
interpretations of the frequency components in HR and BP variability are still not
completely agreed on (Parati, et al., 1995; Eckberg, 1983; Malliani, et al., 1991).
The low frequency (LF) range of the heart rate variability signal is usually defined as
centered around 0.1 Hz, between 0.04 and 0.15 Hz. It physiological interpretation is still
not clear and has been the subject of much debate (Bonnemeier, 2007), since both
sympathetic and parasympathetic contributions can be present in this frequency range
(Akselrod, et al., 1981; Pomeranz, et al., 1985; Akselrod, et al., 1985). Since an increase
in the LF power has been observed as a consequence of sympathetic activation, many
authors have used this power range as a measure of sympathetic activity (Cerutti, et al.,
1995; Malliani, et al., 1991). Different studies have also related this frequency range to
the baroreceptor reflex dynamics (Akselrod, et al., 1981; Khoo, et al., 1999; Bonnemeier,
2007). For this reason, other authors consider the low frequency variation in heart rate to
be a measure of sympathetic and vagal balance. Changes in posture, for instance, alter
this sympathovagal balance (Akselrod, et al., 1985), and this is reflected in the heart rate
power spectrum.
The respiratory frequency, usually between 0.15 and 0.4 Hz (corresponding to 9 to 24
breaths per minute), is generally referred to as the high frequency (HF) range. This
rhythm is mediated by the vagus nerve on the heart (Cerutti, et al., 1995) and it is
generally agreed to be a marker of parasympathetic activity, since the response time of
55
the parasympathetic nervous system is much shorter than that of the sympathetic nervous
system (Pomeranz, et al., 1985; Akselrod, et al., 1981).
The slower response of the sympathetic system leads to the assumption that the high
frequency (HF) components of heart rate variations are mediated by the parasympathetic
system. Pharmacologic studies in humans have shown that HRV in all frequencies
between 0.024 Hz to 1 Hz are mediated by the parasympathetic system, while the
sympathetic system mediates only the low frequency variations in heart rate (Akselrod, et
al., 1981). Akselrod and colleagues (Akselrod, et al., 1985; Akselrod, et al., 1981) have
shown that parasympathetic blockade in trained, conscious, unanesthetized dogs
essentially eliminates high (respiratory) frequency fluctuations in heart rate, as well as in
blood pressure, while -blockade does not significantly alter heart rate variability, nor
blood pressure variability, which indicates that sympathetic activity is not involved in
high, respiratory, frequency events.
Some authors consider the LF to HF power ratio as a measure of sympathovagal balance,
a measure of the relative strength of the sympathetic versus the parasympathetic outflow.
A low vagal/high sympathetic tone promotes ventricular arrhythmias and is associated
with an increase in cardiovascular risk (Davey, 2004).
Pomeranz and colleagues (Pomeranz, et al., 1985) have found that low-frequency
fluctuations are jointly mediated by the sympathetic and parasympathetic nervous
systems and are increased by standing, while high frequency fluctuations are mediated
solely by the vagal system and decreases by assuming the upright posture.
56
A third peak in the power spectrum of the heart rate variability signal is centered around
0.04 to 0.08 Hz and is usually called very low frequency. This response has been related
to thermoregulatory fluctuations in peripheral vasomotor tone (Akselrod, et al., 1981;
Akselrod, et al., 1985). This frequency range will not be considered in this study.
4.4. Transfer function analysis of heart rate variability
An alternative method for obtaining information about cardiovascular variabilities and,
thus, cardiac autonomic control, can be obtained using a systems approach, as discussed
in chapter 5.
The systems approach for the study of the beat-to-beat cardiovascular variabilities can
generate information not only about the oscillations of the cardiovascular variables
themselves, but also about the neural regulatory mechanism or system responsible for
generating these oscillations (Xiao, et al., 2005). In this approach, the system is usually
represented by a mathematical transfer function that represents how the system, in this
case the cardiovascular neural regulatory mechanism, generates its output, e.g.
oscillations in heart rate, as a response to its input, e.g. oscillations in arterial blood
pressure. For instance, the transfer function H
RCC
(t) in Figure 10 mathematically
represents how the input, respiration (or, more specifically, variations in instantaneous
lung volume, ILV) generates the output, variations in R-R intervals, RRI.
Besides a feedforward path from input and output, there can also be a feedback path in
the reverse direction. The systems approach allows for a closed loop representation, in
which both a feedforward and a feedback path are present in the system’s representation
57
(Khoo, 2000). This closed-loop approach is appealing for a cardiovascular model, since
the cardiovascular variables affect one another. For instance, heart rate affects arterial
blood pressure by means of the mechanical coupling between the left ventricle and the
vasculature, as well as the arterial blood pressure affects heart rate through the
baroreceptor reflex (Saul, et al., 1991; Akselrod, et al., 1985). Figure 11 in the next
chapter shows the schematic block diagram of the complete closed-loop minimal model
of cardiovascular control considered in this study.
The transfer function is usually evaluated separately in the low frequency (LF) and high
frequency (HF) bands (Parati, et al., 2004). In our study, the gain G
ABR
is the gain
between heart rate and respiration evaluated in the low frequency band, while the gain
G
RCC
is the gain between heart rate and blood pressure variations evaluated in the high
frequency band.
4.5. Baroreflex sensitivity as a measurement of autonomic function
The baroreceptor-cardiac reflex sensitivity (BRS) is an established measure of cardiac
autonomic function (McNally, et al., 2003; La Rovere, et al., 2008). Impairments in
autonomic cardiovascular regulation seem to be related with increased mortality in
patients with heart disease (Keyl, et al., 2001). In particular, a low BRS has been found to
be an independent marker of cardiovascular risk in myocardial infarction patients
(Karemaker, 2002; La Rovere, et al., 1998). In congestive heart failure (CHF), the
impairment of the baroreflex control of sympathetic activity, which may cause the
marked sympathetic activation present in this condition, diminishes the baroreceptor
58
inhibitory influence on heart rate and may be responsible for the early sympathetic
activation that occurs in the course of CHF (Grassi, et al., 1995).
Patients with hypertension, diabetes, congestive heart failure, or coronary artery disease
have been found to have low baroreflex sensitivity. Severe obstructive sleep apnea
patients were found to present depressed baroreflex sensitivity during sleep, which may
be related to the cardiovascular pathophysiology observed in OSA patients. CPAP
therapy in these patients significantly improved the baroreflex sensitivity measures
(Ryan, et al., 2007).
Arterial pressure receptors or baroreceptors in the carotid sinus (monitoring the blood
being delivered to the head) and in the aortic arch (examining the blood delivered to the
systemic circulation), the primary systemic arterial baroreflex sensors (Batzel, et al.,
2006), are mechanoreceptors that sense pressure changes by detecting the stretch of the
blood vessels walls (Kirchheim, 1976). These receptors are important in the short-term
regulation of systemic arterial blood pressure (Sparks, et al., 1987; Cowley, et al., 1973;
La Rovere, et al., 2008). These sensors respond not only to the amount of stretch but also
to changes in stretch and the rate of change (Sato, et al., 1998; Scher, 1977).
An increase in arterial pressure causes the blood vessel walls to expand, which stimulates
the firing of the arterial baroreceptors. These action potentials are then processed by the
CNS, which interprets the firing rate, proportional to the change in arterial pressure or
stretch of the receptors, and responds by stimulating the vagal nuclei and elevating the
parasympathetic output while simultaneously decreasing the discharge of sympathetic
59
neurons to the heart and peripheral vascular system. This leads to a drop in peripheral
resistance (sympathetic inhibition), bradycardia, and depressed cardiac contractility
(parasympathetic activation). These combined effects work to reduce arterial blood
pressure (La Rovere, et al., 2008). Figure 7 illustrates this short-term neural baroreflex
loop response to a rise in pressure, considering the high-pressure sensor-response loop of
the cardio-arterial baroreceptors.
Hypovolemia Arterial Pressure (-)
Venous Filling Pressure (-)
Cardiac Output (-) CNS
Sympathetic Activity (+) Parasympathetic Activity (-)
Systemic Vascular Venous Tone (+) Contractility (+) Heart Rate (+)
Resistance
P
ra
(+) Stroke Volume (+)
Arterial Pressure (+) Cardiac Output (+)
Figure 7: Baroreceptor control loops, adapted from (Batzel, et al., 2006).P
ra
: right arterial pressure.
Analogously, a decrease in arterial pressure lowers the rate of firing of action potentials
by the baroreceptors, which leads simultaneously to an increase in sympathetic tone,
leading to an elevation in total peripheral resistance by arterial constriction and an
increase in cardiac output by augmenting cardiac contractility and heart rate, and a
Arterial Baroreceptor
Activity
(+)
(+)
60
reduction in parasympathetic output, leading to an increase in arterial blood pressure (La
Rovere, et al., 2008).
The baroreflex sensitivity can, thus, be defined as sensory firing in response to pressure
induced stretch (Batzel, et al., 2006), and is related to a balance between the sympathetic
and parasympathetic nervous system activities. A shift of the autonomic balance towards
a sympathetic dominance decreases the baroreflex sensitivity, while a shift of the
autonomic balance towards a parasympathetic dominance increases the baroreflex
sensitivity (Vanoli, 1997). Therefore, in this study our measure of the baroreflex function,
the baroreflex gain G
ABR
, is interpreted as reflecting the influence of both sympathetic and
vagal activations, such that a decrease in G
ABR
is related to a decrease in vagal activity, an
increase in sympathetic activity, or both.
4.5.1. Assessment of baroreceptor sensitivity
Different methods have been proposed in the literature for assessment of baroreceptor
activity. A common method for evaluating the baroreceptor sensitivity was proposed by
Smyth, Sleight and Pickering (Smyth, et al., 1969). They proposed to study the reflex
heart rate response to physiological activation or deactivation of the baroreceptors by use
of vasoactive drugs to induce changes in arterial pressure. They observed that an increase
in blood pressure induced by a phenylephrine injection is followed by beat-by-beat
increases in heart period. The authors found this beat-to-beat relationship between
systolic blood pressure and the R-R interval of the succeeding cardiac cycle during the
transient pressure changes produced by the injection to be linear. They used the slope of
61
the regression line of the systolic pressure on heart period (ms/mmHg), or the increase in
pulse interval for each millimeter rise in systolic pressure, as an index of the baroreceptor
reflex sensitivity.
The continuous smaller variations in blood pressure throughout the day also activate the
baroreceptors (La Rovere, et al., 2008; Parati, et al., 2000). Spectral analysis of RR
interval variations or HRV have been used to obtain noninvasive measurements of the
baroreceptor function since each spontaneous oscillation in arterial blood pressure brings
about an oscillation in the RR interval at the same frequency via the arterial baroreceptor
reflex (La Rovere, et al., 2008).
An alternative noninvasive technique proposed, albeit time-consuming and complex to
use, is the neck chamber technique, which, by applying a measurable positive and
negative pneumatic pressure to the neck region allows local activation or deactivation of
the carotid baroreceptors (La Rovere, et al., 1995).
In this study, the arterial baroreflex response is evaluated noninvasively and in a time-
efficient manner by determining the gain G
ABR
using the minimal model of
cardiorespiratory control. Mudler (Mulder, 1985) has also indicated that the gain of the
transfer function between variations in blood pressure and heart rate in the frequency
range roughly between 0.07 and 0.14 Hz would be an appropriate quantification of
baroreflex sensitivity. Robbe and colleagues (Robbe, et al., 1987) demonstrated, using the
phenylephrine method and by means of spectral analysis, that this gain in the
62
aforementioned frequency band is indeed an appropriate index of BRS and that it is
sensitive to changes in mental and physiological states.
4.6. Respiratory sinus arrhythmia as a measure of cardiac autonomic
control
Heart rate is also influenced by our respiratory rate. Respiratory sinus arrhythmia (RSA)
is the fluctuation in heart rate synchronous with respiration. In particular, the RR interval
on an ECG is shortened (or heart rate is increased) during inspiration and is prolonged (or
heart rate is decreased) during expiration (Yasuma, et al., 2004). Yasuma and colleagues
(Yasuma, et al., 2004) postulate that this matched timing of heart beat and respiratory
rhythm improves pulmonary gas exchange.
Respiratory frequency variations in heart rate seem to be parasympathetically mediated,
since the sympathetic nervous system dynamics is too slow to mediate variations at the
respiratory frequency (Akselrod, et al., 1985). Therefore, the respiratory sinus
arrhythmia, or respiratory variations in heart rate, is related to the level of efferent vagal
activity to the heart and can be used as a noninvasive quantitative indicator of
parasympathetic cardiac control (Katona, et al., 1975; Eckberg, 1983). However, RSA is
influenced not only by respiration, but also by baroreflex responses to respiratory related
fluctuations in arterial blood pressure (Khoo, 2008). Thus, in this study we are using the
respiratory cardiac coupling gain (G
RCC
), relating changes in respiration to variations in
RRI, as a measure of vagal modulation, as mentioned in the next section.
63
4.6.1. Assessment of respiratory sinus arrhythmia
One measure that has been used to assess respiratory sinus arrhythmia is the relative
frequency histogram of RR-intervals. The standard deviation of the RR-interval (SD
RR
)
has been used in research as an index of cardiovascular autonomic nervous control
(Ewing, et al., 1984; Rusu, et al., 2008; Bittiner, et al., 1986). This index has, for
instance, been used to differentiate diabetics from normal controls. Diabetic subjects
usually have much less variability in heart rate when compared to normal controls, and
this reduction is considered a strong evidence of cardiac autonomic neuropathy (Pfeifer,
et al., 1982).
However, this index presents many disadvantages. For instance, while a reduced
variability is a strong evidence of diminished sinus arrhythmia, a normal value is not
necessarily an indication of a normal autonomic response, since other sources of
variability not related to respiration (e.g. premature ventricular contraction, PVC, and
slow trends in heart rate over time) can result in an increase of SD
RR
, effectively masking
RSA dysfunctions (Weinberg, et al., 1984). Another disadvantage is that SD
RR
is also
influenced by mean heart. A low SD
RR
can be a simple consequence of a faster heart rate,
or shorter RR-intervals, on average (Weinberg, et al., 1984).
Another proposed method for the assessment of RSA is based on successive differences,
or the absolute differences between adjacent RR-intervals. This measure is relatively
independent of mean heart rate, since the mean is effectively subtracted out of the
64
measure. However, this measure is still sensitive to short-term high-frequency heart
period fluctuations (Weinberg, et al., 1984; Berntson, et al., 2005; Task Force, 1996).
In the present study we will use respiratory cardiac coupling gain, G
RCC
, as a measure of
the influence of respiration on heart rate. Respiratory sinus arrhythmia (RSA), on the
other hand, is mediated by both respiratory cardiac coupling and baroreflex responses to
respiratory-related fluctuations in arterial blood pressure (Khoo, 2008; Berntson, et al.,
1997). Thus, G
RCC
is a measure of direct autonomic coupling between respiration and
heart rate, disentangled from baroreceptor influences on respiration, measured separately
as the gain G
ABR
. These gains will be explained in more detail in chapter 5.
4.7. The autonomic nervous system and metabolic and sleep disorders
Studies in adults have shown that diabetic patients have a reduced HRV power at all
frequencies when compared to controls, indicating a depression in both vagal and
sympathetic activities (Lishner, et al., 1987). The Task Force (Task Force, 1996) states
that diabetic autonomic neuropathy is also associated with a failure to increase low
frequency on standing, reflecting an impaired sympathetic response or a depressed
baroreflex sensitivity. Patients with sleep disorders have also been found to have
impaired autonomic functions. Narkiewicz and colleagues (Narkiewicz, et al., 1998) have
shown that cardiovascular variability is altered in patients with obstructive sleep apnea,
and that this alteration is observed even in the absence of hypertension, heart failure, or
other disease states.
65
The previous chapters presented aspects of the metabolic system and sleep disordered
breathing importantly related to the autonomic function. The background presented on
previous findings relating metabolic and autonomic dysfunctions present in sleep
disordered breathing will aid in the interpretation of the data obtained in the present work
and discussed in chapter 9.
66
Chapter 5: Minimal cardiorespiratory model
Physiological system modeling can be defined as a means to summarize experimental
data in a compact mathematical or computational form that aids in elucidating the
functional relationships among the observed physiological variables (Marmarelis, 2004).
As discussed by (Marmarelis, 2004), the model must be able to satisfactorily reproduce
the observed data when simulated, have the minimal mathematical or computational
complexity required to correctly quantify the variables of interest and their relationships,
and retain physiological interpretation as to advance our knowledge of the physiological
system’s behavior and functional properties.
The minimal model of cardiorespiratory control analyzed in this studyis used as a non-
invasive method for assessing autonomic function, based on a computational model of
cardiovascular variability (Chaicharn, et al., 2009; Belozeroff, et al., 2002). This model is
minimal in the sense that all transfer functions or blocks (labeled ‘H
RCC
(t)’, ‘H
DER
(t)’,
‘H
ABR
(t)’, and ‘H
CID
(t)’ in Figure 9 in section 5.2) that characterize the dynamics of the
system can be estimated from the noninvasive observed variables (respiration, heart rate,
blood pressure) obtained during a single experimental procedure (Khoo, 2008).
The parameters characterizing the dynamic response of the minimal model, which are
measures of the autonomic function, are obtained for each patient. These parameters are
estimated from data collected during a daytime study consisting of contiguous 10-minute
periods, with measurements of respiration, ECG, and continuous blood pressure during
the supine (baseline) and standing (orthostatic stress) postures.This chapter explains the
67
minimal cardiovascular model as a systems approach to the study of oscillations of
cardiovascular variables.
As will be discussed in this chapter, this systems approach provides the tools to study the
inter-relationships between varying signals, in this case the autonomically mediated
cardiovascular variables (e.g. heart rate, respiration, arterial blood pressure), not only the
individual oscillations themselves. This formulation permits investigation of the cause-
and-effect relationships between the variables under study, and is also a means to obtain
information about the state of the cardiovascular autonomic nervous system that regulates
these variables.
5.1. Control systems approach to the analysis of cardiovascular variables
The beat-to-beat oscillation of cardiovascular variables such as heart rate (HR) and
arterial blood pressure (ABR) have been studied for many years through different
methodologies (Pagani, et al., 1999; Malliani, 2000; Warner, et al., 1962). The motivation
is that a better understanding of these variabilities implies a better understanding of the
nature of these variabilities as well as the mechanisms and dynamics of the
cardiovascular regulatory system, mediated by the autonomic nervous system, producing
these oscillations. This knowledge can lead to the development of quantitative markers of
autonomic activity (Task Force, 1996; Jo, et al., 2001).
A commonly used methodology to quantitatively characterize the beat-to-beat
cardiovascular regulations is the power spectrum or frequency analysis of heart rate
variability (HRV) (Akselrod, et al., 1981; Malliani, 2000; Pagani, et al., 1999; Pomeranz,
68
et al., 1985), as mentioned in the previous chapter. The term heart rate variability (HRV)
has been used not only to refer to oscillations between consecutive instantaneous heart
rates, as the name suggests, but also to oscillations in the interval between consecutive
heart beats (Task Force, 1996), or R-to-R intervals (RRI).
Analysis of heart rate variability, e.g. power spectrum analysis of the magnitude and
speed of the variations in heart rate, gives important information regarding the state of the
autonomic nervous system (Davey, 2004; Pomeranz, et al., 1985), as presented in section
4.3. Nevertheless, in this analysis only a single signal is considered at a time, e.g. HRV is
analyzed independently of other variations. Moreover, only the output, e.g. heart rate, of
the system under study, not the system itself, is characterized by this procedure.Thus, this
methodology provides information about the output or signal being analyzed, but not
about the underlying dynamics and relationships between cardiovascular oscillations (Jo,
et al., 2003).
An alternative approach to the development of quantitative markers of cardiovascular
autonomic activity is the analysis of these oscillations through a systems perspective.
This approach to the analysis of cardiovascular variabilities (e.g. HR and ABP
variabilities) provides the tools to quantitatively study the dynamic coupling between
pairs of the measured signals, not only the variabilities themselves, thus yielding
important insights and clues to the autonomic mechanisms responsible for such coupling
(Belozeroff, et al., 2002; Xiao, et al., 2005). With this formulation one can gain further
knowledge and investigate the cause-and-effect relationships between the autonomically
69
mediated cardiovascular variables (e.g. respiration, heart rate and arterial blood pressure).
Mukkamala and colleagues (Mukkamala, et al., 1999)also used a closed-loop
cardiovascular regulation model and reported that cardiovascular system identification
provided a more sensitive tool to assess diabetic autonomic neuropathy than standard
autonomic tests.
In a systems approach, a mathematical model of the system under study is developed.
Insights about the original system’s behavior can be obtained from quantitative analyses
of the estimated mathematical model. Different mathematical descriptions of the same
system can be obtained, depending on the objectives of the proposed analysis (McGraw-
Hil, 1977). For instance, an input-output modeldescribes the system’s behavior from the
standpoint of the dynamical relationships between the model’s input and output signals.
This systems approach also allows for the systematic representation of interconnections
among system variables (e.g. oscillations in respiration influencing, and being influenced
by, oscillations in heart rate). This model-based approach is used both to characterize
baseline autonomic activity as well as to detect changes in autonomic control due to
different stimulus (e.g. cold face protocol and prolonged standing).
In order to estimate the proposed minimal model of cardiorespiratory control for each
patient, we apply system identification of impulse responses, using orthogonal Meixner
basis functionsextension, to characterize the dynamic properties of the respiratory sinus
arrhythmia and the baroreflex control on heart rate. More details regarding the system
identification methodology used in the model can be found in chapter 6.
70
5.2. The minimal model of cardiorespiratory control
A schematic representation of the major physiological mechanisms that contribute to
heart rate variability is depicted in Figure 8 (Khoo, 2008). In this study, we will
concentrate on the effects of fluctuations in RRI due to variations in respiration and
arterial blood pressure (ABP). Fluctuations in ABP are related to heart rate variability via
the baroreflexes. Oscillations in respiration are related to heart rate variability through
direct respiratory-cardiac coupling, which involves mechanisms such as vagal feedback
from the lung stretch receptors, respiratory modulation of the cardiovagal neural output,
intrathoracic pressure effects on the cardiopulmonary receptors, and direct mechanical
stretching and compression of the sino-atrial node (Khoo, 2008). It is important to point
out that this is not equivalent to what is usually referred to as respiratory sinus
arrhythmia (RSA), since RSA is mediated by both respiratory-cardiac coupling and
baroreflex responses to respiratory-related fluctuations in arterial blood pressure (ABP)
(Khoo, 2008; La Rovere, et al., 1995).
Figure 8: Schematic representation of the principal physiological mechanisms contributing to heart rate
variability and blood pressure variability (Khoo, 2008).
71
The minimal model of cardiorespiratory control, represented schematically in Figure 9
below, is a closed-loop system that accounts for these dynamic interrelationships between
different pairings of the three measured variables: respiration, heart rate, and systolic
blood pressure (Belozeroff, et al., 2002). These variables are represented respectively by
variations in instantaneous lung volume or ILV(t), RR interval or RRI(t), and
variations in blood pressure or SBP(t). The minimal model of cardiorespiratory control
assumes that oscillations in heart rate (or RRI) are generated via two functional
mechanisms: direct respiratory-cardiac coupling (corresponding to the “block” or transfer
function labeled ‘H
RCC
(t)’ in Figure 9) and the arterial baroreflex (‘H
ABR
(t)’ in Figure 9).
Figure 9: Closed-loop minimal model of cardiorespiratory control (from Belozeroff et al., 2002).
This model summarizes the major physiological mechanisms that can be involved in
generating the observed oscillations in heart rate and blood pressure (Khoo, 2008). This
closed-loop block diagram model allows for a more systematic representation of the
feedforward and feedback paths among the key physiological variables.
SBP(t)
SBP
(t)
Respiratory Cardiac
Coupling Dynamics
72
For instance, blood pressure variations ( SBP) can result from the direct mechanical
effects of respiration – primarily high frequency oscillations, changes in the peripheral
vasculature resistance – low frequency fluctuations, and/or through oscillations in stroke
volume (SV) and RRI – involving both high- and low-frequency fluctuations(Khoo,
2008). The effect of respiration on SBP is represented by H
DER
(t) inFigure 9, and the
combined effects of variations in peripheral vasculature, cardiac contractility, and RRI
influences on fluctuations in blood pressure by H
CID
(t).
Variations in RRI are assumed to be caused from direct respiratory-cardiac coupling
(H
RCC
(t) in the model) and/or by oscillations in arterial blood pressure (ABP) via the
baroreflexes (H
ABR
(t)).
The objective of the minimal model of cardiorespiratory control is not to include every
known mechanism and develop detailed mathematical equations relating all variables
involved in cardiorespiratory control, in order to account for the observed variabilities in
heart rate and blood pressure. A parallel study in the Cardiorespiratory Sleep Laboratory
at the University of Southern California has been the development of a comprehensive
model of circulatory control in SDB. This model contains a large number of parameters
in order to simulate the dynamics of cardiorespiratory control during wakefulness and
sleep, incorporating the respiratory, cardiovascular, and neural control systems (Fan, et
al., 2002; Ivanova, et al., 2004).
Our goal indeveloping the minimal model of cardiorespiratory control is to obtain a
mathematical representation that accounts for most of the dynamic behavior observed in
73
heart rate and blood pressure variabilities, yet that is still simple enough such that its
parameters, which determine the dynamic features of the model and, thus, give a measure
of the autonomic function, can be estimated from measurements acquired from an
individual subject in a single study (Khoo, 2008). This “minimal model” approach has
been employed in different studies by our group in an effort to better delineate which key
physiological mechanisms involved in heart rate and blood pressure variabilities are
affected by chronic exposure to sleep disordered breathing (SDB) (Blasi, et al., 2004;
Belozeroff, et al., 2002).
The systems identification procedure adopted, used to estimate the parameters of the
minimal model of cardiorespiratory control, employs Meixner basis functions for the
estimation of Volterra kernels using least squares minimization (Asyali, et al., 2005).
Since this study is focused on investigating the effects of variations in heart rate
stemming from oscillations in respiration and blood pressure, a subset of the minimal
cardiorespiratory model is currently being used, as depicted in Figure 10.
Figure 10: Subset (2-input 1-output) of the minimal cardiorespiratory model.
RRI
(t)
h
RCC
(t)
h
ABR
(t)
+
Extraneous influences
Heart period
RRI(t)
Respiration
ILV(t)
Blood pressure
SBP(t)
74
5.2.1. Autonomic parameters G
ABR
and G
RCC
As mentioned in the previous section, in the minimal model of cardiorespiratory control,
fluctuations in RRI are assumed to be a result of direct respiratory-cardiac coupling,
RCC, and/or blood pressure fluctuations via the arterial baroreflex, ABR.Other influences
not accounted for by the model are represented as the signal
RRI
(t) in Figure 10. The
dynamics of the relation between respiration and RRI is characterized by the transfer
function ‘H
RCC
(t)’ or, alternatively, the impulse response ‘h
RCC
(t)’ (Figure 11), while the
gains and temporal properties of the arterial baroreflex, ABR, are characterized by the
transfer function ‘H
ABR
(t)’ or, equivalently, the impulse response ‘h
ABR
(t)’ (Figure 11).
The closed-loop nature of the problem and, consequently, of the model used to represent
it, require that the equations that define the model be solved in the time domain, so that
the causality constraints and delays associated with the response at different portions of
the structure can be accounted for (Khoo, 2000).
Figure 11 shows the closed loop minimal model of cardiorespiratory control, with the
transfer functions in each “box” or “block” of Figure 9 replaced by the corresponding
impulse responses. The components circumscribed by the dashed lines constitute the
mathematical model employed in the present study, where the inputs are variations in
respiration, ILV(t), in liters, and variations in systolic blood pressure, SBP(t), in mm
Hg, and the output is variations in R-R interval, RRI(t), in milliseconds.
75
Figure 11: Closed loop minimal model of cardiorespiratory control. The subset indicated by the dashed line
corresponds to the subset of the model considered in the current study.The dynamics of respiratory cardiac-
coupling are represented by the impulse response function h
RCC
(t), while the arterial baroreflex dynamics are
represented by the impulse response function h
ABR
(t).
In linear systems theory, the impulse responseis a time function used to characterize the
response of a dynamic system, directly related to its transfer function. In summary, in the
minimal model of cardiovascular control the impulse response h
ABR
(t) quantifies the time
course of the change in RRI associated with an abrupt increase in SBP of 1 mm Hg, while
h
RCC
(t) quantifies the time course of the fluctuation in RRI as a result of a rapid
inspiration and expiration of 1 L of air (Jo, et al., 2003). The impulse response of a linear
system completely characterizes the dynamic properties of the system under study.
Knowledge of the impulse response of a system provides a means to determine the output
of this system to any arbitrary input (Khoo, 2000).
Accumulated experience from previous studies with this model show that the RCC gain
(G
RCC
), associated with the impulse response h
RCC
(t) and which is a measure of the effects
of respiration on heart rate, provides an index of vagal modulation of heart rate, while the
ABR gain (G
ABR
), associated with the impulse response h
ABR
(t) and which gives a
h
RCC
(t) h
CID
(t)
h
ABR
(t)
h
DER
(t)
SBP(t)
SBP
(t)
Arterial Baroreflex
(ABR) Dynamics
Respiratory Cardiac
Coupling (RCC)
Dynamics
76
measure of the independent effect of blood pressure on respiration and reflects arterial
baroreflex sensitivity, is influenced by both vagal and sympathetic tone (Khoo, 2010).
Thus, a decrease in G
RCC
is associated with a decrease in cardiac vagal modulation, while
a decrease in G
ABR
is related to a decrease in vagal modulation, an increase in sympathetic
modulation, or both.
5.3. Study protocol and instrumentation
5.3.1. Study protocol
Figure 12 illustrates the setup for the autonomic study. With the subject initially in supine
posture, as shown, non-invasive measurements of heart rate (ECG), blood pressure
(Nexfin), and airflow (pneumotachometer and pressure transducers) are performed. Other
measurements we are currently acquiring during the autonomic study includeelectrical
bioimpedance, from which cardiac output can be determined by detecting changes in
impedance related to changes in blood flow (Brazdzionyte, et al., 2007); peripheral
arterial tonometry (PAT), a finger plethysmographic approach that continuously
measures the arterial pulse waveform of the digit which can be used to acquire moment-
to-moment measurement of sympathetic tone (Schattenkerk, et al., 2009); a pulse
oximeter, used to monitor the arterial pulse waveform from the index finger contralateral
to that from which arterial blood pressure is measured, which, combined with ECG
measurements can be used to determine pulse transit time, PTT. More details on the
instrumentation used will be shown in section 5.3.2 of this manuscript.
77
Figure 12: Experimental setup for autonomic study
Measurements performed with the subject in supine posture give baseline values for each
subject’s autonomic activity. With the subject in the supine posture for at least 5 minutes,
the subject’s cuff blood pressure is initially measured and the mean of three
measurements taken at 1 minute intervals is used as reference. We then proceed to the 10-
minute measurement recording procedure from which baseline values of arterial
baroreflex and respiratory cardiac coupling gains are subsequently obtained. These
recordings are subsequently analyzed using the minimal model of cardiovascular control
depicted in Figure 11 in order to obtain the gains G
RCC_supine
and G
ABR_supine
corresponding
to each subject’s baseline autonomic activity, following the procedures detailed in section
5.2.1.
The next step in the autonomic study is a cold face test. In this test, with the subject still
in supine posture, after a 1 minute recording of the subject’s baseline activity, a cold pack
Continuous blood
pressure (Nexfin)
Respiration
(pneumotachometer and
pressure transducers)
Heart rate (ECG)
(not visible)
Peripheral arterial
tonometry (PAT)
Impedance cardiography
leads (from neck and
lower back electrodes)
78
(approximately0
o
C) is applied to the subject’s forehead and held in place for 1 minute
and then removed. The region of the eyes is avoided to prevent stimulation of the
oculocardiac reflex (vagally mediated). The recording is continued for 8 additional
minutes (the total time for this study is also 10 minutes) with the subject still resting in
supine.
The cold face test reproduces the characteristic heart rate and blood pressure changes of
the simulated diving reflex (bradycardia, peripheral vasoconstriction, increase in blood
pressure, increase in sympathetic activity) (Khurana, et al., 1980). The cold face test
results in stimulation of trigeminal brain stem cardiovagal and sympathetic pathways
without essential involvement of the arterial baroreceptors, and is therefore useful as a
test of efferent autonomic function (Hilz, et al., 1999; Brown, et al., 2003). Therefore, the
cold face test elicits an increase in both vagal and sympathetic activities.
Since the interest is in analyzing how the gains G
ABR
and G
RCC
change in time before,
during, and after applying the cold pack to each subject’s forehead, analysis of the cold
face test data using the minimal model of cardiorespiratory control requires the use of a
time-varying version of the model. Although this test was performed in each patient and
initial time-varying analyses were carried out, this will not be discussed in the present
study.
The next step of the autonomic test is recording of the same variables with the subject in
the standing posture. The upright position leads to a shift of the mainly parasympathetic
supine state to a sympathetically dominated standing state (Karemaker, 1997).
79
Cardiovascular adaptations to active standing from a supine posture can be divided into
different categories, depending on how long the change in posture has occurred. These
adaptations can be divided into an initial response, defined within 30 seconds of
assuming the standing posture, followed by an early steady-state response, defined within
1 to 2 minutes of the change in posture, a delayed response, occurring usually within 2 to
5 minutes of standing,and finally a prolonged response, occurring after having assumed
the upright posture for more than 5 minutes.These autonomic reflex responses result in
fluctuations in heart rate and blood pressure which compensate the sudden and significant
blood shift to the lower limbs as a result of both gravitational pooling and muscle
contraction (Appenzeller, et al., 1997).
Appenzeller and Oribe (Appenzeller, et al., 1997) present a thorough description of the
transient and steady-state autonomic response to standing, which will be summarized in
the following section. This short review is presented in order to aid in the interpretation
of the autonomic descriptors obtainedfrom the standing posture. Both transient and
steady-state autonomic responses will be mentioned. Nonetheless, in this study we are
only interested in the steady-state autonomic response to prolonged standing (steady-state
response to orthostatic stress). Recording of the standing autonomic measurements (blood
pressure, heart rate, and respiration) begins after the subject has assumed the upright
posture for at least 5 minutes for hemodynamic equilibration, and variables are recorded
during 10 minutes. The transient responses are discussed as an aid to understand how the
steady-state response is achieved, and to help understand the consequence of impairments
in the autonomic adaptations to postural change.
80
Autonomic adaptations to postural change (supine to standing) (Appenzeller, et al.,
1997)
Healthy subjects have a transient and later a steady-state autonomic response to active
standing. In terms of heart rate, there is initially a fast increase, with a peak at about 3
seconds after assuming the standing posture. A subsequent increase occurs to a maximum
at about 12 seconds after standing (reaching a maximum after about the 15
th
beat)
(Appenzeller, et al., 1997). The early increase in heart rate is credited to a sudden
inhibition of cardiac vagal input due to the exercise reflex resulting from voluntary
muscle contraction. The secondary peak is the result of further reflex inhibition of cardiac
vagal tone from the activation of the baroreceptors, due to the transient fall in pressure
induced by orthostasis, and an increased sympathetic tone (Oribe, 1999).
Seconds after this initial response, the pumping effects of limb and abdominal muscle
contractions during the effort of standing result in a rise in venous return, leading blood
pressure to overshoot transiently. This loading effect on the baroreceptors then lead to
reflex parasympathetic activation, resulting in a rapid vagal inhibition of the sinus node
and thus slowing the heart rate, which reaches a minimum at about 20 seconds (about the
30th heart beat) after active standing (Oribe, 1999). This relative bradycardia is vagally
mediated, but is dependent upon the preceding sympathetically mediated
vasoconstriction. After this decrease in heart rate, a gradual rise to baseline is observed
(Appenzeller, et al., 1997).
The abrupt increase in blood pressure as a result from the change in posture from supine
to standing is attributed to a mechanical increase in peripheral vascular resistance by the
81
contracting muscles on standing. This rapid increase is followed by a transient fall in
systolic and diastolic blood pressure, possibly due to compression of capacitance vessels
by the contracting muscles of the leg and in the abdomen.
This causes an increase in the blood volume in the heart, increasing right atrial and
ventricular filling pressures, which then activate the cardiopulmonary receptors resulting
in reflex vasodilation. A second mechanism that may contribute to the reflex vasodilation
is the activation of arterial baroreceptor reflexes by the early transient increase in arterial
pressure immediately following the onset of the upright posture.
This fall in blood pressure is then followed by a recovery and many times an ‘overshoot’
in arterial pressure during the first 30 seconds after standing. This recovery or occasional
overshoot observed in arterial pressure (occurring about 7 seconds after standing), is
believed to be due to a decrease in the activation of the arterial baroreceptors and
cardiopulmonary receptors.
Healthy subjects adapt quickly to the initial disturbances induced by standing, reaching a
complete readjustment within 1 minute. After this readjustment, only minor changes in
heart rate and blood pressure are observed. Postural change normally increases diastolic
pressure about 10% with no or very little change in systolic pressure, and the average
increase in heart rate observed is around 10 beats/min.
Within the next 1 to 2 minutes of standing, the early steady-state, there is a gradual
stabilization of both heart rate and blood pressure. From 2 to 5 minutes, the combined
82
effect of vagal withdrawal and sympathetic activation lead to increases in heart rate. After
about 5 minutes, a steady-state in heart rate and blood pressure is achieved (Appenzeller,
et al., 1997; Wieling, et al., 1992). The heart rate in this state is mainly due to
sympathetic drive. An excessive heart rate increase in steady state is evidence of
powerful adrenergic drive to the sinus node (Blomqvist, et al., 1983).
In terms of blood pressure, the steady-state is characterized by a fall in arterial pressure,
both systolic and diastolic, or in systolic pressure only. A fall in systolic pressure 20
mm Hg and of diastolic pressure 5 mm Hg due to change in posture from supine to
standing is considered abnormal (Dambrink, et al., 1991).
A small increase in heart rate after prolonged standing in patients with orthostatic
hypotension is interpreted to show impaired sympathetic heart-rate control, while the
complete absence of cardiac acceleration on standing is considered the result of total
cardiac denervation (Appenzeller, et al., 1997).
In relation to the G
RCC
and G
ABR
gains determined by our minimal model of
cardiorespiratory control, when comparing gains obtained in the supine (G
RCC_supine
and
G
ABR_supine
) and standing (G
RCC_stand
and G
ABR_stand
) postures, we expect G
RCC_stand
to be
lower than G
RCC_supine
gain, reflecting a decrease in cardiac vagal tone. In the standing
posture, shorter R-R intervals (or higher heart rate) are a consequence of a decrease in
parasympathetic modulation (Carnethon, et al., 2002). In terms of the baroreflex gain,
G
ABR_stand
is expected to be lower than G
ABR_supine
, suggesting a shift in autonomic balance
towards sympathetic activation.
83
5.3.2. Instrumentation
All patients were instructed to maintain their normal breathing pattern throughout the
study. To measure airflow a snug-fitting mask covering the nose and the mouth was used
onto which a pneumotachometer (model 3700, Hans Rudolph, Kansas City, MO) was
attached. The variation of the lung volume over time was obtained from integration of
airflow measured using the pneumotachograph connected to a differential pressure
transducer, Validyne Model MP45-1-871 variable-reluctance transducer, from Validyne
Engineering Corp., Northridge, CA. Heart rate was monitored with a standard three-lead
configuration and amplified using a BMA-200 bioamplifier, CWE Inc, Ardmore, PA.
Systolic, mean, and diastolic blood pressure signals were obtained for the continuous
blood pressure waveform recorded using Nexfin HD, from BMEYE B. V., Netherlands.
For noninvasive measurement of continuous arterial blood pressure, the Finapres and,
more recently, Nexfin have been used in different studies.
The Finapres uses a finger cuff equipped with an infrared photoplethysmograph to
measure the arterial blood volume under the inflatable cuff. Parati and colleagues (Parati,
et al., 1989) have shown that noninvasive beat-to-beat blood pressure recordings using
Finapres (finger arterial pressure) are comparable to those obtained with invasive intra-
arterial blood pressure monitoring at rest and during laboratory studies. Nevertheless,
although finger pressure tracks intra-arterial pressure, the arterial blood pressure wave
form changes shape while traveling from the aorta to the periphery. This may explain
84
why finger arterial mean pressure measured with Finapres seems to be 5 to 10 mmHg
lower than intra-arterial pressure in the brachial artery (Langewouters, et al., 1998).
The Nexfin monitor (BMEYE B.V., Amsterdam, the Netherlands) uses an updated
implementation of the Finapres method and provides reconstructed brachial arterial blood
pressure from the finger pressure. Using a finger cuff consisting of an inflatable air
bladder, a plethysmograph consisting of an infrared light-emitting diode and an infrared
photodiode for light detection, the Nexfin performs this reconstruction by applying a
physiological model and a regression-based level correction, correcting for the difference
in pressure waveforms and an individual forearm cuff calibration (Schattenkerk, et al.,
2009; Bogert, et al., 2005). Schattenkerk and colleagues (Schattenkerk, et al.,
2009)validated reconstructed brachial pressures obtained by the Nexfin monitor against
Riva-Rocci/Korotkoff (RRK) blood pressure measurements and concluded that Nexfin
provides accurate pressure measurement with good within-subject precision.
One temporary problem we have encountered with the use of finger pressure recording is
cold fingers, as also reported elsewhere (Tanaka, et al., 1993). We have observed that if
the patient has cold fingers, the systolic and diastolic blood pressures indicated by Nexfin
become unrealistically low. Warming of the hand helps reverse the condition. Reduced
blood flow due to the finger being in the cuff for a long time (due, for instance, to the
adjustment of other equipments while the Nexfin is still on) also leads to low blood
pressure indicated by the monitor. When this happens we proceed to turn off and remove
85
the equipment and ask the subject to move his fingers to restore blood flow and reduce
numbness.
