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Model-based phenotyping of obstructive sleep apnea in overweight adolescents for personalized theranostics

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Model-based phenotyping of obstructive sleep apnea in overweight adolescents for personalized theranostics

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Content MODEL-BASED PHENOTYPING OF OBSTRUCTIVE SLEEP
APNEA IN OVERWEIGHT ADOLESCENTS FOR
PERSONALIZED THERANOSTICS
by
Leonardo Nava-Guerra
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BIOMEDICAL ENGINEERING)
May, 2018.

Acknowledgments
I am very thankful to several people who have contributed, either directly or indirectly, to the completion of
my doctoral studies. First and foremost, I wish to thank my parents for their constant support throughout
all these years. Thanks for always creating a loving environment at home and for providing the conditions
for my sister and I to accomplish all of our goals. I am very grateful for being raised in a home with examples
of honesty, humbleness, integrity, perseverance and hard work; those values made me who I am and they
certainly also helped me get to where I am today. In addition, I would like to thank my dear sister and
partner in crime Gabriela Nava Guerra for all the great advice she gave me while I was growing up and
for the memories we have together. Thank you for always checking on me through Facetime while I was
studying abroad, despite the distance you always felt very close to me. Thank you for coming to visit me
in Los Angeles in company of my brother in law Julio Guerrero Pena and my lovely nephew (and godson)
Braulio Guerrero Nava, you all helped creating incredibly amazing new memories.
I am also very grateful to all of my family and friends in Mexico for keeping track of my progress during
my PhD and for your continuous motivation and support. Special thanks go to my late grandfather Rafael
Nava Venegas for being an important part of my education while I was growing up. I want to thank him
for his constant encouragement, which pushed me (and all of his grandchildren) to do well in school and to
excel in what we do. Unfortunately, he is no longer physically among us to witness the end of this journey,
but I am pretty sure that he is around. It is to him that I want to dedicate this dissertation.
I consider myself very lucky to have come across Alejandra Gonzalez Calle while taking some biomedical
engineering classes. I would like to express my sincere gratitude for all her love, support, encouragement
i
and for always being there for me. Thanks for bearing and sharing with me those very stressful moments of
grad school. Also, thanks for patiently listening to all those rehearsal oral presentations and for the provided
feedback, it was critical to the ne tuning of all the materials I presented. Thanks for being a great travel
partner, especially when we attended the IEEE EMBC conferences to present our work, they were certainly
unforgettable experiences. In general, I wish to thank her for being an awesome life companion.
Throughout all these years, I made several friends who made the experience of being away from home a
lot easier and fun. To avoid leaving someone out, I would like to thank you all for all those beach days, road
trips, movie nights, sports we played together, Korean barbecues, etc. Special thanks go to Juan Enrique
Arguelles Morales for being a great roommate but more importantly for his unconditional friendship.
I am deeply indebted to my adviser Dr. Michael C. K. Khoo for believing in me and giving me the
opportunity to join his lab and undertake this research. His patient guidance, encouragement, accessibility
and prompt responsiveness to concerns and questions are denitely an example to me. Also, the care that he
provides to his students go above and beyond one's expectations. His nancial support was critical for me to
complete this work in a timely manner. His support was not only nancial but also academic, providing his
students with great opportunities to present our research at national and international conferences, which
have resulted in great networking experiences and sometimes even collaborations. His support continues
even to date, when I am starting to look for future opportunities by introducing me to people that are part
of his large network and that may be a good t for my research interests. I truly hope we can continue to
collaborate in future projects.
I also must express my gratitude to my dissertation committee members for the supervision and direction
that was provided to my work. Thanks to Dr. Sally L. Davidson Ward and Dr. Thomas G. Keens from
Children's Hospital Los Angeles for their insights related to respiratory physiology and the pathophysiology
of sleep disordered breathing. I would also like to thank Dr. Vasilis Z. Marmarelis and Dr. Krishna S. Nayak
for the great feedback and enlightening discussions regarding the modeling aspects of my project.
I would be remiss if I did not acknowledge the Department of Biomedical Engineering Department at
USC for its excellence in terms of research and teaching. I am grateful for all of the activities that were
ii
organized by students in order to encourage networking within and outside the department such as the annual
Grodins symposium, corporate dinners and other social gatherings. Special thanks go to our graduate adviser
Mischalgrace Diasanta, not only for her invaluable counseling and advice when dealing with administrative
matters, but also for her friendship and great music recommendations.
I wish to thank all the members of the Cardiorespiratory Sleep Lab for all the casual conversations we
had during our in-lab lunches, and also for those more serious ones that were work related. I really want to
thank you all for creating a nice and fun environment to work in. Special thanks go to Winston Tran for
his exceptional work at implementing the setup that was used to carry out our experimental sleep studies
and also for training me to run them. Additionally, I wish to thank Sang for developing some of the signal
visualization and processing tools that I used to analyze my data and also for helping me understanding
some hard concepts of biomedical signal analysis and mathematical modeling. Also, I would like to thank
Toey for aiding in the development of data processing tools as well as for performing part of the signal
processing of our study. Lastly, big thanks to my oce mate and friend, John F. Sunwoo, for all of the great
discussions we had when sharing our research results; for the great advice related to statistical analyses; for
the valuable feedback provided to my work; and, more importantly, for the extraordinary eorts to organize
fun lab activities like dinners, pot lucks, bowling, etc.
Since a large part of my project involved a clinical aspect, I had the opportunity to closely work with people
from the Children's Hospital of Los Angeles. This invaluable experience made me realize the importance of
the interactions between biomedical engineers and medical doctors in order to tackle health-related problems.