Additional equipment used include a HLT100C module transducer, Biopack Systems
Inc., Goleta, CA, used to measure bioimpedance, for noninvasive determination of
cardiac output, and a PAT, Itamar Medical, Caesarea, Israel, for measurement of
peripheral arterial tonometry, a non-invasive measurement of sympathetic tone.
The impedance cardiography signal obtained from bioimpedance measurements is based
on the notion that blood pressure variations in main chest vessels during various changes
of heart cycles cause impedance variations that can be measured (Brazdzionyte, et al.,
2007). Blood is the most electrically conductive (lowest resistance) component in the
thorax (Sramek, 1988). Resistance of the chest is the sum of the resistance of the adipose
tissue, the heart, skeletal muscles, the lungs, vessels, bones, and air (Sodolski, et al.,
2007). Changes in the volume of the lungs during respiration and in the volume and
blood velocity in the large vessels during systole and diastole are responsible for
variations in the resistance of the chest. Changes in resistance caused by respiration can
be eliminated by using electronic filters (Pandey, et al., 2005). This way, there will be a
direct relation between the observed change in chest resistance and variations in blood
outflow (Sramek, 1988). Thus, continuous noninvasive impedance cardiography allows
primary measurement of stroke volume and its changes. Stroke volume is determined
from the measured impedance and oscillations in impedance using the formula originally
suggested by Kubicek (Kubicek, et al., 1966), later modified by Bernstein (Bernstein,
86
1986). Cardiac output can then be determined from the stroke volume and the measured
heart rate.
The PAT system detects sympathetic surge by measuring amplitude attenuation, which
reflects vasoconstriction, and pulse-rate increase (Pillar, et al., 2002).Arterial vascular
beds of the finger tips are very densely innervated by sympathetic vasoconstrictor
efferents, and blood flow through the finger tips is capable of great modulation (Schnall,
et al., 1999). The PAT probe is a noninvasive finger plethysmograph consisting of an
optical sensor housed in a self-pressurized finger-mounted shell, which generates a
uniform pressure surrounding the distal two phalanges of the finger (Pillar, et al., 2002).
Pulsatile volume changes are optically measured while the uniform pressure field unloads
the arterial wall tension. Changes in sympathetic nervous system activity, which are
mediated by alpha adrenoreceptor activation, result in episodic vasoconstriction of the
digital vascular beds with corresponding attenuation of PAT signal (Schnall, et al., 1999).
Thus, increases in sympathetic activity will elicit significant changes in peripheral
vascular cutaneous perfusion and can be readily detected on a beat-to-beat basis (O'Brien,
et al., 2005). O'Brien and colleagues (O'Brien, et al., 2005) showed an increased
sympathetic tone during wakefulness in pediatric SDB, as assessed by more pronounced
PAT signal attenuations during different autonomic challenges.
All the equipmentswere connected to a USB data acquisition device from National
Instruments, DAQPad-6020E, a 12-bit resolution analogue to digital converter (ADC) for
signal integration and synchronization. These synchronized digital signals were sampled
87
at 512 Hz and fed into a computer running Matlab, from Mathworks, Natick, MA, in
which an in-house generated program allowed simultaneous real-time visualization and
storage of all measured variables. All analysis (power spectral analysis, autonomic
descriptors determination etc) at this time are being performed off-line.
5.4. Autonomic compact descriptors
The RRI, blood pressure, and respiratory airflow data were recorded and sampled at 512
Hz. The processing of these signals is similar to that described previously in (Jo, et al.,
2001). In summary, the time series of R-R intervals was obtained from the time-locations
of the QRS complexes in the ECG tracing, initially automatically detected by a computer
algorithm then manually reviewed and edited when necessary to prevent detection errors.
This beat-to-beat succession of spikes was converted into an equivalent uniformly spaced
time-series and subsequently downsampled to 2 Hz.
The systolic (SBP) and diastolic (DBP) blood pressures were automatically extracted on a
beat-to-beat basis from the continuous arterial blood pressure waveform generated by the
Nexfin. The instantaneous lung volume (ILV) was obtained by integration of the airflow.
To synchronize each respiratory value with the corresponding instantaneous R-R interval,
SBP, and DBP values, the airflow, ILV, and blood pressure signals were also resampled
to 2 Hz. Each resampled signal contained thus 1,200 data point (a total of 10 minutes,
with a sample every 0.5 seconds).
These resampled signals were then low-pass filtered in order to remove high frequency
noise (with frequencies above the respiratory frequency). For this step, we are using a
88
Kaiser window of order 21 with a passband of 0 - 0.5 Hz, a stopband of 0.85 - 1 Hz, and
ripples in the pass and stop bands of less than 0.01. The resulting signals were
subsequently processed in order to remove the mean and high-order trend (5th order
polynomial) so that slow trends present in these signals are eliminated. These filtered and
detrended signals RRI, SBP, and ILF were then used as inputs to the minimal model
of cardiorespiratory control.
Since the measured variables were obtained under closed-loop conditions, it was
necessary to impose causality constraints on the system identification procedure. Thus, a
delay of 0.5 sec or higher was assumed in the baroreflex impulse response. Since central
regulation in RSA has been reported to result in an apparent noncausal coupling of
respiration and heart rate, the model was allowed to consider negative values for the
delay D
RCC
.
The transfer functions H
ABR
and H
RCC
were computed by taking the fast Fourier transform
(FFT) of the impulse responses h
ABR
and h
RCC
, respectively. The gains G
ABR
and G
RCC
were then obtained from the transfer functions H
ABR
and H
RCC
, respectively. In particular,
the gain G
ABR
corresponds to the mean of the magnitude of the transfer function H
ABR
in
the low-frequency range (between 0.04 and 0.15 Hz), while the gain G
RCC
corresponds to
the mean of the magnitude of the transfer function H
RCC
in the high-frequency range
(between 0.15 and 0.4 Hz). As discussed earlier, the gain G
RCC
reflects vagal modulation,
while the gain G
ABR
is related to both sympathetic and vagal activity. These gains or
autonomic compact descriptors were generated to facilitate statistical comparison by
89
expressing the relationship between each pairs of variables (between ILV and RRI in
the case of G
RCC
, and SBP and RRI for G
ABR
) as a single quantitative measurement.
5.5. Pulse transit time, PTT
The pulse transit time (PTT) is the time taken for a pulse wave to travel from one arterial
site to another (Wilkinson, et al., 1999). A common method of calculating PTT has been
to use the QRS complex, in particular the R peak, of the ECG as a timing reference, taken
to represent the point at which blood is expelled from the left ventricle (Dingli, et al.,
2008). Due to its ease of measurement, the present study also uses the R-wave of the
ECG as the starting point, although this does introduce an additional delay related to the
duration between the onset of electrical cardiac activity and the beginning of ventricular
ejection (Deb, et al., 2007). The arrival of the wave is represented by the point at which
the photoplethysmographic signal has attained its maximum change during a pulse.
Studies investigating the use of PTT as a surrogate measure of SBP have found that there
is a significant albeit not particularly strong negative correlation between PTT and SBP
(Payne, et al., 2006; Chen, et al., 2000). These same studies, however, also concluded
that beat-to-beat variability of PTT provides a useful measure of blood pressure
variability. PTT has also been employed as a measurement of arterial stiffness,
respiratory efforts, and as an index of sympathetic nervous system effects on the
vasculature (Wong, et al., 2009). Pan and colleagues (Pan, et al., 2007) have shown that
PTT also responds to stress. The authors mention that a reduction in PTT indicates
90
sympathetically-mediated increases in myocardial performance, vasoconstriction, or a
combination of the two.
In the present study we will use alternatively SBP and PTT to derive autonomic metrics
and study the relationships of these parameters with those obtained from the sleep and
metabolic studies. We also aim to compare the PTT and SBP data, as well as the
autonomic descriptors derived from each measurement, in order to gain further
understanding of the relationships between these variables.
PTT is also inversely related to pulse wave velocity, which has been found to be a
sensitive measurement of arterial tree stiffness and a strong predictor of cardiovascular
disease mortality in adults (Alpert, et al., 2007).
Shiina and colleagues (Shiina, et al., 2010) reported that patients with obstructive sleep
apnea have increased arterial stiffness and sympathovagal imbalance, and that CPAP
therapy for 3 months resulted in improvement of the sympathovagal balance. They
mention that this improvement may be related to decreased stiffness of the central to
middle-sized arteries, independent of the changes in blood pressure and vascular
endothelial status.
The direct determination of pulse wave velocity requires the measurement of vessel
diameter and the distance traveled by the pressure wave along the arterial tree, among
others. Moens's original formula for pulse wave velocity (V) involves the coefficient of
91
elasticity of the artery for lateral expansion (E), the thickness of the arterial wall (c), the
radius of the artery in diastole (r), and the density of blood (d), and is given by
r d
c E
V
2
,
(5.1)
(Musser, 1934). There are currently different techniques available for the measurement of
pulse wave velocity, based either on pressure, distension, or Doppler waveforms,
differing as well in the preferred method to measure distance between sites (Boutouyrie,
et al., 2009).
Pulse wave velocity is affected not only by blood pressure, arterial size, and age (pulse
wave velocity increases with age due to increased artery stiffness), but also by arterial
tone, which affects arterial elasticity probably through its effect on smooth muscle
(Musser, 1934).
Pulse wave velocityor assessment of arterial waveforms may add to information obtained
from measurement of peripheral (brachial) pulse pressure alone. Pulse wave velocity is
inversely related to PTT. By assuming that the elongation of the arteries is negligible,
pulse wave velocity can be substituted by a constant divided by the inverse of the time
taken for the pulse wave to travel along the artery and arrive at the periphery, or the pulse
transit time (PTT) (Wilkinson, et al., 1999). This measure is less elaborated than use of
the pulse wave velocity directly.
In this study we aim to use PTT as a surrogate measure of SBP in our minimal model of
cardiorespiratory control, not only as a cuffless approach to arterial blood pressure
92
estimation, but also as a variable related to SBP which may present important additional
information regarding arterial tone and sympathetic influence not present in the SBP
measurements.
93
Chapter 6: Identification of physiological systems
As discussed in chapter 5, this study utilizes a systems approach to the study and analysis
of cardiovascular variabilities. While different single signal analysis techniques, e.g.
power spectral analysis, applied to beat-to-beat cardiovascular variability signals
characterize fluctuations in a single cardiovascular variable (e.g. heart rate variability), a
systems approach can provide a quantitative characterization of the cardiovascular
regulatory mechanisms responsible for the coupling of the beat-to-beat variability
between pairs of signals. For instance, using power spectral analysis of heart rate one can
analyze the fluctuations in heart rate, which is one output of the cardiovascular control
system. However, the heart rate power spectrum does not provide direct information
about how heart rate changes in response to oscillations in the inputs (e.g. respiration or
blood pressure) to the cardiovascular control system (Mukkamala, et al., 1999).
A systems analysis provides us with the tools to directly and noninvasively determine the
couplings of the control mechanism relating pairs of cardiovascular variables.The
technique used for the identification of the parameters that characterize the dynamical
system, in particular the quantification of the cardiovascular regulatory mechanisms
coupling respiration as well as variations in blood pressure to variations in R-R interval,
is the subject of this chapter.
This chapter begins by introducing the mathematical equations that model the
relationships between beat-to-beat variations in respiration and arterial blood pressure
tovariations in RRI in the minimal model of cardiorespiratory control. This is followed by
94
an overview of mathematical modeling of dynamic systems, including the Laguerre
expansion of kernels representation and Meixner basis functions used in the minimal
model of cardiovascular control. Concepts such as impulse response, input-output
representation of a dynamic system, orthonormal basis functions, Laguerre networks, and
Meixer basis functions are discussed for contextualization purposes and to clarify the
system identification approach used in this study, namely impulse response estimation
using Meixner basis functions.In the next chapter, the Laguerre and Meixner expansion
of kernels will be contextualized in the general framework of the Volterra models, a
nonparametric modeling technique based on the notion of the Volterra series, from which
one can mathematically approximate, to any desired degree of accuracy, the output or
response y(t) of a system of interest as a function of the inputs or stimuli.
6.1. Mathematical dynamic equations of the minimal model of
cardiorespiratory control and impulse response estimation
As mentioned in section 5.2.1, the impulse response is a time function used to
characterize the response or output of a dynamic system to any input or stimulus. As
previously discussed, in the minimal model of cardiorespiratory control the impulse
response h
ABR
(t) quantifies the time course of the change in RRI associated with an abrupt
increase in SBP of 1 mm Hg, while h
RCC
(t) quantifies the time course of the fluctuation in
RRI as a result of a rapid inspiration and expiration of 1 L of air (Jo, et al., 2003). The
impulse response of a linear system completely characterizes the dynamic properties of
the system, in the sense that knowledge of a system’s impulse response provides a means
to determine the output of this system to any arbitrary signal at its input (Khoo, 2000).
95
The mathematical equations that characterize the full model are given by
) ( ) ( ) ( ) ( ) ( ) (
1
0
1
0
t D t SBP h D t ILV h t RRI
RRI
p
ABR ABR
p
RCC RCC
(6.1)
) ( ) ( ) ( ) ( ) ( ) (
1
0
1
0
t D t RRI h t ILV h t SBP
SBP
p
CID CID
p
DER
(6.2)
where D
RCC
, D
ABR
, and D
CID
are the latencies or delays associated with the RCC
(respiratory cardiac coupling), ABR(arterial baroreflex), and CID(circulatory dynamics)
mechanisms, respectively. The signals
RRI
(t) and
SBP
(t) represent the stochastic
components of RRI(t) and SBP(t), respectively, as well as any contributions not
accounted for by the model. The model is assumed to be linear, thus complete
characterization of respiratory cardiac coupling and baroreflex dynamics are given by
their respective impulse responses.
The impulse responses h
RCC
(t) and h
ABR
(t) in equation(6.1), as explained previously,
characterize the dynamics of the respiratory cardiac coupling mechanism and the
baroreflexes, respectively. The impulse responses h
CID
(t) and h
DER
(t) in equation(6.2)
characterize the circulatory dynamics (CID) and the direct effect of respiration (DER) on
SBP, respectively. Since we are currently dealing with a subset of the full minimal model
of cardiovascular control,asshown in Figure 10 on page 73, our identification efforts will
be focused on obtaining a representation of the impulse responses h
ABR
(t) and h
RCC
(t).
96
Based on previous studies using this model (Chaicharn, et al., 2009), these impulse
responses were assumed to persist for a maximum duration of M = 50 sampling intervals,
each sampling interval corresponding to 0.5 seconds (sampling frequency f
s
= 2 Hz). As
reported in (Belozeroff, et al., 2002), causality constraints were imposed in an explicit
fashion during the parameter estimation procedure due to the inherent closed-loop
structure of the model.
In particular, a minimum value of 0.5 s, or one sampling interval, was assumed for the
latency D
ABR
in the estimation of the baroreflex dynamics, reflecting the latencies that are
in fact observed in the baroreflex dynamics. In terms of the latency D
RCC
, since there
appears to be a noncausal relationship between ILV(t) and RRI(t), in which changes in
heart rate (the output in the model) precede changes in lung volume (the input to the
model), D
RCC
was allowed to assume negative values. Previous studies (Mukkamala, et
al., 1999) have also reported this anticipatory response, e.g. heart rate transiently
increases in response to respiration, and this increase begins before the actual beginning
of inspiration, indicating a rise in heart rate in anticipation of a corresponding increase in
instantaneous lung volume, ILV(Mukkamala, et al., 1999; Mullen, et al., 1997).This
behavior could be explained by the fact that both lung volume and heart rate respond to
simultaneous nervous stimulation, however actual mechanical inspiration takes effect
later (Belozeroff, et al., 2002; Mullen, et al., 1997).
The causal structure of this model allows us to computationally “open the loop” of the
closed-loop system, effectively separating the feedforward from the feedback
97
components (Khoo, 2008). This approach is adopted in order to estimate the impulse
responses h
ABR
(t) and h
RCC
(t) of the open-loop model of Figure 10. The transfer functions
are then obtained from the estimated impulse responses using FFT, as previously
described.
6.1.1. Impulse response estimation
Since the dynamics of the minimal model of cardiovascular control are characterized by
their corresponding impulse responses, this model is “kernel-based” (Marmarelis, 2004).
The impulse responses of the model components were estimated from their Meixer basis
functions representation (Asyali, et al., 2005), obtained from the Laguerre basis functions
representation (Marmarelis, 1993). Details of this methodology will be discussed later in
this chapter.
In summary, the estimation of an impulse response using basis functions reduces the
number of parameters to be estimated, which may not only improve the numerical
condition of the estimation problem and produce coefficients with less variance(Asyali, et
al., 2005), but also require significantly less data points in the estimation process when
compared to other systems identification methodologies,e.g. finite impulse response
(FIR) models (Marmarelis, 2004). The Laguerre basis functions can effectively represent
physiological systems with kernels that die away after some certain time, corresponding
to the memory of the system. Meixer basis functions have been shown to be a more
suited option to represent kernels that also have a slower initial onset (Asyali, et al.,
2005).
98
Laguerre basis functions for impulse response representation
Marmarelis (Marmarelis, 1993) has shown that the use of Laguerre expansions of system
kernels from input-output data are an efficient and accurate methodology to obtain
estimates of the impulse response of a system from short experimental data records even
in the presence of noise. The discrete-time Laguerre functions are an example of an
orthonormal basis used to expand the kernels and reduce the number of unknown
parameters to be estimated, which enhances the robustness of the parameter estimates.
The unknown parameters, corresponding to the expansion coefficients, are estimated
using least-squares estimation, leading to increased estimation accuracy in the presence
of noise and reduced length required of experimental data records.
In the minimal model of cardiorespiratory control, the unknown impulse responses
h
ABR
(t) and h
RCC
(t) were expanded as a sum of several weighted Laguerre basis functions
as
1
0
) ( ) (
ABR
q
j
j
ABR
j ABR
t L c t h
(6.3)
1
0
) ( ) (
RCC
q
j
j
RCC
j RCC
t L c t h
(6.4)
In these equations, L
j
(t) represents the j-th order discrete time orthonormal Laguerre
function,
and
are the corresponding unknown coefficients or weights assigned
to each L
j
(t) in the ABR and RCC impulse responses, respectively, and q
ABR
and q
RCC
are
the total number of Laguerre basis functions in the ABR and RCC impulse functions,
99
respectively. For an impulse response of maximum duration M, the function L
j
(t) over the
interval 0 t M – 1, corresponding to the duration specified for the impulse response, is
defined by the recursive equations (Jo, et al., 2007):
1 ) (
0
t
t L
(6.5)
and
RCC ABR j j j j
q q j t L t L t L t L , 0 ), 1 ( ) ( ) 1 ( ) (
1 1
(6.6)
The parameter in equations (6.5) and (6.6) (0 1) is the discrete-time Laguerre
parameter which determines the rate of exponential asymptotic decline of the Laguerre
functions (Marmarelis, 1993). This parameter was empirically selected such that, for a
given M, q
RCC
, and q
ABR
, the values of the impulse responses defined by equations
(6.3)and (6.4)become insignificant as t M (Chaicharn, et al., 2009). Substituting
equations (6.3) and (6.4) into equation (6.1), we obtain
) ( ) ( ) ( ) (
1
0
1
0
t t v c t u c t RRI
RRI
q
j
j
ABR
j
q
j
j
RCC
j
ABR RCC
(6.7)
where u
j
(t) and v
j
(t) are defined as
100
1
0
) ( ) ( ) (
M
i
RCC j j
D i t ILV i L t u
(6.8)
1
0
) ( ) ( ) (
M
i
ABR j j
D i t SBP i L t v
(6.9)
Thus, instead of having to identify the M coefficients of h
RCC
(t) and h
ABR
(t) for 0 t M–
1, the identification problem now consists of estimating the unknown parameters
(0
j q
RCC
) and
(0 j q
ABR
) using least squares minimization, where q
RCC
+ q
ABR
<<
2M. The least-squares minimization procedure was repeated for a range of values for the
delays D
ABR
and D
RCC
and Laguerre function orders q
ABR
and q
RCC
in order to determine
the “optimal” set of parameters, as described in (Belozeroff, et al., 2002). Optimality, in
this case, was determined from the minimum description length, MDL (Rissanen, 1982),
computed for each combination of delays and Laguerre function orders.
The minimum description length (MDL) is a metric of the quality of fit of a model, here
used to compare the models obtained from these different combinations of delays and
Laguerre function orders and infer which of the fitted models is the most suitable. It is
based on a tradeoff between goodness-of-fit to the observed data (how well the model
describes the actually observed data points) with the complexity of the model (a more
complex model with a greater number of parameters may provide a better fit to the
measured data points, however it may not be a good or the most simple explanation of the
general behavior of the model). In sum, the minimum description length principle states
101
that we should choose the model that gives the shortest description of the data or, in other
words, that provides a concise description of the data while still being good fit to the
measured data points (Ramos, 2006).
The MDL was computed as
M
M
J MDL
R
) log( ) parameters of # total (
) log(
(6.10)
where J
R
is the variance of the residual errors between the measured data and the
predicted model output. A decrease in the variance J
R
(better model fit) leads to a smaller
MDL, while an increase in the model order (or increase in the number of parameters and,
thus, an increase in model complexity) results in a larger value for MDL. The optimal
candidate model is based on a global search for the minimal MDL (Belozeroff, et al.,
2002). An additional requirement for the optimal solution was that it had to satisfy the
condition that the cross-correlations between the residual errors (errors between actual
measured RRI data and the model predicted RRI output) and past values of the inputs
ILV(t) and SBP(t) had to not be significantly different from zero (Belozeroff, et al.,
2002; Blasi, et al., 2006). Once the optimal parameter values
(0 j q
RCC
) and
(0 j q
ABR
) were determined, the impulse responses h
ABR
(t) and h
RCC
(t) were
calculated from equations (6.3) and(6.4).
102
Meixner basis functions for impulse response representation
The Meixner basis functions can be interpreted as a generalization of the discrete
Laguerre functions. The Meixer basis functions have an additional parameter to
determine. This parameter n = 0, 1, 2, … is called the “order of the generalization”, and
determines how late the family of Meixner basis functions (MBF) will start to fluctuate.
The Meixner basis functions can be obtained from the Laguerre basis, as will be shown in
section 6.3.1.
The following sections provide more detailed aspects of the mathematical modeling of
dynamic systems, in particular the use of impulse responses and transfer functions for the
input-output representation of a dynamic system. In particular, it discusses the
representation of the transfer function of a system as a series expansion in orthonormal
basis functions and compares the finite impulse response (FIR) representation with other
orthonormal basis transfer functions, in particular the Laguerre model.
6.2. Mathematical modeling of dynamic systems
For the mathematical representation or modeling of a dynamic system, there are different
domains and/or approaches that may be followed. For instance, a finite discrete linear
time invariant (LTI) system can be described by its impulse response coefficients. In this
representation, if u(t) is the input to a linear and time invariant system and y(t) is the
output or system response to the stimulus u(t), the impulse response g( ) is such that
103
0
) ( ) ( ) (
t u g t y
(6.11)
This means that the impulse response g( ) characterizes the system’s dynamics such that
knowledge of g( ) permits one to determine the output y(t) of the system to any arbitrary
input u(t). In other words, the impulse response g( ) provides a complete characterization
of the system’s dynamics (Khoo, 2000; Bruce, 2001).
In practice, for an impulse applied at time = 0, the impulse response will be of finite
duration, such that g( ) = 0 for ≥ T. This value of T determines the memory length of
the system, or how long the response to a single impulse lasts or, equivalently, how many
past values or history of the system should be considered when computing the current
output (Westwick, et al., 2003). Thus, equation (6.11) can be rewritten as
1
0
) ( ) ( ) (
T
t u g t y
(6.12)
This description allows for a characterization of the transient characteristics of the
system. However, it requires in general many parameters for a reasonable system
representation. In particular, for the representation in equation (6.12), for a known input
u(t) and output y(t) and an unknown impulse response g( ), there would be a total of T
parameters, corresponding to each value of g( ), 0 T, to be determined. In our
autonomic study, each data sequence has a total of 1200 samples, equivalent to 600 secs,
104
or 10 mins. Thus, a total of 1200 parameters would need to be determined in order to
characterize the impulse response directly using the representation in equation (6.12).
Transfer function and state-space representations
An alternative approach is to represent a LTI system by its rational transfer functionG(s)
or G(z) (representations used for continuous or discrete time, respectively), which can be
obtained directly from the impulse response g( ) (Khoo, 2000). The output is then
obtained as
time discrete ), ( ) ( ) (
time continuous , ) ( ) ( ) (
z U z G z Y
s U s G s Y
(6.13)
where U(s) (U(z)) is the Laplace (Z-) transform of the input u(t), Y(s) (Y(z)) is the Laplace
(Z-) transform of the output y(t), and G(s) (G(z)) is the system’s transfer function (Lathi,
2005).
This is an efficient model representation of the system in terms of number of parameters.
Nevertheless, this input-output representation essentially “hides” internal variables that
may be of interest, and a multiple-input multiple-output (MIMO) system requires
multiple transfer functions for each input-output pair. This latter problem can be
conveniently addressed by a state-space representation of the LTI system, a convenient
choice for the MIMO case (Khoo, 2000). Notwithstanding, the transient characteristics of
the system are not readily available in the state-space model.
105
Basis functions expansion of a system’s impulse response
A dynamic system can also be represented by expanding the system’s impulse response
in terms of basis functions, e.g. Volterra and Wiener models, which is usually an input-
output system representation in which the output is obtained by a combination of
functions which are themselves elements of the system and its inputs (De Hoog, 2001).
In short, the impulse response g(k) of a system, where k is the discrete time sequence (k =
0, 1, …, represents = k×t
s
, where t
s
is the sampling interval in seconds), can be
represented by
1
) ( ) (
i
i i
k c k g
.
(6.14)
The impulse response g(k) can be approximated by the finite representation
n
i
i i
n
i
i i
k c k g k c k g
1 1
) ( ) ( ˆ ) ( ) (
(6.15)
where ) ( , ), ( ), (
2 1
k k k
n
is a set with the n first orthonormal basis functions and
n
c c c , , ,
2 1
are scalars. The error can be made arbitrarily small by choosing an
appropriate number n of basis functions. For n , ) ( ) ( ˆ k g k g (Campello, et al., 2007).
Using the system representation in equation (6.12), the output y(t) can then be
approximated by ) ( ˆ k y as follows:
106
k
m
m k u m g k y
0
) ( ) ( ˆ ) ( ˆ
k
m
n
i
i i
m k u m c
0 1
) ( ) (
k
m
i
n
i
i
m k u m c
0 1
) ( ) (
) (
1
k l c
i
n
i
i
(6.16)
where the term l
i
(k) is the convolution of the input u with the i-th orthonormal function
i
at time k.
The term l
i
can be interpreted as the result of the filtering of the input signal u, i.e.
) ( ) ( ) ( k u q k l
i i
, where ) (q
i
is the discrete transfer function of the i-th orthonormal
function represented by the delay operator q, where ) ( ) ( q k u k u q . The set of transfer
functions of the filters associated with the Laguerre basis functions, for instance, is given
by
, 2 , 1 ,
1 1
) ( ) (
1
2
i
p z
pz
p z
p
k Z z
i
i i
(6.17)
as will be presented in more detail in section 6.3. In this expression, p is the stable pole
that parameterizes this orthonormal function. For instance, if p = 0,
i
i
z z
) ( or,
equivalently,
i
i
q q
) ( , which implies that ) ( ) ( ) ( i k u k u q k l
i
i
. Thus, for p = 0, the
model in equation (6.16) can be rewritten as ) ( ) ( ˆ
1
i k u c k y
n
i
i
, which defines the
finiteimpulse response model, FIR (Nelles, 2001). In this case, c
i
= g(i), i.e. the basis
107
functions coefficients c
i
correspond to the value of the impulse response function at time
= i.
Therefore, the FIR orthonormal basis is a particular case of the Laguerre basis for p = 0.
The FIR basis function representation, however, requires a large n for a satisfactory
approximation of y(t), especially for slow decaying systems. The dynamics present in the
Laguerre filters, defined by the pole p≠ 0, allows the incorporation of a priori
information about the dynamic behavior of the system, leading to a much smaller n or
total number of basis functions for an acceptable approximation of y(t) (Campello, et al.,
2007).
When approximating a system’s impulse response using a Laguerre filter, a design
criterion is the fixed pole position. By adjusting the position of this pole, the rate of decay
of the impulse response can be controlled. Since Laguerre sequences decay exponentially
to zero at a controlled rate, relatively low order Laguerre filters can result in good
approximations for impulse responses that decay exponentially over time (Oliveira e
Silva, 1995).
In system identification usually only the input and output of a system (or subsystems
within a larger system) are available, and the model is then estimated from these input-
output data. Within the different options available for the system’s representation,
Laguerre filters can be an interesting option to approximate a linear dynamical system’s
impulse response with fewer parameters when compared to other approaches such as a
FIR or transversal filter (Oliveira e Silva, 1995).
108
Comparing a FIR estimate and a Laguerre basis estimate of the same order, the latter
performs substantially better. Laguerre models are also robust to the choices of model
order and sampling interval (Walhberg, 1991). The parameter p in the Laguerre model
makes it possible to reduce the number of the parameters necessary for a satisfactory
approximate system model.
However, one drawback of the Laguerre model is that its accuracy diminishes at higher
frequencies (Heuberger, et al., 2005). This means that the estimates of faster dynamic
modes of the system being modeled are not well represented using these basis functions.
Moreover, when the kernels have slow initial onset, the use of Laguerre basis functions
may also not be the better alternative (Asyali, et al., 2005). For this latter case, Meixner
basis functions may be a better option.
Meixner basis functions
The Meixner basis functions are generalizations of the discrete Laguerre basis functions
(den Brinker, 1995). The former can be derived from the latter through a transformation
matrix A
(n)
. This is reviewed in section 6.3.1. The Meixner functions are defined by an
additional parameter called the order of generalization, which determines how fast the
functions begin to deviate from zero. A larger value for this parameter emphasizes the
low frequency components, at the expense of the high frequency components. Thus, the
Meixner basis functions, being more slowly starting functions (depending on the choice
of the order of generalization parameter), may be a better series expansion choice for
109
impulse functions that have a slow start, in terms of requiring fewer total number of terms
for an equally good approximation (den Brinker, 1995).
For nonlinear dynamical systems, the use of discrete Laguerre basis functions for the
kernel expansion of the Volterra series is an interesting nonparametric modeling
approach (Marmarelis, 2004).
Therefore, the choice of which modeling approachto use depends on factors such as the
characteristic one wants to observe of the system and the efficiency of the representation,
usually reflected by the number of parameters necessary for an accurate representation of
the system under study, as well as the robustness of the representation and convergence
issues (De Hoog, 2001).
In this study we are using Meixner basis functions for approximating the impulse
responses h
ABR
(t) and h
RCC
(t). The next section presents a more detailed approach to the
concept of orthonormal basis functions as well as to the implementation of Laguerre
networks as a network of cascaded all-pass filters. It will be shown that the Meixner basis
functions can then be obtained from a modification of this implementation of the
Laguerre networks.
6.2.1. Orthonormal basis functions (OBF)
As shown by equation (6.11), the impulse response representation g(k) of a discrete linear
time-invariant stable dynamical system provides a complete characterization of the
system’s dynamics.
110
If the system is strictly causal, or equivalently the system model or transfer function is
strictly proper (i.e. 0 ) ( lim
| |
z G
z
), there is no assumption of instantaneous transfer of
information between the input and output (Whalley, 1990), so the corresponding discrete
transfer function ) (z G can be denoted by
1
) ( ) (
k
k
z k g z G
(6.18)
This means that at least one delay (k ≥ 1) is assumed between the input and output of the
system (the variable z is the z-transform of the delay operator q, i.e. z
k
= Z(q
k
), or Z(q
k
) =
z
k
).
Assuming the system is l
2
-stable (Wahlberg, 2003), the n-th order truncated finite
impulse response (FIR) approximation G
FIR
(z) and the corresponding FIR output model
y(t) are given by
n
k
k
k
n
k
k FIR
z g z k g z G
1 1
) ( ) ( ) (
n
k
k
k t u g t y
1
) ( ) (
(6.19)
as obtained in the previous section.
With this representation, the identification of this system characterized by the impulse
response ) (k g is accomplished by directly estimating the impulse response parameters
k
g .
Since this model is linear in the unknown parameters g
k
, linear regression estimation
111
techniques can be used for the identification from input-output data (Heuberger, et al.,
2005).
Systems with long impulse responses relative to the sampling interval require a high-
order FIR approximation, since the delay operator expansion function
k
k
z z
) (
requires a large number of coefficients to accurately represent the system dynamics. In
other words, the order n has to be chosen large enough to include all g
k
that are
significantly different from zero (Nelles, 2001).The higher the number of parameters to
be estimated, the higher the variance of the transfer function estimate. By using
orthogonal rational basis functions (OBF), a fixed denominator transfer function model
) (z G
OBF
can be modeled by
n
k
k k OBF
z F c z G
1
) ( ) (
(6.20)
where n k
z A
z
z F
k
k
,..., 1 ,
) (
) (
1
define a set )} ( { z F
k
of orthonormal basis transfer
functions with pre-specified poles and infinite impulse responses (Nelles, 2001). The use
of rational function models,e.g. ) (z F
k
, to approximate mathematical functions enables
one to represent curves which approach asymptotes, not generally possible when using
ordinary polynomials for this approximation. Moreover, ratios of polynomials are able to
approximate known mathematical functions to the same degree of accuracy as ordinary
polynomials, with a smaller number of terms (Ratkowsky, 1987).
112
This parameterization in terms of pre-specified poles allows the incorporation of a priori
information about time constants in the model structure (Heuberger, et al., 2005; Akçay,
2001). Since the pole position is a design criterion, the asymptotic decay rate of the
impulse response can be controlled (Oliveira e Silva, 1995). Moreover, since each basis
function has an infinite impulse response, the representation of a transfer function model
by orthogonal basis functions requires fewer parameters to obtain a good approximation
of a long impulse response than if a FIR model is used. In other words, the number of
} {
k
c parameters to estimate is much less than the required } {
k
g parameters needed to
accurately represent G(z) (McCombie, et al., 2005).
Among the most used orthonormal basis functions are the Laguerre basis, parameterized
by a single pole p, as discussed in the previous section, and the Kautz basis (Wahlberg,
2003), a generalization of the Laguerre basis, where the functions are parameterized by a
pair of complex poles. This characteristic of the Kautz basis functions make them an
interesting option for representing systems with underdamped dominant oscillations.
Other generalized basis functions with additional modes may require less terms to
represent a certain dynamical system. The tradeoff is that these functions also require
additional a priori information about its dominant modes (Campello, et al., 2007).
6.2.2. FIR model and Laguerre expansion of kernels
From equation (6.19), the output y(k) of a dynamic system can be determined from Y(z)
as:
113
) ( ) ( ) ( z U z G z Y
FIR
n
i
i
i
i
i k u c i k u g z Y Z k y
1 1
1
) ( ) ( ) ( ) (
(6.21)
where the coefficients c
i
, n i , , 2 , 1 , are modeling the g
i
.
In the systems identification literature, a general FIR model for the system output y(t) is
more generally described as
) ( ) ( ) 2 ( ) 1 ( ) (
2 1
k v n k u c k u c k u c k y
n
(6.22a)
) ( ) ( ) ( ) (
2
2
1
1
k v k u q c k u q c k u q c
n
n
(6.22b)
where v(k) represents white noise and q
1
is the delay or backward shift operator (Ljung,
1999). With this representation, the FIR model output y(k) is then a weighted sum of
previous inputs.
Figure 13: FIR filter representation
5
5
Adapted from (Nelles, 2001).
q
1
q
2
q
n
u(k)
c
1
c
2
c
n
v(k)
y(k)
114
Figure 13 illustrates the FIR model as a linear combination of the actual input u(k)
filtered by q
k
, n k , , 1 . These filters, having all their poles at zero
k k
z q Z 1
, are
the simplest form of an orthonormal basis function model.
The operator q
1
used in the FIR filter has a very short memory (one sampling step), thus
requiring a large number of parameters for an acceptable representation of the actual
system output. If more general orthonormal filters L
i
(q) are used to represent the system’s
output y(k), as illustrated in Figure 14, the respective model can have a much lower order
than the corresponding FIR model (Wahlberg, et al., 1991; Nelles, 2001).
Figure 14: A more general OBF function
6
The Laguerre and Meixner basis functions are thus interesting alternatives to the FIR
representation.
6.3. Laguerre network derivation from state space representation
The construction of orthonormal basis functions can be more clearly visualized by using
state-space models and matrix algebra, as shown in (Heuberger, et al., 2005). The basic
6
Adapted from (Nelles, 2001).
L
1
(q)
L
2
(q)
L
m
(q)
u(k)
c
1
c
2
c
m
v(k)
y(k)
115
idea is to find a state-space model representation of the dynamic system in which the
components of the input-to-state transfer functions form an orthogonal basis.
A linear system can be described by its general state space model
) ( ) ( ) (
) ( ) ( ) 1 (
k D k C k y
k B k A k
u x
u x x
(6.23)
where u(k)
m×1
is the input vector to the system, x(k)
n×1
is the state vector,y(t)
1×1
is the output of the system,A
n×n
is ann×nstate transmission matrix,B
n×m
is
ann× minput-to-state transmission matrix, C
1×n
is a 1 × n state-to-output transmission
matrix and D
1×m
is a 1 × m input-to-output transmission matrix (Paraskevopoulos,
2002).
A state variable, represented by x(t) in the state space model, describes the time-varying
characteristics of the modeled systemand is a representation of each independent dynamic
element of the system. If the system’s state variables x(k) and initial conditions are
known, the response or output of the system y(k) to any input u(k)can be determined
(Gopal, 2009). The system states x(t) can be interpreted as reflecting the memory of the
system, and they define the not only the number and size of energy storage mechanisms
but also the mechanisms by which energy may be dissipated, absorbed, or transferred
from one energy store (or system state variable) to another within the system (Bruce,
2001).
116
The transfer functions from the input )} ( { ) ( t Z z U u to the states )} ( { ) ( t Z z X x is
given by
B A I z z F z F
z U
z X
z V
T
n
1
1
) ( ) ( ) (
) (
) (
) (
(6.24)
where F
k
(z), k = 1, …, n, are n linearly independent rational transfer functions. Thus, the
set )} ( ) ( {
1
z F z F
n
are a basis (not necessarily orthogonal) for the vector set spanned
by )} ( ) ( {
1
z F z F
n
. The eigenvalues of Ain equations (6.23) and (6.24)are the poles of
)} ( { z F
k
. The state covariance matrix of the stable state space model is given by
]] , [[ )} ( ) ( { V V t x t x E P
T
, where [[V,V]] represents the cross-Gramian or matrix “outer
product”. The Gram matrix of a basis } , , {
1 n
f f of an n-dimensional inner product space
is the n×n matrix whose (i,j)
th
entry is the inner product
j i
f f ,
(Gregson, et al., 1988;
Borowski, et al., 2002). If [[V,V]] = I, where I is the identity matrix, then the
corresponding input to state transfer functions will be orthonormal (Heuberger, et al.,
2005).
Therefore, in order to find a set of orthonormal input-to-state transfer functions, one can
find a square nonsingular transformation matrix Tsuch that the transformed state
variables ) (t x are related to the “original” state variables x(t) by ) ( ) ( t T t x x and the
transformed state covariance matrix I T P T t t E P
T T
)} ( ) ( { x x . The components of
the new input-to-state transfer functions ) ( )] ( ) ( [ ) ( ) (
1
1
z TV z F z F B A zI z V
T
n
,
117
where the new state transmission and input-to-state transmission matrices are given by
1
TAT A and TB B , respectively, now form an orthonormal basis for
)} ( ) ( {
1
z F z F Sp
n
.
6.3.1. Laguerre Networks as a network of cascaded all-pass filters
All-pass transfer functions are a powerful framework for factorization of the state
covariance matrices (Heuberger, et al., 2005).
Assume a single-input single-output (SISO) asymptotically stable all-pass transfer
function H(z) of order m, with real valued impulse response, such that 1 ) / 1 ( ) ( z H z H ,
completely specified by its poles } 1 , 1 | | ; { m i p p
i i
. Such a transfer function can be
represented by a Blaschke product as in equation (6.25) and is often called an inner
function (Heuberger, et al., 2005).
m
i i
i
p z
z p
z H
1
*
1
) (
(6.25)
This function can also be represented by an orthogonal state space realization
) (
) (
) (
) 1 (
t u
t x
D C
B A
t y
t x
, where
I
D C
B A
D C
B A
T
(6.26)
since this directly implies that P = I. Thus, this state space realization of H(z) is
orthogonal.
In the special case of a first order system,
118
a a
a a
D C
B A
2
2
1
1
1 1 ,
1
) (
a
a z
z a
z H
(6.27)
Orthogonality and the all-pass property are preserved through different connections of
all-pass filters (e.g. cascade connections). Thus, an all-pass transfer function H(z) can be
factorized as H(z) = H
1
(z)H
2
(z), where H
1
(z) and H
2
(z) are themselves all-pass transfer
functions, with orders lower than that of H(z), and can be represented in state space by
(A
1
, B
1
, C
1
, D
1
) and (A
2
, B
2
, C
2
, D
2
), respectively. By recursively applying this
factorization procedure, a cascade all-pass filter network can be obtained, as illustrated in
Figure 15. The individual input to state transfer functions H
i
(q), 1 i n, obtained this
way are all orthonormal and therefore define an orthonormal basis functions set
(Wahlberg, 2003).
Figure 15: Cascade all-pass filter network. The H
i
(z) form orthonormal basis functions
7
.
Choosing n identical first order H
i
(z) as defined in (6.27) for the individual transfer
functions of Figure 15, the orthogonal input-to-state transfer functions define the
Laguerre basis functions
7
Adapted from (Heuberger, et al., 2005).
H
1
(q) H
2
(q) H
n
(q)
x
1
(k) x
2
(k)
x
n
(k)
u(k)
119
1
2
1
1
) (
k
k
a z
z a
a z
a
z F , m k , , 1
(6.28)
where m is the order of H(z).
Based on this cascade all-pass filter network, the discrete time Laguerre basis function is
generated in the minimal model of cardiovascular control from the filter structure shown
in the dashed box in Figure 16.
Figure 16: The cascaded filter network to generate the Laguerre (dashed box) and Meixner basis functions
8
.
The Meixner basis functions are then obtained from cascading the Laguerre filter bank
with an orthogonal matrix A
(n)
, as shown in Figure 16, such that the resulting vector of z-
transforms ) ( ) (
) ( ) (
z z G
n n
m
A , where ] [ , ], [ ], [ ) (
) ( ) (
1
) (
0
k L k L k L Z z
n
q
n n
, contains
rational functions in z and the order of the z-transform ) (
) (
z G
n
m
is 1 m n (den Brinker,
1995). The Laguerre basis functions and Meixner basis functions are denoted by L
q
(n)
[k]
and M
q
(n)
[k], respectively. The subscript q( 1 , , 2 , 1 , 0 Q q ) is the order of the basis
functions and k ( 1 , , 2 , 1 , 0 N k ) is the index, where N is the system length or system
8
Adapted from (Asyali, et al., 2005).
2
1 p
] [
) (
0
k L
n
] [
) (
1
k L
n
] [
) (
2
k L
n
] [
) (
k L
n
q
) (n
A
] [
) (
0
k M
n
] [
) (
1
k M
n
] [
) (
2
k M
n
] [
) (
k M
n
q
] [k
discrete
impulse input
p z
z
p z
pz
1
p z
pz
1
p z
pz
1
120
memory (Asyali, et al., 2005). The system identification problem, thus, consists of
estimating the coefficients of the Meixner basis functions in the Meixner basis functions
expansion used to represent the impulse responses h
ABR
(t) and h
RCC
(t). For our minimal
model, the coefficients are estimated based on a search for the global minimum
description length of all candidate models.
6.4. Model evaluation
A measure of how well a model describes an unknown system (or of the accuracy of a
model) can be quantified by the normalized mean square error of the prediction output
(Westwick, et al., 2003), defined as the ratio between the variance of the residuals
) ˆ ( y y
n
and the variance of ) (y , where y is the actual output of the system and
n
y ˆ is the
prediction output. In equation form,
) var(
) ˆ var(
) ˆ (
y
y y
y NMSE
n
n
The NMSE is a value between 0 and 1 and represents the portion of the output signal
power that is not “explained” or accounted for by the model. The value of NMSE ) ˆ (
n
y is a
sufficient means of validation, albeit not a necessary one, since a low signal-to-noise ratio
(SNR) at the output will result in a high NMSE for the predicted outputeven for a
“perfect” model of the system under study (Marmarelis, 2004).
This chapter presented details on the implementation of the estimation of the impulse
responses for the minimal model of cardiorespiratory control. The next chapter will
121
contextualize the Laguerre and Meixner basis functions in the general framework of
Volterra models, for completeness. Chapter 8 will present methods used in the statistical
analysis of the data obtained in the present study, while the results are presented in
chapter 9.
122
Chapter 7: Volterra models and the Meixner expansion of kernels
In this chapter the Laguerre expansion of kernels will be contextualized in the general
framework of the Volterra models. Volterra models are a nonparametric modeling
technique based on the notion of the Volterra series, from which one can mathematically
approximate, to any desired degree of accuracy, the output or response y(t) of a system of
interest as a function of the input(s) or stimulus (stimuli) x
j
(t), j = 1, 2, …, k, where k is
the total number of inputs to the system.
This chapter begins by the presentation of the Volterra models as a mapping or
nonparametric modeling representing the input-output relation of any continuous and
stable nonlinear dynamic system with finite memory. Discrete-time Volterra models are
then presented and the choice of important parameters such as kernel memory length,
system bandwidth, sampling time, and system order are discussed.
This is followed by a presentation of the Laguerre and Meixner orthogonal basis function
expansions as a compact representation of the Volterra kernels, having the additional
advantage of not requiring white or quasi-white inputs for kernel estimation. The chapter
ends by considering the conditions and constraints involved in the estimation of the
optimal model candidates. Final results obtained from this time-invariant analysis of the
cardiovascular data, in particular those relating to the supine and standing postures for
each subject, are shown in the appendix and discussed in chapter 9.
123
7.1. Volterra models
In short, nonparametric modeling is based on employing a functional F such that
t t t x F t y ' ), ' ( ) ( . The functional F represents mathematically how the causal system
being studied transforms the input signal x(t) into the output signal y(t). In other words,
the functional F defines the mapping of the past and present values of the input signal x(t)
onto the present value of the output signal y(t) (Marmarelis, 2004). In contrast, parametric
modeling techniques are based on approximating the output y(t) of a system observed at
time t as a linear combination, or weighted sum, of previous values of the output and/or
previous and present values of the input x(t) as well as the process (Ljung, 1999). These
definitions can also be extended to the case of systems with multiple inputs (x
1
, x
2
,…,x
k
)
and outputs y
i
(t).
In both approaches, it is assumed that we only have a finite number of discrete data
points of the input(s) and output(s) of interest. Thus, t = nT, where n is the sample
number, n = 1, 2, …N, and T is the sampling interval. N is the total number of samples of
each data set available from an experiment. As discussed in (Marmarelis, 2004), the goal
of nonparametric modeling is to obtain an explicit mathematical representation of the
functional F from input-output (i.e. stimulus-response) data.
Volterra models are a nonparametric modeling technique based on the notion of the
Volterra series, which define a functional expansion of an analytical functionalF that
represents the input-output relation of any continuous and stable nonlinear dynamic
system with finite memory (Marmarelis, 2004). In this context, the output y(t) of a single-
124
input single-output stationary stable causal system can be expressed in terms of the input
x(t) by use of the Volterra series expansion as the sum
0
2 1 2 1 2 1 2
0
1 0
) ( ) ( ) , ( ) ( ) ( ) ( d d t x t x k d t x k k t y
r r r r
d d t x t x k
1 1 1
0
) ( ) ( ) , , (
(7.1)
7.1.1. Volterra kernels
In the previous expression, k
r
is the Volterra kernel of order r. The kernels can be
interpreted as causal (k
i
(t) = 0, t< 0) weighting functions that define how the input x(t)
affects the output y(t). In particular, the kernel k
0
, or 0
th
order Volterra kernel, is the
value of the functional (“mapping”) F in the absence of an input. For a stationary model,
k
0
can be interpreted as the average of the spontaneous activity of the system in the
absence of any input (Marmarelis, 2004). For nonstationary systems, k
0
can be expressed
as k
0
(t).
The first-order Volterra kernel k
1
( ) is the linear component of the nonlinear system
defined by the input x(t) and output y(t). Thus, for a linear time-invariant system with k
0
=
0, k
1
( ) would be equivalent to the impulse response of the system. The second-order
Volterra kernel k
2
(
1
,
2
) represents the lowest order nonlinear interactions observable in
the system. It can be interpreted as describing the two-dimensional pattern by which the
system weighs the pairwise product combinations of past and present values of the input
x(t) in order to generate the second-order component of the system output y(t)
125
(Marmarelis, 2004). Higher order kernels have an equivalent interpretation, but are
seldom used in practice (Marmarelis, 2004).
In the minimal model of cardiovascular control, we initially detrend all system inputs,
SBP(t) and ILV(t), defining as inputs only the variations of systolic blood
pressure,SBP(t), and instantaneous lung volume, ILV(t). In this case, k
0
= 0.
Moreover, we are interested in analyzing the first order interactions of SBP(t) and
ILV(t) on the output RRI(t). Thus, the only kernel to be obtained is k
1
(t), which will be
an approximation of the impulse response of the system, or the convolution integral that
represents the input-output relation of a linear time-invariant (LTI) system.
As is the case for impulse responses in linear time-invariant systems, the Volterra
kernels, which define the patterns of nonlinear interactions among different values of the
input signal, allow the prediction of the output y(t) to any input x(t), constituting, thus, a
complete representation of the system functional properties (Marmarelis, 2004). In other
words, the Volterra model characterizes the system functional properties and dynamics
such that it permits the accurate prediction of the output y(t) of a system to any given
input x(t). Consequently, a model of a physiological system can be interpreted as
encompassing our current knowledge of the system under study as well as allowing
further analyzes of the system’s behavior and characteristics (Marmarelis, 2004).
7.2. Discrete-time Volterra models
For discrete input and output data, the discrete-time Volterra model assumes the form
126
1
0
1
0
1
0
2 1 2 1 2
2
1 0
1 2
1
2
2
) ( ) ( ) , ( ) ( ) ( ) (
N
m
N
m
N
m
m n x m n x m m k T m n x m k T k n y
(7.2)
where T is the sampling interval, n is the discrete-time index (n = t / T), k
1
and k
2
are the
first and second order kernels and N
1
and N
2
are their lengths (Marmarelis, 2004; Asyali,
et al., 2007).
7.2.1. Kernel memory length Mand system bandwidth B
s
From this discrete representation, a few important remarks must be made. First of all, we
are assuming that each kernel k
i
is finite in length. In other words, we are assuming that
the system under study has a finite memory length. For a system with memory length M,
we must have the sample input-output data length N>M for an accurate representation of
the system dynamics. Moreover, we must also have N>N
1
and N>N
2
.
The kernel length (N
1
, N
2
, etc.) defines how long the influence of an input applied at
discrete-time n will influence the output. For instance, if we define the memory length of
the kernel to be N
1
, we are assuming that the input (stimulus) at discrete-time n will
influence the output (response) until discrete-time n + N
1
. In the minimal model of
cardiorespiratory control, we are assuming the memory length of the kernels to be equal
to 50 samples. Since we are using a sampling time T = 0.5 secs (i.e. one sample every 0.5
secs, or 2 samples per second), this means that we are assuming that each kernel’s length
corresponds to 25 seconds. Thus, an input applied at time tis considered to influence the
output until time t + 25 secs. The memory length of the system should be defined based
127
on the system bandwidth. The memory length M is an important parameter to be
specified prior to the actual system identification procedure.
In our minimal model, since we are interested in analyzing frequency components present
in RRI, SBP, and ILV from 0.04 Hz to 0.5 Hz (see chapter 4, item 4.3), the inputs
SBP(t) and ILV(t) are initially filtered by a Kaiser filter with passband from 0 to 0.5
Hz and a stopband from 0.85 to 1 Hz (as discussed in chapter 5, item 5.4), prior to the
estimation process. Thus, the effective system bandwidth B
s
for the minimal model of
cardiorespiratory control can be considered to be around 0.8 Hz.
In general we should have M ≥ 2 B
s
, where is the effective kernel memory, i.e. the
domain of the lag for which the respective kernel has values significantly different from
zero (Marmarelis, 2004). For M = 50 samples and B
s
= 0.8 Hz, we have ≤ 31.25 secs.
From the results obtained by using our minimal model, we have observed that the
estimated kernels are generally very close to zero around t = 26 secs. Therefore, the
choice of using M = 50 for our application has been shown to be appropriate.
As indicated by the previous equation of the discrete-time Volterra models, the memory
length M is directly related to the total number of parameters or unknowns that need to be
estimated, which increase geometrically with the order r of the kernel (Marmarelis,
2004). The use of kernel expansions greatly reduces the number of unknowns to be
estimated and is one of the strong motivations for its use. This will be addressed later in
this chapter. Moreover, the memory length choice will be addressed again when
discussing the Volterra kernels expansions later in this chapter.
128
7.2.2. Sampling time T
Another important parameter to be defined in the modeling process is the sampling time
T. As mentioned previously, the effective system bandwidth B
s
for the minimal model
can be considered to be around 0.8 Hz. To avoid aliasing (Proakis, et al., 2002) and thus
obtain an accurate discretization of the Volterra model, the sampling time Tshould be
sufficiently small relative to the bandwidth, i.e. T ≤ 1 / 2B
s
. Therefore, we should have T
≤ 1 / 2(0.8) or T ≤ 0.625. Thus, T = 0.5 secs is an appropriate choice relative to the
system bandwidth.
Although a smaller sampling time could theoretically improve the approximation of the
discretized model when compared to the continuous-time Volterra model, the smaller the
sampling time, the greater the number of parameters needed for the model identification
from input-output data. This would require more experimental data to be collected,
resulting in an increased experiment time with each subject, not desirable especially in
the pediatric population, the subjects in this study. Moreover, an increase in the number
of parameters to be estimated could potentially lead to an increase in variance error, thus
to an increased model error, as discussed below.
7.2.3. Model error and model complexity
The model error, which is the difference between the estimated model output and the
actual measured output, can be interpreted as being composed of two parts: the bias error
and the variance error. The bias erroris the part of the model error that is due to the
restricted flexibility of the model. Thus, the bias error is related to the model structure.
129
The variance error, on the other hand, is the part of the model error that is due to
uncertainties in the estimated parameters, or to a deviation of the estimated parameters
from their optimal values (Nelles, 2001). In practice, there is a tradeoff between bias and
variance errors. An increase in model complexity decreases the bias error but increases
the variance error (Nelles, 2001).
While a low order model with a small number of parameters may not be capable of
representing all of the system dynamics due to underfitting, too high an order or too many
parameters in the model may lead to overfitting, in which the model is usually not only
representing the underlying dynamics of the system but is also modeling the noise
dynamics, which is not desirable. Since the actual system dynamics is unknown, there
needs to be a compromise in model complexity in order to generate a model that results
in an acceptable model error but still represents the unknown system dynamics
reasonably well. In our model of cardiorespiratory control, we use the minimum
description length, described previously, as a criterion to choose a model with reasonable
complexity that still represents the system dynamics with reasonable accuracy.
7.2.4. System order r
The system order r, which defines the total number of Volterra kernels k
i
, i = 0, 1, …, r to
be used to model the input-output relation of a system, is yet another important parameter
to define in the system identification problem utilizing the Volterra model approach.
Approximating an infinite order system using a finite order Volterra model leads to some
correlation among the residuals of the estimation, due to model truncation errors that
130
depend on the input signal (Marmarelis, 2004). This correlation leads to biases in the
kernel estimates determined, for instance, by applying a least-squares estimation
algorithm. The less significant the model truncation error is, the less significant the bias
will be. In other words, systems satisfactorily described by lower-order models can be
expected to present smaller bias in the estimated kernels.
7.2.5. Model evaluation: use of information criteria
As mentioned in the previous chapter, the optimal candidate model is chosen based on a
global search for the minimal description length (MDL) in order to avoid overfitting. In
this case, the whole data set is used in the estimation process. Overfitting is avoided by
using the information criterion MDL, defined in equation (6.10), to determine the optimal
fit. In this case, the parameters of the models are still determined by minimizing the sum
of square errors, represented by J
R
in equation (6.10), with the additional requirement that
the choice of the “optimal” model must also take into consideration the model
complexity. The “best” model is then that defined as the model with the lowest
information criterion, which reflects the loss function value (minimum sum of squares)
and the model complexity (Nelles, 2001).
7.2.6. Cross-correlation between residuals and input sequence
As also mentioned in the previous chapter, the optimal solution had to satisfy the
additional condition of minimal cross-correlation between the residual errors and past
values of the inputs. The residuals or prediction errors are the difference between the
131
actual measured output and the output estimated from the model at each data point and
represent the part of the data that the model could not reproduce (Ljung, 1999).
A correlation between the residual errors and past values of an input is an indication that
the model does not describe how part of the output relates to the corresponding input,
and, thus, that there are more system dynamics to be described that the model did not
pick up (Ljung, et al., 1994).
Since this correlation quantifies how “similar” the residual errors are to past inputs, a
significantly large correlation at, for instance, lag k, means that the output at time t, y(t),
that originates from the input at time t – k, u(t – k), is not properly described by the model
(Ljung, 1988).
7.2.7. Estimation of Volterra kernels
The discrete-time Volterra model represented in equation (7.2) can be written in matrix
form as
ε k X y
(7.3)
where )]' ( , ), 2 ( ), 1 ( [ N y y y y is the output data vector, ), ( ), 1 ( ), 0 ( , [
1 1 1 0
M Tk Tk Tk k k
), 1 , ( 2 , ), 2 , 2 ( ), 1 , 2 ( 2 ), 0 , 2 ( 2 ), 1 , 1 ( ), 0 , 1 ( 2 ), 0 , 0 (
2
2
2
2
2
2
2
2
2
2
2
2
2
2
M M k T k T k T k T k T k T k T
]' ), , (
2
2
M M k T is the vector of unknown kernel values (to be estimated), X is the input
data matrix that can be constructed according to equation(7.2) and the definition for k,
and = [ (1), (2), …, (N)]' is the error or residuals vector, which is the difference
132
between the model predicted output ) ( ˆ n y and the actual measured output y(n) values at
each sample time n, n = 1, …, N (Marmarelis, 2004).
From this equation, we can observe that the size P of the unknown kernel vector k
depends on the memory length M and on the (nonlinear) order of the systemQ = max(r).
As the system’s memory length and/or model order increase, the greater the number of
kernel values to be estimated. This, in turn, requires a larger/longer experimental data set
(sometimes impractically long, depending on the parameters P, M, and Q) for an accurate
estimation and increases the computational burden of the estimation problem. The kernel
expansions approach, as adopted in the current study, is a means to compact the kernel
representation, thus significantly reducing the total number of parameters or unknowns to
be estimated. Previous studies have found a reduction in the required data length by a
factor of 10
Q
by the adoption of the kernel expansions approach for the Volterra model,
besides improvement in estimation accuracy and a reduction in computational costs
(Marmarelis, 2004).
7.3. Wiener kernels
Wiener proposed the use of orthogonal functional spaces to effectively decouple the
kernels. He suggested the use of Gaussian white noise (GWN) as an effective test input
for the identification of nonlinear dynamic systems and introduced the procedure of
kernel estimation from input-output data by orthogonalization of the Volterra series for a
GWN test input. Use of a GWN test input not only efficiently tests the input space at all
frequencies (ideal constant power spectrum over all frequencies), but also allows the
133
orthogonalization of the Volterra functional expansion by making the residuals
orthogonal to the estimated model output (Marmarelis, 2004).
The resulting orthogonal functional series, the Wiener functionals, define a Wiener series
expansion of the output signal using Wiener kernels, which are in general distinct from
the Volterra kernels of a system. Among the advantages of the orthogonality of the series
are the fact that the Wiener kernel estimates do not change if additional higher-order
terms are addedand that the conversion of the estimation algorithm of the expansion for a
GWN input is faster, since a GWN input results in the least truncation error for a given
model order (Marmarelis, 2004).
A GWN, however, cannot be generated physically, due to its infinite bandwidth and
infinite variance (Victor, 1991). An approximation can be made by using a band-limited
GWN input, with a sufficient bandwidth to cover the bandwidth of the system of interest.
This, however, can lead to functionals that are not strictly orthogonal. Moreover, the
estimation of the Wiener kernels from input-output data require long data records in order
to reduce the considerable estimation variance of the obtained kernel estimates. Also, the
Wiener kernels are input dependent (the estimation variance depends on the input length
and bandwidth). The Volterra kernels, on the other hand, are independent of any input
characteristics (Marmarelis, 2004). Another advantage of the Volterra kernels is that their
physiological interpretation is more direct when compared to the form of the output
expression obtained by the Wiener model consisting of the Wiener series expansion
coefficients (Marmarelis, 2004).
134
In order to obtain a more efficient representation of the Volterra kernels, requiring thus
shorter data lengths for an accurate estimation, as well as to be able to use arbitrary (non-
white, but still broadband) inputs, more appropriate for physiological systems since data
can thus be obtained through a more spontaneous or natural operation of the system, the
Volterra kernel expansion approach was proposed. This method will be discussed in the
next section.
7.4. Volterra kernel expansion approach
The Volterra kernel expansion approach is used to address the issues previously
mentioned on the estimation of the Volterra kernels. One of the important issues this
approach addresses is the biases in the Volterra kernel estimates from model truncation,
due to the resulting correlated residuals that are dependent on the specific input used for
kernel estimation, as a result of the coupling of the functional terms of the Volterra
models. The Volterra kernel expansion technique allows a much more compact
representation of the Volterra kernels, resulting in higher estimation accuracy and
reduced computational burden, thus requiring much less input-output data for an accurate
modeling of the dynamics of the system under study. Another important advantage of the
kernel expansion approach is the removal of the requirement for white or quasiwhite
inputs (Marmarelis, 2004).
From the expression of the discrete-time Volterra model (7.2), we can observe that even a
second order Volterra model is highly parameterized, thus noise-sensitive. By projecting
the Volterra kernels onto a small number of orthogonal basis functions, the kernels can be
135
represented with a relatively small number of basis functions, which can considerably
reduce the number of parameters to be estimated. This in turn may improve the numerical
condition of the estimation problem and produce coefficient estimates with less variance
and, consequently, a more reliable model (Asyali, et al., 2007).
For a basis of L causal functions {L
j
(n)}, j = 1, …, Q
j
, where Q
j
is the total number of
basis functions used for expansion of a certain Volterra kernel, we have, for the first two
kernels k
1
and k
2
in equation(7.2), the expansions:
1 , , 1 , 0 , ) ( ) (
1
1
0
1
1
N m m L c m k
Q
q
q q
(7.4a)
1 , , 1 , 0 , ) ( ) ( ) , (
2 2 , 1
1
0
1
0
2 1 , 2 1 2
2
1
2
2
2 1 2 1
N m m L m L c m m k
Q
q
Q
q
q q q q
(7.4b)
7.4.1. The Laguerre basis expansion
A widely used orthogonal function for the expansion of the Volterra kernels are the
discrete Laguerre functions, represented in equation (6.28) andFigure 16 (page 119). The
parameter a in that equation (or parameter p in Figure 16), or more specifically the
parameter a
2
, is the decay parameter and determines the rate of exponential asymptotic
decline of the Laguerre functions L
q
(k). The value of a should be chosen such that, given
the memory length M assumed for the impulse response of the dynamic system under
study and the order q of the expansion (or the total number of basis functions used in the
estimation), the values of all q Laguerre functions in the expansion become
approximately zero as the time index k approaches the memory length M.
136
In other words, each function should die out as k M. Figure 17 shows the first 5
Laguerre functions (order i = 0 to i = 4) for a
2
= 0.25, 0.5, and 0.7 (or a = 0.5, 0.71, and
0.84). From this figure it can be observed that the greater the value of a, the longer each
function oscillates. Also, the greater the order i of the function, the more oscillating the
function is.
Figure 17: First 5 Laguerre basis functions (order i = 0 to order i = 4) for a
2
= 0.25, 0.5, and 0.7, respectively.
7.4.2. The Meixner basis expansion
As mentioned in the previous chapter, we are using Meixner basis functions to expand
the Volterra kernels in this study. This involves the determination of an additional
parameter, the order of generalization n. This parameter determines how late each
function starts to oscillate.
5 10 15 20 25 30 35 40 45 50
-0.5
0
0.5
Lags (sample number)
Amplitude L
i
(k)
p = 0.5, k (numb. BF) = 5, n (ord. gen.) = 0
i = 0
i = 1
i = 2
i = 3
i = 4
5 10 15 20 25 30 35 40 45 50
-0.4
-0.2
0
0.2
0.4
0.6
p = 0.707107, k (numb. BF) = 5, n (ord. gen.) = 0
Lags (sample number)
Amplitude L
i
(k)
5 10 15 20 25 30 35 40 45 50
-0.4
-0.2
0
0.2
0.4
p = 0.83666, k (numb. BF) = 5, n (ord. gen.) = 0
Lags (sample number)
Amplitude L
i
(k)
a
2
= 0.25
a
2
= 0.50
a
2
= 0.70
137
This behavior is depicted in Figure 18. For a fixed decay parameter, a
2
= 0.25, the greater
the order of generalization n, the longer it takes for the functions to start to oscillate. It is
this feature of the Meixner basis functions that make them particularly interesting to use
as expansion basis for systems with a slow onset (Asyali, et al., 2005). For a null order of
generalization, n = 0, the Meixner basis functions are equivalent to the Laguerre basis
functions for the same decay parameter.
Figure 18: First 5 Meixner basis functions (order i = 0 to order i = 4) for decay parameter a
2
= 0.25 and order of
generalization n = 2, 4, and 8, respectively.
As previously mentioned, the system identification problem, thus, consists of estimating
the coefficients c
j
ABR
and c
j
RCC
of the Meixner basis functions M
j
in the Meixner basis
functions expansion used to represent the impulse responses h
ABR
(t) and h
RCC
(t):
5 10 15 20 25 30 35 40 45 50
-0.5
0
0.5
Lags (sample number)
Amplitude M
i
(k)
p = 0.5, k (numb. BF) = 5, n (ord. gen.) = 2
i = 0
i = 1
i = 2
i = 3
i = 4
5 10 15 20 25 30 35 40 45 50
-0.5
0
0.5
p = 0.5, k (numb. BF) = 5, n (ord. gen.) = 4
Lags (sample number)
Amplitude M
i
(k)
5 10 15 20 25 30 35 40 45 50
-0.5
0
0.5
p = 0.5, k (numb. BF) = 5, n (ord. gen.) = 8
Lags (sample number)
Amplitude M
i
(k)
a
2
= 0.25, n = 2
a
2
= 0.25, n = 4
a
2
= 0.25, n = 8
138
1
0
) ( ) (
ABR
q
j
j
ABR
j ABR
t M c t h
(7.5)
1
0
) ( ) (
RCC
q
j
j
RCC
j RCC
t M c t h
(7.6)
In these equations, similar to the equations involving the Laguerre basis functions in the
previous chapter, M
j
(t) represents the j-th order discrete time orthonormal Meixner
function,
and
are the corresponding unknown coefficients or weights assigned
to each M
j
(t) in the ABR and RCC impulse responses, respectively, and q
ABR
and q
RCC
are
the total number of Laguerre basis functions in the ABR and RCC impulse functions,
respectively. Using this representation, the inputs ILV(t) and SBP(t) and the output
RRI(t) are then used to estimate the unknown coefficients from following expression:
) ( ) ( ) ( ) (
1
0
1
0
t t v c t u c t RRI
RRI
q
j
j
ABR
j
q
j
j
RCC
j
ABR RCC
(7.7)
where u
j
(t) and v
j
(t) are defined as
1
0
) ( ) ( ) (
M
i
RCC j j
D i t ILV i M t u
(7.8)
1
0
) ( ) ( ) (
M
i
ABR j j
D i t SBP i M t v
(7.9)
139
Model requirements and the optimal model candidate
For our minimal model, the coefficients are estimated based on a search for the global
minimum description length of all candidate models. The choice of the optimal candidate
model also takes into consideration the correlation between residual errors and past
inputs. This correlation should ideally be not statistically different from zero (Ljung,
1999), indicating that the model is able to correctly account for the influence of each
input on the system output, so no oscillation in the error should be associated with an
oscillation in a past input. In practice, however, due to inherent noise in the
measurements and to the fact that the system is in reality a closed-loop system, for cases
in which the correlation condition was not satisfied for a particular data set, the chosen
model candidate would then have to be chosen among those that had at least the
minimum amount of correlation between residual errors and inputs considering all
possible model candidates.
An additional requirement for the chosen model is that the impulse responses must reflect
the corresponding physiological behavior expected. For instance, it is required that the
chosen model for the RCC impulse response present an initial negative peak, reflecting
the fast increase in heart rate (decrease in RRI) following a rapid inspiration (positive
increase in ILV). In terms of the ABR impulse response, the chosen model is required to
result in an impulse response that presents an initial positive peak, related to a decrease in
heart rate (increase in RRI) as a response to a rapid increase in SBP (Jo, et al., 2003).
140
Since the minimal model of cardiorespiratory control is in practice a closed-loop system,
in order to prevent errors in parameter estimation due to the dependence of the system
inputs on its output, the model equations are formulated in the time-domain so that the
model output is mathematically dependent only on past values of the inputs. This way,
“causality” constraints can be imposed and the closed-loop system can be
computationally “opened” (Jo, et al., 2003; Khoo, 2000). For instance, present changes in
RRI are mathematically constrained to be influenced only by past oscillations in blood
pressure. This constraint forces the estimation algorithm to converge towards a solution
reflecting the effect of blood pressure on RRI (through the baroreceptors), rather than the
other way around (Jo, et al., 2003).
Delays present in the baroreflex and respiratory cardiac coupling dynamics are also
considered in the model. A delay of at least 0.5 secs (or 1 sample) is assumed in the ABR
impulse response (D
ABR
), reflecting actual delays observed in experimental studies (Jo, et
al., 2003). For the RCC impulse response, since noncausal relationships have been
observed between ILV and HR (Chon, et al., 1996), in which variation in heart rate
associated with respiration precedes the actual change in lung volume, we assume that the
delay associated with the RCC impulse response (D
RCC
) is 0.
The model candidates were thus defined by a combination of all possible model orders
assumed reasonable (q
ABR
and q
RCC
are varied from 4 to 8), of all possible delays ( 3
D
RCC
0 s, 0.5 D
ABR
3 s), and of all possible orders of generalization (0 n 5) of the
Meixner basis functions. The decay parameter a was chosen from the combination of
141
number of basis function used and the order of generalization considered, in order to
assure that the functions are essentially zero around 25 s (or 50 samples), corresponding
to the assumed memory length of each impulse response. For instance, a larger number of
basis functions would require a smaller value for the decay parameter so that the
corresponding impulse response decays to zero around 25 s.
Likewise, a larger order of generalization would mean that the impulse response
generated from the respective Meixner basis functions not only starts to oscillate later
when compared to the impulse response obtained if using only Laguerre basis functions
of the same order, but also takes longer to decay to zero. Thus, there is a compromise that
must be made in the combination of these parameters, as to guarantee that the resulting
impulse responses have effectively decayed to zero by the assumed memory length of 25
s. The optimal model candidate for h
ABR
(t) and h
RCC
(t) are, thus, chosen from the total set
of possible candidates by using the constraints and conditions described above.
The objective of this chapter was to contextualize the Laguerre and Meixner basis
functions in the general framework of Volterra models, as well as to further detail the
constraints and conditions imposed on the model to better assure that the estimation
algorithm will converge to optimal models for h
ABR
(t) and h
RCC
(t) that are physiologically
reasonable and adequately model the dynamics observed in the actual system. The final
models obtained for each subject are shown in the appendix. The next chapter will cover
the time-varying model of cardiorespiratory control in order to analyze data from the cold
142
face test, as well as discuss the physiological relevance of this test in the analysis of a
subject's autonomic function.
143
Chapter 8: Statistical analysis
To test the hypothesis that the autonomic nervous system (ANS) is adversely affected by
OSA and metabolic dysfunctions in obese children, and that OSA severity is also linked
to alterations in glucose metabolism, the parameters of the autonomic control model were
tested for correlations with the Bergman minimal model parameters and indices of OSA
severity. To account for differences in age and adiposity, we used partial correlation
coefficients, as well as multiple linear regression models. This chapter reviews the
statistical methods used in the data analysis in order to test our hypothesis.
8.1. Multiple linear regression
Regression analysis not only tests but also describes a relationship between a continuous
outcome, the dependent variable, and one or more explanatory or independent variables
(Hassard, 1991). If there is an actual influence of the independent variables on the
outcome, regression analysis quantifies this relationship by determining the extent in
which changes in each explanatory variable are reflected by corresponding changes on
the outcome.
An often used measure of the strength of the regression relationship is the proportion or
percentage of the total variance in the outcome y that can be successfully explained by
the regression equation and is given by the coefficient of determinationr
2
,
y
reg
SS
SS
r
2
(8.1)
144
where SS
reg
is the variation in the outcome variable that can be successfully explained or
described by the regression model and SS
y
is the total variation in y. In this equation, the
denominator is total variance in the outcome or dependent variable y, given by the sum of
squared deviations from the mean of the y, i.e.,
n
i
i tot
y y SS
1
2
, where y
i
is the i
th
measurement of the dependent variable y and y is the mean of all y
i
’s, i = 1..n. Since
SS
err
n
i
i i
y y
1
ˆ
is the sum of squared errors between the actual observed outcome value
y
i
and the expected value
i
y ˆ predicted by the regression equation at the associated values
of the independent variables,the numerator, defined mathematically as
n
i
i i
n
i
i reg
y y y y SS
1
2
1
2
ˆ
n
i
i err tot
y y SS SS
1
2
ˆ
, quantifies the reduction
in the total variance of the output y, SS
tot
, due to using the independent variables to
predict y, or the variation in y that is explained by the linear relationship with all x
j
, j =
1..k, where k is the number of independent variables in the linear regression (Glantz, et
al., 2001; Kleinbaum, et al., 2007). The greater the coefficient of determination, the
stronger and clearer the regression relationship is.
Multiple linear regression analysis both describes the joint influence of the various
explanatory variables on the outcome variable and also measures the effect on the
outcome variable due to the influence of each explanatory variable by itself. This will be
discussed in more detail in the next section.
145
When using linear regression analysis, there are some assumptions made about this
relationship. First of all, it’s assumed that the dependent and independent variables are
linearly related. Besides, for any given value of the independent variables, the possible
values of the outcome are independent and normally distributed. In particular, the errors
or residuals are assumed to be normally distributed with zero mean. It is also assumed
that the standard deviation of the outcomes y is constant for all values of x. In other
words, the variance around the regression line is the same for all values of the
independent variable x, a property know as homoscedasticity (Rawlings, et al., 1998).
Thus, in analyzing our data, our first step was to check that all parameters to be analyzed
were normal. Non-normal distributions of the dependent and/or the independent variables
can lead to a non-normal error or residual distribution. Thus, even though normality of
the explanatory or independent variables is not a required assumption for the least
squares estimation algorithm, we first checked the dependent and independent variables
for normality prior to calculating the multiple linear regression model. Any variable
found to be non-normal were log-transformed. This transformed variable was then
rechecked for normality.
8.2. Standardized regression coefficients
To test the relationship between the autonomic and metabolic parameters, considering the
influence of age and adiposity, we used a multiple linear regression model assuming the
autonomic parameters as the dependent variable and age, adiposity, and metabolic
parameters as the independent variables, as shown in equation (8.2),
146
i i age i adip i ivgtt i aut
x b x b x b a y
, 3 , 2 , 1 ,
(8.2)
where y
aut,i
is the response or dependent variable, in this case a specific autonomic
parameter, for the i
th
patient, and x
ivgtt,i
, x
adip,i
and x
age,i
are the values of the known
independent variables, i.e. a specified metabolic and adiposity parameter and the patient’s
age, respectively, measured on the i
th
patient. The regression coefficients b
j
, j= 1..3,
describe the influence of each corresponding independent variable on the dependent
variable y
aut
. In particular, b
1
, b
2
and b
3
describe the change in the autonomic parameter
y
aut
due to a unit change in the corresponding metabolic, adiposity or age parameter,
respectively. The intercept a is interpreted as the value of the autonomic parameter y
aut
if
x
ivgtt
= x
adip
= x
age
= 0.
The error term
i
describes the variability in the sample data. As previously mentioned,
this model assumes that
i
has a normal distribution with mean 0 and standard deviation
. Moreover, the error terms
1
,
2
, …,
n
, where n is the sample size, are assumed
mutually independent.The variance
2
of the error term
i
can be estimated by s
2
,
) 1 ( / ) ˆ (
2
1
2
k n y y s
n
i
i i
(8.3)
where n is the sample size and k is the number of parameters or independent variables
considered in the multiple linear regression model (Dupont, 2002).
The multiple linear regression analysis provides a means to untangle the unique influence
of each explanatory or independent variable on the outcome (Hassard, 1991). The
147
regression coefficients are a means to quantify the extent to which the different, albeit
related, factors each uniquely contribute to the outcome. Due to the difference in units of
each regression coefficient, e.g. b
1
is in y
aut
/ x
ivgtt
units, they cannot be directly compared.
Nevertheless, by using standardized regression coefficients, with standardized units, the
relative strength of each explanatory variable on the outcome can be measured.
The standardized regression coefficient
i
for explanatory variable iis defined as
i
y
i
i
b
SD
SD
(8.4)
where SD
i
is the standard deviation of explanatory or independent variable i, SD
y
is the
standard deviation of the outcome or dependent variable, and b
i
is the regression
coefficient for explanatory variable i (Hassard, 1991).
8.3. Partial correlations for autonomic and metabolic parameters,
controlling for adiposity and age
A frequently used measure of the relationship between two continuous variables e.g. x
and y,is the correlation coefficient, also known as Pearson’s correlation coefficient, which
can be interpreted as the standardized covariance of these two variables. For instance, the
correlation coefficient between variablesx and y is defined as
y x
n
i
i i
s s
y y x x
n
r
) ( ) (
1
1
1
(8.5)
148
with 1 1 r . For simple linear regressions, the correlation coefficient requires the
estimation of the mean of two variables, e.g. x and y in equation (8.5). In this case, the
degrees of freedom df for the correlation coefficient is given by
df = n – 2
where n is the sample size. The standard error of the correlation coefficient is determined
by
2
1
) (
2
n
r
r SE
(8.6)
where the numerator can be interpreted as a measure of the proportion of variation that is
not shared by the two variables x and y, and the denominator contains the degrees of
freedom in the correlation calculation (Hassard, 1991).
The significance of this correlation can be calculated from the statistic
2
1
2
) (
0
r
n
r
r SE
r
t
(8.7)
Assuming the variables } , , {
1 n
x x x and } , , {
1 n
y y y are normally distributed and
that the pairs of observations (x
i
, y
i
) for each individual in the sample were randomly
obtained, this statistic has a t distribution with df = n – 2 (Pagano, et al., 2000).
It is well known that a test of significance for the correlation coefficient is
mathematically equivalent to a test of significance on the regression coefficient b or on
the standardized regression coefficient (Pagano, et al., 2000).
149
In the multiple linear regression case, when testing the null hypothesis H
0
: b
i
= 0 against
the alternative hypothesis H
A
: b
i
0, the test statistic
)
ˆ
(
ˆ
i
i
b SE
b
t , where
i
b
ˆ
is the estimate
for the regression coefficient b
i
and SE(
i
b
ˆ
) is the standard error of
i
b
ˆ
, has a t-distribution
with n – k – 1 degrees of freedom, where k is the number of independent or explanatory
variables in the regression model and n is the number of samples. In this analysis, all
other independent variables x
j
x
i
remain constant.
Partial correlation coefficient
The multiple correlation coefficient r in the multiple linear regression analysis is a
measure of the degree of correlation considering all k independent variables, x
1
, …,x
k
. In
order to consider the correlation between a pair of variables, while holding the other
variables constant, a partial correlation coefficient can be used. This allows the study of
the correlation of two variables of interest, usually the dependent y and one of the
independent variables x
i
, while keeping the other independent variables x
j
x
i
constant.
This eliminates any effects of the interaction of the other variables x
j
x
i
on the
relationship between y and x
i
(Zar, 1999). This partial correlation coefficient is referred to
as
k j i
x x x x y
r
1
, j i. In other words, the partial correlation coefficient can be
interpreted as an adjustment to the simple linear regression coefficient between y and x
i
to
take into account the influence of additional explanatory or control variables x
j
, j = 1, …,
k, j i (Kleinbaum, et al., 2007).
150
Another interpretation of the partial correlation coefficient is that it represents the
correlation of the residuals in a regression. Assume, for instance, that three variables x, y
and z are jointly normally distributed. Suppose that the linear regression model for the
relation of y with z is given by
1 1 1
e z b a y , while the model for the relation of x with
z is given by
2 2 2
e z b a x . The estimate y ˆ
and x ˆ for a given z from the respective
models are given by z b a y
1 1
ˆ and z b a x
2 2
ˆ . Thus, the residuals ) ˆ (
i i
y y and
) ˆ (
i i
x x , i = 1, …, n, from predicting y from z and x from z, respectively, represent the
information or variation that cannot be explained by z in the variables y and x separately
by use of each linear regression model. By correlating these n pairs of residuals, we find
the correlation coefficient
) ˆ )( ˆ ( x x y y
r
, which is independent of any effect of z. It can be
shown that the partial correlation between y and x, controlling for z, is the correlation
between the aforementioned residuals (Kleinbaum, et al., 2007; Waliczek, 1996), i.e.
) ˆ )( ˆ ( x x y y z x y
r r
(8.8)
This is referred to as a first order correlation, since only one variable is being controlled
in the correlation, namely z. In a second order correlation, two variables are being
controlled, e.g.
w z x y
r
, where z and w are the control variables, and so on. A Pearson’s
correlation can be referred to as a zero order correlation, since no variables are being
partialed out of the correlation (Waliczek, 1996). The square of the partial correlation
coefficient, e.g.
w z x y
r
2
, measures the proportion of the variation in ythat can be
explained by variations in x while controlling for z and w.
151
8.4. Significant F-test in the multiple linear regression
To test the hypothesis that there is no interrelationship among the dependent and
independent variables in the multiple linear regression model, we can use the F-test such
that
e
r
df SSE
df SSR
residual square means
regression square means
F
/
/
(8.9)
where SSR is the regression sum of squares, df
r
is the regression degrees of freedom, SSE
is the residual sum of squares, and df
e
is the residual degrees of freedom (Zar, 1999). In
the multiple linear regression analysis, the F statistic tests the null hypothesis H
0
that the
slopes are all not significantly different from zero, against the alternative hypothesis H
A
that at least one slope or partial regression coefficient is significantly different from zero,
i.e.
0 :
2 1 0
k
H
) 1 0 ( s ' more or one for , 0 : , ..., k , i i H
i A
(8.10)
where k is the total number of independent variables being considered in the analysis.
A significant F statistic in the test for dependence of the outcome yon all of the
explanatory variablesx
i
is usually associated to a significance of at least one of the partial
regression coefficients
i
. However, there may be situations in which a significant F is
obtained without any significant t-test for the regression coefficients, as well as a
significant t-test for one or more regression coefficients without a significant F value.
152
These latter cases usually indicate a high degree of correlation among the different
explanatory or independent variables (Zar, 1999). Multicollinearity in the explanatory
variables may lead to large standard errors of the partial regression coefficients
i
’s,
which means that the
i
’s are imprecise estimates of the relationships of the explanatory
variables on the outcome (Zar, 1999). Thus, even if there is a relation between y and
some x
i
, the corresponding b
i
may be found not to be statistically significantly different
from zero.