I wish to express my gratitude to the study coordinators and the sleep medicine fellows for their participation
in the recruitment, screening and consent of our research subjects; as well as for sharing information when
needed. Special thanks go to Dr. Emily Gillett for carrying out the analyses on the clinical data in a timely
manner and also for her great contributions to our manuscripts. Moreover, I would like to thank all of the
sleep technicians who helped running our experimental sleep studies, especially to Brian Meehan and Aaron
Bernardo for their professionalism at looking after the integrity of the recordings and also for making those
sleepless data collection nights less tedious.
iii
A person who was key for me to come to USC, thus deserving my complete gratitude, was Dr. Francisco
Valero-Cuevas. His eorts of having more Mexican students pursuing graduate studies in the US resulted in
an incredible Summer research internship program at USC. This program gave me the opportunity to meet
Dr. Khoo and exposed me for the rst time to the research that is carried out at the Cardiorespiratory Sleep
Lab. I hope this amazing Summer research internship program continues to bring more and more talented
students from Mexico to show their capabilities. Also, I would like to thank Dr. Angela McCracken, the
representative of USC in Mexico, for all the support that she provided since I rst started the grad school
application process, and for her help that continues to date with my postgraduate applications.
Also, none of this would have been possible without the funding sources that supported me. First, I wish
to thank the National Council of Science and Technology (CONACyT) for serving as a leverage for Mexican
young professionals to continue their training. I am especially grateful for being selected as a recipient of
the prestigious USC-CONACyT fellowship. Second, I want to thank the National Institute of Health (NIH)
for its commitment into the advancement of science to enhance health by improving current diagnostic,
preventive and treatment strategies of human diseases. Your continuous support provided the means for our
group to successfully carry out this research. Lastly, I would also like to thank the Biomedical Simulations
Resource (BMSR) for the provided funds towards the end of my stay at USC and for sponsoring amazing
events at the IEEE EMBC conference that I was lucky to be a part of.
iv
Contents
Acknowledgments i
Contents v
List of Tables x
List of Figures xiii
Abstract xxii
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Adult vs. pediatric obstructive sleep apnea . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Poor eciency and adherence to current treatment strategies in children . . . . . . . . 3
1.1.3 Complement current OSA diagnostic tools . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.4 Personalized therapy design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Specic aims and objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Document organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Literature review. Anatomy, physiology and pathophysiology of the respiratory and
sleep regulation systems. 8
2.1 Respiratory system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
v
2.1.1 Anatomy and morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.2 Gas exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.3 Ventilatory control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Sleep system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Sleep architecture and associated physiological changes . . . . . . . . . . . . . . . . . 16
2.2.2 Sleep-wake regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Eects of sleep on respiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Sleep-related breathing disorders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.6 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.7 Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 Model-based stability assessment of ventilatory control in overweight adolescents with
obstructive sleep apnea during NREM sleep 27
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Experimental methods and data preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1 Experimental methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1.1 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1.2 Standard polysomnography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1.3 Pulmonary function test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1.4 Experimental polysomnography . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.2 Data preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.2.1 Sleep state monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.2.2 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Mathematical modeling and stability feature extraction . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 Mathematical modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.1.1 Volterra series and basis expansion technique . . . . . . . . . . . . . . . . . . 42
vi
3.3.1.2 Meixner basis functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3.1.3 Model formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3.1.3.1 Gas exchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3.1.3.2 Chemore
ex loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.3.1.4 Model selection criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.3.2.1 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.2.1.1 Parallel coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3.3 Stability feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.3.1 Plant, controller and loop gain . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3.3.2 Relative stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.3.4 Statistical analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4.1.1 Robustness to noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4.1.2 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.4.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4.2.1 Induced sighs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.4.2.2 No intervention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4.2.3 Relative stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.4.2.4 Stability feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.4.2.5 Correlation of stability parameters with OSA severity . . . . . . . . . . . . . 78
3.4.2.6 Eects of gender and NREM sleep stage on ventilatory control stability . . . 81
3.4.2.6.1 Gender . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.4.2.6.2 NREM Sleep stages . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
vii
3.5.1 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.5.2 Physiological interpretation of experimental models . . . . . . . . . . . . . . . . . . . . 87
3.5.3 Stability markers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.5.4 Correlation analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.5.5 Eects of gender and NREM sleep stages on stability quantiers . . . . . . . . . . . . 95
3.5.5.1 Gender . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.5.5.2 NREM sleep stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.5.6 Methodological considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4 Model-based phenotyping of obstructive sleep apnea in overweight adolescents for per-
sonalized theranostics 101
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.2.1 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.2.2 Standard polysomnography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.2.3 Pulmonary function test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.2.4 Experimental polysomnography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.2.5 Upper airway collapsibility determination . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.2.6 Ventilatory control stability quantication . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.2.7 Arousal components extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.2.8 Classication model incorporating all traits . . . . . . . . . . . . . . . . . . . . . . . . 113
4.2.8.1 Cross-validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.2.9 Statistical analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.3.1 Upper airway collapsibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.3.2 Ventilatory control stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
viii
4.3.3 Arousal components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.3.4 Classication model incorporating all traits . . . . . . . . . . . . . . . . . . . . . . . . 122
4.3.4.1 Cross-validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.4.1 Upper airway anatomy and collapsibility . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.4.2 Pulmonary function test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.4.3 Ventilatory control stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.4.4 Arousal components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.4.5 Classication model incorporating all traits . . . . . . . . . . . . . . . . . . . . . . . . 140
4.4.6 Design of therapeutic strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
4.4.7 Methodological considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.4.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5 Conclusions 150
6 Future Work 154
6.1 Estimation of other OSA traits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.2 Sleep-state eects on OSA traits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.3 Adaptive estimation of OSA traits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.4 Experimentally-derived personalized models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
6.5 Prescribing the subjects with the therapies predicted by the model . . . . . . . . . . . . . . . 158
Bibliography 159
ix
List of Tables
1.1 Comparison of the obstructive sleep apnea snydrome in children versus adults. CPAP, Con-
tinuous Positive Airway Pressure; REM, Rapid Eye Movement; T&A, Tonsillectomy and
adenoidectomy; UVPP, uvulopharyngopalatoplasty. Table adopted from Marcus (2001). . . . 3
2.1 Behavioral and physiological characteristics of the main sleep-wake states. Note that NREM
encompasses all of the 4 sleep stages. Adopted from Phillipson (1978) and Asyali (1998). . . . 17
2.2 Summary of costs related to sleep disorders in Australia. Note that costs are presented in
2004 US dollars. Adopted from AlGhanim et al. (2008). . . . . . . . . . . . . . . . . . . . . . 24
3.1 Subject pool anthropometric and polysomnographic characteristics. BMI, body mass index;
OAHI, obstructive apnea hypopnea index; CPAP, continuous positive airway pressure. *
indicates that there is one missing value. ** indicates that there are two missing values.