The statistical tools presented in this chapter were used to analyze the data from the
different studies performed in our sample of subjects, in order to test our hypothesis of
interactions among sleep apnea severity, autonomic imbalance, and metabolic
dysfunction, controlling for age and adiposity. The data analyses and results obtained are
presented and discussed in the next chapter.
153
Chapter 9: Results and discussion
This chapter presents the results obtained from the tests of metabolic and autonomic
function, as well as sleep studies, conducted in a total of 30 obese male subjects (age:
13.2 ± 2.2 years (mean ± SD), BMI>95% for age) with varying degrees of OSA severity
(obstructive apnea-hypopnea index (OAHI): 1 events/h; desaturation index:
0.140.1). Exclusion criteria included diabetes, systemic hypertension, and treatment for
OSA. Of these 30 boys, while all had autonomic studies, 28 had both autonomic and
sleep studies, 22 had both autonomic and FSIVGTT studies, 22 had both sleep and
FSIVGTT studies, while 21 had all three (autonomic, sleep, and IVGTT) studies.
The subjects were recruited via Sleep, Endocrinology, and Obesity clinics at Children’s
Hospital Los Angeles (CHLA). The procedures were carried out in the Sleep Lab and
General Clinical Research Center (GCRC) at CHLA. The experimental protocol was
fully approved by the Committee on Clinical Investigations (institutional review board)
of Children’s Hospital Los Angeles. Written informed consent was obtained from the
parents of each subject before participation in the study. Assent was obtained from the
subjects themselves.
As previously mentioned, our hypothesis in this study is that the autonomic nervous
system (ANS) and glucose metabolism are adversely affected by OSA in children. We
also wish to investigate if autonomic abnormalities are linked to alterations in glucose
metabolism.
154
Table 1 gives an overview of the 22 male subjects who had both sleep and IVGTT
studies.
Table 1: Descriptive statistics of male subjects in study
Variable Mean SD Range
Age (years) 13.4 ± 2.1 10.3 – 17.9
BMI
*
(kg/m
2
) 34.4 ± 6.3 25.3 – 52.5
Total % Body Fat 41.0 ± 5.0 29.9 – 50.0
BMI (z-Score) 2.4 ± 0.3 2.0 – 3.2
OAHI
**
(events/h) 4.1± 3.2 1.0 – 14.1
TAI (events/h) 11.7 ± 6.6 4.1 – 29.0
Desaturation index (event/h) 9.8 ± 11.1 0 – 40.1
Fasting Glucose (mg/dl) 84.7 ± 7.4 70.5 – 100
Fasting Insulin ( U/ml) 15.2 9.5 2.0 – 39.5
SI (×10
-4
min
-1
/ U/ml) 4.1 ± 4.8 0.9 – 22.2
SBP (baseline, mmHg)
123.9 16.5 99.0 – 152.0
RRI (baseline, msec)
839.3 134.6 596.8 – 1094.0
Heart rate (baseline, beats/min)
73.3 12.0 54.8 – 100.5
*
BMI 90
th
percentile for age and gender
**
Upper limit of normal in this age group = 1.5 events/h
Exclusion criteria: diabetes, systemic hypertension, and treatment for OSA
The subjects participated in a series of procedures that included: (1) polysomnography;
(2) morning fasting blood samples, followed by a frequently-sampled intravenous
glucose tolerance test (FSIVGTT); (3) dual energy X-ray absorptiometry for assessing
adiposity; and (4) measurement of respiration, heart rate and noninvasive continuous
blood pressure during supine and standing postures. Insulin sensitivity, disposition index
(DI, a measure of pancreatic beta cell function) and other Bergman minimal model
parameters were derived from the FSIVGTT data, as discussed in chapter 3.
Baroreflex gain (G
ABR
), a measure of sympathovagal balance, and respiratory cardiac
coupling gain (G
RCC
), a measure of vagal modulation, were computed from the
autonomic measurements using theminimal model of cardiorespiratory control. As
155
reviewed in chapter 5, a decrease in the respiratory cardiac coupling gain is related to a
decrease in vagal modulation, and vice-versa. In terms of the baroreflex gain, a decrease
in this gain corresponds to a decrease in vagal modulation, an increase in sympathetic
modulation, or both.
In order to evaluate our hypothesis that both autonomic dysfunctions and metabolic
impairments are related to OSA in overweight and obese children, as well as the
existence of a direct association between autonomic and metabolic imbalances, pairwise
correlations between sleep, autonomic, and metabolic parameters were performed,
adjustingfor age and adiposity, as well as multiple linear regression analyses, considering
the effect of OSA and metabolic variables on the autonomic function, as well as
considering the effects of OSA and autonomic function simultaneously on metabolic
variables (metabolic parameters as the dependent variable in a multiple linear regression
model). These analyses are performed in both baseline conditions (supine posture) and
considering autonomic adjustments to postural change (from supine to standing). This is
followed by a discussing of the results obtained.
9.1. SBP vs. PTT as input to the ABR transfer function in the minimal
model of cardiorespiratory control
As discussed in the proposal manuscript presented previously (Oliveira, 2010), PTT was
found to be negatively correlated with SBP (p < 0.003), although these correlations were
not very strong (0.00046 R
2
0.46, median R
2
= 0.24, mean R
2
= 0.23). These results
were in agreement with other studies (as discussed in section 5.5), which report a
156
significant but not particularly strong negative correlation between PTT and SBP (Payne,
et al., 2006; Chen, et al., 2000).
These same studies mention that beat-to-beat variations in PTT, instead of the PTT data
themselves, provide a useful measure of blood pressure variability. This was also found
in the present study. Variations in SBP and PTT, described by the signals
) 1 ( ) ( ) ( k SBP k SBP k SBP and ) 1 ( ) ( ) ( k PTT k PTT k PTT , n k , , 1 , where n is
the total number of data points (n = 1200), were also shown previously to have a stronger
correlation than that found between the raw PTT and SBP data.
Moreover, the autonomic descriptors determined using either SBP or PTT as input to the
ABR transfer functionwere compared, in both the supine and standing postures. From
those results, it was found that using SBP or PTT as input to the ABR transfer function
results in autonomic measures that are correlated, but not perfectly. In other words,
autonomic parameters determined using either SBP or PTT seem to contain overlapping
information, but also each parameter contains information unique to the particular choice
of input.
In this study, the autonomic descriptors using either SBP or PTT as input will be
analyzed in the correlations with sleep and metabolic parameters, since this information
may be useful for subsequent studies. In the present study the Nexfin, described
previously, was used, from which continuous measurement of blood pressure can be
obtained. Since the Nexfin and similar equipments are expensive, if the continuous blood
157
pressure measurement is not available in a particular study, then an alternative would be
to use PTT as a surrogate measure for SBP.
Since the autonomic parameters depend on variations of SBP and PTT, and not on the
signals themselves, a significant correlation is expected between the same autonomic
measure determined using either input. Tables 2 through 4 show the correlations between
each autonomic parameterconsidered in this study, determined in the supine, standing,
and as the stand/supine ratio, respectively, using either input.
From these tables, it can be seen that for the supine and standing postures, the autonomic
descriptors using SBP as input to the ABR transfer function were significantly correlated
to the corresponding parameters determined using PTT as input (values in principal
diagonal of the tables). For the stand/supine ratio, the corresponding parameters were also
significantly correlated, except for the high frequency component of ABR
(ABR
_HF_stand/supine
). These results confirm that, for practically all cases, the autonomic
parameters determined using either SBP or PTT are significantly correlated.
The results from these tables also show that the correlationsbetween the RCC parameters
using either SBP or PTT as input to the ABR transfer function are much stronger than
those between the ABR parameters. This result was expected. Although the estimation of
the RCC parameters does depend on the input to ABR (the arterial baroreflex “block” or
transfer function, as shown in Figure 10), the change in input to ABR from SBP to PTT
should not have a strong influence in the estimation of the RCC transfer function (which
158
measures the relationship between variations in respiration, ILV, to oscillations in RRI,
RRI).
Table 2: Pearson’s correlation coefficient (r) and corresponding p-value between the ABR and RCC autonomic
parameters, determined in the supine posture, with either SBP or PTT as input to the ABR transfer function.
ABR
_LF_supine_PTT
ABR
_HF_supine_PTT
RCC
_LF_supine_PTT
RCC
_HF_supine_PTT
ABR
_LF_supine_SBP
0.5*
(0.0074)
0.063
(0.75)
0.39*
(0.043)
0.27
(0.16)
ABR
_HF_supine_SBP
0.16
(0.43)
0.52*
(0.0051)
0.4*
(0.033)
0.34
(0.074)
RCC
_LF_supine_SBP
0.34
(0.079)
0.36
(0.059)
0.96*
(<0.001)
0.67*
(<0.001)
RCC
_HF_supine_SBP
0.39*
(0.042)
0.43*
(0.023)
0.62*
(<0.001)
0.98*
(<0.001)
* Significant correlations (p < 0.05)
Table 3: Pearson’s correlation coefficient (r) and corresponding p-value between the ABR and RCC autonomic
parameters, determined in the standing posture, with either SBP or PTT as input to the ABR transfer function.
ABR
_LF_stand_PTT
ABR
_HF_stand_PTT
RCC
_LF_stand_PTT
RCC
_HF_stand_PTT
ABR
_LF_stand_SBP
0.85*
(<0.001)
0.65*
(<0.001)
0.39*
(0.043)
0.22
(0.26)
ABR
_HF_stand_SBP
0.44*
(0.018)
0.58
(0.0011*)
0.34
(0.074)
0.43*
(0.023)
RCC
_LF_stand_SBP
0.33
(0.089)
0.27
(0.16)
0.98*
(<0.001)
0.76*
(<0.001)
RCC
_HF_stand_SBP
0.18
(0.35)
0.30
(0.13)
0.71*
(<0.001)
0.99*
(<0.001)
* Significant correlations (p < 0.05)
Table 4: Pearson’s correlation coefficient (r) and corresponding p-value between the ABR and RCC autonomic
parameters, determined as the ratio of the gain in the standing posture to the gain in the supine posture, with
either SBP or PTT as input to the ABR transfer function.
ABR
_LF_stand/sup_PTT
ABR
_HF_stand/sup_PTT
RCC
_LF_stand/sup_PTT
RCC
_HF_stand/sup_PTT
ABR
_LF_stand/sup_SBP
0.56*
(0.0019)
0.21
(0.29)
0.03
(0.87)
0.09
(0.66)
ABR
_HF_stand/sup_SBP
-0.05
0.787
-0.185
0.347
-0.0024
(0.99)
-0.037
(0.85)
RCC
_LF_stand/sup_SBP
0.40*
(0.037)
0.33
(0.084)
0.85*
(<0.001)
0.707*
(<0.001)
RCC
_HF_stand/sup_SBP
0.14
(0.49)
0.041
(0.84)
(0.40) *
(0.034)
0.90*
(<0.001)
* Significant correlations (p < 0.05)
159
9.2. Autonomic reactivity to posture change: supine to standing
The next step was to compare the G
RCC
and G
ABR
gains in the supine (baseline conditions)
against the standing postures. From previous experience with the model, changes in these
gains from supine to standing should reflect a shift from parasympathetic dominance in
the supine posture to sympathetic dominance upon standing. Since the G
RCC
gain reflects
vagal modulation, a decrease of this gain is expected upon standing. In terms of the G
ABR
gain, a shift to sympathetic modulation would be related to a decrease in this gain. Since
the baroreflex gain also reflects parasympathetic modulation, a decrease in G
ABR
could be
the result of a decrease in parasympathetic modulation, an increase in sympathetic
modulation, or both.
160
Figure 19: G
RCC
supine vs. standing, determined using either (a) SBP or (b) PTT.
Figure 19 shows, for each subject, the respiratory cardiac coupling gain in the supine and
standing postures, using both SBP (left figure) and PTT (right figure). These results show
that G
RCC
supine is statistically significantly different from G
RCC
standing (p < 0.0001). In
particular, G
RCC
decreased substantially from the supine to the standing posture,
indicating a decreased vagal modulation due to the standing posture.
In terms of the baroreflex gain G
ABR
, some subjects showed a decrease in this gain from
supine to standing, while others showed an increase, as illustrated in Figure 20. The
overall difference between G
ABR
supine and G
ABR
standing was, therefore, not statistically
significantly different from zero, using either SBP or PTT as the input. Since the
baroreflex gain reflects both sympathetic and parasympathetic modulations, both of these
0.5 1 1.5 2 2.5
0
50
100
150
200
250
300
350
400
450
AMD 2
AMD 4
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AMD 6
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AMD 21
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AMD 31
AMD 35
AMD 36
AMD 37
AMD 38
AMD 40
AMD 43
AMD 47
AMD 48
AMD 50
AMD 54
RCC (HF) SBP: Supine vs. Standing
Supine and standing values are statistically significantly different (p < 0.001)
Mann-Whitney Rank Sum Test
0.5 1 1.5 2 2.5
0
50
100
150
200
250
300
350
400
450
AMD 2
AMD 4
AMD 5
AMD 6
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AMD 19
AMD 21
AMD 22
AMD 25
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AMD 29
AMD 30
AMD 31
AMD 35
AMD 36
AMD 37
AMD 38
AMD 40
AMD 43
AMD 47
AMD 48
AMD 50
AMD 54
RCC (HF) PTT: Supine vs. Standing
Supine and standing values are statistically significantly different (p < 0.001)
Mann-Whitney Rank Sum Test
supine standing standing supine
(a)G
RCC
using SBP (b)G
RCC
using PTT
161
changed from supine to standing, but in different proportions in different subjects. From
the results for G
RCC
, all subjects showed a significant decrease in this gain from supine to
standing, indicating a decrease in vagal modulation. Consequently, the difference in
behavior seen for the baroreflex gain for the different postures suggests a different degree
of sympathetic modulation (increase, decrease, or no change, depending on the subject).
Some subjects, for instance AMD 11, showed a strong decrease in baroreflex gain
G
ABR
from supine to standing, indicating a decrease in vagal modulation (confirmed by the
decrease in G
RCC
) and/or an increase in sympathetic modulation, while others, i.e. AMD
29, showed a shift in G
ABR
in the opposite direction. In this case, since G
RCC
decreased
from supine to standing for all subjects, indicating vagal withdrawal, this increase in
G
ABR
seems to indicate that the magnitude of increase in sympathetic modulation, if any,
was not enough to result in an overall decrease in G
ABR
.In fact, a decrease in sympathetic
modulation greater than the decrease observed in the parasympathetic modulation as
measured by G
RCC
could explain the increase observed in G
ABR
for these patients.
162
Figure 20: G
ABR
supine vs. standing, determined using either (a) SBP or (b) PTT as input.
9.3. Correlations between sleep apnea and metabolic parameters
Our hypothesis is that an increase in OSA severity in children is related to metabolic
impairments, such as an increase in insulin resistance. To test this hypothesis, the
association between sleep and metabolic parameters were investigated by performing
linear regression analysis between these parameters, controlling for age and adiposity.
For adiposity measures, we are using total percent body fat, total fat in grams, trunk
percent fat, and trunk fat in grams, obtained from the DEXA scan, as well as BMI and
BMI z-score. For this group of subjects, BMI and total percent body fat (as well as trunk
0.5 1 1.5 2 2.5
0
0.5
1
1.5
2
2.5
3
3.5
4
AMD 2
AMD 4
AMD 5
AMD 6
AMD 8
AMD 9
AMD 10
AMD 11
AMD 12
AMD 18
AMD 19
AMD 21
AMD 22
AMD 25
AMD 28
AMD 29
AMD 30
AMD 31
AMD 35
AMD 36
AMD 37
AMD 38
AMD 40
AMD 43
AMD 47
AMD 48
AMD 50
AMD 54
ABR (LF) SBP: Supine vs. Standing
Supine and standing values are not statistically significantly different (p = 0.36)
Mann-Whitney U Statistic
0.5 1 1.5 2 2.5
0
0.5
1
1.5
2
2.5
3
3.5
4
AMD 2
AMD 4
AMD 5
AMD 6
AMD 8
AMD 9
AMD 10
AMD 11
AMD 12
AMD 18
AMD 19
AMD 21
AMD 22
AMD 25
AMD 28
AMD 29
AMD 30
AMD 31
AMD 35
AMD 36
AMD 37
AMD 38
AMD 40
AMD 43
AMD 47
AMD 48
AMD 50
AMD 54
ABR (LF) PTT: Supine vs. Standing
Supine and standing values are not statistically significantly different (p = 0.995)
T-test statistic
supine standing standing supine
(a) G
ABR
using SBP (b) G
ABR
using PTT
163
percent fat) were not significantly correlated, as can be seen from the correlation results
shown in Table 5.
Table 5: Pearson’s correlation coefficient (and corresponding p-value) between the obesity measures considered
in this study.
Obesity
measure
BMI
r
(p-value)
BMI Z Score
r
(p-value)
Total body fat
(g)
r
(p-value)
Trunk fat (g)
r
(p-value)
Trunk % fat
r
(p-value)
Total % body fat
0.217
(0.331)
0.240
(0.282)
0.593*
(0.00363)
0.538*
(0.00984)
0.953*
(7.424E-012)
BMI
0.967*
(2.151E-013)
0.713*
(0.000197)
0.712*
(0.000204)
0.122
(0.590)
BMI Z Score
0.691*
(0.000365)
0.690*
(0.000380)
0.154
(0.495)
Total body fat (g)
0.977*
(5.997E-015)
0.481*
(0.0234)
Trunk fat (g)
0.473*
(0.0263)
*
Significant correlations (p 0.05).
Since BMI does not distinguish between lean body mass and fat, the relationship between
BMI and body fatness varies according to body composition and proportions (Garn, et al.,
1986). Adiposity results from the DEXA scan provide a more precise estimate of body fat
mass (Punjabi, et al., 2009).
164
Table 6: Metabolic parameters for the subjects analyzed in this study
Subject AIRg DI SI Sg Fast. gluc. Fast. Insul. HOMA
2 732.0 1879.90 2.57 0.0035 85.00 13.00 2.73
4 1758.2 3444.50 1.96 0.0141 88.00 21.50 4.67
5 1768.6 2040.00 1.15 0.0030 80.50 26.00 5.17
8 313.3 1601.50 5.11 0.0169 75.00 6.40 1.19
9 382.5 537.20 1.40 0.0178 92.50 17.00 3.88
10 1946.0 2390.40 1.23 0.0181 80.00 19.50 3.85
11 281.0 1021.80 3.64 0.0175 70.50 3.45 0.60
12 803.0 1572.00 1.96 0.0189 95.00 19.00 4.46
17 834.0 1241.30 1.49 0.0164 85.00 17.50 3.67
18 147.6 1917.10 12.99 0.0235 81.50 9.45 1.90
19 3360.0 3034.20 0.90 0.0249 81.50 18.50 3.72
21 845.9 2291.10 2.71 0.0157 83.00 9.85 2.02
22 507.5 959.88 1.89 0.0259 92.00 23.00 5.22
25 2003.9 4060.40 2.03 0.0289 82.50 9.90 2.02
26 1179.00 1773.20 1.50 0.0045 97.50 39.50 9.51
29 639.0 4251.00 6.65 0.0387 80.00 4.00 0.79
30 239.0 5302.10 22.18 0.0300 81.50 2.00 0.40
31 726.0 1427.50 1.97 0.0242 100.00 12.00 2.96
36 581.61 2442.60 4.20 0.0072 86.00 8.50 1.80
37 821.0 2313.20 2.82 0.0183 85.50 13.50 2.85
38 190.3 598.14 3.14 0.0235 90.50 6.00 1.34
43 1714.0 8328.10 4.86 0.0255 79.00 10.00 1.95
48 1124.5 2864.50 2.55 0.0234 77.50 11.50 2.20
The metabolic parameters for each patient considered in this study are summarized in
Table 6, while the sleep parameters are listed in Table 7. From the OAHI data, 19
subjects (65.6%) have mild OSA (between 1.5 and 5 events/h), 6 subjects (20.7%) have
moderate OSA (between 5 and 10 events/h), 3 subjects (10.3%) have severe OSA (> 10
events/h), and 1 subject (3.4%) is considered normal (< 1.5 events/h), according to
criteria for this age group.
165
Table 7: Sleep parameters for the subjects analyzed in this study
Subject OAHI TAI Desat index SpO2_low TST (min) Effic. (%)
2 4.3 9.3 3.9 90 276.0 66
4 3.2 8.2 0.4 94 336.0 84
5 9.5 22.9 12.7 81 372.0 88
6 20.0 7.8 14.5 88 285.0 77
8 4.9 5.1 1.4 92 282.5 83
9 14.1 15.7 22.0 87 321.5 77
10 2.9 24.0 8.0 88 307.0 84
11 2.3 5.8 1.5 86 319.0 78
12 4.6 29.0 2.0 79 248.0 55
18 1.0 15.6 0.1 93 316.0 72
19 2.1 7.5 4.3 91 366 97
21 1.5 16.2 13.6 84 200.0 74
22 5.6 13.3 7.4 88 163.0 84
25 1.8 8.6 19.0 79 413.0 92
26 1.5 8.0 30.8 83 352.0 81
28 2.4 7.3 24.8 81 331.0 79
29 6.4 12.1 6.8 91 327.0 90
30 1.6 4.1 0.2 93 304.5 82
31 2.4 10.9 1.6 81 444.0 89
35 18.0 12.2 29.6 83 299.0 69
36 1.8 5.8 25.1 88 236.5 62
37 7.4 9.5 40.1 86 308.0 76
38 2.2 4.9 5.7 87 294.0 90
40 3.5 13.2 2.2 92 276.5 69
43 7.1 9.1 8.1 83 433.5 92.9
47 3.9 4.8 1.9 92 273.5 62.2
48 2.0 12.5 0.5 89 335.0 77
50 7.7 9.6 2.9 92 287.5 67.2
54 2.2 9.2 3.5 89 332 80.5
From Table 8, it can be observed that there are 22 subjects that have both sleep and
IVGTT studies. These were, thus, the subjects considered for the pairwise correlations
between sleep and metabolic parameters. To perform the linear regression analysis
between these parameters, we used the methodology described in section 8.3 to define the
partial correlation coefficient between two variables, in this case the sleep and metabolic
parameters, controlling for the influence of additional independent variables, in this case
age and adiposity.
166
Table 8: Studies for each subject
Subject IVGTT
study?
Sleep
study?
Autonomic
study?
2
4
5
6 No
8
9
10
11
12
17
No
18
19
21
22
25
26
No
28 No
29
30
31
35 No
36
37
38
40 No
43
47 No
48
50 No
54 No
The results of the regressions between sleep and metabolic parameters are summarized in
Table 9, using the measures of adiposity displayed in Table 5. Figures 21 through 25
show the regression line and each the individual data points for each metabolic and sleep
parameter correlation presented in Table 9, controlling for age and adiposity (total
percent body fat).
167
Table 9: Partial correlation between key polysomnographic and metabolic parameters (after adjustment for age
and adiposity)
Metabolic
parameter (Y
adj
)
Sleep parameter
(X
adj
)
Adiposity parameter Partial
p-value
Partial
corr. coeff.
(r)
log10(SI) log10(Desat.)
BMI 0.041 0.46*
BMI z-score 0.022 0.51*
Total Body Fat (g) 0.077
% Body Fat 0.043 *
Total trunk fat 0.069
log10(% Trunk Fat) 0.036 *
Sg Efficiency (%)
BMI 0.036 0.47*
BMI z-score 0.039 0.46*
Total Body Fat (g) 0.029 0.49*
% Body Fat 0.044 0.45*
Total trunk fat 0.015 0.53*
log10(% Trunk Fat) 0.041 0.46*
log10(Fast Ins) log10(TAI)
BMI 0.095 0.38
BMI z-score 0.097 0.38
Total Body Fat (g) 0.019 0.52*
% Body Fat 0.016 0.53*
Total trunk fat 0.019 0.52*
log10(% Trunk Fat) 0.016 0.53*
log10(HOMA) log10(TAI)
BMI 0.11 0.37
BMI z-score 0.11 0.37
Total Body Fat (g) 0.024 0.50*
% Body Fat 0.019 0.52*
Total trunk fat 0.024 0.50*
log10(% Trunk Fat) 0.020 0.52*
log10(QUICKI) log10(TAI)
BMI 0.094 -0.38
BMI z-score 0.10 -0.38
Total Body Fat (g) 0.022 -0.51*
% Body Fat 0.017 -0.53*
Total trunk fat 0.021 -0.51*
log10(% Trunk Fat) 0.018 -0.52*
log10(FGIR) log10(TAI)
BMI 0.089 -0.39
BMI z-score 0.087 -0.39
Total Body Fat (g) 0.016 -0.53*
% Body Fat 0.013 -0.54*
Total trunk fat 0.016 -0.53*
log10(% Trunk Fat) 0.014 -0.54*
*
Significant correlations (p 0.05).
Figure 21 shows the correlation between log10(SI) and log10(desaturation index),
controlling for age and adiposity (total percent body fat). This result indicates that an
168
increase in exposure to hypoxia, as measured by the desaturation index, is related to a
decrease in insulin sensitivity (or, equivalently, an increase in insulin resistance).
Figure 21: Linear regression between log10(SI) and log10(desaturation index), controlling for age and adiposity
(total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.21, partial correlation coefficient = 0.46, partial p-value = 0.043, =
0.59, = 0.23, standardized
sleep
= 0.50, standardized
adiposity
= 0.099, standardized
age
= 0.022.
Figure 22 shows the correlation between glucose effectiveness, Sg, and sleep efficiency
(%), controlling for age and adiposity (total % body fat). This plot shows that a decreased
sleep efficiency is related to a decreased glucose effectiveness. This result agrees with
results from Punjabi and colleagues (Punjabi, et al., 2009) in nondiabetic adults. They
found that, in subjects with sleep disordered breathing, Sg was negatively correlated with
the apnea-hypopnea index (events/hour), and not with the degree of oxyhemoglobin
desaturation.
-1 -0.5 0 0.5 1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Adjusted log10_Desat---
Adjusted log10_SI----
(N = 22) Linear regression for Y
adj
= log10_SI---- vs. X1
adj
= log10_Desat---, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.208, corr. coeff. (Yadj vs. X1adj) = -0.456, partial corr. coeff = -0.456, partial p-value = 0.0431,
p-value (Yadj vs X1adj) = 0.0327.
= 0.59428, (X1adj) = -0.23476.
Pearson's Corr. Coeff. (Yadj vs. Xadj_sleep) = -0.45644, p-value (SIMPLE LIN REGR) = 0.03274.
bRelSLEEP = -0.50472, bRelOBES = -0.0989, bRelAGE = -0.021971
Adjusted log(Desat index)
Adjusted log(SI)
169
This could mean that sleep disruption, such as a decrease in sleep efficiency, is related to
a decrease in the effect of glucose per se on its own peripheral disposal, at basal insulin
levels. Since an increase in epinephrine levels, suggesting increased sympathetic tone,
has been found to be associated with decreased glucose effectiveness (Avogaro, et al.,
1996), the link between the decrease in sleep effectiveness associated with a decrease in
Sg could be through an impairment in autonomic control. As will be shown in section
9.6, sleep efficiency was found to be significantly correlated to the high frequency
component of baseline baroreceptor function, quantified by the autonomic parameter
ABR
_HF_supine_PTT
, when adjusting for age, adiposity, and the disposition index, a measure
of pancreatic -cell function. The parameter ABR
_HF_supine_PTT
is related to baroreceptor
vagal modulation, such that a decrease in this parameter is related to a decrease in
baroreceptor mediated vagal tone.
170
Figure 22: Linear regression between Glucose Effectiveness (Sg) and Sleep Efficiency (%), controlling for age
and adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.21, partial correlation coefficient = 0.45, partial p-
value = 0.044, =-0.013, = 0.00040, standardized
sleep
= 0.46, standardized
adiposity
= -0.089, standardized
age
= -0.071.
The correlation between fasting insulin and total arousal index (TAI), controlling for age
and adiposity (total percent body fat), is shown in Figure 23. This positive correlation
indicates that an increase in sleep fragmentation, as measured by the total number of
arousals per hour of sleep, is related to an increase in fasting insulin levels. Increased
fasting insulin levels are an evidence of insulin resistance. These results are consistent
with findings from Redline and colleagues (Redline, et al., 2007). In their community-
based sample of predominantly postpubertal adolescents, they found a strong association
of sleep disordered breathing with fasting insulin and the HOMA index, even after
adjusting for BMI percentile. Their study in fact indicates that sleep disordered breathing
is a risk factor for the development of the metabolic syndrome. They found that
adolescents with SDB have a sevenfold increased odds of developing the metabolic
55 60 65 70 75 80 85 90 95 100
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Adjusted nolog_Eff-Perc
Adjusted nolog_Sg----
(N = 22) Linear regression for Y
adj
= nolog_Sg---- vs. X1
adj
= nolog_Eff-Perc, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.207, corr. coeff. (Yadj vs. X1adj) = 0.455, partial corr. coeff = 0.455, partial p-value = 0.0437,
p-value (Yadj vs X1adj) = 0.0332.
= -0.012841, (X1adj) = 0.0003984.
Pearson's Corr. Coeff. (Yadj vs. Xadj_sleep) = 0.45528, p-value (SIMPLE LIN REGR) = 0.033242.
bRelSLEEP = 0.4606, bRelOBES = -0.088868, bRelAGE = -0.071568
Adjusted Sg
Adjusted Sleep Efficiency (%)
171
syndrome when compared to children without SDB. In their study population, they found
the metabolic syndrome to be strongly associated with sleep-related desaturation and low
sleep efficiency, but not arousal frequency. Since the metabolic syndrome is
characterized by insulin resistance, this result agrees with the findings in the present
study of the association between SI and desaturation index (Figure 21).
Figure 23: Linear regression between Fasting Insulin and Total Arousal Index (TAI), controlling for age and
adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.28, partial correlation coefficient = 0.53, partial p-value =
0.016, = 0.31, = 0.73, standardized
sleep
= 0.55, standardized
adiposity
= 0.0066, standardized
age
= 0.044.
The measures of fasting insulin, HOMA, QUICKI, and FGIR were found to be
significantly correlated in our study population. These correlation results are summarized
in Table 10. The HOMA and QUICKI indexes were also significantly correlated with
fasting glucose. For our study population, we also found insulin sensitivity (S
I
) obtained
from the FSIVGTT study to be significantly correlated with HOMA, QUICKI, and FGIR,
as well as with fasting insulin values, but not with fasting glucose. The correlation
0.5 1 1.5
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Adjusted log10_TAI-----
Adjusted log10_FstIns
(N = 22) Linear regression for Y
adj
= log10_FstIns vs. X1
adj
= log10_TAI-----, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.284, corr. coeff. (Yadj vs. X1adj) = 0.533, partial corr. coeff = 0.533, partial p-value = 0.0155,
p-value (Yadj vs X1adj) = 0.0106.
= 0.31409, (X1adj) = 0.72781.
Pearson's Corr. Coeff. (Yadj vs. Xadj_sleep) = 0.53319, p-value (SIMPLE LIN REGR) = 0.010611.
bRelSLEEP = 0.54557, bRelOBES = 0.0066209, bRelAGE = 0.043763
Adjusted log(Fasting Insulin)
Adjusted log(TAI)
172
coefficients and corresponding p-values for these correlations are also summarized in
Table 10.
Table 10: Pearson’s product moment correlation between measures of insulin resistance and sensitivity (HOMA,
QUICKI, FGIR, S
I
), as well as IVGTT parameters such as acute insulin response to glucose (AIRg), disposition
index (DI), and glucose effectiveness (Sg), and fasting glucose and insulin.
QUICKI
r
(p-value)
FGIR
r
(p-value)
AIRg
r
(p-value)
DI
r
(p-value)
S I
r
(p-value)
Sg
r
(p-value)
Fast. Gluc.
r
(p-value)
Fast. Ins.
r
(p-value)
HOMA
-0.827*
(< 0.001)
-0.642*
(0.0013)
0.338
(0.12)
-0.263
(0.24)
QUICKI
0.934*
(<0.001)
-0.448*
(0.037)
0.288
(0.19)
0.718*
(<0.001)
0.475
(0.025)
-0.559*
(0.0069)
-0.849*
(<0.001)
FGIR
-0.444*
(0.039)
0.289
(0.19)
0.822*
(<0.001)
0.453*
(0.034)
-0.33
(0.13)
-0.679*
(<0.001)
AIRg
0.368
(0.092)
-0.417
(0.053)
-0.0356
(0.88)
-0.111
(0.62)
0.414
(0.055)
DI
0.373
(0.087)
0.38
(0.081)
-0.345
(0.12)
-0.238
(0.29)
SI
0.38
(0.081)
-0.255
(0.25)
-0.502*
(0.017)
Sg
-0.15
(0.51)
-0.522*
(0.013)
Fast.
Gluc.
0.514*
(0.014)
*
Significant correlations (p 0.05).
From these correlations between fasting insulin, HOMA, QUICKI, and FGIR, it seems
that the correlation found between log(fasting insulin) and log(TAI), adjusted for age and
adiposity, as well as the correlations between log(HOMA), log(QUICKI), and log(FGIR)
with log(TAI) are all conveying equivalent information.An increase in sleep
fragmentation, as measured by the total arousal index, is related with an increase in
fasting insulin and, consequently, also with an increase in HOMA (a surrogate measure
of insulin resistance based on fasting glucose and insulin levels), QUICKI, and FGIR
(these surrogate measures of insulin sensitivity, the inverse of insulin resistance, also
based on fasting plasma glucose and insulin levels), all highly correlated with fasting
173
insulin. The plots for these correlations, controlling for age and total % body fat, are
displayed in the figures below.
Figure 24: Linear regression between HOMA and Total Arousal Index (TAI), controlling for age and adiposity
(total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.27, partial correlation coefficient = 0.52, partial p-value = 0.019, =
-0.39, = 0.75, standardized
sleep
= 0.53, standardized
adiposity
= 0.0049, standardized
age
= 0.058.
0.5 1 1.5
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
Adjusted log10_TAI-----
Adjusted log10_HOMA--
(N = 22) Linear regression for Y
adj
= log10_HOMA-- vs. X1
adj
= log10_TAI-----, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.269, corr. coeff. (Yadj vs. X1adj) = 0.519, partial corr. coeff = 0.519, partial p-value = 0.0191,
p-value (Yadj vs X1adj) = 0.0134.
= -0.39366, (X1adj) = 0.75444.
Pearson's Corr. Coeff. (Yadj vs. Xadj_sleep) = 0.51862, p-value (SIMPLE LIN REGR) = 0.013401.
bRelSLEEP = 0.52974, bRelOBES = 0.0049137, bRelAGE = 0.058105
Adjusted log(HOMA)
Adjusted log(TAI)
174
Figure 25: Linear regression between QUICKI and Total Arousal Index (TAI), controlling for age and adiposity
(total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.28, partial correlation coefficient = 0.53, partial p-value = 0.012, =
-0.72, = -0.12, standardized
sleep
= -0.53, standardized
adiposity
= 0.00069, standardized
age
= 0.084.
Figure 26: Linear regression between FGIR and Total Arousal Index (TAI), controlling for age and adiposity
(total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.30, partial correlation coefficient = -0.54, partial p-value = 0.013,
= 1.59, = -0.70, standardized
sleep
= -0.56, standardized
adiposity
= -0.0085, standardized
age
= -0.027.
0.5 1 1.5
-0.95
-0.9
-0.85
-0.8
-0.75
-0.7
Adjusted log10_TAI-----
Adjusted log10_QUICKI
(N = 22) Linear regression for Y
adj
= log10_QUICKI vs. X1
adj
= log10_TAI-----, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.277, corr. coeff. (Yadj vs. X1adj) = -0.527, partial corr. coeff = -0.527, partial p-value = 0.0171,
p-value (Yadj vs X1adj) = 0.0118.
= -0.71573, (X1adj) = -0.11624.
Pearson's Corr. Coeff. (Yadj vs. Xadj_sleep) = -0.52652, p-value (SIMPLE LIN REGR) = 0.011823.
bRelSLEEP = -0.53471, bRelOBES = 0.00069241, bRelAGE = -0.084488
0.5 1 1.5
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Adjusted log10_TAI-----
Adjusted log10_FGIR--
(N = 22) Linear regression for Y
adj
= log10_FGIR-- vs. X1
adj
= log10_TAI-----, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.295, corr. coeff. (Yadj vs. X1adj) = -0.543, partial corr. coeff = -0.543, partial p-value = 0.0133,
p-value (Yadj vs X1adj) = 0.00897.
= 1.5856, (X1adj) = -0.70119.
Pearson's Corr. Coeff. (Yadj vs. Xadj_sleep) = -0.54329, p-value (SIMPLE LIN REGR) = 0.0089731.
bRelSLEEP = -0.55716, bRelOBES = -0.008476, bRelAGE = -0.027024
Adjusted log(QUICKI)
Adjusted log(TAI)
Adjusted log(FGIR)
Adjusted log(TAI)
175
Although insulin sensitivity (S
I
) obtained from the FSIVGTT study was significantly
correlated with these same metabolic measures, log(S
I
) was not found to be significantly
correlated with log(TAI), even after controlling for age and adiposity (e.g. r = -0.37, p =
0.11, controlling for age and total % body fat; r = -0.15, p = 0.44, controlling for age and
BMI z-score; r = -0.37, p = 0.11, controlling for age and trunk % fat).
The positive correlation between HOMA and total arousal index indicates that an
increase in sleep fragmentation, as measured by TAI, is related to an increase in insulin
resistance, as measured by the HOMA index, for these subjects. Analogously, the
negative correlation between QUICKI and FGIR with TAI indicates that an increase in
sleep fragmentation is related to a decrease in insulin sensitivity, as measured by these
latter metabolic indexes.These results are consistent with findings by Stamatakis and
Punjabi (Stamatakis, et al., 2010). By experimentally inducing sleep fragmentation across
all sleep stages for two nights in normal healthy adults (age < 40 years) with BMI < 30
kg/m
2
, they showed that sleep fragmentation was negatively correlated with both insulin
sensitivity (S
I
), which can be understood as the inverse of insulin resistance, and glucose
effectiveness (Sg).
These combined results show that an increase in sleep-related oxygen desaturation, as
well as an increase in sleep fragmentation, are related to an increase in insulin resistance
or, equivalently, a decrease in insulin sensitivity, and increased fasting insulin levels.
Although we also found the disposition index, a measure of -cell function, to be
significantly correlated with total sleep time when controlling for age and total body fat
176
in grams (r = 0.44, p = 0.049) and age and trunk fat in grams (r = 0.47, p = 0.047), these
correlations were not very strong and were not significant for any other adiposity
measure. This correlation, therefore, was not included in Table 9.
Besides the correlation with indices of insulin resistance, we also found a positive
correlation between sleep efficiency and glucose effectiveness (Sg), indicating that a
decrease in sleep efficiency is related to a decrease in Sg. Glucose effectiveness (Sg) and
the disposition index (DI) have been shown to independently predict conversion to
diabetes across race/ethnic groups, varying states of glucose tolerance, family history of
diabetes, obesity (BMI and waist circumference), and age (Lorenzo, et al., 2010). Sg has
been shown to contribute to glucose tolerance even in individuals with significant insulin
resistance, including diabetes (Best, et al., 1996). Although Sg is independent of the
dynamic insulin response, it does depend on the basal insulin level (Bergman, 1989).
Thus, diminished sleep efficiency is related to a deficiency in the effect of glucose on its
own disposal, which may further contribute to decreased glucose tolerance. These
combined results confirm our initial hypothesis of an association between measures
related to sleep apnea severity and metabolic dysfunction.
QUICKI and FGIR as measures of insulin sensitivity
Conwell and colleagues (Conwell, et al., 2004), in their study involving obese prepubertal
(Tanner stage 1) children and pubertal (Tanner stages 2-5) adolescents, compared fasting
indexes of insulin sensitivity and secretion with metabolic measures obtained from the
modified frequently sampled intravenous glucose tolerance test (FSIVGTT), such as
177
insulin sensitivity (S
I
). They found HOMA, QUICKI, FGIR, and fasting insulin levels to
correlate strongly with S
I
assessed by the FSIVGTT in their study population.This strong
correlation was also found in the present study.
Keskin and colleagues (Keskin, et al., 2005), on the other hand, argue that, among the
fasting methods to measure insulin resistance, HOMA is a more reliable measure of
insulin resistance among obese children and adolescents when compared to the fasting
glucose/insulin ratio(FGIR) and the quantitative insulin sensitivity check index
(QUICKI) methods. Keskin and colleagues also mention that the cutoff point for
diagnosis of insulin resistance in this population using the HOMA index was 3.16.
The QUICKI index (Katz, et al., 2000) is a measure of insulin sensitivity and is derived
from the expression )] log( ) [log( 1
f f
G I , where I
f
and G
f
are the measures of fasting
insulin and glucose, respectively. An increased insulin resistance is related to a decrease
in the QUICKI index. Silfen and colleagues (Silfen, et al., 2001) have shown the QUICKI
and the FGIR indexes to be highly correlated with oral glucose tolerance test measures of
insulin sensitivity in their study population (prepubertal girls with premature adrenarche
or obesity).
As the name suggests, the FGIR index is calculated from the ratio of fasting glucose to
fasting insulin. Legro and colleagues (Legro, et al., 1998) found the FGIR index to be
useful as a screening test for insulin resistance in obese non-Hispanic white PCOS
women. They found that the FGIR index had both high sensitivity and specificity for
detecting insulin resistant women in their study group.Silfen and colleagues (Silfen, et al.,
178
2001) have shown that an FGIR less than 7 in young girls with premature adrenarche or
obesity is helpful in the early identification of children at risk for complications of insulin
resistance. Vuguin and colleagues (Vuguin, et al., 2001) have shown that the FGIR is a
useful measure for insulin resistance screening in prepubertal Caribbean Hispanic and
African American girls with premature adrenarche. Nevertheless, as discussed by Quon
(Quon, 2001), the FGIR only behaves as a physiologically appropriate index of insulin
sensitivity in subjects with normal fasting glucose levels, while the HOMA and QUICKI
indexes are more robust, both behaving qualitatively as expected across a broad spectrum
of insulin sensitivity and resistance.
9.4. Correlations between sleep apnea and autonomic parameters
We also hypothesize that an increase in OSA severity is associated to autonomic
dysfunction in this group of obese children. In order to test this hypothesis, the linear
regressions between the sleep and autonomic parameters were analyzed, controlling for
age and adiposity.
The autonomic parameters investigatedwere the gains G
ABR
and G
RCC
, corresponding to
the low frequency gain of the ABR transfer function (ABR_LF) and to the high
frequency gain of the RCC transfer function (RCC_HF), respectively, as previously
mentioned. The autonomic parameters were determined for both the supine (G
ABR_sup
,
G
RCC_sup
) and standing (G
ABR_std
, G
RCC_std
) postures, calculated using either SBP or PTT as
input to the ABR transfer function. An additional autonomic parameter analyzed is the
179
high frequency component of ABR, or ABR_HF, also in the supine (baseline) and
standing postures. This parameter reflects baroreceptor mediated vagal modulation.
Baseline (supine) autonomic parameters and the standing/supine ratio
We are interested in analyzing the correlations of the sleep parameters with both the
baseline autonomic parameters (G
ABR
, G
RCC
, and ABR_HF determined in the supine
posture) as well as with autonomic reactivity to orthostatic stress, measured as the ratio
between the standing and supine parameters, e.g. G
ABR
ratio = G
ABR_stand
/ G
ABR_supine
and
G
RCC
ratio = G
RCC_stand
/ G
RCC_supine
. An equivalent measure is the autonomic reactivity,
defined as 1 the ratio of the standing and supine parameters (i.e., ABR autonomic
reactivity = 1 G
ABR
ratio and RCC autonomic reactivity = 1 G
RCC
ratio).
Therefore, a large variation in gain associated to change in posture from supine to
standing, meaning a large autonomic reactivity due to change in posture, is quantified by
a small G
ABR
or G
RCC
ratio. This is illustrated in Figure 27. In normal subjects, we expect
large variations in gain from supine to standing. Therefore, we expect to see smaller G
ABR
and/or G
RCC
ratios in normal subjects, indicating normal autonomic reactivity to change
in posture. On the other hand, in those subjects with higher degrees of OSA, we expect to
see larger G
ABR
and/or G
RCC
ratios, meaning autonomic impairment to change in posture.
At the extreme, a value of e.g. G
RCC
ratio = 1, or autonomic reactivity = 0, would mean
no change in G
RCC
from supine to standing.
180
Figure 27: A high stand/supine ratio (e.g. a high G
ABR
and/or G
RCC
ratios) means a smaller autonomic reactivity
to postural change, an indication of autonomic impairment, while a low stand/supine ratio is an indication of a
higher autonomic reactivity to postural change.
G
RCC
ratio
As shown in section 9.2, all subjects showed a decrease in the gain G
RCC
from supine to
standing, determined using either SBP or PTT as input to the ABR transfer function,
indicating vagal withdrawal in the standing posture when compared to baseline (supine)
conditions, as would be expected. Consequently, for all patients we find that G
RCC
ratio <
1, or, equivalently, RCC autonomic reactivity > 0, an indication of vagal withdrawal.
Nevertheless, some patients showed a greater change from supine to standing (e.g. AMDs
29, 21, 31), while others showed a smaller postural change in the G
RCC
gain (e.g. AMDs
5, 10, 25). Smaller changes from supine to standing may indicate a lower G
RCC
baseline
gain (supine posture) than normal, associated with lower baseline vagal modulation,
which could be an indication of increased baseline sympathetic tone for these subjects.
G
ABR
ratio
In terms of the baroreflex gain, the expected outcome is to observe a shift towards
sympathetic modulation when comparing the supine G
ABR
to the standing G
ABR
gains.
Thus, a decrease in G
ABR
from supine to standing would be the expected behavior,
supine standing
G
ABR
or
G
RCC
Stand
Supine
ratio = high
ratio = low
Stand
Supine
181
indicating a decrease in parasympathetic modulation and/or an increase in sympathetic
drive due to the change in posture. Therefore, we would also expect a smaller G
ABR
ratio
for less severe OSA patients, indicating larger autonomic reactivity and, thus, the
expected shift towards sympathetic dominance in the standing posture when compared to
baseline conditions (supine). A larger G
ABR
ratio, indicating less reactivity to postural
change, could be an indication of autonomic impairment. A ratio > 1 (or, equivalently, an
ABR reactivity < 0) means an increase in G
ABR
from supine to standing.
Linear regression results, controlling for age and adiposity
Baseline autonomic parameters and sleep
The results obtained from the linear regressions between autonomic and sleep parameters
showed no statistically significant correlation of the baseline (supine) G
ABR
or G
RCC
gains,
defined using either SBP or PTT, with any of the sleep parameters, even after controlling
for age and adiposity. The only significant correlation found was with the high frequency
ABR gain (PTT input) and the desaturation index, when controlling for total % body fat
or trunk % fat only, as shown in Table 11. These correlations, however, were not very
strong (R
2
= 0.18 and 0.19, respectively). The plot for this correlation, controlling for
total % body fat and age, is depicted in Figure 28.
182
Table 11: Partial correlation between log(ABR
_HF_sup_PTT
) and log(Desat) (after adjustment for age and
adiposity)
Autonomic parameter
(Y
adj
)
Sleep parameter
(X
adj
)
Adiposity parameter
Partial
p-value
Partial
corr. coeff.
(r)
log(ABR
_HF_sup_PTT
) log(Desat.)
BMI 0.10 0.33
BMI z-score 0.071 0.36
log(Total Body Fat (g)) 0.058
% Body Fat 0.046 *
Total trunk fat 0.058
% Trunk Fat 0.044 *
*
Significant correlations (p 0.05).
Figure 28: Linear regression between log(ABR
_HF_sup_PTT
) and log(Desat), controlling for age and adiposity (total
percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.16, partial correlation coefficient = -0.40, partial p-value = 0.046, = -
0.25, = -0.32, standardized
sleep
= -0.43, standardized
adiposity
= 0.10, standardized
age
= 0.0034.
The primary systemic arterial baroreflex sensors, comprising the carotid and aortic
baroreceptors, constitute a high pressure sensor-response loop, which responds to
pressure induced stretch (Batzel, et al., 2006). This response defines the baroreflex
sensitivity. These sensors relay information about the systemic arterial pressure to the
central nervous system, which is then translated into sympathetic and parasympathetic
-1 -0.5 0 0.5 1 1.5 2 2.5
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Adjusted log10_Desat---
Adjusted log10_ABR_HF_sup_PTT
(N = 28) Linear regression for Y
adj
= log10_ABR_HF_sup_PTT vs. X1
adj
= log10_Desat---, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.156, corr. coeff. (Yadj vs. X1adj) = -0.396, partial corr. coeff = -0.396, partial p-value = 0.0455,
p-value (Yadj vs X1adj) = 0.0372.
= -0.24737, (X1adj) = -0.31765.
Pearson's Corr. Coeff. (Yadj vs. Xadj_sleep) = -0.39559, p-value (SIMPLE LIN REGR) = 0.037188.
bRelSLEEP = -0.43491, bRelOBES = 0.099617, bRelAGE = 0.003411
Adjusted log(ABR
_HF_sup_PTT
)
Adjusted log(Desat)
183
control responses to bring the mean arterial pressure back to its baseline level (Batzel, et
al., 2006).
The high frequency component of the arterial baroreflex gain can be interpreted as
measuring the vagal limb of baroreflex responses, since cardiovagal function is also an
important determinant of baroreflex gain (Lipman, et al., 2003). While the gain of the
transfer function between arterial blood pressure as input and heart rate as output in the
frequency band 0.07 to 0.14 Hz, considered in the low frequency band in this study, has
been validated against the phenylephrine method as a measure of baroreflex sensitivity
(Robbe, et al., 1987), and used as such in different studies (deBoer, et al., 1987;
Pomeranz, et al., 1985; Linden, et al., 1996), some researchers use the high frequency
gain (corresponding to the respiratory rate) for estimation of baroreflex sensitivity
(Veerman, et al., 1994; Blaber, et al., 1995).
Autonomic parameters obtained in the standing posture and sleep
While no standing autonomic parameter, determined using SBP as input, was found to be
correlated with any sleep parameter, the high frequency component of the arterial
baroreflex gain, determined using PTT as input, or log(ABR
_HF_stand_PTT
), is significantly
correlated with total sleep time for all adiposity measures, as summarized in Table 12.
184
Table 12: Partial correlation between log(ABR
_HF_stand_PTT
)and total sleep time (in minutes)(after
adjustment for age and adiposity)
Autonomic parameter (Y
adj
)
Sleep parameter
(X
adj
)
Adiposity parameter
Partial
p-value
Partial
corr. coeff.
(r)
log(ABR
_HF_stand_PTT
)
Total sleep time
(minutes)
BMI 0.020* 0.45
BMI z-score 0.022* 0.45
log(Total Body Fat (g)) 0.023*
% Body Fat 0.018*
Total trunk fat 0.047*
% Trunk Fat 0.019*
*
Significant correlations (p 0.05).
These results suggest that a decrease in total sleep time is related to a decrease in the high
frequency ABR gain, indicating a decrease in baroreceptor mediated vagal modulation in
the standing posture with a decrease in total sleep time. The corresponding plot is shown
in Figure 29 (controlling for age and total % body fat).
Figure 29: Linear regression between log(ABR
_HF_stand_PTT
) and total sleep time (in minutes), controlling for age
and adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
) = 0.21, partial correlation coefficient = 0.46, partial p-
value = 0.017, = -1.18, = 0.0019, standardized
sleep
= 0.45, standardized
adiposity
= -0.21, standardized
age
= -
0.22.
150 200 250 300 350 400 450
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
Adjusted nolog_TotSlpT-
Adjusted log10_ABR_HF_std_PTT
(N = 28) Linear regression for Y
adj
= log10_ABR_HF_std_PTT vs. X1
adj
= nolog_TotSlpT-, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.212, corr. coeff. (Yadj vs. X1adj) = 0.461, partial corr. coeff = 0.461, partial p-value = 0.0178,
p-value (Yadj vs X1adj) = 0.0136.
= -1.18, (X1adj) = 0.0019038.
Pearson's Corr. Coeff. (Yadj vs. Xadj_sleep) = 0.46082, p-value (SIMPLE LIN REGR) = 0.01359.
bRelSLEEP = 0.45483, bRelOBES = -0.2092, bRelAGE = -0.22067
Adjusted log(ABR
_HF_stand_PTT
)
Adjusted Total Sleep Time
185
Interpretation of the standing data by itself, however, is not very clear, since each subject
starts from a different baseline gain value. Low standing values could be an indication of
either high reactivity to postural change, if the initial baseline value is high, or low
reactivity to postural change, if baseline gain is already low.
For instance, Burke and colleagues (Burke, et al., 1977), in a study involving the
measurement of bursts of muscle sympathetic nerve activity related to change in posture,
observed that the magnitude of change in bursts incidence related to a change in posture
from lying (recumbent position) to sitting and from sitting to standing was inversely
related to the initial burst incidence. Subjects with low initial values (suggesting lower
resting sympathetic tone) usually showed greater increases in burst incidence than those
with initial high values (suggesting higher levels of resting sympathetic tone). They also
observed that some subjects with high initial values showed a decrease in their burst
incidence with change in posture. They speculate that subjects with high resting burst
incidence may be orthostatically more vulnerable than those with low resting burst
incidence.
Thus, although the significant results obtained using standing autonomic parameters will
be reported for completeness, they will not be used as basis for analysis in the discussion
and conclusion sections.
186
Autonomic stand/supine ratio and sleep
SBP input
When analyzing the correlation results obtained considering the ratios G
ABR_std
/G
ABR_sup
and G
RCC_std
/G
RCC_sup
, determined using SBP as input, the only significant correlations
found were between log(G
RCC_stand/supine
) and both TAI and total sleep time (TST),
controlling for age and adiposity, as summarized in Table 13. The corresponding plots for
these linear regressions are plotted in Figure 30 and Figure 31 (controlling for age and
total % body fat).
Table 13: Partial correlation coefficients and corresponding p-values for correlations between
log(G
RCC_stand/supine_SBP
) and log(TAI) as well as log(G
RCC_stand/supine_SBP
) and TST, both controlling for age and
adiposity.
Autonomic parameter
(Y
adj
)
Sleep
parameter
(X
adj
)
Adiposity parameter
Partial
p-value
Partial
corr. coeff.
(r)
log(G
RCC_stand/supine_SBP
) log(TAI)
BMI 0.055
BMI z-score 0.061 0.37
log(Total Body Fat (g)) 0.041 *
% Body Fat 0.017 *
Total trunk fat 0.017 *
% Trunk Fat 0.013 *
log(G
RCC_stand/supine_SBP
) TST
BMI 0.0092 0.50*
BMI z-score 0.0090 0.50*
log(Total Body Fat (g)) 0.011 *
% Body Fat 0.021 *
Total trunk fat 0.026 *
% Trunk Fat 0.028 *
*
Significant correlations (p 0.05). (TST = Total sleep time, in minutes)
187
Figure 30: Linear regression between log(G
RCC_stand/supine_SBP
) and total arousal index (TAI), controlling for age
and adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.21, partial correlation coefficient = 0.46, partial p-
value = 0.017, = -1.09, = 0.61, standardized
sleep
= 0.45, standardized
adiposity
= -0.31, standardized
age
= -
0.36.
Figure 31: Linear regression between log(G
RCC_stand/supine_SBP
) and total sleep time (TST), controlling for age and
adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
)= 0.20, partial correlation coefficient = -0.45, partial p-value =
0.021, = 0.16, = 0.0021, standardized
sleep
= -0.44, standardized
adiposity
= -0.16, standardized
age
= -0.29.
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
Adjusted log10_TAI-----
Adjusted log10_RCC_HF_ssp_SBP
(N = 28) Linear regression for Y
adj
= log10_RCC_HF_ssp_SBP vs. X1
adj
= log10_TAI-----, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.214, corr. coeff. (Yadj vs. X1adj) = 0.462, partial corr. coeff = 0.462, partial p-value = 0.0174,
p-value (Yadj vs X1adj) = 0.0133.
= -1.0902, (X1adj) = 0.60854.
Pearson's Corr. Coeff. (Yadj vs. Xadj_sleep) = 0.46219, p-value (SIMPLE LIN REGR) = 0.013279.
bRelSLEEP = 0.45109, bRelOBES = -0.31426, bRelAGE = -0.35791
150 200 250 300 350 400 450
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
Adjusted nolog_TotSlpT-
Adjusted log10_RCC_HF_ssp_SBP
(N = 28) Linear regression for Y
adj
= log10_RCC_HF_ssp_SBP vs. X1
adj
= nolog_TotSlpT-, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.202, corr. coeff. (Yadj vs. X1adj) = -0.449, partial corr. coeff = -0.449, partial p-value = 0.0213,
p-value (Yadj vs X1adj) = 0.0164.
= 0.15703, (X1adj) = -0.002066.
Pearson's Corr. Coeff. (Yadj vs. Xadj_sleep) = -0.44938, p-value (SIMPLE LIN REGR) = 0.016438.
bRelSLEEP = -0.43502, bRelOBES = -0.16266, bRelAGE = -0.29287
Adjusted log(G
RCC_stand/supine_SBP
)
Adjusted log(TAI)
Adjusted log(G
RCC_stand/supine_SBP
)
Adjusted TST
188
The positive correlation of the G
RCC
ratio (G
RCC_stand/supine_SBP
) with TAI shows that an
increase in sleep fragmentation is related to an increase in G
RCC
ratio or, equivalently, a
decrease in G
RCC
reactivity associated with orthostatic stress. In other words, increased
levels of sleep fragmentation are related to a less pronounced change in G
RCC
from supine
to standing, indicating a blunted vagal withdrawal.
The negative correlation found between the same G
RCC
ratio (G
RCC_stand/supine_SBP
) and total
sleep time (TST) suggests that an increase in total sleep time is related to a greater RCC
reactivity (or, equivalently, a smaller G
RCC
ratio) due to change in posture from supine to
standing, indicating a greater vagal withdrawal related to change in posture with
increased TST. Considered together, these results suggest that decreased total sleep time
and increased sleep fragmentation, both indications of sleep disruption, are both related to
a decreased vagal withdrawal related to orthostatic stress, an indication of cardiovagal
dysfunction. This confirms our initial hypothesis of impaired autonomic modulation in
OSA.
PTT input
When using PTT as input, log(G
RCC_stand/supine_PTT
) was also found to be correlated
significantly correlated to total sleep time (TST), controlling for age and adiposity, while
the correlation with TAI was significant only for trunk fat in grams and trunk % fat.
These results are summarized in Table 14. The corresponding plots for these linear
regressions are plotted in Figure 32 and Figure 33 (controlling for age and total % body
fat).
189
Table 14: Partial correlation coefficients and corresponding p-values for correlations between
log(G
RCC_stand/supine_SBP
) and log(TAI) as well as log(G
RCC_stand/supine_SBP
) and TST, both controlling for age and
adiposity.
Autonomic parameter
(Y
adj
)
Sleep
parameter
(X
adj
)
Adiposity parameter
Partial
p-value
Partial
corr. coeff.
(r)
log(G
RCC_stand/supine_PTT
) log(TAI)
BMI 0.10
BMI z-score 0.13 0.31
log(Total Body Fat (g)) 0.11
% Body Fat 0.055
Total trunk fat 0.050
% Trunk Fat 0.050
log(G
RCC_stand/supine_PTT
) TST
BMI 0.029
BMI z-score 0.026
log(Total Body Fat (g)) 0.024
% Body Fat 0.050
Total trunk fat 0.061
% Trunk Fat 0.067
*
Significant correlations (p 0.05). (TST = Total sleep time, in minutes)
Figure 32: Linear regression between log(G
RCC_stand/supine_PTT
) and total arousal index (TAI), controlling for age
and adiposity (total % body fat). R
2
(Yadj vs. Xadj) = 0.14, partial correlation coefficient = 0.38, partial p-value
= 0.055, = -0.90, = 0.40, standardized
sleep
= 0.38, standardized
adiposity
= -0.29, standardized
age
= -0.29.
0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
-1.1
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
Adjusted log10_TAI-----
Adjusted nolog_lRC_HF_ssp_PTT
(N = 28) Linear regression for Y
adj
= nolog_lRC_HF_ssp_PTT vs. X1
adj
= log10_TAI-----, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.145, corr. coeff. (Yadj vs. X1adj) = 0.381, partial corr. coeff = 0.381, partial p-value = 0.0549,
p-value (Yadj vs X1adj) = 0.0455.
= -0.89537, (X1adj) = 0.40096.
Pearson's Corr. Coeff. (Yadj vs. Xadj_sleep) = 0.38091, p-value (SIMPLE LIN REGR) = 0.045524.
bRelSLEEP = 0.3766, bRelOBES = -0.29434, bRelAGE = -0.29048
Adjusted log(G
RCC_stand/supine_PTT
)
Adjusted log(TAI)
190
Figure 33: Linear regression between log(G
RCC_stand/supine_PTT
) and total sleep time (TST), controlling for age and
adiposity (total % body fat). R
2
(Yadj vs. Xadj) = 0.15, partial correlation coefficient = -0.39, partial p-value =
0.050, = -0.053, = -0.0014, standardized
sleep
= -0.38, standardized
adiposity
= -0.16, standardized
age
= -0.24.
Since G
RCC_stand/supine
defined using either SBP or PTT were significantly and strongly
correlated, it would be expected that the significant correlations found for SBP would be
similar to those found using PTT. The signs of the correlations are the same as for the
parameters determined using SBP as input. In other words, an increase in TAI or a
decrease in TST is correlated with impairment in vagal autonomic reactivity, as measured
by the G
RCC_stand/supine
parameter, determined using PTT as input to the ABR transfer
function.
9.5. Correlations between autonomic and metabolic parameters
In the current study it is also hypothesized that there is an association between impaired
glucose metabolism and autonomic dysfunction in overweight and obese children. In
order to test this hypothesis, the correlations between autonomic and metabolic
150 200 250 300 350 400 450
-1.1
-1
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
Adjusted nolog_TotSlpT-
Adjusted nolog_lRC_HF_ssp_PTT
(N = 28) Linear regression for Y
adj
= nolog_lRC_HF_ssp_PTT vs. X1
adj
= nolog_TotSlpT-, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.151, corr. coeff. (Yadj vs. X1adj) = -0.388, partial corr. coeff = -0.388, partial p-value = 0.0499,
p-value (Yadj vs X1adj) = 0.0411.
= -0.053028, (X1adj) = -0.0014274.
Pearson's Corr. Coeff. (Yadj vs. Xadj_sleep) = -0.38835, p-value (SIMPLE LIN REGR) = 0.04113.
bRelSLEEP = -0.38084, bRelOBES = -0.16441, bRelAGE = -0.23763
Adjusted log(G
RCC_stand/supine_PTT
)
Adjusted TST
191
parameters were analyzed, controlling for age and adiposity. Significant correlations were
found only when using SBP as input to the ABR transfer function.
Baseline autonomic function and metabolic parameters
There was no correlation found between baseline G
ABR
, ABR_HF, or G
RCC
with any
metabolic parameter.
Autonomic parameters determined in the standing posture and metabolic parameters
The only significant correlation found, considering all adiposity measures used, was
between G
ABR
in the standing posture and fasting glucose, as summarized in Table 15.
Table 15: Results for the correlations log(G
ABR_stand_SBP
) and fasting glucose, correcting for age and adiposity.
Autonomic parameter
(Y
adj
)
Metabolic
parameter (X
adj
) Adiposity parameter
Partial
p-value
Partial
corr.
coeff. (r)
log(G
ABR_stand_SBP
)
Fasting
Glucose
BMI 0.022 *
BMI z-score 0.021 0.51*
Total Body Fat (g) 0.020 *
% Body Fat 0.023 *
Total trunk fat 0.027 *
% Trunk Fat 0.026 *
*
Significant correlations (p 0.05).
As mentioned above, the standing posture is characterized by a smaller baroreflex
sensitivity when compared to the supine posture, indicative of vagal withdrawal and/or
increased sympathetic modulation. The positive correlation found between standing G
ABR
gain and fasting glucose suggests a decreased sympathetic drive and/or an increase in
vagal modulation with increasing fasting plasma glucose levels.
These combined results indicate that there could be a relationship between autonomic
dysfunctions and impaired glucose metabolism. In particular, these results suggest that
192
higher fasting glucose and HOMA levels are related to impaired sympathetic modulation
as well as decreased vagal modulation.
Autonomic stand/supine ratios and metabolic parameters
The results obtained are summarized in Table 16. The corresponding plots are displayed
in Figure 34 and Figure 35, adjusting for age and adiposity (total % body fat).
Table 16: Results for the correlations between sleep and the ratios standing/supine of the autonomic parameters,
controlling for age and adiposity.
Autonomic parameter
(Y
adj
)
Metabolic
parameter (X
adj
) Adiposity parameter
Partial
p-value
Partial
corr.
coeff. (r)
log(G
RCC_stand/supine_SBP
) HOMA
BMI 0.25 0.27
BMI z-score 0.26 0.26
Total Body Fat (g) 0.076
% Body Fat 0.11
Total trunk fat 0.047 *
% Trunk Fat 0.086
log(G
ABR_stand/supine_SBP
)
Fasting
Glucose
BMI 0.049 *
BMI z-score 0.058 0.43
Total Body Fat (g) 0.059
% Body Fat 0.056
Total trunk fat 0.058
% Trunk Fat 0.065
*
Significant correlations (p 0.05).
The correlation of G
ABR
and G
RCC
ratios with fasting glucose and HOMA, respectively,
were mostly marginal.
As previously mentioned, an increase in G
RCC
ratio (G
RCC_std/sup_SBP
) is related to a decrease
in vagal withdrawal associated with change in posture from supine to standing.
Therefore, the positive trend found between G
RCC
ratio and HOMA, controlling for age
and adiposity, may indicate that there is a trend relating increased HOMA to decreased
193
vagal withdrawal during orthostatic stress. This correlation, however, is not significant
across adiposity measures.
Figure 34: Linear regression between log(G
RCC_stand/supine_SBP
) and HOMA, controlling for age and adiposity (total
percent body fat). R
2
(Y
adj
vs. X
adj
) = 0.14, partial correlation coefficient = 0.37, partial p-value = 0.11, = -0.71,
= 0.074, standardized
metab
= 0.37, standardized
adiposity
= -0.21, standardized
age
= -0.25.
The correlation between ABR ratio, or log(G
ABR_stand/supine_SBP
), and fasting glucose is also
marginal (significant only for BMI as the adiposity measure), which seems to indicate a
trend between an increase in fasting glucose and a decreased baroreflex reactivity to
postural change (quantified by a larger ABR ratio (G
ABR_stand/supine_SBP
) or, equivalently, by
a smaller ABR reactivity). This lack of significance could be related to the fact that all
subjects presented fasting glucose measures considered normal (range = 70.5 to 100.0
mg/dL, mean ± SD = 84.8 ± 7.4) (American Diabetes Association, 2010). A population
sample with higher fasting glucose levels could show a significant relation to autonomic
dysfunction, as measured by increased G
RCC
ratios.
0 1 2 3 4 5 6
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
Adjusted nolog_HOMA--
Adjusted log10_RCC_HF_ssp_SBP
(N = 22) Linear regression for Y
adj
= log10_RCC_HF_ssp_SBP vs. X1
adj
= nolog_HOMA--, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.136, corr. coeff. (Yadj vs. X1adj) = 0.369, partial corr. coeff = 0.369, partial p-value = 0.109,
p-value (Yadj vs X1adj) = 0.0908.
= -0.70909, (X1adj) = 0.074116.
Pearson's Corr. Coeff. (Yadj vs. Xadj_ivgtt) = 0.36921, p-value (SIMPLE LIN REGR) = 0.090831.
bRelIVGTT = 0.37162, bRelOBES = -0.20747, bRelAGE = -0.24786
Adjusted log(G
RCC_stand/supine_SBP
)
Adjusted HOMA
194
Figure 35: Linear regression between log(G
ABR_stand/supine_SBP
) and fasting glucose, controlling for age and
adiposity (total percent body fat). R
2
(Y
adj
vs. X
adj
) = 0.19, partial correlation coefficient = 0.43, partial p-value =
0.056, = -1.72, = 0.021, standardized
metab
= 0.44, standardized
adiposity
= -0.17, standardized
age
= -0.39.
The normal reaction to a change in posture from supine to standing is a decrease in
baroreflex sensitivity (Bahjaoui-Bouhaddi, et al., 1998), indicating a shift from vagal
(supine) to sympathetic (standing) dominance (Hartikainen, et al., 1993; Gibbons, et al.,
2006). A smaller ABR reactivity to change in posture is related to a smaller difference
between the baroreflex gain (G
ABR
) determined in the standing posture (sympathetically
modulated) when compared to baseline G
ABR
obtained in the supine posture (vagally
modulated), resulting in an increased G
ABR
ratio. This increased G
ABR
ratio may indicate a
decreased vagal withdrawal upon standing and/or a decreased baseline G
ABR
, suggesting
an increased baseline sympathetic modulation than normal during restful supine.
As discussed by Punjabi and colleagues (Punjabi, et al., 2004), many studies have shown
that patients with sleep-disordered breathing present high levels of sympathetic neural
70 75 80 85 90 95 100 105
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Adjusted nolog_FstGlu
Adjusted log10_ABR_LF_ssp_SBP
(N = 22) Linear regression for Y
adj
= log10_ABR_LF_ssp_SBP vs. X1
adj
= nolog_FstGlu, corrected for obesity (nolog_TotB-Pfat) and age
R
2
= 0.188, corr. coeff. (Yadj vs. X1adj) = 0.433, partial corr. coeff = 0.433, partial p-value = 0.0564,
p-value (Yadj vs X1adj) = 0.044.
= -1.7164, (X1adj) = 0.02068.
Pearson's Corr. Coeff. (Yadj vs. Xadj_ivgtt) = 0.43319, p-value (SIMPLE LIN REGR) = 0.044021.
bRelIVGTT = 0.43551, bRelOBES = -0.16798, bRelAGE = -0.38828
Adjusted log(G
ABR_stand/supine_SBP
)
Adjusted Fasting Glucose
195
activity. It has been shown that both the sympathetic and parasympathetic nervous
systems are important modulators of hepatic metabolism, while also regulating glycogen
breakdown and synthesis (Shimazu, 1981). Thus, this increased sympathetic activity
could further degrade glucose homeostasis by increasing glycogen breakdown and
stimulating gluconeogenesis.
Therefore, although in the present study we found no direct association of fasting glucose
with any sleep parameter, we did find that the correlations found between the autonomic
indices and fasting glucose may be an indication that the link between sleep related
breathing disorders and fasting glucose could be through an impairment in autonomic
control, through decreased vagal activity and increased sympathetic modulation related to
OSA.
9.6. Multiple linear regression analysis
Based on the correlations obtained between sleep and metabolic, sleep and autonomic, as
well as metabolic and autonomic parameters, the next step was to investigate the
hypothesis that variations in the autonomic parameters could be explained by variations
in both sleep and metabolic parameters considered at the same time, controlling for age
and adiposity. The next section (9.7) will investigate the hypothesis that variations in
metabolic indices can be explained by variations in both sleep and metabolic parameters,
controlling for age and adiposity.
This was accomplished by applying multiple linear regression analysis, considering the
autonomic parameter as the dependent variable, and the sleep indices,
196
metabolicparameters, age, and adiposity measures as the independent variables. The
hypothesis is that both sleep and metabolic abnormalities have a deleterious effect on
autonomic modulation.
As discussed in chapter 8, the multiple linear regression analysis allows a description of
the combined influence of the various explanatory variables on the outcome variable by
yielding a regression equation that relates the outcome or dependent variable to all the
explanatory or independent variables in the study. Moreover, this analysis also measures
the effect on the outcome variable due to each explanatory variable alone by means of
each of the latter’s regression coefficient. Since each regression coefficient describes the
influence of its corresponding explanatory variable on the outcome, it is a means of
untangling the influences of several explanatory variables and measuring the unique
contribution of each one to the outcome (Hassard, 1991).
Moreover, in multiple linear regression, there are instances in which the regression of a
dependent variable on a set of explanatory variables results on a greater R
2
than the sum
of the individual R
2
’s related to the separate pairwise regressions on each of the
independent variables. In other words, the complete regression can explain more of the
variance observed on the outcome than can the sum of parts. Therefore, simultaneous
regression on all relevant variables is crucial to obtain a correct understanding of the
underlying process (Bertrand, et al., 1988).
As in the previous correlations, the autonomic parameters were obtained in both the
supine (baseline) and standing (orthostatic stress) postures, using either SBP or PTT as
197
input to the ABR transfer function. The autonomic parameters considered in the
following analysis are those at baseline (supine posture), determined from standing data,
and the standing/supine ratios.
Each variable was first tested for normality
9
and log transformed whenever the normality
test was not satisfied. The transformed variable was then rechecked for normality.
Although a normal distribution of the independent variables is not necessary for the least
squares estimates of the regression parameters (Rawlings, et al., 1998), this
transformation was used to insure better statistical properties of the residuals and thus a
greater power for the multiple linear regression model.
The model assumed for the relationship between the autonomic (Y
aut
), sleep (X
sleep
), and
metabolic (X
met
) parameters, also considering age (X
age
) and adiposity (X
adip
), is given by
adip adip age age sleep sleep met met aut
X b X b X b X b a Y
(9.1)
where a is the estimated intercept of the hyperplane of the multiple linear regression
model, which mathematically corresponds to the mean value of the response Y when all
explanatory variables X
i
take the value 0, and b
met
, b
sleep
, b
age
, and b
adip
are the slopesor
9
This test of normality uses the function ‘ s w test . m’, available at
http://www.mathworks.com/matlabcentral/fileexchange/13964-shapiro-wilk-and-shapiro-francia-
normality-tests, which performs the Shapiro-Francia test (Shapiro, et al., 1972) when the data are
leptokurtic (having a coefficient of kurtosis K > 0, or higher peaks around the mean compared to normal
distributions, leading to thick tails on both sides) and the Shapiro-Wilk test (Shapiro, et al., 1965) when the
data are platykurtic (negative kurtosis value, K < 0, meaning a shallow or more spread out distribution, less
peaked about its mean than the normal distribution, resulting in less probability in the tails than the normal
distribution).
198
regression coefficients for the metabolic (X
met
), sleep (X
sleep
), age (X
age
), and adiposity
(X
adip
) measures, respectively.
As discussed in section 8.2, in order to be able to compare the regression coefficients and
measure the relative strength of each explanatory variable on the outcome, their units
should be standardized by using the standardized regression coefficients, as defined by
equation (8.4). The standardized regression coefficient related to the independent variable
x
i
, i = 1, …, k, where k is the number of parameters or independent variables considered
in the multiple linear regression, is defined as
i
= SD
i
/ SD
y
b
i
, where SD
i
is the standard
deviation of the independent variable x
i
, SD
y
is the standard deviation of the dependent
variable y, and b
i
is the regression coefficient associated with x
i
.
The standardized regression coefficient
i
measures the extent of a unit change in the
standardized value of x
i
on the standardized value of the outcome y. The larger the
magnitude of
i
, the more x
i
contributes to the prediction of y (Hassard, 1991). The value
of the standardized
i
is, in many cases, is similar, although not equal to, the value of the
partial correlation coefficient of x
i
on y, when the influence of the other variables x
j
, j ≠ i,
on the outcome y are controlled, or accounted, for. For this reason, in the following
multiple linear regressions, the relative strength of each variable on the outcome will be
quantified by using its corresponding standardized regression coefficient.For these
multiple linear regressions, the 21 subjects who had all 3 studies were considered.
199
9.6.1. Baseline autonomic parameters, OSA, and metabolic function
SBP as input to the ABR transfer function
For baseline conditions, the multiple linear regression between Y
aut
= G
ABR
, using SBP as
input, and the independent variables X
met
= fasting insulin, X
sleep
= REM (as % of total
sleep time), age, and adiposity (total % body fat, trunk % fat, and trunk fat in grams, but
not BMI, BMI z-score, or total body fat in grams, for which there seems to be only a
trend), shows that baseline baroreflex gain becomes significantly correlated with REM
(% of total sleep time). This multiple linear regression has the form:
adip adip age age sleep met SBP ABR
X b X b TST REM b Insulin Fasting b a G ) (% ) (
sup_ _
From a partial correlations perspective, this can be interpreted as meaning that G
ABR
is
significantly correlated with REM (% of total sleep time) when accounting for fasting
insulin values, age, and adiposity (total % body fat, trunk fat in grams, and trunk % fat,
but not for BMI, BMI z-score, or total body fat in grams, for which there seems to be
only a trend). This seems to indicate that this correlation is dependent on fat distribution
(e.g. total trunk fat) and the proportion of fat content to total mass (e.g. total % body fat),
but not on total fat content itself (e.g. total body fat in grams,BMI). The p-values
associated with each variable, for each adiposity measure, together with each
corresponding standardized , are presented in Table 17, while the standardized 's for
the significant correlations are listed separately in Table 18.
200
Table 17: Multiple linear regression analysis (dependent variable Y = G
ABR_sup_SBP
; independent variables: X
met
=
fasting insulin, X
sleep
= REM (%TST), X
age
, X
adip
) for the supine posture, showing that G
ABR_sup_SBP
is significantly
correlated with the sleep parameter for 3 of the 6 adiposity parameters considered when also controlling for
fasting insulin levels, age, and adiposity.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
met
) 0.081
( = 0.46)
0.063
( = 0.50)
0.17
( = 0.34)
0.19
( = 0.32)
0.24
( = 0.30)
0.21
( = 0.31)
p (X
sleep
) 0.074
( = -0.46)
0.063
( = -0.47)
0.057
( = -0.51)
0.038
( = -0.55*)
0.037
( = -0.56*)
0.040
( = -0.54*)
p (X
adip.
) 0.21
( = -0.41)
0.15
( = -0.43)
0.71
( = -0.10)
0.83
( = 0.048)
0.81
( = 0.079)
0.51
( = 0.14)
p (X
age
) 0.74
( = -0.99)
0.65
( = -0.12)
0.35
( = -0.28)
0.18
( = -0.34)
0.23
( = -0.39)
0.20
( = -0.32)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Table 18: Standardized and corresponding p-values for the multiple linear regression analysis (dependent
variable Y = G
ABR_sup_SBP
; independent variables: X
met
= fasting insulin, X
sleep
= REM (%TST), X
age
, X
adip
) for the
supine posture, showing that G
ABR_sup_SBP
is significantly correlated with X
sleep
= REM (%TST) for 3 of the 6
adiposity parameters considered when also controlling for fasting insulin levels, besides age and adiposity. The
power of this multiple linear regression is > 0.63 all adiposity measures related to a significant correlation.
Auton.
Parameter
(Y)
Explanatory variable
(X)
Adiposity parameter (X adip)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
G
ABR_sup_SBP
X sleep= REM (% TST)
Standardized
(p-value)
-0.46
(0.074)
-0.47
(0.063)
-0.52
(0.057)
-0.55*
(0.038)
-0.56*
(0.037)
-0.54*
(0.040)
X met = fasting insulin
Standardized
(p-value)
0.46
(0.081)
0.49
(0.063)
0.34
(0.18)
0.32
(0.19)
0.30
(0.24)
0.31
(0.21)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat, TST: total sleep time.
This result suggests that, when controlling for age, adiposity (total % body fat, trunk fat
in grams, and trunk % fat), and fasting insulin levels, an increase in REM (% of total
sleep time) is correlated with a decrease in baseline baroreflex gain, suggesting an
increase in baseline sympathetic drive and/or a decrease in baseline vagal modulation
associated with the increased REM measure.
These same results are obtained when the metabolic parameter X
met
considered is HOMA,
a surrogate measure of insulin resistance using fasting glucose and insulinlevels. The
associated multiple linear regression expression is:
201
adip adip age age sleep met SBP ABR
X b X b TST REM b HOMA b a G ) (% ) (
sup_ _
The significance of each variable, quantified by the p-value associated with each
regression coefficient, together with each corresponding standardized , is shown in
Table 19, while the standardized 's for the significant correlations are separately listed in
Table 20.
Table 19: Multiple linear regression analysis (dependent variable Y = G
ABR_sup_SBP
; independent variables: X
met
=
HOMA, X
sleep
= REM (%TST), X
age
, X
adip
) for the supine posture, showing that G
ABR_sup_SBP
is significantly
correlated with the sleep parameter for 3 of the 6 adiposity parameters considered when also controlling for
HOMA levels, age, and adiposity.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
met
) 0.083
( = 0.44)
0.064
( = 0.48)
0.16
( = 0.34)
0.18
( = 0.33)
0.23
( = 0.31)
0.18
( = 0.32)
p (X
sleep
) 0.083
( = -0.44)
0.072
( = -0.45)
0.060
( = -0.51)
0.038
( = -0.54*)
0.038
( = -0.55*)
0.040
( = -0.53*)
p (X
adip.
) 0.24
( = -0.38)
0.17
( = -0.41)
0.71
( = -0.10)
0.80
( = 0.054)
0.80
( = 0.080)
0.48
( = 0.15)
p (X
age
) 0.71
( = -0.11)
0.64
( = -0.13)
0.35
( = -0.28)
0.18
( = -0.34)
0.23
( = -0.40)
0.20
( = -0.32)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Table 20: Standardized and corresponding p-values for the multiple linear regression analysis (dependent
variable Y = G
ABR_sup_SBP
; independent variables: X
met
= HOMA, X
sleep
= REM (%TST), X
age
, X
adip
) for the supine
posture, showing that G
ABR_sup_SBP
is significantly correlated with X
sleep
= REM (%TST) for 3 of the 6 adiposity
parameters considered when also controlling for HOMA levels, besides age and adiposity. The power of this
regression is > 0.68 and R
2
> 0.27 for the significant correlations.
Auton.
Parameter
(Y)
Explanatory variable
(X)
Adiposity parameter (X adip)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
G
ABR_sup_SBP
X sleep= REM (% TST)
Standardized
(p-value)
-0.44
(0.083)
-0.45
(0.072)
-0.51
(0.060)
-0.54*
(0.038)
-0.55*
(0.038)
-0.53*
(0.040)
X met = HOMA
Standardized
(p-value)
0.44
(0.083)
0.48
(0.064)
0.34
(0.16)
0.33
(0.18)
0.31
(0.23)
0.32
(0.18)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat, TST: total sleep time.
We have shown previously that HOMA and fasting insulin are significantly correlated in
our study group. Thus, an increase in REM (% of total sleep time) seems to be also
202
correlated with a decrease in baseline baroreflex gain when controlling for age, adiposity
(total % body fat, trunk fat in grams, and trunk % fat), and HOMA values.
It’s important to point out that, although X
met
= fasting insulin or HOMA are not
significantly correlated with the outcome variable G
ABR_sup_SBP
, if X
met
is not considered in
the multiple regression, X
sleep
= REM (% TST) is not significantly correlated with
G
ABR_sup_SBP
. Nevertheless, this correlation is not very strong. Also, the positive
correlation found between HOMA (or fasting insulin) and baseline G
ABR
gain, although
not significant, does not make intuitive sense. It suggests that an increase in HOMA is
related to an increase in baseline baroreflex gain. The expected behavior would be for
increased insulin resistance to be related to decreased baseline arterial baroreflex gain, as
found in studies in adults. This, together with the low statistical, could be an indication
that this correlation should not be considered physiologically meaningful.
PTT as input to the ABR transfer function
For baseline conditions, the multiple linear regression between the high frequency
baroreflex gain, when using PTT as input, or log(ABR
_HF_sup_PTT
), and the independent
variables X
met
= log(DI), X
sleep
= sleep efficiency (%), besides age and adiposity
measures, shows that the autonomic parameter becomes significantly correlated with the
sleep parameter. From the pairwise correlation results, log(ABR
_HF_sup_PTT
) was not found
to be significantly correlated with sleep efficiency, when adjusting for age and adiposity
only. The autonomic parameter was also not significantly correlated with log(DI), if
203
controlling only for age and adiposity. Likewise, log(DI) and sleep efficiency were also
not found to be significantly correlated, when controlling for age and adiposity only.