Values are presented as mean SD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Subject pool pulmonary function test measurements. FRC, functional residual capacity; FVC,
forced vital capacity; FEV1, forced expired volume in one second; FEF 25/75, forced expira-
tory
ow between 25% and 75% of FVC; PEF, peak expiratory
ow; Vmax 80%, percentage
of FVC remaining. Values are presented as means SEM. * Missing data from six subjects.
** Missing data from seven subjects.yy indicates that the results are statistically signicantly
dierent between the groups at p 0.05. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
x
3.3 Description of frequency content of the EEG signal and its interpretation in sleep analysis.
The frequency ranges that are dened herein are not standard and could be slightly dierent
to some other conventions found in the literature. N1-N3 denote the multiple sleep stages in
accordance with the notation proposed by the American Academy of Sleep Medicine (Iber,
2007). Table adapted from Asyali et al. (2007). . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.4 Nominal values of the parameters used for data generation. Values were adopted from previous
studies (Bellville et al., 1979; Khoo, 2000b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.5 Summary of the model-derived stability markers comparison between the non-OSA and OSA
groups. Variables are presented as mean SEM. * indicates that for Plant Gain the sample
size was dierent (non-OSA = 22 and OSA = 23).x is used to highlight the variables that did
not pass the normality test and required the application of a nonparametric statistical test.
y indicates that the results are marginally signicantly dierent between the groups with 0.1
> p > 0.05. yy indicates that the results are statistically signicantly dierent between the
groups at p 0.05. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.6 Correlation analysis between the model-derived stability markers and OSA severity measured
by the amount of obstructive apnea/hypopnea vents per hour of sleep. The symbolx indicates
that the variable was log-transformed to pass normality prior to the correlation analysis. y
indicates that the variables were marginally signicantly associated with 0.1 > p > 0.05. yy
indicates that the variables were signicantly associated at p 0.05. . . . . . . . . . . . . . . 81
3.7 Contingency table showing the distribution of males and females within our non-OSA and OSA
groups. A statistically signicant interaction was found between gender and the presence of
OSA (
2
(1) = 4.677 ; p = 0.031). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
xi
3.8 Contingency table showing the frequency distribution of the sleep stages of the induced sighs
segments measured on a total of 38 subjects (19 non-OSA and 19 OSA). Note that each induced
sighs segment was considered to be coming from a dierent non-OSA and OSA subject in this
case. No signicant interaction was found between the frequency of NREM2 and NREM3 and
the presence of OSA (
2
(1) = 0.132 ; p = 0.715). . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.1 Summary of population demographics and OSA traits. BMI, body mass index; OAHI, ob-
structive apnea hypopnea index; FRC, functional residual capacity; FVC, forced vital capac-
ity; FRC Pleth, forced residual capacity measured by plethysmography; FEV1, forced expired
volume in one second; FEF 25/75, forced expiratory
ow between 25% and 75% of FVC;
PEF, peak expiratory
ow; Vmax 80%, percentage of FVC remaining; FRC Upright N2 and
FRC Supine N2, functional residual capacity measured in the upright and positions using
the nitrogen washout technique. x is used to highlight the variables that did not pass the
normality test and required the application of a nonparametric statistical test. y indicates
that the results are marginally signicantly dierent between the groups with 0.1 > p> 0.05.
yy indicates that the results are statistically signicantly dierent between the groups at p
0.05. Correlation analyses using the nonparametric Spearman correlation on ranks were
carried out between the variables and OAHI. * indicates that there is a marginally signicant
association. ** indicates that there is a statistically signicant association between the variables.124
4.2 Inter-rater agreement statistical test summary for the dierent number of traits considered in
the classication process.yy indicates that the classication agreement between our method-
ology and the polysomnography is statistically signicant at p 0.05. . . . . . . . . . . . . . 127
4.3 Out-of-sample predictive accuracy of the classier with the for the four dierent cross-validation
schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
xii
List of Figures
2.1 Anatomical changes occurring in the thoracic cavity associated with the inspiratory and ex-
piratory phases of respiration. Adopted from Britannica (2016). . . . . . . . . . . . . . . . . . 9
2.2 Schematic of the cardiovascular and respiratory interactions that allow the oxygen to reach
the cells and tissues and the carbon dioxide to be expelled out of the body. Figures extracted
from Germann and Staneld (2002). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Parasagital slice of the lower brainstem of a rodent showing the location and projection of
the RTN neurons and the regions participating in the breathing pattern generation. Adapted
from Guyenet et al. (2012). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Schematic of the elements that participate in the control of respiration during sleep. . . . . . 15
2.5 Schematics showing the key components and neuronal projections of the sleep and wake-
generating systems. Adopted from Saper et al. (2005). . . . . . . . . . . . . . . . . . . . . . . 18
2.6 Schematic showing how the neural implant provides a stimulation pattern to the hypoglossal
nerve based on the respiratory activity measured at the intercoastal muscles. Adapted from
Strollo Jr et al. (2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1 Schematic of the full body plethysmography and spirometry tests that are part of the pul-
monary function test along with sample measurements that are obtained from various maneu-
vers. Figure adapted from Siberry and Iannone (2000). . . . . . . . . . . . . . . . . . . . . . . 33
xiii
3.2 A. Schematic of the breathing circuit and the integrated control and data acquisition system
utilized for protocol execution. B. Picture of the experimental setup taken on a subject who
participated in the study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 Sample induced sighs recording that resulted in arousal. The top panel shows a forty second
window of the continuous recording of EEG activity that includes the region were the arousal
was detected. The second panel depicts, in the form of a heat map, the normalized power
spectrum of the EEG recording as a function of time. Note that the frequency axis has been
limited to the frequencies that are relevant in sleep analysis. The lower three panels show the
continuous measurements of pressure, air
ow and PCO
2
, respectively. The arrow indicates
the portions of these measurements that are discarded from our analysis. . . . . . . . . . . . . 38
3.4 Breath-by-breath derivation of ventilatory time series from the continuous recording of air
ow. 40
3.5 Breath-by-breath derivation of P
ET
CO
2
time series from the continuous recordings of air
ow
and PCO
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.6 Graphical representation of the expansion of the impulse response function as a weighted sum
of Meixner basis functions. In this example the memory of impulse response of the system M
was selected to be 100 seconds and was expanded using a total of basis functions Q = 4. . . . 44