This multiple linear regression equation is given by:
adip adip age age sleep met PTT HF
X b X b Efficiency b DI b a ABR (%) ) log( ) log(
sup_ _ _
Interpreting this result in the partial correlation context, the high frequency component of
the baroreflex gain in the supine posture (baseline conditions), using PTT as input to the
ABR transfer function, becomes significantly correlated with sleep efficiency (%) when
controlling for age, the disposition index, and adiposity (except for total % body fat and
trunk % fat, where there seems to be only a trend towards significance). The significance
of each variable in this model, quantified by the p-value associated with each regression
coefficient, together with each standardized , is shown in Table 21, while the
standardized 's for the significant correlations are listed separately in Table 22.
Table 21: Multiple linear regression analysis (dependent variable Y = log(ABR
_HF_sup_PTT
); independent
variables: X
met
= log(DI), X
sleep
= Efficiency (%), X
age
, X
adip
) for the supine posture, showing that
log(ABR
_HF_sup_PTT
) is significantly correlated with the sleep parameter (except for total % body fat and trunk %
fat), when also controlling for log(DI) levels, age, and adiposity. The R
2
of this multiple linear regression is > 0.29
for the significant correlations.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
met
) 0.11
( = -0.35)
0.084
( = -0.37)
0.074
( = -0.40)
0.13
( = -0.34)
0.11
( = -0.37)
0.13
( = -0.34)
p (X
sleep
) 0.030
( = 0.49*)
0.024
( = 0.50*)
0.026
( = 0.51*)
0.064
( = 0.42)
0.047
( = 0.46*)
0.062
( = 0.42)
p (X
adip.
) 0.20
( = -0.33)
0.12
( = -0.37)
0.19
( = -0.33)
0.89
( = 0.028)
0.51
( = -0.19)
0.67
( = 0.089)
p (X
age
) 0.31
( = -0.26)
0.26
( = -0.26)
0.22
( = -0.29)
0.050
( = -0.45)
0.24
( = -0.33)
0.051
( = -0.44)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
204
Table 22: Standardized and corresponding p-values for the multiple linear regression analysis (dependent
variable Y = log(ABR
_HF_sup_PTT
); independent variables: X
met
= log(DI), X
sleep
= Efficiency (%), X
age
, X
adip
) for the
supine posture, showing that log(ABR
_HF_sup_PTT
) is significantly correlated with X
sleep
= Efficiency (%) for 4 of
the 6 adiposity parameters considered, when also controlling for log(DI) levels, besides age and adiposity.
Auton.
Parameter (Y)
Explanatory
variable
(X)
Adiposity parameter (X adip)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
log(ABR
_HF_sup_PTT
)
X sleep= Effic. (%)
Standardized
(p-value)
0.49*
(0.030)
0.50*
(0.024)
0.51*
(0.026)
0.42
(0.064)
0.46*
(0.047)
0.42
(0.062)
X met = log(DI)
Standardized
(p-value)
-0.35
(0.11)
-0.37
(0.084)
-0.40
(0.074)
-0.34
(0.13)
-0.37
(0.11)
-0.34
(0.13)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat, Effic (%): sleep efficiency, as percentage of total sleep time.
Since the disposition index is an integrated measure of pancreatic -cell function and
quantifies an increase in insulin secretion to compensate for insulin resistance, this result
suggests that, when controlling for age, adiposity, and increased insulin secretion, a
decrease in sleep efficiency (%) is correlated with a decrease the high frequency
component of the baroreflex. This suggests that decreased baroreceptor mediated vagal
modulation is associated with decreased sleep efficiency if, conceptually, insulin
secretion is maintained constant or, equivalently, if the effects of insulin secretion are
removed. This is equivalent to considering that all subjects’ data have been adjusted such
that they now have the same -cell function, as measured by DI. This way, the effect of
log(DI) as a confounder can be mathematically removed.
9.6.2. Autonomic parameters in the standing posture, OSA, and metabolic function
SBP input
The significant pairwise correlation found previously between log(G
ABR_stand_SBP
) and
fasting glucose, controlling for age and adiposity, is maintained when adding any sleep
parameter as an additional independent variable, as shown in Table 23.
205
In this case, the multiple linear regression equation is given by:
adip adip age age sleep sleep met SBP stand ABR
X b X b X b glucose fasting b a G ) ( ) log(
_ _
The sleep parameters, age, and adiposity, however, are not significantly correlated with
log(G
ABR_stand_SBP
) using this multiple linear regression model.
This reinforces the idea that increasing fasting glucose levels are related to increasing
standing baroreflex gain, indicating decreased sympathetic drive and/or increased vagal
modulation in the standing posture related tohigher fasting glucose values. It also shows
that, if addition of sleep parameters does not change the significance of the correlations,
then most probably sleep is not directly correlated with fasting glucose. Indeed, by
referring back to Table 9, which shows the partial correlations between sleep and
metabolic parameters adjusting for age and adiposity only, fasting glucose was not found
to be correlated with any sleep parameter. Nevertheless, the p-values associated with the
correlation between log(G
ABR_stand_SBP
) and fasting glucose when adding X
sleep
as an
additional explanatory variable are higher than those obtain when controlling only for age
and adiposity. This may be an indication of some indirect correlation between X
sleep
and
fasting glucose. If fasting glucose and X
sleep
were completely independent, the addition of
X
sleep
would not influence the correlation between fasting glucose and log(G
ABR_stand_SBP
).
206
Table 23: Standardized and associated p-values for the multiple linear regressionfor log(G
ABR_stand_SBP
) and
fasting glucose, considering the autonomic parameter as the dependent variable (Y) and IVGTT, sleep, age, and
adiposity as the independent, or explanatory, variables (X
met
, X
sleep
, X
age
, and X
adip
), respectively. The power of
any of these tests is greater than 0.80, and R
2
> 0.42.
Auton.
Parameter (Y)
Metab. param.
(X met)
controlling for X sleep= log(OAHI), X age, X adiposity
Standardized
(p-value)
log(G
ABR_stand_SBP
)
Fasting Glucose
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.46*
(0.035)
0.47*
(0.034)
0.48*
(0.028)
0.46*
(0.037)
0.46*
(0.038)
0.45*
(0.042)
log(G
ABR_stand_SBP
)
Fasting Glucose
controlling for X sleep= log(TAI), X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.44
(0.051)
0.46*
(0.042)
0.48*
(0.039)
0.45*
(0.049)
0.46*
(0.050)
0.44
(0.056)
log(G
ABR_stand_SBP
)
Fasting Glucose
controlling for X sleep= log(Desat) , X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.49*
(0.033)
0.50*
(0.031)
0.51*
(0.030)
0.48*
(0.036)
0.47*
(0.042)
0.47*
(0.040)
log(G
ABR_stand_SBP
)
Fasting Glucose
controlling for X sleep= SpO2_low, X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.53*
(0.027)
0.54*
(0.025)
0.54*
(0.024)
0.52*
(0.029)
0.53*
(0.027)
0.52*
(0.031)
log(G
ABR_stand_SBP
)
Fasting Glucose
controlling for X sleep= Efficiency (%), X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.52*
(0.027)
0.53*
(0.026)
0.54*
(0.023)
0.51*
(0.030)
0.50*
(0.038)
0.49*
(0.035)
log(G
ABR_stand_SBP
)
Fasting Glucose
controlling for X sleep= TST, X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.50*
(0.031)
0.51*
(0.028)
0.52*
(0.025)
0.48*
(0.033)
0.48*
(0.040)
0.47*
(0.039)
log(G
ABR_stand_SBP
)
Fasting Glucose
controlling for X sleep= REM (% of TST) , X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.49*
(0.034)
0.50*
(0.033)
0.50*
(0.032)
0.48*
(0.036)
0.47*
(0.044)
0.47*
(0.041)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat, TST: total sleep time, REM: rapid eye movement.
207
The last significant correlation found involving standing autonomic parameters
determined using SBP as input was for Y = log(G
RCC_stand_SBP
), X
sleep
= TST, and X
met
=
log(AIRg), log(DI), or Sg, besides X
age
and X
adip
(except total body fat in grams in all
cases and trunk fat in grams for one case). This multiple regression model is given by
adip adip age age sleep met met SBP stand RCC
X b X b b X b a G TST ) log(
_ _
In this case, Y = log(G
RCC_stand_SBP
) was found to be significantly correlated with X
sleep
=
TST only when also considering log(AIRg), log(DI), or Sg as the metabolic parameters
(X
met
) in the regression, besides age and adiposity. The correlation between
log(G
RCC_stand_SBP
) and TST, adjusting only for age and adiposity, is not significant.
These results are summarized in Table 24. These metabolic parameters, age, and
adiposity, however, are not significantly correlated with log(G
RCC_stand_SBP
) in this
multiple linear regression model.
208
Table 24: Multiple linear regression analysis for Y = log(G
RCC_stand_SBP
) as the dependent variable and age, total
sleep time, adiposity, and the listed metabolic parameters as the independent variables. This shows that
log(G
RCC_stand_SBP
) is significantly correlated with total sleep time when the listed metabolic parameters are added
as independent variables, along with age and adiposity.
Auton.
Parameter (Y)
Sleep
parameter
(X sleep)
controlling for X met= log(AIRg), X age, X adiposity
Standardized
(p-value)
log(G
RCC_stand_SBP
)
TST
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
-0.48*
(0.037)
-0.49*
(0.041)
-0.39
(0.11)
-0.49*
(0.046)
-0.49
(0.061)
-0.50*
(0.042)
log(G
RCC_stand_SBP
)
TST
controlling for X met = log(DI), X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
-0.51*
(0.030)
-0.53*
(0.028)
-0.44
(0.080)
-0.54*
(0.023)
-0.58*
(0.029)
-0.54*
(0.021)
log(G
RCC_stand_SBP
)
TST
controlling for X met = Sg, X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
-0.45*
(0.047)
-0.46*
(0.043)
-0.38
(0.10)
-0.48*
(0.037)
-0.52*
(0.045)
-0.49*
(0.036)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat, TST: total sleep time, REM: rapid eye movement.
These results indicate that a decrease in total sleep time is related to an increase in G
RCC
in the standing posture, when considering not only age and adiposity, but also X
met
=
AIRg, the acute insulin response to glucose, or first phase insulin response to the initial
glucose bolus of the FSIVGTT test, X
met
= DI, the disposition index, which quantifies the
increase in insulin secretion to compensate for insulin resistance and is an integrated
measure of pancreatic -cell function, or X
met
= Sg, the glucose effectiveness index,
which quantifies the effect of glucose on its own disposal, independent of an increase in
insulin from baseline. G
RCC
is related to vagal modulation such that an increase in this
gain is related to an increase in vagal modulation. This suggests that a decrease in total
sleep time is related to an increased standing vagal modulation, or a decreased standing
vagal withdrawal, in the standing posture, when considering insulin secretion (AIRg and
209
DI) or glucose effectiveness (Sg), besides age and adiposity. This suggests an impairment
in vagal withdrawal in the standing posture for smaller values of TST, when also
considering the aforementioned independent variables.
PTT input
When considering the multiple linear regressions for autonomic parameters usingPTT as
input to the ABR transfer function, we find Y =log(ABR
_HF_stand_PTT
) to be correlated with
both X
met
= log(DI) and X
sleep
= log(OAHI), considering also age, and adiposity. This
multiple linear regression equation is given by:
adip adip age age sleep met PTT stand HF
X b X b b DI b a ABR (OAHI) log ) ( log ) log(
_ _
The significance of X
met
= log(DI) andX
sleep
= log(OAHI) on explaining
log(ABR
_HF_stand_PTT
), quantified by the p-values associated with each regression
coefficient, together with each standardized , is shown in Table 25, while the
standardized 's for the significant correlations are listed separately in Table 26.
210
Table 25: Multiple linear regression analysis (dependent variable Y = log(ABR
_HF_stand_PTT
); independent
variables: X
met
= log(DI), X
sleep
= log(OAHI), X
age
, X
adip
) for the supine posture, showing that log(ABR
_HF_stand_PTT
)
is significantly correlated with both the sleep parameter and the metabolic parameter, for all adiposity
measures. The power of this multiple linear regression is > 0.90 and R
2
> 0.45 for any adiposity measure.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
met
) 0.033
( = 0.44*)
0.038
( = 0.43*)
0.036
( = 0.44*)
0.036
( = 0.44*)
0.031
( = 0.45*)
0.032
( = 0.44*)
p (X
sleep
) 0.016
( = 0.51*)
0.019
( = 0.50*)
0.021
( = 0.50*)
0.017
( = 0.51*)
0.029
( = 0.47*)
0.016
( = 0.51*)
p (X
adip.
) 0.38
( = -0.21)
0.55
( = -0.13)
0.76
( = 0.070)
0.63
( = -0.094)
0.43
( = 0.21)
0.46
( = -0.14)
p (X
age
) 0.54
( = -0.15)
0.38
( = -0.20)
0.18
( = -0.31)
0.16
( = -0.28)
0.12
( = -0.40)
0.15
( = -0.29)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Table 26: Multiple linear regression analysis (dependent variable Y = log(ABR
_HF_stand_PTT
); independent
variables: X
met
= log(DI),X
sleep
= log(OAHI),X
age
, X
adip
) for the supine posture, showing that log(ABR
_HF_stand_PTT
)
is significantly correlated with both the sleep parameter, log(OAHI), and the metabolic parameter, log(DI), for
all adiposity measures. The power of this multiple linear regression is > 0.90 and R
2
> 0.45 for any adiposity
measure.
Auton.
Parameter (Y)
Explanatory
variable
(X)
Adiposity parameter (X adip)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
log(ABR _HF_stand_PTT)
X sleep = log(OAHI)
Standardized
(p-value)
0.51
(0.016*)
0.50
(0.019*)
0.50
(0.021*)
0.51
(0.017*)
0.47
(0.029*)
0.51
(0.016*)
X met = log(DI)
Standardized
(p-value)
0.44
(0.033*)
0.43
(0.038*)
0.44
(0.036*)
0.44
(0.036*)
0.45
(0.031*)
0.45
(0.032*)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
When interpreted in a partial correlations view, the high frequency component of the
baroreflex gain in the standing posture, determined using PTT as input to the ABR
transfer function, becomes significantly correlated with the disposition index DI, when
controlling for age, adiposity, and OSA severity (OAHI). This indicates that, when the
degree of OSA severity is controlled for, along with age and adiposity, an increase in the
disposition index, a measure of increase in -cell function, is correlated with an increase
in the high frequency ABR gain in the standing posture. This may suggests an increase in
baroreceptor mediated vagal modulation in the standing posture associated with increased
211
insulin secretion, if age, adiposity, and sleep apnea severity are kept constant. Since we
would not expect an increase in vagal modulation in the standing posture, this could
mean an impairment in baroreceptor mediated vagal withdrawal in the standing posture
due to increased insulin secretion to compensate for insulin resistance.
This correlation is not observed when using any other measure of OSA. Likewise, the
high frequency component of ABR, determined in the standing posture, was not
significantly correlated to any other metabolic parameter, even after controlling for age,
adiposity, and OSA severity.
A complementary interpretation in terms of partial correlation can be made considering
the pairwise correlation between the high frequency component of ABR and log(OAHI),
controlling for age, adiposity, and insulin secretion, as measured by the disposition index
DI. In this case, an increase in OSA severity, as measured by OAHI, is correlated with an
increase in the high-frequency ABR gain, when insulin secretion is controlled for. This
suggests an increase in baroreceptor mediated vagal modulation in the standing posture
associated with increased OSA severity, which could indicate an impairment in
baroreceptor mediated vagal withdrawal in the standing posture due to increased OSA
severity, when adjusting for age, adiposity, and -cell function.
In fact, as shown in Table 27, log(ABR
_HF_stand_PTT
) is significantly correlated with OSA
severity, as measured by log(OAHI), controlling not only for insulin secretion (log(DI))
as the metabolic parameter but also for X
met
= insulin sensitivity (S
I
),X
met
= glucose
effectiveness (Sg), X
met
= fasting insulin, X
met
= HOMA, X
met
= log(QUICKI), or X
met
=
212
log(FGIR), along with age and adiposity. These metabolic parameters, however, are not
significant in those regression models.
Since QUICKI and FGIR are highly correlated with both fasting insulin and HOMA, the
results using these metabolic parameters have been omitted from Table 27 for easier
readability. Since the correlation between log(ABR
_HF_stand_PTT
) and log(OAHI)
controlling only for age and adiposity is not significant, this multiple regression result
indicates that both OSA severity and the different measures of metabolic function are
important when considering baroreceptor reflex in orthostatic stress.
213
Table 27: Standardized and associated p-values for the multiple linear regression for Y = log(ABR
_HF_stand_PTT
)
as the dependent variable and age, X
sleep
= log(OAHI), adiposity, and the listed metabolic parameters X
met
as the
independent variables. Interpreted from a partial correlation perspective, this appears to show that
log(ABR
_HF_stand_PTT
) is significantly correlated with log(OAHI) when controlling for age, adiposity, and all listed
metabolic parameters.
Auton.
Parameter (Y)
Sleep. param.
(X sleep)
controlling for X met= log(S I), X age, X adiposity
Standardized
(p-value)
log(ABR _HF_stand_PTT)
log(OAHI)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.51*
(0.041)
0.52*
(0.041)
0.51*
(0.034)
0.52*
(0.034)
0.45*
(0.031)
0.49*
(0.042)
log(ABR _HF_stand_PTT)
log(OAHI)
controlling for X met=Sg, X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.49*
(0.032)
0.48*
(0.036)
0.49*
(0.038)
0.49*
(0.034)
0.45*
(0.031)
0.45
(0.053)
log(ABR _HF_stand_PTT)
log(OAHI)
controlling for X met= Fasting Insulin , X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.56*
(0.031)
0.59*
(0.031)
0.56*
(0.026)
0.56*
(0.025)
0.45*
(0.031)
0.53*
(0.029)
log(ABR _HF_stand_PTT)
log(OAHI)
controlling for X met= HOMA, X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.57*
(0.030)
0.59*
(0.030)
0.56*
(0.026)
0.57*
(0.024)
0.45*
(0.031)
0.54*
(0.029)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat, TST: total sleep time, REM: rapid eye movement.
It is important to observe that neither the pairwise correlation of log(ABR
_HF_stand_PTT
) and
log(DI), controlling for age and adiposity, nor the pairwise correlation of
log(ABR
_HF_stand_PTT
) and log(OAHI), controlling for age and adiposity only, were
significant. As discussed by Hamilton (Hamilton, 1987), the importance of one
explanatory variable can be enhanced by the inclusion of another in the regression
equation. This can happen when the added explanatory variable is a “suppressor
variable”. Suppose a multiple regression in which the explanatory variables are given by
X
1
and X
2
, and the outcome variable is given by Y. X
2
is said to be a suppressor variable
214
when the addition of X
2
to the multiple regression suppresses some of the variance in X
1
not relevant to Y, therefore increasing X
1
’s importance in the regression (Lynn, 2003). On
the extreme, for instance, it is possible to have R
2
= 1 for a multiple correlation involving
two explanatory variables even though one of the simple correlations is 0 and the other is
arbitrarily close to 0 (Hamilton, 1987).
Therefore, in order to understand the variable log(ABR
_HF_stand_PTT
), it seems to be
necessary to consider both log(DI) and log(OAHI) simultaneously, along with age and
adiposity, even if their separate pairwise correlations with log(ABR
_HF_stand_PTT
) is not
significant. Moreover, an explanatory variable does not necessarily need to be
significantly correlated with the outcome variable to be considered important in
understanding the underlying process. While the explanatory variable may not be
quantitatively useful in terms of mathematically predicting the output, it may be useful in
the interpretation of the obtained results (Courville, et al., 2001).
A significant correlation with Y = log(ABR
_HF_stand_PTT
) was also found for X
sleep
= TST
(total sleep time, in minutes). As reported in Table 12, log(ABR
_HF_stand_PTT
) is
significantly correlated with total sleep time (in minutes) when controlling for age and
adiposity only. When performing a multiple linear regression for the same autonomic
parameter as the dependent variable Y, and X
sleep
= TST as one of the independent
variables, along with age, adiposity, and X
met
, the multiple linear regression equation is
given by:
215
adip adip age age sleep met met PTT stand HF
X b X b b X b a ABR TST ) log(
_ _
In this case, the significance between Y = log(ABR
_HF_stand_PTT
) and X
sleep
= TST is
maintained for almost all adiposity measures (except total body fat in grams and trunk fat
in grams), for X
met
= log(S
I
), X
met
= Sg, X
met
= fasting glucose, X
met
= fasting insulin, X
met
=
HOMA, X
met
= QUICKI, orX
met
= FGIR. These results are summarized in Table 28. For
reasons previously explained, the results for QUICKI and FGIR have been omitted from
the table. These metabolic parameters, however, are not significant in the multiple linear
regression model. These metabolic parameters have been found to be correlated with
each other in our study population. In particular, fasting insulin is correlated with log(S
I
)
(r = -0.68, p < 0.001*), Sg (r = -0.52, p = 0.013*), fasting glucose (r = 0.51, p = 0.014*),
HOMA (r = 0.99, p < 0.001*), QUICKI (r = -0.85, p < 0.001*), and FGIR (r = -0.68, p <
0.001*). Besides these variables, fasting insulin is also correlated with log(AIRg) (r =
0.51, p = 0.016*), but not with log(DI).
Since the addition of these X
met
doesn’t seem to affect the correlation between
log(ABR
_HF_stand_PTT
) and X
sleep
= TST found previously adjusting for age and adiposity
only, this is an indication that these metabolic parameters X
met
are not correlated with
total sleep time. This is consistent with the results for the pairwise correlations between
metabolic and sleep parameters presented in Table 9, adjusting for age and adiposity.
For X
met
= log10(AIRg) or X
met
= log10(DI), however, then X
sleep
= TST is no longer
significantly correlated with Y = log(ABR
_HF_stand_PTT
). This may indicate that these
metabolic parameters are somewhat correlated with total sleep time, since the addition of
216
any of these parameters as a separate explanatory variable has the effect of diminishing
the significance of an otherwise significant correlation. Nevertheless, from the results
presented in Table 9, consisting of the pairwise correlations between sleep and metabolic
parameters, adjusting for age and adiposity, log(DI) was found to be significantly
correlated with total sleep time only when adjusting for total body fat in grams and total
trunk fat in grams, besides age, while log(AIRg) was not found to be significantly
correlated with any sleep parameter, adjusting for age and adiposity.
Nevertheless, results obtained considering autonomic parameters in the standing posture
should be interpreted with caution, as previously mentioned. A higher absolute standing
autonomic parameter could be related to either a low, high, or null autonomic reactivity
to postural change, depending on the respective baseline value of each subject. For this
reason, while the results involving the standing autonomic parameters have been reported
for completeness, they will not be considered in the discussion and conclusion sections.
217
Table 28: Multiple linear regression analysis for Y = log(ABR
_HF_stand_PTT
) as the dependent variable and age,
X
sleep
= total sleep time (TST), adiposity, and the listed metabolic parameters X
met
as independent variables. This
shows that log(ABR
_HF_stand_PTT
) is significantly correlated with TST even when the listed metabolic parameters
are added as independent variables, along with age and adiposity, an indication that these X
met
are uncorrelated
with X
sleep
= TST.
Auton.
Parameter (Y)
Sleep. param.
(X sleep)
controlling for X met= log(S I), X age, X adiposity
Standardized
(p-value)
log(ABR _HF_stand_PTT)
TST
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.55*
(0.021)
0.55*
(0.022)
0.50
(0.059)
0.52*
(0.031)
0.42
(0.096)
0.52*
(0.029)
log(ABR _HF_stand_PTT)
TST
controlling for X met=Sg, X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.53*
(0.028)
0.52*
(0.029)
0.47
(0.083)
0.49*
(0.046)
0.37
(0.17)
0.49*
(0.043)
log(ABR _HF_stand_PTT)
TST
controlling for X met= Fasting Glucose , X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.56*
(0.018)
0.56*
(0.017)
0.52*
(0.048)
0.51*
(0.032)
0.44
(0.084)
0.51*
(0.031)
log(ABR _HF_stand_PTT)
TST
controlling for X met= Fasting Insulin, X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.58*
(0.017)
0.58*
(0.017)
0.49
(0.065)
0.51*
(0.035)
0.40
(0.12)
0.51*
(0.033)
log(ABR _HF_stand_PTT)
TST
controlling for X met= HOMA, X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
0.58*
(0.017)
0.58*
(0.017)
0.49
(0.066)
0.51*
(0.036)
0.40
(0.12)
0.51*
(0.033)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat, TST: total sleep time, REM: rapid eye movement.
218
9.6.3. Standing/supine ratio, sleep indices, and metabolic parameters
SBP input
G
ABR_stand/supine_SBP
or G
ABR
ratio
There was no significant pairwise correlation found for the ratio between the ABR gain
determined in the standing posture and the ABR gain determined in the supine posture,
called G
ABR_stand/supine_SBP
or G
ABR
ratio, a measure of autonomic reactivity, with any
metabolic or sleep parameter, controlling only for age and adiposity. However, when an
additional independent variable is considered, in particular X
sleep
= sleep efficiency (%),
G
ABR
ratio becomes significantly correlated with X
met
= fasting glucose. The
corresponding multiple linear regression equation in this case is given by:
adip adip age age sleep met supine_SBP ABR_stand/
X b X b b ucose Fasting Gl b a G y(%) Efficienc ) ( ) log(
The sleep, age, and adiposity measures, however, were not found to be correlated to G
ABR
ratio in this multiple regression model.
The p-values associated with each independent variable in the above model are listed in
Table 29, together with each respective standardized , while the standardized ’s for the
independent variable X
met
= fasting glucose in the multiple regression model are listed
separately in Table 30.
219
Table 29: Multiple linear regression analysis (dependent variable Y = log(G
ABR_stand/supine_SBP
); independent
variables: X
met
= fasting glucose, X
sleep
= sleep efficiency (%), X
age
, X
adip
) for the stand/supine ratio, showing that
log(G
ABR_stand/supine_SBP
) is significantly correlated with the sleep efficiency, when also controlling for fasting
glucose levels, age, and adiposity. The power of this multiple linear regression is > 0.75 and R
2
> 0.30 for all
adiposity measures.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
met
) 0.043
( = 0.49*)
0.048
( = 0.48*)
0.040
( = 0.51*)
0.039
( = 0.49*)
0.040
( = 0.51*)
0.045
( = 0.46*)
p (X
sleep
) 0.28
( = 0.24))
0.28
( = 0.24)
0.21
( = 0.29)
0.17
( = 0.30)
0.20
( = 0.29)
0.17
( = 0.29)
p (X
adip.
) 0.54
( = 0.17)
0.55
( = 0.15)
0.78
( = -0.074)
0.32
( = -0.21)
0.74
( = -0.098)
0.15
( = -0.30)
p (X
age
) 0.094
( = -0.48)
0.088
( = -0.46)
0.19
( = -0.35)
0.078
( = -0.40)
0.27
( = -0.32)
0.068
( = -0.41)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Table 30: Multiple linear regression analysis (dependent variable Y = log(G
ABR_stand/supine_SBP
); independent
variables: X
met
= fasting glucose, X
sleep
= sleep efficiency (%), X
age
, X
adip
) for the G
ABR
stand/supine ratio, showing
that log(G
ABR_stand/supine_SBP
) is significantly correlated with X
met
= fasting glucose only after considering X
sleep
=
sleep efficiency (%), besides age and adiposity.
Auton. Parameter
(Y)
Metabolic
parameter
(X met)
controlling for X sleep= sleep efficiency (%) , X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%F
at
log(G
ABR_stand/supine_SBP
)
X met = Fasting
Glucose
Standardized
(p-value)
0.49*
(0.043)
0.48*
(0.048)
0.51*
(0.040)
0.49*
(0.039)
0.51*
(0.040)
0.46*
(0.045)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
From these results, an increase in fasting glucose is correlated with an increase in G
ABR
ratio, when also considering age, adiposity, and sleep efficiency. Since an increased G
ABR
ratio is related to a decreased autonomic reactivity, this means that increased levels of
fasting glucose are associated with decreased autonomic reactivity to change in posture
from supine to standing, indicating autonomic impairment with higher fasting glucose
values. In particular, an increase in G
ABR
ratio is related to a smaller degree of change in
baroreceptor gain from supine to standing. This could be related to a lower supine
baseline G
ABR
gain than normal, which then does not decrease much more upon standing.
220
A low baseline G
ABR
gain is indicative of a high sympathetic baseline tone, a low vagal
baseline modulation, or both.
However, the positive, albeit not significant, correlation found between G
ABR
ratio and
sleep efficiency, in which a larger degree of sleep efficiency is related to a higher G
ABR
ratio and, thus, to a smaller autonomic reactivity, does not seem to make much sense.
This point will be again considered when Y
met
= fasting glucose is assumed to be the
dependent variable in the multiple linear regression model, in the next section (9.7).
G
RCC_stand/supine_SBP
or G
RCC
ratio
There was no significant pairwise correlation found for the ratio between the RCC gain
determined in the standing posture and the RCC gain determined in the supine posture,
called G
RCC_stand/supine_SBP
or G
RCC
ratio, also a measure of autonomic reactivity, with any
metabolic parameter, controlling for age and adiposity only. However, when adding X
sleep
= log(OAHI) as an additional independent variable, G
RCC
ratio becomes significantly
correlated with HOMA (except for BMI and BMI z-score). This multiple linear
regression modelis given by:
adip adip age age sleep met supine_SBP RCC_stand/
X b X b b H b a G log(OAHI) OMA) ( ) log(
G
RCC
ratio was not correlated with any other explanatory variable in the model. If the
multiple linear regression for Y = log(G
RCC_stand/supine_SBP
) (or G
RCC
ratio) as the dependent
variable and X
sleep
= log(OAHI), X
met
= HOMA, age, and adiposity as the independent or
explanatory variables, is interpreted in a partial correlation context, this means that an
221
increase in insulin resistance, as measured by HOMA, is correlated with an increase in
G
RCC
ratio, when also considering age, adiposity, and OSA severity.
Since a larger G
RCC
ratio means a decreased G
RCC
reactivity to postural change, this
suggests that increased insulin resistance is related to a lower degree of vagal withdrawal
from supine to standing, when age, fat distribution (or fat content, but not BMI), and
OSA severity are considered, indicating autonomic dysfunction. This could be related to
lower G
RCC
gain at baseline, which then doesn’t go much lower upon standing. A lower
baseline G
RCC
gain is related to a smaller degree of vagal modulation during supine,
which could also contribute to a higher baseline sympathetic tone.
The p-values associated with each independent variable in the above model are listed in
Table 31, together with each respective standardized , while the standardized ’s for the
independent variable X
met
= HOMA in the multiple regression model are listed separately
in Table 32.
Table 31: Multiple linear regression analysis (dependent variable Y =log(G
RCC_stand/supine_SBP
); independent
variables: X
met
= HOMA, X
sleep
= log(OAHI), X
age
, X
adip
) for the G
RCC
stand/supine ratio, showing that
log(G
RCC_stand/supine_SBP
) is significantly correlated with the HOMA index, when also controlling for age, adiposity,
and OSA severity. measured by log(OAHI). The power of this multiple linear regression is > 0.73 and R
2
> 0.28
all adiposity measures related to a significant Y vs. X
met
correlation.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
met
) 0.12
( = 0.48)
0.12
( = 0.50)
0.033*
( = 0.56)
0.040*
( = 0.53)
0.022*
( = 0.62)
0.027*
( = 0.54)
p (X
sleep
) 0.30
( = -0.27)
0.30
( = -0.28)
0.29
( = -0.26)
0.21
( = -0.31)
0.32
( = -0.24)
0.17
( = -0.32)
p (X
adip.
) 0.83
( = 0.071)
0.95
( = 0.020)
0.31
( = -0.27)
0.25
( = -0.25)
0.18
( = -0.42)
0.077
( = -0.38)
p (X
age
) 0.49
( = -0.20)
0.53
( = -0.17)
0.89
( = -0.037)
0.40
( = -0.19)
0.77
( = 0.083)
0.33
( = -0.21)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
222
Table 32: Multiple linear regression analysis (dependent variable Y = log(G
RCC_stand/supine_SBP
);independent
variables: X
met
= HOMA, X
sleep
= log(OAHI),X
age
, X
adip
) for the stand/supine ratio, showing that
log(G
RCC_stand/supine_SBP
)is significantly correlated with X
met
= HOMA only after considering OSA severity,
measured by log(OAHI), besides age and adiposity. The power of this multiple linear regression is > 0.73 and R
2
> 0.28 all adiposity measures related to a significant Y vs. X
met
correlation.
Auton. Parameter
(Y)
Metabolic
parameter
(X met)
controlling for X sleep= log(OAHI) , X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%F
at
log(G
RCC_stand/supine_SBP
)
X met = HOMA
Standardized
(p-value)
0.48
(0.12)
0.51
(0.12)
0.56*
(0.033)
0.53*
(0.040)
0.62*
(0.022)
0.54*
(0.027)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
The negative correlation between Y = G
RCC
ratio and X
sleep
= log(OAHI), however,
although not significant, does not seem to make intuitive sense. It implies that a decrease
in OAHI, a measure of OSA severity, is related to an increase in G
RCC
ratio, indicating
autonomic reactivity impairment, when the opposite would make more sense. This point
will be later addressed when considering HOMA as the dependent variable in the
multiple linear regression model in the next section (9.7).
The correlation between G
RCC
ratio and HOMAalso becomes significant when controlling
for REM (% of total sleep time) as the sleep parameter, along with age and adiposity
(except for BMI and BMI z-score). In this case, when controlling for age, adiposity, and
REM (% of total sleep time), G
RCC
ratio was significantly correlated not only for X
met
=
HOMA, but also for X
met
= fasting insulin. The results for X
sleep
= REM (% of total sleep
time) are summarized in the following tables. Table 33 lists the p-values associatedwith
each independent variable for X
sleep
= REM (% of total sleep time) and X
met
= HOMA,
together with each respective standardized , while Table 34 lists separately the p-values
223
and each respective standardized for the same X
sleep
and X
met
= fasting insulin. The
associated significant standardized ’s are listed separately in Table 35.
Table 33: Multiple linear regression analysis (dependent variable Y = log(G
RCC_stand/supine_SBP
); independent
variables: X
met
= HOMA, X
sleep
= REM (% TST), X
age
, X
adip
) for the G
RCC
stand/supine ratio, showing that
log(G
RCC_stand/supine_SBP
) is significantly correlated with the HOMA, when also controlling for age, adiposity, and
REM (% TST). The power of this multiple linear regression is > 0.72 and R
2
> 0.29 for all adiposity measures
related to a significant Y vs. X
met
correlation.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
met
) 0.13
( = 0.39)
0.13
( = 0.39)
0.036
( = 0.53*)
0.040
( = 0.50*)
0.020
( = 0.60*)
0.023
( = 0.52*)
p (X
sleep
) 0.095
( = -0.43)
0.11
( = -0.41)
0.26
( = -0.29)
0.16
( = -0.34)
0.22
( = -0.29)
0.10
( = -0.37)
p (X
adip.
) 0.29
( = 0.34)
0.36
( = 0.28)
0.46
( = -0.21)
0.30
( = -0.22)
0.20
( = -0.40)
0.070
( = -0.38)
p (X
age
) 0.086
( = -0.55)
0.10
( = -0.49)
0.46
( = -0.22)
0.14
( = -0.36)
0.80
( = -0.079)
0.087
( = -0.40)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat, TST: total sleep time (in minutes).
Table 34: Multiple linear regression analysis (dependent variable Y = log(G
RCC_stand/supine_SBP
); independent
variables: X
met
= fasting insulin, X
sleep
= REM ( % TST), X
age
, X
adip
) for the G
RCC
stand/supine ratio, showing that
log(G
RCC_stand/supine_SBP
) is significantly correlated with fasting insulin, when also controlling for age, adiposity,
and REM (% TST). The power of this multiple linear regression is > 0.72 and R
2
> 0.29 for all adiposity
measures related to a significant Y vs. X
met
correlation.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
met
) 0.17
( = 0.37)
0.18
( = 0.37)
0.045
( = 0.51*)
0.048
( = 0.49*)
0.025
( = 0.59*)
0.026
( = 0.52*)
p (X
sleep
) 0.096
( = -0.44)
0.11
( = -0.42)
0.24
( = -0.31)
0.15
( = -0.36)
0.20
( = -0.32)
0.090
( = -0.40)
p (X
adip.
) 0.31
( = 0.34)
0.37
( = 0.28)
0.46
( = -0.21)
0.28
( = -0.23)
0.21
( = -0.40)
0.062
( = -0.40)
p (X
age
) 0.095
( = -0.54)
0.11
( = -0.48)
0.47
( = -0.22)
0.14
( = -0.36)
0.81
( = -0.077)
0.086
( = -0.41)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat, TST: total sleep time (in minutes).
224
Table 35: Multiple linear regression analysis for Y = log(G
RCC_stand/supine_SBP
) as the dependent variable and age,
adiposity, X
sleep
= REM (% of total sleep time), and X
met
= HOMA or fasting insulin as the independent variables.
Interpreted from a partial correlation perspective, this shows that log(G
RCC_stand/supine_SBP
) is significantly
correlated with both HOMA and fasting insulin levels (the latter only for trunk fat and trunk % fat), when
REM (% of total sleep time) is added as an additional explanatory variable, along with age and adiposity (except
for BMI and BMI z-score).
Auton. Parameter
(Y)
Metabolic
parameter
(X met)
controlling for X sleep= REM (% TST) , X age, X adiposity
Standardized
(p-value)
BMI BMI z-
score
TBF (g) T%BF TrkFat
(g)
Trk%Fat
log(G
RCC_stand/supine_SBP
)
X met = HOMA
Standardized
(p-value)
0.39
(0.13)
0.39
(0.13)
0.53*
(0.036)
0.50*
(0.040)
0.60*
(0.020)
0.52*
(0.023)
log(G
RCC_stand/supine_SBP
)
X met = Fasting
Insulin
Standardized
(p-value)
0.37
(0.17)
0.37
(0.18)
0.51*
(0.045)
0.49*
(0.048)
0.59*
(0.025)
0.52*
(0.026)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat, TST: total sleep time (in minutes).
These correlations, however, were not very strong. For X
met
= HOMA, the power of the
multiple linear regression is > 0.72 (R
2
> 0.29) for all adiposity measures related to a
significant correlation, while for X
met
= fasting insulin the power was > 0.52 (R
2
> 0.27).
Moreover, the negative correlation between REM (% TST) and G
RCC
ratio may not be
correct. It implies that a decrease in REM is related to an increase in G
RCC
ratio,
indicating impaired autonomic reactivity. Since an increase in REM could be related to
an increased sleep sympathetic tone, which could still be present during wakefulness in
OSA patients, the contrary relationship would be expected. This point will be further
investigated when Y
met
= HOMA is considered as the dependent variable, in the next
section (9.7).
G
RCC
ratio had been found to be correlated with log(TAI) when controlling for age and
adiposity only (except for BMI and BMI z-score), if a metabolic parameter is added as an
additional explanatory variable, this correlation no longer exists. This is an indication that
there is a correlation between log(TAI) and metabolic parameters. Indeed, from the
225
pairwise correlations between log(TAI) and metabolic parameters, controlling for age and
adiposity, listed in Table 9, we see that log(TAI) is significantly correlated with
log(Fasting Insulin), log(HOMA), log(QUICKI), and log(FGIR). The correlation with
other metabolic parameters was not significant.
The autonomic parameter G
RCC
ratio had also been found to be correlated with total sleep
time, controlling for age and adiposity (all measures). In this case, the correlation
continues to be significant by adding any metabolic parameter as additional explanatory
or independent variable, with an even smaller p-value in most cases. The G
RCC
ratio is not
correlated to any metabolic parameter in this multiple linear regression analysis,
however.
PTT input
The only significant correlation when considering ABR stand/supine ratio, using PTT as
input, as the dependent variable in the multiple linear regression model, was found for the
high frequency component of ABR ratio, or ABR
HF
stand/supine ratio, X
sleep
= Sleep
efficiency (%), X
met
= log(DI), as described by the multiple regression model:
adip adip age age sleep met ne_PTT stand/supi HF
X b X b b b a ABR (%) efficiency Sleep (DI) log ) log(
_
The autonomic parameter log(ABR
HF_stand/supine_PTT
) had not been found to be correlated
with any sleep or metabolic parameter when adjusting for age and adiposity only. In the
equation above, the autonomic parameter is significantly correlated to log(DI) for all
adiposity measures except BMI and total % body fat, for which it seems to be a trend.
226
Table 36 contains the p-values for the multiple linear regression model with Y =
log(G
ABR_HF_stand/supine_PTT
), X
met
= log(DI), and X
sleep
= Sleep efficiency (%).
Table 36: Multiple linear regression analysis (dependent variable Y = log(ABR
_HF_stand/supine_PTT
); independent
variables: X
met
= log(DI), X
sleep
= Sleep efficiency (%), X
age
, X
adip
) for the G
ABR
stand/supine ratio (PTT input),
showing that log(ABR
_HF_stand/supine_PTT
) is significantly correlated with X
met
= log(DI), when also controlling for
age, adiposity, and X
sleep
= Sleep efficiency (%). The power of this multiple linear regression is > 0.71 and R
2
>
0.29 for all adiposity measures related to a significant correlation.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
met
) 0.054
( = 0.47)
0.047
( = 0.48*)
0.028
( = 0.53*)
0.055
( = 0.47)
0.034
( = 0.52*)
0.049
( = 0.48*)
p (X
sleep
) 0.20
( = -0.31)
0.17
( = -0.32)
0.11
( = -0.38)
0.25
( = -0.27)
0.14
( = -0.34)
0.24
( = -0.27)
p (X
adip.