3.7 Cascaded lter structure used to generate the Laguerre and the Meixner set of basis functions.
Figure was adopted from Asyali and Juusola (2005). . . . . . . . . . . . . . . . . . . . . . . . 45
3.8 Generated Meixner basis functions of memory M = 100 lags and for n = 0; 2; 4; 6 and Q =
3; 4; 5; 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.9 Simulation discrete model used to emulate the experimental interventions and generate the
articial data segments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
xiv
3.10 Data characterization and visualization framework for multi-dimensional sensitivity analysis
using parallel coordinates. Values of each parameter are represented on the corresponding
vertical axes and each line connecting the n parameter values represent a single parameter
set. Note that all of the sampling parameter ranges have been normalized to the [0,1] range
to facilitate visualization and system's behavior comparison for the multiple parameter sets.
Adapted from Nguyen et al. (2015). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.11 Parallel coordinates used to summarize an all-at-a-time sensitivity analysis of the stability
characteristics of the feedback dynamic system presented in Section 3.3.2. Note that while in
the top panel the outcome variable is dichotomous, in the bottom panel the outcome variable
is given by a continuous variable. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.12 Schematic of the Nyquist stability criterion and relative stability parameter denition. The
dashed circle with a unity radius delimits the stability boundaries on the complex plane with
Im andRe representing the imaginary and real axes. LG(e
j!T
), loop gain taking values of up
to half of the sampling frequency; T , sampling period;PM, phase margin;GM, gain margin;
!
pc
, phase crossover frequency; !
gc
, phase crossover gain. . . . . . . . . . . . . . . . . . . . . 57
3.14 Schematic showing the feedback conguration that was utilized iteratively to search for the
relative stability parametersGM and!
pc
. The open loop impulse response functionLG(m
D) is an actual estimation from a subject from the induced sighs protocol. . . . . . . . . . . . 60
3.15 Simulation example of the induced sigh protocol for dierent levels of noise around a nominal
value. The noise realizations followed a gaussian distribution with zero mean. Results are
shown for dierent noise variances: 0.5 L
2
min
-2
(A), 1 L
2
min
-2
(B) and 1.5 L
2
min
-2
(C).
The estimated impulse response and dynamic loop gain are presented as mean SD over 100
trials with dierent noise realizations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
xv
3.16 Sample of the simulated no intervention protocol for three dierent levels of noise present in
the data. Noise realizations followed a Gaussian distribution with zero mean. Results are
shown for dierent noise variances in ventilation and P
ET
CO
2
: 0.5 L
2
min
-2
, 0.25 mmHg
2
(A); 1 L
2
min
-2
, 0.5 mmHg
2
(B); and 1.5 L
2
min
-2
, 0.75 mmHg
2
(C). The estimated impulse
response and dynamic plant gain are presented as mean SD over 100 trials with dierent
noise realizations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.17 One-at-a-time (A), Two-at-a-time (B) and All-at-a-time (C) sensitivity analyses of the per-
cent error between the estimated and the theoretical loop gain within the periodic breathing
frequency band. In A and B, each data point represents the ensemble average over 100 trials
with dierent noise realizations but with constant statistics. In C, each line connects all the
elements of the parameter set that was used to generate the multiple data sets with color
representing the average percent error over 100 trials as well. Note that the ranges over which
the parameters were varied are presented on top of the gure. . . . . . . . . . . . . . . . . . . 66
3.18 All-at-a-time sensitivity analysis performed on the percent error of the estimated plant gain
from the simulated spontaneous breathing protocol. Each line connects all the elements of
the parameter set that was used to generate the multiple data sets with color representing the
average percent error over 100 trials with dierent noise realizations. Note that the ranges
over which the parameters were varied are presented on top of the gure. . . . . . . . . . . . 67
3.19 Sample induced sighs recording. The top two panels represent the continuous recordings of
pressure and air
ow. The bottom three panels depict the derived breath by breath measure-
ments of tidal volume, ventilatory drive and P
ET
CO
2
, respectively. Note that the bottom-
most panel also shows the continuous recording ofPCO
2
from which the end-tidal values were
derived. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
xvi
3.20 Sample results obtained from the induced sighs protocol on a non-OSA subject (top panels)
and an OSA patient (bottom panels). Column A shows the measured responses to the sighs
in addition to the predictions provided by the estimated models. Column B shows the corre-
sponding estimated impulse responses. Column C depicts the associated frequency responses. 70
3.21 Average loop impulse responses (A) and dynamic loop gains (B) of the non-OSA and OSA
groups. Median responses in the time and frequency domains were used to represent each
individual and were obtained from the multiple induced sighs that were performed per exper-
imental sleep study. The mean and variability of both responses were computed at each point
to obtain a representation of the group. Results are displayed as mean SEM. . . . . . . . . 71
3.22 Sample no intervention recording. The top two panels represent the continuous recordings
of pressure and air
ow. The bottom three panels depict the derived breath by breath mea-
surements of tidal volume, ventilation andP
ET
CO
2
, respectively. Note that the bottom-most
panel also shows the continuous recording of PCO
2
from which the end-tidal values were
derived. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.23 Sample results obtained from the no intervention protocol on a non-OSA subject (top panels)
and an OSA patient (bottom panels). Columns A and B show breath-to-breath ventilation
and P
ET
CO
2
with the corresponding model predictions, respectively. Column C depicts the
estimated impulse responses and D the associated frequency responses of the estimated models. 74
3.24 Average plant impulse responses (A) and dynamic plant gains (B) of the non-OSA and OSA
groups. The mean and variability of both responses were computed at each point to obtain a
representation of the group. Results are displayed as mean SEM. . . . . . . . . . . . . . . . 75
3.25 Relative stability analysis comparison between a non-OSA and an OSA individual. Simulation
results show that the OSA subject requires the incorporation of more feedback gaink in order
to exhibit self-sustained oscillations as compared to its OSA counterpart. . . . . . . . . . . . 77
xvii
3.26 Model-derived stability markers comparison between the non-OSA and OSA groups. Vari-
ables are presented as mean SEM.y indicates that the results are marginally signicantly
dierent between the groups with 0.1> p> 0.05.yy indicates that the results are statistically
signicantly dierent between the groups at p 0.05. . . . . . . . . . . . . . . . . . . . . . . 79
3.27 Correlation plots of the signicant associations between the model-derived stability parameters
and OSA severity represented by the OAHI. Note that the OAHI was log-transformed prior
to the correlation analysis and is plotted in logarithmic scale. . . . . . . . . . . . . . . . . . . 81
3.28 Two way analysis of variance results that permit the interaction between phenotype and
gender. Controller gain (A), loop gain evaluated at the phase crossover frequency (B) and
gain margin (C). Results are presented as mean SEM. Note that controller gain and gain
margin were log-transformed prior to statistical testing.yy indicates that the mean values of
the variables were found to be statistically signicantly dierent among the two phenotypes
after allowing for the gender dierences at p 0.05. . . . . . . . . . . . . . . . . . . . . . . . 83
3.29 Two-way repeated measures ANOVA results for the log-transformed loop gain and phase
crossover frequency. Results are presented as mean SEM. ** indicates that the interaction
term of sleep-stagephenotype is statistically signicant.yy indicates that the main eect of
sleep stage was found to be statistically signicantly dierent after allowing for phentotypic
dierences. In both cases statistical signicance was set at p 0.05. . . . . . . . . . . . . . . 85
4.1 Left. Schematic of the breathing circuit and the integrated control and data acquisition system
that was utilized for protocol execution. Right. Sample recordings of the main physiological
measurements that were used for the extraction of the physiological traits. . . . . . . . . . . . 107
4.2 A. Sample continuous recordings of pressure and air
ow during the intermittent CPAP drops
protocol. Shaded areas correspond to the instances where CPAP pressure was lowered to the
various subtherapeutic levels. B. Scatter plot of peak inspiratory
ow and mask pressure for
the
ow limited breaths along with the results from the linear regression analysis that lead to
the extraction of the upper airway collapsibility features. . . . . . . . . . . . . . . . . . . . . . 109
xviii
4.3 A. Sample measurements of pressure (top) and air
ow (bottom) throughout the induced sighs
intervention. The shaded area indicates the time during which the hyperventilatory sighs are
being provoked. B. Corresponding breath-by-breath ventilatory drive measurement (solid)
and prediction provided by the optimal model (dashed). . . . . . . . . . . . . . . . . . . . . . 111
4.4 A. Sample continuous recording of brain activity by means of the EEG (top panel), pressure
(middle panel) and air
ow. B. Zoom in to the pressure panel during the application of the
occlusion. The time of arousal is represented by the vertical dashed line and is used as
a reference to extract the two components of the arousal mechanism. Note that both the
arousal threshold and the arousal drive are referenced to the therapeutic pressure. . . . . . . 113
4.5 Schematic of the diagnostic and therapy suggestion methodology for a subject with OSA. The
abnormal upper airway anatomy in combination with an abnormal ventilatory control stability
leads to a therapeutic strategy that combines weight loss and the application of supplemental
oxygen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.6 Flow chart describing the procedure that was followed to nd the optimal parameters of our
classication model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.7 Sample regression results for three subjects with dierent critical pressures as well as with
dierent slopes. Note that the air
ow and pressure data correspond to those breaths that were

ow limited during the CPAP pressure drops. Critical pressures are referenced to aptmospheric
pressure which is represented by the dashed line. . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.8 Sample breath-by-breath measurements of the induced sighs protocol in three subjects with
dierent degrees of oscillatory responses. The dashed line represents the prediction provided
by the dynamics model from which respiratory stability was quantied. . . . . . . . . . . . . 121
4.9 Sample continuous recordings of mask pressure during the application of the inspiratory oc-
clusion in two dierent individuals. The solid line marks the therapeutic pressure. The broken
vertical line indicates the time at which cortical arousal was detected. The horizontal dashed
line marks the pressure of the respiratory measurement following arousal. . . . . . . . . . . . 122
xix
4.10 Schematic of the rank normalization procedure that was used to transform all of the OSA
traits to range between zero and one. Note that the normalization was carried out using all
of the available data from all subjects including those with incomplete measurements. . . . . 126
4.11 Receiver operating curves for the dierent number of features considered in the classica-
tion process. The red line represents the optimal threshold that simultaneously maximized
sensitivity and specicity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.12 Spider plot representations of the model-extracted features of the nineteen subjects with
complete measurements. Subjects are ordered from lower to higher OAHI with the seven
subjects on the top row having an OAHI 5 (non-OSA), while the twelve subjects in the
bottom two rows had an OAHI 5 (OSA). The green area in the pentagons indicates the
region that is considered as normal, while the red represents the abnormal region. Note that
the loop gain, arousal threshold and FEV1/FVC parameters were inverted in order to have
the abnormal region on the upper part of the pentagon. The red broken boxes highlight the
three erroneous classications performed by our model. . . . . . . . . . . . . . . . . . . . . . . 130
4.13 Summary of the abnormal traits found in the OSA group with the threshold set at the 62
nd
percentile along with the summary of the therapeutic strategies that are suggested by our
methodology. A. Proportion of subjects with a determined number of traits exceeding the
cut-o point. B. Proportion of subjects whose therapeutic strategies target the upper airway.