) 0.61
( = 0.14)
0.43
( = 0.21)
0.18
( = 0.36)
0.65
( = -0.10)
0.26
( = 0.34)
0.44
( = -0.17)
p (X
age
) 0.43
( = 0.22)
0.44
( = 0.20)
0.59
( = 0.13)
0.21
( = 0.29)
0.75
( = 0.091)
0.21
( = 0.29)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat, TST: total sleep time (in minutes).
These results show that the autonomic parameter is significantly correlated to the
disposition index, when controlling for age, adiposity, and sleep efficiency. The positive
correlation indicates that an increase in the disposition index DI is related to an increase
in the high frequency component of the baroreflex stand/supine gain determined using
PTT as input.
The high frequency component of the baroreflex gain is a measure of the vagal limb of
the baroreflex response. A higher ratio is related to a lower reactivity, indicating that
increased insulin secretion to compensate for insulin resistance, as measured by DI, is
related to a decreased vagal reactivity of the baroreflex response, when the sleep
efficiency parameter is also taken into consideration. In other words, since DI is a
measure of increased insulin secretion to compensate for insulin resistance, this suggests
that those subjects with a greater DI could have increased insulin production, as a
227
response to decreased insulin sensitivity, and this would be associated with a lower
degree of baroreceptor mediated vagal reactivity related to change in posture.
For the following model involving G
RCC
ratio, using PTT as input, the correlation with
X
sleep
= TST for any X
met
and all X
adip
, was significant:
adip adip age age sleep met supine_PTT RCC_stand/
X b X b b X b a G TST
met
The correlation between G
RCC
ratio (PTT input) and TST, controlling for age and
adiposity only, had been found to be significant for all adiposity values expect trunk fat in
grams and trunk % fat. With the addition of X
sleep
= TST to the multiple regression model,
G
RCC
ratio (PTT input) becomes significantly correlated with TST for all adiposity and all
metabolic measures. In fact, the p-values associated with this correlation are much
smaller than when considering age and adiposity alone. All p-values are < 0.031, while
many are < 0.001. To illustrate this point, Table 37 contains the p-values for the multiple
linear regression model with Y = G
RCC_stand/supine_PTT
, X
met
= log(DI), and X
sleep
= TST. This
may indicate that, while log(DI) and TST were not found to be directly correlated, there
could still be an indirect interaction between log(DI) and TST.
228
Table 37: Multiple linear regression analysis (dependent variable Y = G
RCC_stand/supine_PTT
; independent variables:
X
met
= log(DI), X
sleep
= TST, X
age
, X
adip
) for the G
RCC
stand/supine ratio (PTT input), showing that
G
RCC_stand/supine_PTT
is significantly correlated with X
sleep
= TST, when also controlling for age, adiposity, and X
met
.
The results are similar for any metabolic parameter X
met
. The power of this multiple linear regression is > 0.87
and R
2
> 0.36 for all adiposity measures related to a significant correlation.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
met
) 0.088
( = 0.32)
0.056
( = 0.35)
0.11
( = 0.37)
0.23
( = 0.27)
0.15
( = 0.33)
0.22
( = 0.27)
p (X
sleep
) 0.00037
( = -0.83*)
0.00024
( = -0.84*)
0.0034
( = -0.83*)
0.0097
( = -0.66*)
0.0069
( = -0.76*)
0.013
( = -0.62*)
p (X
adip.
) 0.0091
( = 0.63*)
0.0055
( = 0.62*)
0.19
( = 0.36)
0.93
( = 0.019)
0.41
( = 0.26)
0.48
( = -0.15)
p (X
age
) 0.027
( = -0.53*)
0.028
( = -0.47*)
0.21
( = -0.33)
0.58
( = -0.12)
0.32
( = -0.30)
0.55
( = -0.13)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat, TST: total sleep time (in minutes).
9.7. Metabolic parameters as the dependent variable
As stated previously, the hypothesis in this study is that obstructive sleep apnea,
metabolic function, and the autonomic system are correlated. More specifically, this
investigation also includes trying to identify different pathways that could be involved in
the associations among sleep apnea, autonomic dysfunction, and metabolic imbalance.
The diagram in Figure 36 illustrates the different working hypothesis in this study.
Hypothesis (1) assumes that sleep apnea would lead to metabolic dysfunction through
impairment in autonomic control. Hypothesis (2) assumes a direct association between
sleep apnea and metabolic dysfunction, which would then lead to autonomic impairment.
The third hypothesis assumes a direct link between sleep apnea and autonomic
impairments, as well as between sleep apnea and metabolic dysfunction, including insulin
resistance. An additional hypothesis would be the existence of direct interactions between
abnormal autonomic control and metabolic dysfunctions.
229
Figure 36: Hypotheses for different pathways that could be involved in the association among sleep apnea,
autonomic dysfunction, and metabolic imbalance.
Although the present study is cross-sectional, the results obtained using the different
regression models could give a clue as to which pathway seems more probable. In order
to obtain more information on the different interactions among sleep apnea, autonomic
function, and metabolic parameters, this section analyzes the multiple linear regression
model assuming the metabolic index as the dependent variable in the model.
In section 9.6, the multiple linear regression model used allows one to investigate if the
autonomic parameter can be explained by variations in sleep indices, metabolic
parameters, age, and adiposity. If, instead, the hypothesis is stated considering the
metabolic parameter as the dependent variable, and the autonomic and sleep parameters,
Sleep
Apnea
Abnormal
ANS
Metabolic
Dysfunction
Other
factors
(Obesity)
Sleep
Apnea
Sleep
Apnea
Metabolic
Dysfunction
Abnormal
ANS
(1)
(2)
(3)
Abnormal
ANS
Metabolic
Dysfunction
(?)
Hypotheses
230
besides age and adiposity, as the explanatory or independent variables, this tests if the
metabolic parameter can be explained by variations in sleep and autonomic measures,
besides age and adiposity.
In this model considering the metabolic parameter as the dependent variable, the p-values
that relate the metabolic and autonomic values do not change from those when
considering the autonomic parameter as the dependent variable Yand the metabolic
parameter as an explanatory variable. This result was expected, since it is still a measure
of the partial correlation of the autonomic with the corresponding metabolic parameter,
accounting for the effects of sleep, age, and adiposity. Nevertheless, the p-values relating
the metabolic parameter (dependent variable) with the remaining explanatory variables
are, understandably, new information, since the correlation of these independent variables
with the metabolic parameter had not been calculated in the previous model. The multiple
linear regression model is now stated as:
adip adip age age sleep sleep aut aut met
X b X b X b X b a Y
(9.2)
The results of this multiple linear regression considering the metabolic parameter as the
dependent variable Y
met
and the autonomic (X
aut
) and sleep parameters (X
sleep
), besides age
(X
age
) and adiposity (X
adip
), as the explanatory variables, if interpreted from a partial
correlation coefficient perspective, could be understood as determining the effects of the
autonomic function on the metabolic index, accounting for the effects of sleep, age, and
adiposity. Alternatively, the results can also be interpreted as determining the effects of
231
sleep parameters on metabolic function, accounting for the effects of autonomic function,
age, and adiposity.
Performing the multiple linear regressions considering the metabolic parameters as the
dependent variable Y
met
, the results obtained are described below.
9.7.1. Baseline autonomic parameters, metabolic function, and OSA
SBP as input to the ABR transfer function
In the previous section (9.6), we had found that, for the multiple linear regression model
with Y = G
ABR
(baseline), X
met
= fasting insulin, X
sleep
= REM (% TST), X
age
, and X
adip
(total % body fat, trunk % fat, and trunk fat in grams, but not BMI, BMI z-score, or total
body fat in grams), there was a significant correlation between baseline G
ABR
and REM
(% TST) only when considering all of these explanatory variables (G
ABR
and REM (%
TST) were not significantly correlated controlling for age and adiposity only). The
previous equation implied the assumption that both sleep indices and metabolic
parameters influence the autonomic system. G
ABR
and REM (% TST) were also
significantly correlated for X
met
= HOMA.
Since the above is significant only if all the aforementioned explanatory variables are
considered, this seems to indicate that there is an interaction betweenX
sleep
and X
met
. In
particular, it seems that X
met
is a suppressor variable in the previous multiple regression
equation, since the importance of X
sleep
= REM (% TST) is enhanced by the inclusion of
X
met
in the equation (Hamilton, 1987). As discussed previously, X
met
can be suppressing
232
some of the variance in X
sleep
not relevant to Y = G
ABR
, therefore increasing X
sleep
’s
importance in the regression (Lynn, 2003).
To test the alternative hypothesis that the metabolic system is influenced by sleep and
autonomic function, besides age and adiposity, we defined the following model
adip adip age age sleep SBP ABR aut met
X b X b TST REM b G b a Y ) (% ) (
sup_ _
where Y
met
= fasting insulin or Y
met
= HOMA.
Table 38 shows the corresponding p-values for the significance of each explanatory
variable for Y
met
= fasting insulin, together with each respective standardized , while
Table 39 shows separately the corresponding p-values for the significance of each
explanatory variable when Y
met
= HOMA, together with each respective standardized .
Table 38: Multiple linear regression analysis (dependent variable Y
met
= fasting insulin; independent variables:
X
aut
= G
ABR_sup_SBP
, X
sleep
= REM (%TST), X
age
, X
adip
) for the supine posture, showing that Y
met
= fasting insulin is
not significantly correlated with either X
sleep
or X
aut
.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.081
( = 0.39)
0.063
( = 0.40)
0.17
( = 0.33)
0.19
( = 0.33)
0.24
( = 0.28)
0.20
( = 0.32)
p (X
sleep
) 0.20
( = 0.31)
0.16
( = 0.33)
0.12
( = 0.43)
0.069
( = 0.49)
0.14
( = 0.39)
0.070
( = 0.49)
p (X
adip.
) 0.031
( = 0.61*)
0.018
( = 0.61*)
0.45
( = 0.21)
0.99
( = 0.0027)
0.22
( = 0.38)
0.89
( = 0.030)
p (X
age
) 0.98
( = -0.0085)
0.87
( = 0.041)
0.34
( = 0.29)
0.098
( = 0.42)
0.69
( = 0.13)
0.096
( = 0.42)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
233
Table 39: Multiple linear regression analysis (dependent variable Y
met
= HOMA; independent variables: X
aut
=
G
ABR_sup_SBP
, X
sleep
= REM (%TST), X
age
, X
adip
) for the supine posture, showing that HOMA is not significantly
correlated with either X
sleep
or X
aut
.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.083
( = 0.40)
0.064
( = 0.41)
0.16
( = 0.35)
0.17
( = 0.34)
0.23
( = 0.29)
0.18
( = 0.34)
p (X
sleep
) 0.25
( = 0.29)
0.22
( = 0.29)
0.16
( = 0.39)
0.094
( = 0.46)
0.18
( = 0.36)
0.094
( = 0.46)
p (X
adip.
) 0.049
( = 0.57*)
0.026
( = 0.59*)
0.46
( = 0.20)
0.94
( = -0.018)
0.24
( = 0.36)
0.98
( = -0.005)
p (X
age
) 0.95
( = 0.017)
0.83
( = 0.053)
0.34
( = 0.29)
0.10
( = 0.41)
0.68
( = 0.14)
0.10
( = 0.41)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
These results show that neither X
sleep
= REM (% TST) nor X
aut
= G
ABR_sup_SBP
seem to be
significant in determining Y
met
. The direct correlations between fasting insulin or HOMA
and REM (% TST), as well as between these metabolic indices and G
ABR
, controlling only
for age and adiposity, were also not significant. Also, the positive correlation found
between HOMA and baseline G
ABR
gain, as was the case when assuming the autonomic
parameter to be the dependent variable, does not make intuitive sense, since this would
suggest an increase in baseline baroreflex gain with increased HOMA. This could also be
an indication that this correlation should not be considered as providing meaningful
information.
PTT as input to the ABR transfer function
Using PTT as input to the ABR transfer function, it had been found in section 9.6 that Y
aut
= log(ABR
_HF_sup_PTT
) was significantly correlated with X
sleep
= sleep efficiency (%)when
also considering X
met
= log(DI) in the multiple regression model, besides age and
adiposity. The parameter log(ABR
_HF_sup_PTT
) and sleep efficiency (%) were not
significantly correlated when considering only age and adiposity in the model. This result
234
seems to suggest an interaction between log(DI) and sleep efficiency (%), although the
direct correlation between these parameters, controlling for age and adiposity, is not
significant. Nevertheless, the metabolic parameter log(DI) had been found to be
significantly correlated with TST, controlling for age and adiposity (total body fat in
grams and trunk fat in grams only, however, as shown in Table 9), while TST is
significantly correlated with sleep efficiency (%) (r = 0.59, p < 0.001).
When analyzing the hypothesis considering Y
met
= log(DI) as the dependent variable and
X
aut
= log(ABR
_HF_sup_PTT
) and X
sleep
= sleep efficiency (%), besides age and adiposity, as
the explanatory variables, the multiple linear regression model can be represented by
adip adip age age sleep PTT HF aut
X b X b b ABR b a DI (%) y Efficienc ) log( ) log(
sup_ _
.
The significance of each variable in the model above is listed in Table 40.
Table 40: Multiple linear regression analysis (dependent variable Y
met
= log(DI); independent variables: X
aut
=
log(ABR
_HF_sup_PTT
), X
sleep
= Efficiency (%), X
age
, X
adip
) for the supine posture. These results show that none of the
explanatory variables are significant for determining log(DI) for the multiple linear regression equation above.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.11
( = -0.44)
0.084
( = -0.48)
0.074
( = -0.47)
0.13
( = -0.40)
0.11
( = -0.42)
0.13
( = -0.41)
p (X
sleep
) 0.10
( = 0.43)
0.079
( = 0.45)
0.059
( = 0.48)
0.13
( = 0.38)
0.088
( = 0.43)
0.13
( = 0.38)
p (X
adip
) 0.55
( = -0.18)
0.36
( = -0.26)
0.21
( = -0.34)
0.93
( = 0.020)
0.35
( = -0.28)
0.72
( = 0.082)
p (X
age
) 0.32
( = -0.29)
0.31
( = -0.27)
0.39
( = -0.22)
0.14
( = -0.37)
0.51
( = -0.20)
0.14
( = -0.37)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
These results show that none of the explanatory variables are significant for determining
Y
met
= log(DI) for the multiple linear regression model above. Since log(DI) was also not
significant to either log(ABR
_HF_sup_PTT
) or to sleep efficiency (%) when considered
235
separately, controlling for age and adiposity only, it seems that the previous assumption
that both X
met
= log(DI) and X
sleep
= sleep efficiency (%) are important for the
determination of Y
aut
= log(ABR
_HF_sup_PTT
) is more plausible. Moreover, since X
met
seems
to be a suppressor variable in the multiple linear regression, once its addition to the model
is what makes X
sleep
= sleep efficiency become significantly correlated with Y
aut
=
log(ABR
_HF_sup_PTT
), this is an indication that there is some indirect interaction between
X
met
= log(DI) and X
sleep
= sleep efficiency.
Other results for Y
met
and X
sleep
= sleep efficiency (%)
Y
met
= Sg
When analyzing the correlations between sleep and metabolic parameters, controlling for
age and adiposity only, Sg and sleep efficiency (%) were found to be significantly
correlated (Table 9). When investigating the multiple linear regression for Y
met
= Sg, X
sleep
= sleep efficiency (%), besides X
aut
, X
age
, and X
adip
, expressed by the equation
adip adip age age sleep aut aut
X b X b b X b a Sg (%) y Efficienc
,
the correlation between Y
met
= Sg and X
sleep
= sleep efficiency (%) is still significant for
any autonomic parameter X
aut
and all adiposity measures. Since the addition of the
autonomic parameter seems to make no difference in the significance of the relation
between Sg and sleep efficiency, this suggests that sleep efficiency is not correlated with
any measure of the autonomic function in the above model. Indeed, from the results
obtained previously, the only significant correlation found between sleep efficiency and
236
an autonomic parameter was for Y
aut
= log(ABR
_HF_sup_PTT
), X
sleep
= sleep efficiency (%),
and X
met
= log(DI), also considering X
age
and X
adip
(all adiposity measures except total %
body fat and trunk % fat) in the multiple regression model.
Results for Y
met
= Fasting Insulin and X
sleep
= log(TAI)
Fasting insulin and log(TAI) had been found to be significantly correlated (Table 9),
controlling for age and adiposity, except for BMI and BMI z-score. For the multiple
linear regression for Y
met
= fasting insulin, X
sleep
= log(TAI), besides X
aut
, X
age
, and X
adip
,
expressed by the equation
adip adip age age sleep aut aut
X b X b b X b a Insulin Fasting log(TAI)
,
the correlation between Y
met
= fasting insulin and X
sleep
= log(TAI) is still significant for
any autonomic parameter X
aut
, determined using either SBP or PTT, and practically all
adiposity measures (0.05 < p < 0.083 for BMI and BMI z-score for very few cases). The
addition of the autonomic parameter in all cases seems to enhance the correlation
between fasting insulin and log(TAI), making the associated p-values smaller than if X
aut
is not considered. This seems to indicate that there is some interaction between log(TAI)
and autonomic measures, even though the pairwise correlation between autonomic
measures and log(TAI), controlling for age and adiposity only, had only shown a
significant correlation between log(G
RCC_stand/supine_SBP
) and log(TAI), except for BMI and
BMI z-score.
237
Results for Y
met
= HOMA and X
sleep
= log(TAI)
From the correlations between sleep and metabolic parameters, controlling for age and
adiposity, HOMA and log(TAI) had been found to be significantly correlated (Table 9),
except for BMI and BMI z-score. When investigating the multiple linear regression for
Y
met
= HOMA, X
sleep
= log(TAI), besides X
aut
, X
age
, and X
adip
, expressed by the equation
adip adip age age sleep aut aut
X b X b b X b a HOMA log(TAI)
,
the correlation between Y
met
= HOMA and X
sleep
= log(TAI) is also significant for any
autonomic parameter X
aut
, determined using either SBP or PTT, and practically all
adiposity measures (0.05 < p < 0.083 for BMI and BMI z-score for very few cases). As
for Y
met
= fasting insulin, for Y
met
= HOMA the added explanatory variable X
aut
in all
cases seems to enhance the correlation between HOMA and log(TAI), making the
associated p-values smaller than if X
aut
is not considered. This may also be an indication
of probably some interaction between log(TAI) and autonomic measures.
Results for Y
met
= log(QUICKI) and X
sleep
= log(TAI)
The metabolic parameter log(QUICKI) had also been found to be significantly correlated
with log(TAI) when controlling for age and adiposity (except BMI and BMI z-score).
When investigating the multiple linear regression for Y
met
= log(QUICKI), X
sleep
=
log(TAI), besides X
aut
, X
age
, and X
adip
, expressed by the equation
adip adip age age sleep aut aut
X b X b b X b a QUICKI log(TAI) ) log(
,
238
the correlation between Y
met
= log(QUICKI) and X
sleep
= log(TAI) is also significant for
any autonomic parameter X
aut
, determined using either SBP or PTT, and all adiposity
measures (except for even fewer cases in which 0.05 < p < 0.083 for BMI and BMI z-
score). As in the case for Y
met
= HOMA, for Y
met
= log(QUICKI), the addition of the
autonomic parameter in all cases seems to enhance the correlation between HOMA and
log(TAI), making the associated p-values smaller than if X
aut
is not considered. This may
also be an indication of the existence of some interaction between log(TAI) and all
autonomic measures in the model considering Y
met
= log(QUICKI), as was the case for
the multiple regression model considering Y
met
= HOMA.
Results for Y
met
= log(FGIR) and X
sleep
= log(TAI)
Similarly, the metabolic parameter log(FGIR) had been found to be significantly
correlated with log(TAI) when controlling for age and adiposity (except BMI and BMI z-
score) only. Analyzing the multiple linear regression results for Y
met
= log(FGIR), X
sleep
=
log(TAI), besides X
aut
, X
age
, and X
adip
, expressed by the equation
adip adip age age sleep aut aut
X b X b b X b a FGIR log(TAI) ) log(
,
the correlation between Y
met
= log(FGIR) and X
sleep
= log(TAI) is also significant for any
autonomic parameter X
aut
, determined using either SBP or PTT, and all adiposity
measures (except for only a single case, in which the correlation for X
adip
= BMI had p =
0.052). As in the previous results for X
sleep
= log(TAI), for Y
met
= log(FGIR) the addition
of any autonomic parameter X
aut
seems to enhance the correlation between FGIR and
log(TAI), making the associated p-values smaller than if X
aut
is not considered.
239
9.7.2. Autonomic parameters in the standing posture, metabolic function, and OSA
SBP input
Y
met
= Fasting Glucose
Fasting glucose had been found to be correlated with log(G
ABR_stand_SBP
) controlling for
age and adiposity only (Table 15). This correlation was still significant when considering
Y
aut
= log(G
ABR_stand_SBP
) as the dependent variable and X
met
= fasting glucose, X
sleep
, X
age
,
and X
adip
as the explanatory variables. Since the significance of the correlation between
log(G
ABR_stand_SBP
) and fasting glucose was not affected by any sleep parameter, this may
be an indication that X
met
= fasting glucose and X
sleep
are not highly correlated (their
direct correlation, controlling for age and adiposity only, is indeed not significant). To
further test this result, the next step was to consider Y
met
= fasting glucose as the
dependent variable and X
aut
= log(G
ABR_stand_SBP
), X
sleep
, X
age
, and X
adip
as the explanatory
variables, in the multiple linear regression model expressed as:
adip adip age age sleep sleep SBP stand ABR aut
X b X b X b G b a Glucose Fasting ) log(
_ _
,
The significance of the correlation between fasting glucose and log(G
ABR_stand_SBP
) is
maintained for any X
sleep
, with the same p-values found when considering the autonomic
parameter as the dependent and the metabolic parameter one of the explanatory variables,
as expected. Nevertheless, the associated p-values for the correlation between the
autonomic and metabolic parameter, are larger when adding X
sleep
as an additional
explanatory variable than the p-values obtained from the direct correlation between
240
fasting glucose and log(G
ABR_stand_SBP
), controlling for age and adiposity only. This may
be an indication of some degree of correlation between X
sleep
and G
ABR_stand_SBP
.
X
aut
= log(G
RCC_stand_SBP
)
In the previous section, Y
aut
= log(G
RCC_stand_SBP
) was found to be correlated with X
sleep
=
TST for X
met
= log(AIRg), X
met
= log(DI), or X
met
= Sg, besides X
age
and X
adip
(except total
body fat in grams in all cases and trunk fat in grams for one case). The direct correlation
between log(G
RCC_stand_SBP
) and TST controlling for age and adiposity only was not
significant. This may be an indication that these metabolic parameters are correlated in
some extent to TST.
From Table 9, log(DI) had been found to be significantly correlated with TST only when
controlling for age and either total body fat in grams or trunk fat in grams, but not for any
other adiposity measure, while neither log(AIRg) nor Sg had been found to be
significantly correlated to TST. In fact, log(AIRg) had not been found to be significantly
correlated with any sleep measure when controlling for age and adiposity, while Sg had
been found to be significantly correlated with sleep efficiency (%) only. In terms of
correlations between the different sleep measures, sleep efficiency (%) is significantly
correlated with total sleep time (r = 0.59*, p < 0.001) and REM (% TST) (r = 0.58*, p =
0.0013), but not with any other sleep measure.
To further understand correlations that might be present between log(AIRg), log(DI), or
Sg, and total sleep time, the following multiple regression model was assumed:
241
adip adip age age sleep SBP stand RCC aut met
X b X b T b G b a Y ST ) log(
_ _
,
whereY
met
= log(AIRg), log(DI), or Sg. The significance of each explanatory variable in
the model for Y
met
= log(AIRg) is listed in Table 41, together with each standardized ,
while the results for Y
met
= log(DI) and Y
met
= Sg are listed separately in Table 42 and
Table 43, respectively.
Table 41: Multiple linear regression analysis (dependent variable Y
met
= log(AIRg); independent variables: X
aut
=
log(G
RCC_stand_SBP
), X
sleep
= TST, X
age
, X
adip
).
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.24
( = 0.31)
0.33
( = 0.26)
0.47
( = 0.22)
0.50
( = 0.19)
0.53
( = 0.17)
0.47
( = 0.20)
p (X
sleep
) 0.090
( = 0.43)
0.10
( = 0.43)
0.11
( = 0.45)
0.094
( = 0.47)
0.13
( = 0.44)
0.096
( = 0.46)
p (X
adip.
) 0.052
( = 0.58)
0.11
( = 0.45)
0.57
( = 0.18)
0.52
( = 0.15)
0.56
( = 0.20)
0.36
( = 0.22)
p (X
age
) 0.85
( = -0.053)
0.89
( = 0.040)
0.57
( = 0.17)
0.29
( = 0.28)
0.73
( = 0.12)
0.27
( = 0.29)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Table 42: Multiple linear regression analysis (dependent variable Y
met
= log(DI); independent variables: X
aut
=
log(G
RCC_stand_SBP
), X
sleep
= TST, X
age
, X
adip
).
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.17
( = 0.39)
0.19
( = 0.37)
0.30
( = 0.29)
0.17
( = 0.39)
0.18
( = 0.35)
0.16
( = 0.39)
p (X
sleep
) 0.058
( = 0.52)
0.052
( = 0.54)
0.035
( = 0.59*)
0.058
( = 0.52)
0.025
( = 0.63*)
0.059
( = 0.52)
p (X
adip.
) 0.95
( = 0.019)
0.79
( = -0.075)
0.36
( = -0.28)
0.95
( = 0.015)
0.22
( = -0.39)
0.85
( = 0.045)
p (X
age
) 0.94
( = 0.024)
0.80
( = 0.071)
0.57
( = 0.16)
0.89
( = 0.036)
0.35
( = 0.31)
0.87
( = 0.041)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
242
Table 43: Multiple linear regression analysis (dependent variable Y
met
= Sg; independent variables: X
aut
=
log(G
RCC_stand_SBP
), X
sleep
= TST, X
age
, X
adip
).
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.29
( = 0.33)
0.27
( = 0.33)
0.38
( = 0.28)
0.29
( = 0.32)
0.34
( = 0.27)
0.33
( = 0.29)
p (X
sleep
) 0.22
( = 0.35)
0.23
( = 0.35)
0.20
( = 0.38)
0.22
( = 0.35)
0.091
( = 0.49)
0.19
( = 0.38)
p (X
adip.
) 0.87
( = 0.053)
0.77
( = 0.086)
0.75
( = -0.11)
0.93
( = 0.023)
0.15
( = -0.49)
0.67
( = -0.11)
p (X
age
) 0.94
( = 0.022)
0.98
( = 0.0088)
0.75
( = 0.10)
0.85
( = 0.054)
0.27
( = 0.39)
0.90
( = 0.035)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
From these results it can be observed that the significance of the correlations found
between the listed metabolic parameters and total sleep time (Table 9) does not change
when adding X
aut
= log(G
RCC_stand_SBP
) as an additional explanatory variable. This seems
to be an indication that X
aut
= log(G
RCC_stand_SBP
) and X
sleep
= TST are not directly
correlated. Moreover, it seems that the previous assumption that both X
sleep
= TST and
X
met
= log(AIRg), log(DI), or Sg are important for the determination of Y
aut
=
log(G
RCC_stand_SBP
) is more plausible. In fact, since X
sleep
= TST only becomes
significantly correlated to Y
aut
= log(G
RCC_stand_SBP
) if X
met
= log(AIRg), log(DI), or Sg are
considered, this is an indication that there is some interaction between these X
met
variables and TST, even though their direct correlation, even after controlling for age and
adiposity, is not significant.
PTT input
Using PTT as input, the autonomic parameter Y
aut
= log(ABR
_HF_stand_PTT
) had been found
to be correlated with both X
met
= log(DI) and X
sleep
= log(OAHI), in the multiple linear
regression model:
243
adip adip age age sleep met PTT stand HF
X b X b b DI b a ABR (OAHI) log ) ( log ) log(
_ _
as shown in Table 26. Since the direct correlation between log(ABR
_HF_stand_PTT
) and
log(OAHI), controlling for age and adiposity only, is not significant, this indicates that
there is some correlation between log(DI) and log(OAHI), even though their direct
correlation, even after controlling for age and adiposity, is not significant.
It had also been found (Table 27) that Y
aut
= log(ABR
_HF_stand_PTT
) is significantly
correlated with X
sleep
= log(OAHI) when also considering X
met
= log(S
I
), X
met
= glucose
effectiveness (Sg), X
met
= fasting insulin, X
met
= HOMA, X
met
= log(QUICKI), or X
met
=
log(FGIR) as an additional explanatory variable. In this case, however, these metabolic
parameters are not correlated with Y
aut
= log(ABR
_HF_stand_PTT
) in the above model.
To better understand the relationships between these variables, the significance of the
following model was tested:
adip adip age age sleep PTT stand HF aut met
X b X b b ABR b a Y (OAHI) log ) log(
_ _
for Y
met
= log(S
I
), Sg, fasting insulin, HOMA, log(QUICKI), or log(FGIR). The
significance between each of these metabolic parameters as the dependent variable and
X
aut
= log(ABR
_HF_stand_PTT
), X
sleep
= log(OAHI), X
age
, and X
adip
as the explanatory
variables are listed in Table 44 through Table 49.
244
Table 44: Multiple linear regression analysis (dependent variable Y
met
= log(S
I
); independent variables: X
aut
=
log(ABR
_HF_stand_PTT
), X
sleep
= log(OAHI), X
age
, X
adip
).
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.47
( = 0.16)
0.43
( = 0.18)
0.27
( = 0.27)
0.35
( = 0.24)
0.19
( = 0.32)
0.37
( = 0.23)
p (X
sleep
) 0.086
( = -0.39)
0.060
( = -0.43)
0.16
( = -0.35)
0.11
( = -0.42)
0.18
( = -0.33)
0.11
( = -0.41)
p (X
adip.
) 0.022*
( = -0.61)
0.017*
( = -0.59)
0.13
( = -0.39)
0.36
( = -0.21)
0.075
( = -0.53)
0.30
( = -0.23)
p (X
age
) 0.42
( = 0.20)
0.50
( = 0.16)
0.80
( = 0.066)
0.51
( = -0.16)
0.45
( = 0.22)
0.49
( = -0.17)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Table 45: Multiple linear regression analysis (dependent variable Y
met
= Sg; independent variables: X
aut
=
log(ABR
_HF_stand_PTT
), X
sleep
= log(OAHI), X
age
, X
adip
).
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.21
( = 0.36)
0.20
( = 0.37)
0.22
( = 0.35)
0.22
( = 0.35)
0.17
( = 0.38)
0.23
( = 0.34)
p (X
sleep
) 0.27
( = -0.30)
0.28
( = -0.30)
0.30
( = -0.29)
0.28
( = -0.30)
0.37
( = -0.24)
0.28
( = -0.30)
p (X
adip.
) 0.75
( = 0.096)
0.67
( = 0.12)
0.89
( = -0.040)
0.84
( = 0.048)
0.29
( = -0.35)
0.81
( = -0.057)
p (X
age
) 0.91
( = -0.034)
0.89
( = -0.040)
0.90
( = 0.039)
0.92
( = 0.025)
0.46
( = 0.25)
0.97
( = 0.0099)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Table 46: Multiple linear regression analysis (dependent variable Y
met
= fasting insulin; independent variables:
X
aut
= log(ABR
_HF_stand_PTT
), X
sleep
= log(OAHI), X
age
, X
adip
).
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.33
( = -0.21)
0.28
( = -0.22)
0.21
( = -0.32)
0.23
( = -0.31)
0.14
( = -0.36)
0.24
( = -0.31)
p (X
sleep
) 0.025*
( = 0.51)
0.013*
( = 0.54)
0.059
( = 0.49)
0.046*
( = 0.53)
0.067
( = 0.46)
0.046*
( = 0.53)
p (X
adip.
) 0.016*
( = 0.61)
0.0065*
( = 0.63)
0.36
( = 0.24)
0.89
( = 0.031)
0.11
( = 0.47)
0.81
( = 0.054)
p (X
age
) 0.20
( = -0.31)
0.19
( = -0.29)
0.73
( = -0.091)
0.90
( = 0.031)
0.34
( = -0.28)
0.88
( = 0.036)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
245
Table 47: Multiple linear regression analysis (dependent variable Y
met
= HOMA; independent variables: X
aut
=
log(ABR
_HF_stand_PTT
), X
sleep
= log(OAHI), X
age
, X
adip
).
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.32
( = -0.22)
0.27
( = -0.23)
0.20
( = -0.32)
0.22
( = -0.32)
0.14
( = -0.36)
0.23
( = -0.31)
p (X
sleep
) 0.026*
( = 0.52)
0.014*
( = 0.55)
0.053
( = 0.51)
0.042*
( = 0.54)
0.060
( = 0.47)
0.042*
( = 0.54)
p (X
adip.
) 0.031*
( = 0.55)
0.012*
( = 0.59)
0.41
( = 0.21)
0.96
( = 0.0099)
0.14
( = 0.43)
0.91
( = 0.024)
p (X
age
) 0.27
( = -0.27)
0.25
( = -0.26)
0.78
( = -0.073)
0.89
( = 0.034)
0.39
( = -0.25)
0.88
( = 0.037)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Table 48: Multiple linear regression analysis (dependent variable Y
met
= log(QUICKI); independent variables:
X
aut
= log(ABR
_HF_stand_PTT
), X
sleep
= log(OAHI), X
age
, X
adip
).
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.42
( = 0.19)
0.38
( = 0.20)
0.27
( = 0.28)
0.29
( = 0.28)
0.19
( = 0.32)
0.30
( = 0.27)
p (X
sleep
) 0.092
( = -0.39)
0.061
( = -0.43)
0.15
( = -0.38)
0.11
( = -0.42)
0.17
( = -0.34)
0.11
( = -0.41)
p (X
adip.
) 0.048*
( = -0.52)
0.024*
( = -0.55)
0.36
( = -0.24)
0.95
( = -0.014)
0.14
( = -0.44)
0.83
( = -0.049)
p (X
age
) 0.66
( = 0.11)
0.68
( = 0.098)
0.83
( = -0.057)
0.47
( = -0.18)
0.70
( = 0.12)
0.46
( = -0.18)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Table 49: Multiple linear regression analysis (dependent variable Y
met
= log(FGIR); independent variables: X
aut
= log(ABR
_HF_stand_PTT
), X
sleep
= log(OAHI), X
age
, X
adip
).
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.25
( = 0.25)
0.22
( = 0.27)
0.16
( = 0.36)
0.18
( = 0.35)
0.11
( = 0.40)
0.19
( = 0.34)
p (X
sleep
) 0.046*
( = -0.45)
0.028*
( = -0.49)
0.092
( = -0.44)
0.071
( = -0.48)
0.10
( = -0.40)
0.072
( = -0.47)
p (X
adip.
) 0.024*
( = -0.58)
0.012*
( = -0.59)
0.37
( = -0.23)
0.91
( = -0.024)
0.13
( = -0.45)
0.73
( = -0.077)
p (X
age
) 0.33
( = 0.24)
0.35
( = 0.21)
0.90
( = 0.033)
0.72
( = -0.087)
0.47
( = 0.21)
0.69
( = -0.096)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
These results show that, for the multiple regression model considering the Y
met
= HOMA
or fasting insulin as the dependent variable and X
aut
= log(ABR
_HF_stand_PTT
), X
sleep
=
log(OAHI), X
age
, and X
adip
as the explanatory variables, Y
met
= fasting insulin is
significantly correlated with X
sleep
= log(OAHI), except for total body fat in grams (p =
246
0.059) and trunk fat in grams (p = 0.067); and Y
met
= HOMA is significantly correlated
with X
sleep
= log(OAHI)), except for total body fat in grams (p = 0.053) and trunk fat in
grams (p = 0.060). It’s important to point out that the correlation between either fasting
insulin or HOMA with log(OAHI) when controlling for age and adiposity only is not
significant. Their correlation only becomes significant when adding the autonomic
parameter as an additional explanatory variable. This may be an indication of an
interaction between sleep apnea severity, as measured by OAHI, and the autonomic
measure ABR
_HF_stand_PTT
.
In fact, as previously mentioned, if the autonomic parameter is assumed to be the
dependent variable in the multiple linear regression model
adip adip age age sleep met PTT stand HF
X b X b b X b a ABR (OAHI) log ) log(
met _ _
Y
aut
= log(ABR
_HF_stand_PTT
) was only significantly correlated with X
sleep
= log(OAHI)
when also considering X
met
= fasting insulin and X
met
= HOMA as additional explanatory
variables. These results taken together seem to show that sleep apnea severity, insulin
resistance (HOMA) or fasting insulin levels, and autonomic function are interrelated.
247
9.7.3. Stand/supine ratios, metabolic parameters, and OSA
SBP input
G
ABR_stand/supine_SBP
or G
ABR
ratio
As discussed previously, G
ABR
ratio (G
ABR_stand/supine_SBP
) was found to be significantly
correlated with X
met
= fasting glucose only if also considering X
sleep
= sleep efficiency (%)
to the multiple regression model, besides age and adiposity, according to the equation
y(%) Efficienc ) ( ) log(
sleep met supine_SBP ABR_stand/
b ucose Fasting Gl b a G
adip adip age age
X b X b
The sleep, age, and adiposity measures, however, were not found to be correlated to G
ABR
ratio in this multiple regression model. Since X
sleep
seems to behave as a suppressor
variable in the above correlation, this suggests some correlation between X
sleep
= sleep
efficiency (%) and fasting glucose, even though the correlation between these two
variables, controlling for age and adiposity only, was not found to be significant. From a
partial correlation coefficient perspective, this means that G
ABR
ratio is correlated with
fasting glucose when controlling for age, adiposity, and sleep efficiency. This way, the
effects of age, adiposity, and sleep efficiency can be mathematically removed from the
correlation between G
ABR
ratio and fasting glucose. This has an effect of mathematically
adjusting the data such that all subjects have comparable age, adiposity, and sleep
efficiency characteristics. However, this model also indicated that sleep efficiency was
positively correlated with G
ABR
ratio, indicating autonomic impairement with increased
sleep efficiency. Although the correlation with sleep efficiency was not found to be
248
significant, the effect of sleep efficiency on the outcome G
ABR
ratio does not seem to
make physiological sense.
To further investigate the correlations among these variables, the significance of the
following model was tested:
adip adip age age sleep supine_SBP ABR_stand/ aut
X b X b b G b a Glucose Fasting ) (% y Efficienc ) log(
.
The significance between fasting glucose and the explanatory variables X
aut
=
log(G
ABR_stand/supine_SBP
), X
sleep
= sleep efficiency (%), X
age
, and X
adip
are listed in Table 50,
together with each respective standardized .
Table 50: Multiple linear regression analysis (dependent variable Y
met
= Fasting Glucose; independent variables:
X
aut
= log(G
ABR_stand/supine_SBP
), X
sleep
= Efficiency (%), X
age
, X
adip
). The power of this multiple linear regression is >
0.79 and R
2
> 0.33 for all adiposity measures related to a significant Y vs. X
aut
correlation.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.043*
( = 0.48)
0.048*
( = 0.46)
0.040*
( = 0.47)
0.039*
( = 0.49)
0.040*
( = 0.47)
0.045*
( = 0.50)
p (X
sleep
) 0.21
( = -0.28)
0.19
( = -0.29)
0.14
( = -0.33)
0.18
( = -0.30)
0.15
( = -0.31)
0.19
( = -0.29)
p (X
adip.
) 0.92
( = -0.028)
0.87
( = 0.042)
0.43
( = 0.20)
0.69
( = 0.085)
0.37
( = 0.25)
0.77
( = 0.065)
p (X
age
) 0.13
( = 0.43)
0.14
( = 0.39)
0.22
( = 0.31)
0.062
( = 0.43)
0.38
( = 0.25)
0.065
( = 0.43)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
As expected, these results show the same p-values between the autonomic and metabolic
variables, whether the autonomic or the metabolic parameter is assumed to be the
dependent variable. The results also show that X
sleep
= sleep efficiency (%) is not
correlated with Y
met
= fasting glucose in this model. However, in this case the direction of
this correlation makes more sense. In this model, although their correlation is not
significant, a decrease in sleep efficiency is related to an increase in G
ABR
ratio, indicating
249
autonomic dysfunction. Moreover, as was the case for the autonomic parameter as the
dependent variable, the correlation between Y
met
= fasting glucose and X
aut
=
log(G
ABR_stand/supine_SBP
) is only significant if X
sleep
= sleep efficiency (%) is added to the
multiple regression model. Thus, an increase in fasting glucose is correlated with an
increase in G
ABR
ratio, indicating autonomic dysfunction when controlling for age,
adiposity, sleep efficiency, and the effect of sleep efficiency on fasting glucose in terms
of the sign of the associated standardized makes physiological sense.
These combined analyses seem to indicate that the multiple regression considering Y
met
=
fasting glucose as the dependent variable is more plausible than when considering Y
aut
=
G
ABR
ratio as the outcome. In other words, it seems that both sleep and autonomic
parameters are necessary to explain variations in fasting glucose. This result also suggests
some interaction between the sleep and autonomic parameters, since the correlation
between Y
met
= fasting glucose and X
aut
= G
ABR
ratio is only significant when considering
X
sleep
= sleep efficiency as an additional explanatory variable.
G
RCC_stand/supine_SBP
or G
RCC
ratio
Considering the autonomic parameter as the dependent variable, G
RCC
ratio, or
log(G
RCC_stand/supine_SBP
), had been found to be significantly correlated with HOMA only
when also considering X
sleep
= log(OAHI) or X
sleep
= REM (% TST) as an additional
independent variable (except for BMI and BMI z-score), as shown in Table 32 and Table
35. The autonomic parameter log(G
RCC_stand/supine_SBP
) was also found to be significantly
correlated with fasting insulin if X
sleep
= REM (% TST) is added to the regression model
250
(except for BMI and BMI z-score), as also shown in Table 35. The autonomic parameter
was not found to be significantly correlated with any other explanatory variable in the
multiple linear regression model for Y
aut
= log(G
RCC_stand/supine_SBP
). The negative
correlation between G
RCC
ratio and OAHI, however, although not significant, did not
make sense from a physiological perspective.