C. Distribution of the 28 dierent treatments that were suggested to the ten subjects who
were correctly diagnosed as having OSA by our methodology. . . . . . . . . . . . . . . . . . . 131
4.14 Variability of the receiver operating curves, optimal threshold and the classier performance
metrics using the Leave-M-Out sampling technique for M = 1, 2, 3 and 4. The results are
shown for all of the

N
M

possible training subsamples. . . . . . . . . . . . . . . . . . . . . . . 132
6.1 Minimal feedback model of respiratory control during sleep that combines the anatomical with
the nonatanomical traits predisposing to OSA. . . . . . . . . . . . . . . . . . . . . . . . . . . 157
xx
6.2 Simulation results of the model shown in Figure 6.1 after incorporating the experimentally
derived parameters from two subjects with dierent degrees of upper airway collapsibility. . . 157
xxi
Abstract
Obstructive sleep apnea (OSA) is one of the most common sleep-related breathing disorders and is charac-
terized by recurrent episodes of upper airway narrowing or collapse occurring during sleep. These apneic
events are often accompanied by hypoxia and arousal which might lead, in the long term, to hypertension
and other cardiovascular and cerebrovascular diseases, as well as to metabolic dysfunction, neurocognitive
impairment and poor professional performance. There are also importnat short term implications of OSA.
For instance, the constant episodes of arousal throughout the night have shown to have a negative impact
on mood and alertness. The excessive daytime sleepiness and impaired vigilance have been even associated
with motor vehicle crashes and occupational injuries. As can be seen, OSA is an important health problem
that is associated with multiple adverse behavioral and health outcomes that could translate into major
societal consequences and costs. The sum of direct and indirect annual costs associated with OSA have
been estimated to range between 70 and 160 billion dollars. Such economic burden surpasses other common
respiratory disorders such as asthma and chronic obstructive pulmonary disease. The problem is that less
than 5% of the estimated cost of OSA is associated with the diagnostic and treatment of the disease itself
and the rest corresponds to the indirect expenses such as long-term medical care as a result of a vehicle
or a work-related injury, legal assistance, damage repair, loss of productivity, etc. We believe that in order
to prevent the health and economic eects that OSA represents, there is a need to develop more accurate
diagnostic tools as well as better therapeutic strategies.
The current gold standard diagnostic tool for OSA (i.e. polysomnography) is highly eective at detecting
the presence of OSA; however, it is not specic enough to identify the causes of the breathing disorder.
xxii
Moreover, the rst line of treatment (i.e. continuous positive airway pressure CPAP), which targets to x
the upper airway anatomy, has proven to be ecacious at reducing the severity of OSA; however, it fails
to completely eradicate the disease. The reason for this is that OSA involves the interplay of anatomical
mechanisms, such as an unfavorable upper airway structure and/or a collapsible upper airway; as well as
non-anatomical mechanisms, including an unstable respiratory control system, a low arousal threshold, and
an overly strong respiratory response to arousal. The multifactorial nature of OSA makes the selection of
treatment to be rather challenging to clinicians, especially because the mechanisms interact dierently in
each individual. These observations warrant the development of novel diagnostic and therapeutic strategies
for OSA that are patient specic.
The idea of phenotyping for the development of personalized therapies for OSA subjects has recently
gained considerable attention because of its potential role at eliminating the disorder. However, most of the
studies have been carried out in the adult population. This can be attributed to the higher prevalence of
OSA in adults (3%) as compared to children with ages ranging between 2-18 years (1.6%). However, the
prevalence of OSA in children and adolescents could be increased due in large part to the growing prevalence of
childhood overweight, which is a known risk factor. Therefore, there is a need to implement this phenotypic
approach in the pediatric population. In this study, we are particularly interested in studying a cohort
of adolescents. Adolescence marks the transition from childhood into adulthood, and is characterized by
changes in sexual development in addition to somatic growth and cortical processing. Moreover, adolescence
has been associated with an increase in upper airway collapsibility, with attenuation of important protective
upper airway muscle re
exes, which represents an increased risk to develop OSA. Despite these anatomical
and physiological changes, little is known about the pathophysiology in adolescent OSA. It is of critical
importance to eectively diagnose and treat the disorder at an early age, so that the deleterious eects of
OSA can be avoided.
The OSA phenotyping approach requires the development of experimental interventions along with the
analytical tools that enable the study and quantication of important traits that predispose to the disease
during sleep. In order to measure the hypotonic collapsibility of the upper airway, pressure sequences con-
xxiii
sisting of four abrupt drops in CPAP level of increasing amplitudes and ve breaths duration were delivered
to the subjects. The four levels to which the pressure was dropped lay within the range of the individuals'
therapeutic pressure and the minimal CPAP pressure of 3 cmH
2
O. Each pressure drop was followed by a
rapid return to therapeutic pressure lasting ve breaths as well. The impact that the progressive decrease
in mask pressure had on the amplitude of the air
ow signal was quantied by performing a linear regression
on the peak inspiratory
ow and mask pressure values of those
ow limited breaths occurring at subthera-
peutic CPAP pressures. We extracted two parameters that represented the upper airway collapsibility: the
slope of the regression line (Slope
pf
), which represents the ratio between changes in air
ow and changes
in mask pressure; and the projection of the tted line to the point of zero air
ow (P
crit
). Statistical testing
comparing data from 16 OSA and 12 non-OSA subjects showed no statistical dierences in the two upper
airway collapsibility quantiers (p = 0.59 and p = 0.15, respectively). Although none of the parameters
showed dierences between the groups, a correlation analysis between the Slope
pf
and the obstructive
apnea-hypopnea index (a quantier of OSA severity) revealed a moderate though statistically signicant
positive association (r = 0.45 ; p = 0.016). Our results suggest that the hypotonic collapsibility character-
istics of the upper airway greatly contribute to the presence of more events of hypopnea or apnea and they
appear to agree with what has been previously found in the adolescent population. As compared to the
adult population, adolescents in general have an upper airway that remains sti at subtherapeutic pressure
levels, even in the presence of OSA.
To better understand the characteristics of ventilatory control dynamics in this population, our group
developed a novel experimental intervention that allowed us to perturb the respiratory system by manipulat-
ing the inspiratory pressure, to induce sighs after upper airway stabilization. Furthermore, we developed the
modeling framework that utilizes the noninvasively measured ventilatory responses to the induced sighs and
spontaneous breathing data to obtain representations of the processes involved in the chemical regulation of
respiration. Classical control theory was then utilized as a means to quantify the propensity towards instabil-
ity from the derived models and extract biomarkers that would help us identify the contribution of ventilatory
control instabilities to the development of OSA. After validation with simulated data, our methodology was
xxiv
applied to data collected experimentally from 23 OSA and 22 non-OSA overweight adolescents. Statistical
analyses revealed that the OSA group had a signicantly lower controller gain (p = 0.05). In addition, we
found that OSA severity, following a log-transformation, was statistically signicantly negatively correlated
with the overall loop gain evaluated at the phase crossover frequency (r = -0.350 ; p = 0.02). On the other
hand, the log-transformed OSA severity measurement was found to be statistically signicantly positively
correlated with the log-transformed phase-crossover frequency and gain margin (r = 0.300 ; p = 0.05 and
r = 0.384 ; p = 0.01, respectively). Contrary to what has been found in adults, our overall results suggest
that in overweight adolescents, OSA does not initiate as a result of an overly sensitive chemore
ex but,
on the contrary, could result from an inappropriate compensation to ventilatory stimulation. An increased
hyperventilatory response upon arousal, in combination with such a blunted compensatory action from the
chemore
ex, could lead to a reduction ofCO
2
beyond the apneic threshold and thus inducing an apnea when
sleep is resumed. These cyclic transitions between arousal and apnea lead to a dierent type of ventilatory
instability, which is not mediated by the chemore
ex.
An experimental protocol that elicited an arousal from sleep was implemented with the aim of investi-
gating the contribution of the arousal mechanism to OSA. After a period of stable NREM sleep, arousal
was induced by applying a mechanical load that completely blocked the pass of air from the CPAP machine
into the mask. Specically, we were interested in measuring the arousal threshold, which we dened as the
breathing eort, against a blocked airway, that is required to disturb the sleeping state and elicit an arousal.
In addition, it was of interest for us to quantify the maximum increase in respiratory drive, associated with
arousal, that results from the transient restoration of the wakefulness drive. Statistical testing comparing
data from 16 non-OSA and 15 OSA individuals showed no statistical dierences in none of the extracted
arousal components (p = 0.54 and p = 0.63, respectively). In addition, no signicant association was detected
between OSA severity and our arousal measurements. Although the arousal mechanisms might appear not
to play an important role in adolescent OSA as a population, in some patients they can still interact with
the rest of the traits to cause unstable sleeping patterns that, at the same time, would cause ventilatory
instabilities.
xxv
Lastly, we developed a model that combined the aforementioned traits representing upper airway collapsi-
bility, ventilatory control stability and the arousal mechanism; along with measurements of upper airway
anatomy and lung mechanics, as a means to detect the potential cause of OSA in a personalized manner.
Our OSA detection model using our experimentally-derived traits shows a substantial and statistically sig-
nicant agreement with the clinical polysomnography (Cohen's Kappa = 0.67 ; p = 0.004). We utilized this
information in order to suggest a therapy that would be patient-specic and would be targeted to the specic
trait that is causing OSA. Our preliminary results indicate that the vast majority of our OSA subjects would
benet from the combination of therapies that target the anatomical as well as the non-anatomical traits.
We speculate that by also targeting the non-anatomical traits, we can greatly improve the outcomes of OSA
therapy in the pediatric population.
In summary, we have developed a methodology that combines experimental interventions along with the
analytical tools that allowed the quantication of the traits that predispose to OSA in a population of obese
adolescents. Moreover, we developed a model that integrated various of these OSA traits, in addition to
measurements of upper airway anatomy and lung mechanics, in order to identify the cause of OSA at an
individualized level. We believe that our methodology can be generalized to younger children and the adult
populations and could be used to aid clinicians in the selection of therapy that can be personalized and
targeted to improve a specic trait and could perhaps help resolve OSA completely.
xxvi
Chapter 1
Introduction
1.1 Motivation
1.1.1 Adult vs. pediatric obstructive sleep apnea
In the United States, OSA is more prevalent in adults (3%) (Punjabi, 2008) compared to the 1.6% found in
children and adolescents with ages ranging between 2-18 years (Lumeng and Chervin, 2008). However, the
prevalence of OSA in children could be increased due in large part to the growing prevalence of childhood
overweight (Ogden et al., 2012), which is a known risk factor (Redline et al., 1999).
Although there are similarities in the diverse forms of SRBD between adults and children, there are also
important dierences in treatment and diagnosis (Messner and Pelayo, 2000). Table 1.1 summarizes the
main discrepancies found in OSA between these two populations. For instance, while OSA aects males and
females equally in the pediatric population (Redline et al., 1999), in the adult case it is more predominant
in males with an increased incidence in postmenopausal females only (Young et al., 2002a). It is also of note
that although OSA is mostly associated with anatomical and structural abnormalities in both populations,
in children it is attributed to adenotonsillar hypertrophy (Jain and Sahni, 2002), whereas in adults is largely
associated with obesity. This is why, when it comes to treatment strategies, adenoids and tonsils removal
through surgical intervention is frequently used in children (American Academy of Pediatrics, 2002); whereas,
1
continuous positive airway pressure (CPAP) is a more common therapy in adults (Loube et al., 1999). Lastly,
in terms of diagnostics there are also dierences that should be pointed out. Polysomnography (PSG) is the
gold standard for both adults and children; nevertheless, there are dierences in the way OSA is dened
based on the number of obstructive respiratory events per hour of sleep. In adults, ve events/hour are
considered as mild OSA (Force et al., 2009); while in young children, 1.5 events/hour are already considered
abnormal (Marcus et al., 1996).