Since these results suggest that there may be some correlation between X
sleep
=
log(OAHI) or REM (%TST) and either HOMA and/or fasting insulin, the following
multiple linear regression model was investigated:
adip adip age age sleep sleep supine_SBP RCC_stand/ aut met
X b X b X b G b a Y ) log(
for Y
met
= HOMA or fasting insulin and X
sleep
= log(OAHI) or REM (%TST).
The significance of each explanatory variable for the different combinations of Y
met
=
HOMA or fasting insulin and X
sleep
= log(OAHI) or REM (% TST), together with the
standardized , are listed in tables Table 51 through Table 54. As expected, the
associated standardized values for the metabolic vs. autonomic parameters are the same
when considering either the autonomic or metabolic parameter as the dependent variable.
251
Table 51: p-values for the multiple linear regression analysis (dependent variable Y
met
= HOMA; independent
variables: X
aut
= log(G
RCC_stand/supine_SBP
), X
sleep
= log(OAHI), X
age
, X
adip
). The associated standardized -values for
X
sleep
are also displayed. The power of this multiple linear regression is > 0.87 and R
2
> 0.42 all adiposity
measures related to a significant correlation.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.12
( = 0.31)
0.12
( = 0.29)
0.033
( = 0.45*)
0.040
( = 0.45*)
0.022
( = 0.46*)
0.027
( = 0.50*)
p (X
sleep
) 0.026
( = 0.44*)
0.015
( = 0.47*)
0.068
( = 0.39)
0.042
( = 0.44*)
0.097
( = 0.34)
0.035
( = 0.45*)
p (X
adip.
) 0.050
( = 0.49*)
0.021
( = 0.53*)
0.25
( = 0.28)
0.49
( = 0.14)
0.084
( = 0.47)
0.27
( = 0.23)
p (X
age
) 0.60
( = -0.12)
0.57
( = -0.12)
0.83
( = 0.05)
0.34
( = 0.20)
0.67
( = -0.10)
0.29
( = 21)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Table 52: Multiple linear regression analysis (dependent variable Y
met
= HOMA; independent variables: X
aut
=
log(G
RCC_stand/supine_SBP
), X
sleep
= REM (% TST), X
age
, X
adip
). The power of this multiple linear regression is > 0.81
and R
2
> 0.34 for all adiposity measures related to a significant correlation.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.13
( = 0.36)
0.13
( = 0.34)
0.036
( = 0.47*)
0.040
( = 0.48*)
0.020
( = 0.49*)
0.023
( = 0.54*)
p (X
sleep
) 0.29
( = 0.27)
0.29
( = 0.26)
0.18
( = 0.32)
0.090
( = 0.40)
0.17
( = 0.30)
0.066
( = 0.42)
p (X
adip.
) 0.30
( = 0.32)
0.20
( = 0.35)
0.35
( = 0.24)
0.61
( = 0.11)
0.075
( = 0.49)
0.27
( = 0.24)
p (X
age
) 0.60
( = 0.17)
0.56
( = 0.17)
0.34
( = 0.26)
0.070
( = 0.43)
0.84
( = 0.055)
0.049
( = 0.46*)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Table 53: Multiple linear regression analysis (dependent variable Y
met
= Fasting Insulin; independent variables:
X
aut
= log(G
RCC_stand/supine_SBP
), X
sleep
= log(OAHI), X
age
, X
adip
). The associated standardized -values for X
sleep
are
also displayed. The power of this multiple linear regression is > 0.88 and R
2
> 0.39 for all adiposity measures
related to a significant correlation.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.18
( = 0.26)
0.18
( = 0.24)
0.051
( = 0.42)
0.059
( = 0.42)
0.034
( = 0.43*)
0.039
( = 0.47*)
p (X
sleep
) 0.027
( = 0.43*)
0.016
( = 0.46*)
0.084
( = 0.37)
0.051
( = 0.43)
0.12
( = 0.32)
0.043
( = 0.44*)
p (X
adip.
) 0.025
( = 0.56*)
0.011
( = 0.59*)
0.23
( = 0.29)
0.47
( = 0.15)
0.075
( = 0.49)
0.25
( = 0.25)
p (X
age
) 0.44
( = -0.18)
0.44
( = -0.16)
0.90
( = 0.031)
0.37
( = 0.19)
0.61
( = -0.13)
0.32
( = 0.21)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
252
Table 54: Multiple linear regression analysis (dependent variable Y
met
= Fasting Insulin; independent variables:
X
aut
= log(G
RCC_stand/supine_SBP
), X
sleep
= REM (% TST), X
age
, X
adip
). The power of this multiple linear regression is >
0.82 and R
2
> 0.34 for all adiposity measures related to a significant correlation.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.17
( = 0.31)
0.18
( = 0.30)
0.045
( = 0.44*)
0.048
( = 0.46*)
0.025
( = 0.47*)
0.026
( = 0.52*)
p (X
sleep
) 0.26
( = 0.28)
0.25
( = 0.28)
0.14
( = 0.36)
0.064
( = 0.44)
0.12
( = 0.33)
0.043
( = 0.47*)
p (X
adip.
) 0.20
( = 0.39)
0.15
( = 0.40)
0.35
( = 0.24)
0.56
( = 0.12)
0.068
( = 0.50)
0.22
( = 0.27)
p (X
age
) 0.71
( = 0.12)
0.63
( = 0.14)
0.34
( = 0.26)
0.066
( = 0.43)
0.86
( = 0.050)
0.044
( = 0.47*)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Y
met
= HOMA and X
sleep
= log(OAHI)
From these results, for Y
met
= HOMA, X
aut
= log(G
RCC_stand/supine_SBP
) and X
sleep
=
log(OAHI), the correlation between HOMA and X
aut
is the same, whether HOMA or the
autonomic parameter is the dependent variable, as expected. However, for Y
met
= HOMA,
X
sleep
= log(OAHI) is also significantly correlated with HOMA (except for total body fat
in grams and trunk fat in grams). This confirms the suspected correlation between
HOMA and log(OAHI) from the previous results for the multiple linear regression model
considering the autonomic parameter as the dependent variable. Moreover, the positive
correlation between HOMA and OAHI, now also significant, makes more sense
physiologically, since it implies that an increase in OSA severity, as measured by an
increase in OAHI, is related to an increase in insulin resistance, as measured by the
HOMA index. These results taken together seem to suggest that both sleep and
autonomic function are important in explaining variations in HOMA, and not the other
way around.
253
Y
met
= HOMA and X
sleep
= REM (% TST)
For Y
met
= HOMA, X
aut
= log(G
RCC_stand/supine_SBP
) and X
sleep
= REM (% TST), HOMA is
correlated with log(G
RCC_stand/supine_SBP
) (except for BMI and BMI z-score), as before, but
not with REM (% TST). This correlation, however, is not significant if X
sleep
= REM (%
TST) is not included in the model. Moreover, the positive correlation between REM (%
TST) and HOMA, although not significant, relating an increase in REM to increased
insulin resistance, seems to make more sense than the negative correlation previously
found between REM and G
RCC
ratio when considering the autonomic parameter as the
dependent variable.
Y
met
= Fasting Insulin
For Y
met
= fasting insulin, X
aut
= log(G
RCC_stand/supine_SBP
) and X
sleep
= log(OAHI), fasting
insulin is found to be correlated with log(OAHI) only for BMI, BMI z-score, and trunk %
fat.
For Y
met
= fasting insulin, X
aut
= log(G
RCC_stand/supine_SBP
) and X
sleep
= REM (% TST),
fasting insulin is correlated with log(G
RCC_stand/supine_SBP
) only (except for BMI and BMI z-
score), as before. As was the case for Y
met
= HOMA, the correlation between Y
met
=
fasting insulin and X
aut
= log(G
RCC_stand/supine_SBP
) is not significant if X
sleep
= REM (%
TST) is not included in the model. In these two cases as well, the positive correlation
between fasting insulin and either OAHI or REM (% TST), although not significant,
relating an increase in OSA severity or REM sleep to increased fasting insulin, indicating
254
metabolic dysfunction, seems to make more physiological sense than the correlations
found between these sleep variables and Y
aut
= G
RCC
ratio in the previous section. This is
also an important indication that the assumption that both sleep and autonomic reactivity
function are necessary to explain variations in either insulin resistance or fasting insulin
levels is more plausible than the other way around.
It is also important to point out that all of these mentioned correlations are only
significant when considering the multiple linear regression with all these explanatory
variables. No pairwise correlation involving the autonomic, metabolic, and sleep
parameters mentioned above, controlling only for age and adiposity, was found to be
significant.
Y
met
= log(DI) and X
sleep
= TST
From previous results, the correlation between log(DI) and TST, controlling for age and
adiposity, was significant only when adjusting for total body fat in grams and trunk fat in
grams. On the other hand, the correlation between TST and G
RCC_stand/supine_PTT
(or G
RCC
ratio, for PTT as input) was found to be significant for all adiposity measures except
trunk fat in grams and trunk % fat. The following multiple regression model was defined
in order to investigate the relationships among these three variables:
adip adip age age sleep supine_PTT RCC_stand/ aut
X b X b b G b a DI TST ) log(
The significance of each explanatory variable in this equation is listed in Table 55.
255
Table 55: Multiple linear regression analysis (dependent variable Y
met
= log(DI); independent variables: X
aut
=
G
RCC_stand/supine_PTT
, X
sleep
= TST, X
age
, X
adip
). The power of this multiple linear regression is > 0.75 and R
2
> 0.31 all
adiposity measures related to a significant correlation.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.088
( = 0.64)
0.056
( = 0.59)
0.11
( = 0.42)
0.22
( = 0.33)
0.15
( = 0.37)
0.22
( = 0.34)
p (X
sleep
) 0.027*
( = 0.75)
0.016*
( = 0.81)
0.015*
( = 0.73)
0.067
( = 0.54)
0.021*
( = 0.70)
0.071
( = 0.52)
p (X
adip.
) 0.21
( = -0.42)
0.11
( = -0.50)
0.093
( = -0.48)
0.83
( = -0.049)
0.13
( = -0.48)
0.88
( = 0.037)
p (X
age
) 0.50
( = 0.23)
0.40
( = 0.25)
0.42
( = 0.22)
0.70
( = -0.088)
0.40
( = 0.27)
0.72
( = -0.083)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
Comparing the results of the correlation between Y
met
= log(DI) and X
sleep
= TST with the
correlation between these two same parameters, but controlling for age and adiposity
only (Table 9), it can be seen that including X
aut
= G
RCC_stand/supine_PTT
as an additional
explanatory variable enhances the significance between log(DI) and TST. Thus, the
correlation previously found between X
aut
and X
sleep
is such that X
aut
seems to behave as a
suppressor variable, enhancing the correlation between log(DI) and TST. This result
suggests that an increase in TST is correlated with an increase in insulin secretion to
compensate for insulin resistance, as measured by DI, when controlling for age, adiposity
(except total % body fat and trunk % fat), and the degree of vagal autonomic reactivity to
postural change.
Y
met
= log(DI), X
sleep
= Sleep efficiency (%), and X
aut
= log(ABR
_HF_stand/supine_PTT
)
From previous results, the correlation between log(DI) and log(ABR
_HF_stand/supine_PTT
),
when the later is assumed as the dependent variable, becomes significant only when sleep
efficiency is also considered, besides age and adiposity. To further investigate the
correlations among these variables, the following regression model was investigated:
256
adip adip age age sleep upine_PTT HF_stand/s aut
X b X b b ABR b a DI (%) y Efficienc Sleep ) log( ) log(
The significance of each explanatory variable in this equation is listed in Table 56.
Table 56: Multiple linear regression analysis (dependent variable Y
met
= log(DI); independent variables: X
aut
=
log(ABR
HF_stand/supine_PTT
), X
sleep
= Sleep efficiency (%), X
age
, X
adip
). The power of this multiple linear regression is
> 0.75 and R
2
> 0.31 for all adiposity measures related to a significant correlation.
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.054
( = 0.45)
0.047
( = 0.47*)
0.028
( = 0.50*)
0.055
( = 0.45)
0.034
( = 0.49*)
0.049
( = 0.46*)
p (X
sleep
) 0.14
( = 0.34)
0.12
( = 0.35)
0.071
( = 0.41)
0.17
( = 0.31)
0.093
( = 0.37)
0.16
( = 0.31)
p (X
adip.
) 0.73
( = -0.096)
0.51
( = -0.17)
0.18
( = -0.35)
0.80
( = 0.054)
0.23
( = -0.34)
0.58
( = 0.12)
p (X
age
) 0.34
( = -0.26)
0.36
( = -0.23)
0.54
( = -0.15)
0.17
( = -0.31)
0.72
( = -0.098)
0.17
( = -0.31)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
These results show that log(DI) is significantly correlated with log(ABR
HF stand/supine PTT
)
when adjusting for age, adiposity, and sleep efficiency. The significance is observed for
all adiposity measures except BMI and total % body fat, where the significance is
marginal (p = 0.054 and p = 0.055, respectively). The parameter log(DI), however, is not
significantly correlated with sleep efficiency. Nevertheless, the correlation of log(DI) and
sleep efficiency is positive, which may indicate that decreased sleep efficiency is related
to a decreased DI. When the autonomic parameter log(ABR
HF stand/supine PTT
) is assumed to
be the dependent parameter, the correlation between the autonomic parameter and sleep
efficiency, although also not significant, had been found to be negative, indicating that
decreased sleep efficiency could be related to increased stand/supine ratio or,
equivalently, decreased autonomic reactivity, as measured by log(ABR
HF stand/supine PTT
).
Both linear regression models (results in Table 36 and in Table 56) have a similar power
and convey information that is physiologically reasonable. In sum, both suggest that
257
increased disposition index is correlated with decreased baroreceptor mediated vagal
reactivity, when adjusting for age, adiposity, and sleep efficiency.
Y
met
= log(S
I
) and X
sleep
= log(Desat)
From the results listed in Table 9, the correlation between log(S
I
) and log(Desat) was
significant controlling for age and adiposity, except total body fat in grams and trunk fat
in grams. If Y
met
= log(S
I
) is assumed to be the dependent variable, with the explanatory
variables defined as X
sleep
= log(Desat), X
age
, X
adip
, and an autonomic parameter is added
as an additional explanatory variable X
aut
, the multiple linear regression equation can be
expressed as:
adip adip age age sleep aut aut I
X b X b (Desat) b X b a S log ) log(
In this case, the correlation between Y
met
= log(S
I
) and X
sleep
= log(Desat) is only
significant for X
aut
= log(ABR
_HF_stand/supine_PTT
) (for BMI, BMI z-score, and trunk % fat
only), as shown in Table 57. The variable Y
met
= log(SI), however, is not significant with
any autonomic parameter X
aut
. In this case, the addition of the autonomic parameter
seems to be diminishing, as opposed to enhancing, the correlation between log(S
I
) and
log(Desat). This indicates that the model without X
aut
as an additional independent
variable is more probable when explaining the variations in log(S
I
) by variations in
log(Desat).
258
Table 57: Multiple linear regression analysis (dependent variable Y
met
= log(S
I
); independent variables: X
aut
=
log(ABR
_HF_stand/supine_PTT
), X
sleep
= log(Desat), X
age
, X
adip
).
BMI BMI z-score TBF (g) T%BF TrkFat (g) Trk%Fat
p (X
aut
) 0.16
( = 0.27)
0.095
( = 0.31)
0.20
( = 0.27)
0.27
( = 0.25)
0.17
( = 0.29)
0.30
( = 0.23)
p (X
sleep
) 0.037
( = -0.49*)
0.013
( = -0.56*)
0.094
( = -0.46)
0.051
( = -0.56)
0.059
( = -0.48)
0.050
( = -0.54*)
p (X
adip.
) 0.024
( = -0.55*)
0.0085
( = -0.59*)
0.23
( = -0.31)
0.81
( = -0.052)
0.090
( = -0.47)
0.55
( = -0.13)
p (X
age
) 0.29
( = 0.26)
0.24
( = 0.27)
0.78
( = -0.070)
0.86
( = -0.045)
0.40
( = 0.23)
0.81
( = -0.059)
*
Statistically significant results ( < 0.05). TBF: total body fat, T%BF: total % body fat, TrkFat (g): trunk
fat in grams, Trk%Fat: trunk % fat.
9.8. Discussion
In order to better visualize the associations found, they have been summarized in the
diagrams below. To facilitate the interpretation of the results, they have been separated in
those involving autonomic variables determined using SBP as input to the ABR transfer
function and in those involving the autonomic parameters when PTT is used as input.
9.8.1. SBP as input
This first diagram (Figure 37) contains the associations found for the autonomic variables
defined using SBP as input to the ABR transfer function. Moreover, the diagram contains
only those autonomic parameters defined in either the supine posture (baseline autonomic
function) or as the stand/supine ratio (autonomic reactivity).
259
Figure 37: Diagram showing the associations found in the present group of subjects
While the autonomic parameters determined from supine data are a measure of each
subject’s baseline autonomic function, analysis of the standing parameter by itself does
not provide a clear picture of the change in autonomic response due to change in posture
from supine to standing, since there is no reference involved in this measure. This is
accomplished by the stand/supine ratio, which is a measure of the relative increase or
decrease in autonomic function from baseline as a response to the change in posture.
Once these more basic correlations are determined, the standing autonomic measures may
serve as an additional guide to the understanding the relationships found.
*
OSA
Intermittent
Hypoxia
Sleep
Fragmentation
(TAI)
SI
HOMA
Fast.
insulin
Fast.
Glucose
Autonomic reactivity
( G
RCC
ratio)
Sleep
Efficiency
Sg
Total sleep
time
Autonomic reactivity
( G
ABR
ratio)
Sleep
Efficiency
REM
(%TST)
OSA
severity
(OAHI)
260
9.8.2. Controlling for age and adiposity: summary
Sleep and metabolic correlations
When considering the correlations between sleep and metabolic indices, controlling for
age and adiposity only, intermittent hypoxia (as measured by the desaturation index) was
found to be negatively correlated with insulin sensitivity, while sleep fragmentation (as
measured by TAI) was found to be positively correlated with both insulin resistance (as
measured by the HOMA index) and fasting insulin. Sleep efficiency was also found to be
positively correlated with glucose effectiveness. Thus, in this study population an
increase in hypoxic events is related to a decrease in insulin sensitivity (or the inverse of
insulin resistance), while an increase in sleep fragmentation is related to an increase in
both HOMA and fasting insulin levels. A decrease in sleep efficiency is associated with a
decrease in glucose effectiveness.
These results are consistent with studies in adults. Punjabi and colleagues (Punjabi, et al.,
2004) found sleep apnea to be associated with glucose intolerance, independently of age,
gender, body mass index, and waist. In a more recent study including IVGTT
measurements (Punjabi, et al., 2009), they also found sleep apnea to be associated with a
decrease in insulin sensitivity (SI), glucose effectiveness (Sg), and pancreatic -cell
function (DI), independent of adiposity (percent body fat), age, sex, and race. Ip and
colleagues (Ip, et al., 2002) showed, by using stepwise multiple linear regression, that
while obesity was the major determinant of insulin resistance in their cohort, sleep
disordered breathing parameters such as the apnea-hypopnea index (AHI) and minimum
oxygen saturation were also independent determinants of insulin resistance (measured by
261
the homeostasis model assessment method, HOMA-IR). They also mention that this
association between OSA and insulin resistance was seen in both obese and nonobese
subjects. They also found insulin resistance to be a significant factor for hypertension in
this study sample.
Correlations between obstructive sleep apnea and sleep architecture measures
Sleep related disordered breathing is related to low sleep efficiency (Redline, et al.,
2004), a measure of sleep duration as a percentage of total time in bed after lights off to
the time of final awakening. Sleep efficiency can be interpreted as an additional marker
of sleep fragmentation, although it may not be significantly different across categories of
sleep-related disordered breathing severity (Laffan, 2008). In our study group, we found
that sleep efficiency was significantly correlated with total sleep time and REM (% of
total sleep time), but not with OAHI, TAI, or the desaturation index (nor their log-
transformed values). Nevertheless, we found OAHI to be significantly correlated with the
desaturation index, but not with TAI. The same is true for their log-transformed variables.
These correlations are summarized in Table 58 below.
262
Table 58: Pearson’s correlation coefficient (and corresponding p-value) between the sleep architecture and OSA measures considered in this study.
OAHI
r
(p-value)
TAI
r
(p-value)
Desat.
r
(p-value)
TST
r
(p-value)
REM
(%TST)
r
(p-value)
log(OAHI)
r
(p-value)
log(Desat)
r
(p-value)
log(TAI)
r
(p-value)
Sleep
efficiency
(%)
-0.11
(0.58)
-0.20
(0.31)
-0.079
(0.69)
0.59*
(<0.001)
0.58*
(0.0013)
-0.092
(0.64)
0.057
(0.78)
-0.14
(0.48)
OAHI
0.12
(0.56)
0.44*
(0.012)
-0.037
(0.85)
-0.13
(0.52)
0.93*
(<0.001*)
0.46*
(0.014)
0.18
(0.37)
TAI
-0.0082
(0.97)
-0.11
(0.57)
0.024
(0.90)
0.16
(0.41)
0.079
(0.69)
0.96*
(<0.001)
Desat.
-0.039
(0.85)
-0.22
(0.25)
0.38*
(0.049)
0.82*
(<0.001)
0.059
(0.76)
TST
0.50
(0.0062*)
-0.040
(0.84)
-0.062
(0.75)
-0.055
(0.78)
REM
(%TST)
-0.10
(0.60)
-0.24
(0.21)
0.092
(0.64)
log(OAHI)
0.49*
(0.0086)
0.21
(0.28)
log(Desat)
0.14
(0.48)
*
Significant correlations (p 0.05). TST: total sleep time.
263
Sleep deprivation has been implicated as a risk factor for glucose intolerance and/or
diabetes. Gottlieb and colleagues (Gottlieb, et al., 2005), in a study with 1486 adult
patients (roughly half male and half female), found sleep time to be associated with
impaired glucose regulation in men and women, in subjects 70 years and older and also in
those younger than 70 years, and in those with and without obstructive sleep
apnea/hypoponea, with no significant effect modification by these factors. They also
showed short sleep time to be associated to diabetes mellitus and impaired glucose
tolerance, even after adjustment for known diabetes risk factors as well as age, sex, race,
obesity, and AHI. The association was also found to be independent of the presence of
insomnia symptoms.
A similar result was found by Spiegel and colleagues (Spiegel, et al., 1999). In their study
involving healthy young adults, they experimentally restricted sleep duration to 4 hours
per night (mean total sleep time = 3 hours, 49 minutes) for 6 nights and found that this
reduction in sleep duration caused impaired glucose tolerance. This sleep restriction
period was followed by seven nights of sleep recovery (mean total sleep time = 9 hours, 3
minutes). They also found that both glucose effectiveness, a measure of the effect of
glucose on its own disposal, independent of insulin dynamics, and the acute insulin
response to glucose, a measure of pancreatic -cell responsiveness, was 30% lower in the
sleep-debt period than after the sleep-recovery period, while they found no differences in
insulin sensitivity.
264
They speculate that, since the brain is an important site of non-insulin dependent glucose
uptake, the decrease observed in glucose effectiveness during the sleep deprivation period
could be associated with lower cerebral glucose uptake. In terms of the observed decrease
in acute insulin response to glucose, they speculate that this could be related to an
alteration in the importance of sympathetic (inhibitory) and parasympathetic
(stimulatory) control of pancreatic function.Their study showed estimates of
sympathovagal balance derived from heart rate variability analysis to be significantly
higher in the sleep-restriction condition than in the sleep recovery condition, indicating
increased sympathetic modulation and/or increased vagal function during the sleep
deprivation period.
Sleep and autonomic correlations
From the correlations between sleep and autonomic parameters, controlling for age and
adiposity only, we found sleep fragmentation (as measured by TAI) to be negatively
correlated with autonomic reactivity (as measured by the G
RCC
stand/supine ratio). This
indicates that decreased autonomic reactivity is related with increased sleep. This result is
also consistent with adult studies.
Narkiewics and colleagues (Narkiewicz, et al., 1998) observed that OSA subjects present
increased sympathetic nerve activity, reduced heart rate variability, and increased blood
pressure variance when compared to control subjects also during wakefulness, even in the
absence of hypertension, heart failure, or other disease states, and this may be linked to
the severity of OSA. Tamisier and colleagues (Tamisier, et al., 2011) observed sustained
265
activation of the sympathetic nervous system in subjects with obstructive sleep apnea,
and suggest that this could be due to increased excitatory influences and/or to decreased
sympathoinhibition. The discharge rate of muscle sympathetic nerve activity in awake
OSA patients has been shown to be about double that of healthy controls, independent of
obesity, and similar to that of patients with advanced heart failure (Leuenberger, et al.,
2001).
Autonomic and metabolic correlations
No measure of autonomic function was found to be directly correlated to any metabolic
parameter, when considering SBP as input to the ABR transfer function and analyzing the
results involving only baseline autonomic function and autonomic reactivity measures.
9.8.3. Multiple linear regression model: summary
Sleep and baseline autonomic function
No multiple linear regression model involving baseline autonomic function that was
statistically significant imply physiologically meaningful correlations.
Autonomic reactivity and insulin resistance
While there was no direct correlation found between any measure of autonomic function
and insulin resistance, when REM (% TST) is added as an additional control variable,
HOMA becomes positively correlated with G
RCC
ratio. In fact, when evaluating the
multiple linear regression model considering Y
aut
= log(G
RCC_stand/supine
), or G
RCC
ratio, as
the dependent variable and the explanatory variables X
sleep
= REM (% TST), X
met
=
HOMA or insulin resistance, X
age
and X
adiposity
, X
met
becomes positively correlated to G
RCC
266
ratio (X
sleep
was not found to be significantly correlated to G
RCC
ratio). In this case, both
REM (% TST) and either HOMA or fasting insulin need to be considered in order to
explain the variations observed in Y
aut
= log(G
RCC_stand/supine
).
This correlation is also significant when Y
met
= HOMA or fasting insulin are assumed to
be the dependent variable in the multiple linear regression, with X
aut
=
log(G
RCC_stand/supine
), X
sleep
= REM (% TST),X
age
, and X
adiposity
as the explanatory variables.
X
sleep
is also not found to be correlated to Y
met
= HOMA or fasting insulin in this model.
An increase in G
RCC
ratio means a decrease in autonomic reactivity to postural change. In
this case, higher levels of HOMA or fasting insulin are associated with less autonomic
reactivity to orthostatic stress, as measured by G
RCC
ratio, indicating vagal autonomic
reflex dysfunction, when controlling for age, adiposity, and REM (% TST).
REM sleep and sympathetic activation
During sleep, in particular during non-rapid eye movement (NREM) sleep, in healthy
subjects there is increased vagal activity and decreased sympathetic nervous system
activity, heart rate, cardiac output, and systemic vascular resistance. Since NREM sleep
accounts for approximately 85% of total sleep time, average blood pressure and heart rate
are lower than during wakefulness (Bradley, et al., 2003).
Obstructive sleep apnea subjects, however, do not present the normal decrease in average
arterial pressure during sleep usually observed in healthy subjects. Instead, they show
elevated sympathetic nerve activity (Leuenberger, et al., 2001), artery blood pressure
267
fluctuations, and increased heart rate (Leuenberger, et al., 2005; Bradley, et al., 2003)
related to the apnea. Somers and colleagues (Somers, et al., 1995) report that adult sleep
apnea patients showed significant increases in peak levels of blood pressure during stage
II sleep and REM sleep, with peak mean values higher than wakefulness. They also
showed that the sympathetic activity increased mainly during stage II and REM sleep,
when apnea severity and oxygen desaturation were greatest. They found no significant
correlations between sympathetic nerve activity (both during wakefulness and sleep) and
body mass index, apnea-hypopnea index, or blood pressure. Therefore, an increase in
REM (% TST) may be related to increased sympathetic activity observed in OSA
patients, even during wakefulness. This increased sympathetic activity observed in OSA
subjects could be related to a decreased arterial baroreflex control of sympathetic
outflow, as suggested by (Tamisier, et al., 2011).
Similarly, Reynolds and colleagues (Reynolds, et al., 2007) report that, independent of
AHI, the low frequency to high frequency ratio (LF/HF) of heart rate variability (HRV), a
measure of sympathovagal balance, was the only HRV measure to distinguish stage II
sleep, REM sleep, and wakefulness from each other. They found stage II sleep to have
the lowest LF/HF ratio, followed by wakefulness and then by REM sleep. This finding
reflects the relative sympathetic dominance of HRV in REM sleep in adult obese OSA
patients.
268
Autonomic reactivity, insulin resistance, and OSA severity
A similar result is observed between G
RCC
ratio and HOMA when controlling for
log(OAHI). In particular, when evaluating the multiple linear regression model
considering Y
aut
= log(G
RCC_stand/supine
), or G
RCC
ratio, as the dependent variable and the
explanatory variables X
sleep
= log(OAHI), X
met
= HOMA, X
age
and X
adiposity
, HOMA
becomes positively correlated to G
RCC
ratio (X
sleep
was not found to be significantly
correlated to Y
aut
= G
RCC
ratio). However, in this model the correlation between Y
aut
=
G
RCC
ratio and X
sleep
= log(OAHI), although not significant, implies that a decrease in
OSA severity, as measured by OAHI, is related to an increase in G
RCC
ratio, indicating
vagal autonomic reactivity impairment.
A more physiologically meaningful correlation between these same variables is obtained
when assuming Y
met
= HOMA to be the dependent variable in the multiple linear
regression, with X
aut
= log(G
RCC_stand/supine
), X
sleep
= log(OAHI),X
age
, and X
adiposity
as the
explanatory variables. Moreover, in this case, X
sleep
is also found to be significantly
correlated to Y
met
= HOMA.Both the positive correlation between OAHI and HOMA and
the positive correlation now present between G
RCC
ratio and HOMA, indicating decreased
vagal autonomic reactivity with increased insulin resistance as measured by the HOMA
index, seems more physiologically plausible. This indicates that both log(OAHI) and
G
RCC
ratio are necessary to determine HOMA.
This result also suggests that both OSA severity and autonomic reactivity dysfunction are
interrelated, since the correlations found are only significant when both are
269
simultaneously considered. Also, since variations in HOMA can only be meaningfully
explained by considering both OAHI and G
RCC
ratio, this seems to suggest that both sleep
and autonomic function are necessary to determine insulin resistance (HOMA), and not
the other way around.
Autonomic reactivity and fasting glucose
When considering Y
aut
= log(G
ABR_stand/supine
), or G
ABR
ratio, as the dependent variable and
X
sleep
= sleep efficiency (%), X
met
= fasting glucose, X
age
, and X
adiposity
, fasting glucose is
found to be positively correlated with G
ABR
ratio, but not with X
sleep
. Nevertheless, if X
sleep
is omitted from the equation, the significance is lost. However, this model implies a
positive, although not significant, correlation between G
ABR
ratio and sleep efficiency
(decreased autonomic reactivity with increased sleep efficiency), which does not seem to
be a meaningful description. On the other hand, when assuming the metabolic parameter
Y
met
= fasting glucose and the parametersX
aut
= G
ABR
ratio and X
sleep
= sleep efficiency
(%) as the dependent variables, fasting glucose is still significantly correlated to G
ABR
ratio, but now the negative correlation between sleep efficiency and fasting glucose
makes more sense physiologically (decreased sleep efficiency related to increased fasting
glucose).
The G
ABR
gain is a measure of baroreflex gain and is such that a decrease in G
ABR
is
related to a decrease in vagal modulation, an increase in sympathetic modulation, or both.
When comparing baseline G
ABR
gain and the same gain in the standing posture, the
normal reaction would be to observe a decrease in G
ABR
gain from supine to standing,
270
indicating a decreased vagal modulation and/or an increased sympathetic modulation
related to the change in posture from supine to standing. The greater the decrease in
standing gain when compared to baseline, the larger the reactivity to change in posture,
and, consequently, the smaller the G
ABR
ratio. Thus, a larger G
ABR
ratio related to
increased fasting glucose suggests less change in gain from supine to standing. This is an
indication of impaired baroreflex reactivity to change in posture associated with higher
fasting plasma glucose levels, when controlling for age, adiposity, and sleep efficiency.
9.8.4. PTT as input
The diagram in Figure 38 includes only those autonomic parameters determined using
PTT as input to the ABR transfer function.
Figure 38: Diagram showing the associations found in our present group of subjects
OSA
Intermittent
Hypoxia
Sleep
Fragmentation
(TAI)
SI
Fast. insulin
HOMA
Baseline autonomic function
(ABR
HF supine PTT
)
Autonomic reactivity
( G
RCC stand/supine PTT
)
Total sleep
time
OSA severity
(OAHI)
Sleep
efficiency
Sg
Autonomic reactivity
( ABR
HF stand/supine PTT
)
DI
271
When PTT is used as input to the ABR transfer function, baseline autonomic function, as
measured by the high frequency component of the ABR gain (ABR
HF supine PTT
), is found
to be negatively correlated with the desaturation index, when adjusting for age and either
total % body fat or trunk % fat. This seems to indicate that an increased intermittent
hypoxia is correlated with a decreased baseline baroreceptor mediated vagal modulation.
Vagal autonomic reactivity to postural stress, as measured by the G
RCC
stand/supine ratio,
determined from PTT measurements, is significantly correlated to sleep fragmentation
(TAI) and total sleep time, when adjusting for age and adiposity. The correlation with
total sleep time is still significant for the multiple linear regression model considering the
autonomic reactivity measure as the dependent variable and age, adiposity, and any
metabolic measure as the independent or explanatory variables. This seems to indicate
that total sleep time is not correlated with any metabolic parameter. This also indicates
that the correlation between vagal autonomic reactivity and total sleep time is
independent of metabolic function.
As with the results obtained using SBP, no autonomic reactivity measure (stand/supine
ratios) determined from PTT is found to be significantly correlated with any metabolic
parameter when adjusting for age and adiposity only.
Nevertheless, the high frequency component of the baroreceptor reactivity, measured as
ABR
HF stand/supine PTT
, is significantly correlated with the disposition index DI when
adjusting for age, adiposity, and sleep efficiency. In this case, the multiple linear
regression models assuming either the metabolic or the autonomic parameter as the
272
dependent variable were found to be equally probable, with equivalent statistical power.
Sleep efficiency was not correlated with either the autonomic or the metabolic
parameters.
The positive correlation found between ABR
HF stand/supine PTT
and log(DI) indicates that
increased levels of insulin secretion as a response to insulin resistance is associated with
decreased baroreceptor mediated vagal reactivity to change in posture, indicating
autonomic reactivity control impairement.
Baseline autonomic function, as measured by the high frequency component of the ABR
gain (ABR
HF supine PTT
), is significantly correlated to sleep efficiency when adjusting for
age, adiposity, and the disposition index DI. The disposition index is not correlated with
the autonomic variable. Considering these same variables but assuming DI as the
dependent variable, no significant correlation is found. This may indicate that both sleep
efficiency and the disposition index are important in determining the high frequency
component of baseline baroreceptor function, and not the other way around.
9.9. Conclusion
Baseline autonomic function and autonomic reactivity to orthostatic stress were not
directly correlated to insulin sensitivity or any other measure of insulin resistance,
contrary to initial expectations. However, autonomic reactivity was found to be correlated
with HOMA when OSA severity (log(OAI)) is also taken into consideration. In this case,
both autonomic reactivity and OSA severity were correlated with HOMA, a surrogate
measure of insulin resistance. Fasting insulin levels were found to be significantly
273
correlated to autonomic reactivity, when controlling for age, adiposity, and REM (%
TST).
For this sample of patients, no measure of OSA severity seems to directly influence
baseline autonomic function determined using SBP as input. For baseline autonomic
function determined from PTT, the high frequency component of the baroreflex response
(ABR
HF supine PTT
) is negatively correlated to the desaturation index, indicating decreased
baroreceptor mediated vagal modulation with increased desaturation. Exposure to
intermittent hypoxia (desaturation index), in turn, is correlated to decreased insulin
sensitivity, while sleep fragmentation (TAI) is associated to increased insulin resistance
(HOMA index) and increased fasting insulin levels. Sleep fragmentation is also
associated with decreased autonomic reactivity (G
RCC_stand/supine
) to orthostatic tress,
indicating impaired vagal withdrawal associated with change in posture. Considering
autonomic reactivity variables determined from PTT measurements, a decrease in total
sleep time is associated with a decrease in vagal autonomic reactivity
(G
RCC_stand/supine_PTT
), which also suggests impaired vagal withdrawal reflex to orthostatic
stress.
Baseline autonomic function, as measured by ABR
HF supine PTT
, was positively correlated
with sleep efficiency, when adjusting for age, adiposity, and the disposition index DI.
This indicates a decrease in baroreceptor mediated vagal tone with decresed sleep
efficiency, when age, adiposity, and increased insulin secretion to compensate for insulin
resistance (DI) are taken into consideration. The disposition index was not correlated
274
with either the autonomic measure or to sleep efficiency. Nevertheless, the disposition
index is found to be positively correlated with the high frequency component of the
arterial baroreflex stand/supine ratio determined from PTT, when adjusting for age,
adiposity, and sleep efficiency. Since an increased ratio is related to a decreased
reactivity, this suggests decreased baroreceptor mediated vagal reactivity to orthostatic
stress with increased insulin secretion, as a compensatory mechanism to insulin
resistance, when age, adiposity, and sleep efficiency are adjusted for.
Elevated fasting glucose levels were found to be correlated with smaller autonomic
adjustments to postural change (or, equivalently, larger G
ABR
ratios) when controlling for
age, adiposity, and sleep efficiency, indicating impaired autonomic reactivity.
The combined results suggest that insulin resistance is related not only to intermittent
hypoxia (high desaturation index), by decreased insulin sensitivity, and sleep
fragmentation (high TAI), by increasing HOMA, that accompany OSA, but also to
increased OSA severity when accompanied by autonomic dysfunction (decreased vagal
withdrawal reflex to orthostatic stress). Autonomic dysfunction appears to stem primarily
from sleep fragmentation (high TAI) that accompanies OSA. These results suggest that
both sleep apnea and autonomic dysfunction contribute to insulin resistance in our study
population.
Baroreflex reactivity dysfunction, as measured by G
ABR
ratio, which may be related to
higher levels of baseline sympathetic modulation, further contributes to metabolic
275
dysfunction by increased fasting glucose levels, when considered simultaneously with
sleep efficiency.
In conclusion, from these results it can be speculated that sleep apnea has both a direct
effect on insulin resistance (desaturation index directly correlates to insulin sensitivity
and TAI directly correlates to the HOMA index), as well as an indirect effect, through
autonomic dysfunction (in this case, insulin resistance is measured by the HOMA index).
An additional speculation is that increased levels of baseline sympathetic modulation
related to decreased sleep efficiency further contribute to metabolic dysfunction by
increased fasting glucose levels, through sympathetically induced glycogen breakdown
and gluconeogenesis.
9.10. Future directions
The discussions in this dissertation were based on autonomic parameters determined by
using the minimal model of cardiorespiratory control, which is a means to more
specifically delineate the mechanisms responsible for the observed heart rate variabilities.
This study focused on evaluating the influence of oscillations in respiration (RCC gain)
and blood pressure (ABR gain) on heart rate variability, in both baseline conditions and as
a response to orthostatic stress. Nevertheless, it would be interesting to compare the
results obtained using the minimal model with more conventional measures of heart rate
variability, in the same conditions.
It would also be interesting to analyze the cold face data, which was gathered in the
autonomic test but not analyzed in this study. The cold face test measures stimulation of
276
both the sympathetic and vagal systems. This would require the definition of autonomic
markers to quantify the response to the cold face test, in order to investigate the
relationships among these autonomic markers, OSA indices, and metabolic function.
277
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Abstract (if available)
Abstract
The current evidence in adults suggests that, independent of obesity, obstructive sleep apnea (OSA) can lead to both autonomic dysfunction and impaired glucose metabolism. These relationships have been less well studied in children. Since sleep-disordered breathing occurs in over 13% of the obese pediatric population, knowledge about the autonomic and metabolic effects of OSA is crucial in determining the importance of OSA as an independent factor in promoting the development of childhood metabolic syndrome. The hypothesis in this study is that OSA severity in overweight/obese children is associated with both autonomic abnormality and insulin resistance. This study will also investigate if there is a direct association between autonomic dysfunction and insulin resistance. ❧ To evaluate this hypothesis, overnight polysomnographic studies and tests of metabolic and autonomic function were conducted in 22 obese male subjects (age: 13.4 ± 2.1 years (mean ± SD), BMI>95% for age) with varying degrees of OSA severity (obstructive apnea-hypopnea index (OAHI): 1-14.1 events/h
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Asset Metadata
Creator
Oliveira, Flavia Maria Guerra de Sousa Aranha
(author)
Core Title
Autonomic and metabolic effects of obstructive sleep apnea in childhood obesity
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Biomedical Engineering
Publication Date
07/22/2011
Defense Date
06/16/2011
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
autonomic nervous system,cardiorespiratory minimal model,childhood obesity,insulin resistance,OAI-PMH Harvest,obstructive sleep apnea,sleep disordered breathing
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Khoo, Michael C.K. (
committee chair
), D’Argenio, David Z. (
committee member
), Keens, Thomas G. (
committee member
), Ward, Sally L. Davidson (
committee member
)
Creator Email
flavia.sousa.aranha@gmail.com,foliveir@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c127-642197
Unique identifier
UC1349379
Identifier
usctheses-c127-642197 (legacy record id)
Legacy Identifier
etd-OliveiraFl-157-0.pdf
Dmrecord
642197
Document Type
Dissertation
Rights
Oliveira, Flavia Maria Guerra de Sousa Aranha
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Repository Email
cisadmin@lib.usc.edu
Tags
autonomic nervous system
cardiorespiratory minimal model
childhood obesity
insulin resistance
obstructive sleep apnea
sleep disordered breathing