It remains unclear whether the pathophysiology of OSA changes with growth and development, but there
are certainly marked dierences in body size and composition, sexual maturation and metabolic rates that
may alter the mechanisms predisposing to OSA with aging. Another question that is still unresolved is
whether childhood OSA evolves and develops into adulthood OSA, or whether these are two completely
dierent phenomena (Marcus, 2001). To answer this question, longitudinal studies should be carried out
on subjects who were diagnosed with OSA as children and monitor the progression of the disease until the
adult age. To the best of our knowledge, such studies are not yet available, possibly due to the diculty in
following up with the subjects for a long period of time. Less ambitious but equally enlightening longitudinal
studies have been carried out to address the incidence and progression of OSA and its risk factors throughout
childhood (Spilsbury et al., 2015). Notable is the work of Topol and Brooks (2001) and Marcus et al. (1998a),
who found a progression from primary snoring to OSA in 8-10% of the children studied over a period of
1-3 years. On the other hand the study conducted by Li et al. (2013) reported a strikingly development
of primary snoring into OSA in almost 40% of the children monitored over approximately 5 years. These
results might indicate that there are indeed dierences associated with aging; however, data are still scarce
to draw a denite conclusion.
Considerable research has been devoted to the study of OSA in adults; however, less attention has been
paid to the pathophysiology of the disease in the pediatric population (Redline et al., 1999). Therefore,
this study aims at lling this gap concerning the elucidation of the mechanisms that are responsible for the
development of OSA in pubertal and postpubertal children (13-21 years).
2
Table 1.1: Comparison of the obstructive sleep apnea snydrome in children versus adults. CPAP, Continuous
Positive Airway Pressure; REM, Rapid Eye Movement; T&A, Tonsillectomy and adenoidectomy; UVPP,
uvulopharyngopalatoplasty. Table adopted from Marcus (2001).
Children Adults
Clinical Characteristics
Peak age Preschoolers Elderly
Sex ratio Equal Predominantly males
Etiology Adenotonsillar hypertrophy Obesity
Weight Failure to thrive, normal, obese Obese
Excessive daytime somnolence Uncommon Very common
Neurobehavioral Hyperactivity, developmental Cognitive impairment,
delay impaired vigilance
Polysomnographic
characteristics
Obstruction Cyclic obstruction or prolonged Cyclic obstruction
obstructive hypopneas
Sleep architecture Normal Decreased delta and REM sleep
State with OSA Predominantly REM REM or non-REM
Cortical arousal 50 % of apneas At termination of each apnea
Treatment
Surgical T&A (majority of cases) UVPP (selected cases)
Medical CPAP occasionally CPAP
1.1.2 Poor eciency and adherence to current treatment strategies in children
Given the association between OSA and overweight/obesity, the rst-line treatments in children would be
behavioral modications including weight loss and avoiding sleeping on the supine position (Loube et al.,
1994; Tuomilehto et al., 2009). Weight loss requires some lifestyle changes such as switching to a healthier diet
and/or start doing exercise regularly. Although these changes appear to be simple in principle, overweight
subjects show very poor adherence to them and often fail to lose weight (Crawford et al., 2000; Ball et al.,
2002; Castellani et al., 2003).
Given the major role that upper airway anatomy and collapsibility play in the development of OSA, there
are more specialized treatments that would target to x the abnormal upper airway. Surgical intervention
like adenotonsillectomy is used in the majority of the pediatric cases (American Academy of Pediatrics,
2002), with continuous positive airway pressure (CPAP) being the second line of treatment (Marcus et al.,
2006). Despite the relatively high eectiveness of these two methods at alleviating the symptoms of OSA,
3
there are also problems associated with OSA recurrence after surgical interventions (Spilsbury et al., 2015)
and low adherence to CPAP (Weaver and Grunstein, 2008). The low adherence to the latter method can be
attributed to the discomfort that results from wearing the device for long periods of time and for having the
need to use it on a day-to-day basis. On the other hand, poor adherence to CPAP treatment could be due
to OSA not being associated to a compromised anatomy or an increased collapsibility of the upper aiway
problem but rather to a dierent mechanism in some patients. Therefore there is a need for the investigation
of alternative therapeutic strategies that are not only focused on xing the upper airway anatomy and/or
collapsibility.
1.1.3 Complement current OSA diagnostic tools
The current gold standard diagnostic tool for OSA (i.e. polysomnography) provides a detailed description
of the sleep architecture of the subjects with a quantier of the amount of arousals or awakenings per hour
of sleep. In addition, it provides a summary of all the respiratory events, that could be central obstructive
or mixed apneas and hypopneas, along with the maximum eect they had on oxygen saturation. The rate of
these respiratory events per hour of sleep is then calculated to have an estimate of how often these episodes
occur. Another quantier that is provided by the PSG is the number of oxygen desaturations, dened as a
drop by 3% in oxygen saturation, occurring per hour of sleep. Other relevant values include average heart
rate, maximal oxygen desaturation and end-tidal carbon dioxide level recorded throughout the night. Based
solely on the aforementioned metrics, sleep clinicians carry out the diagnostic of OSA and must decide what
therapy to suggest which is quite challenging and can be therefore subject to error. Therefore, we believe
that by having access to measurements of the OSA traits, in addition to results from the PSG, clinicians
would have a better understanding of the pathophysiology in each individual and could potentially help them
in better planning the treatment strategy.
4
1.1.4 Personalized therapy design
Until now, the management of OSA has been carried out in a trial and error one-size-ts-all basis, where
the rst recommended treatment is that one that would target the upper airway anatomy. While we agree
that the vast majority of the subjects with OSA have some degree of anatomical compromise, the way
the anatomy interacts with the rest of the traits is unique in all patients. For instance, in one subject a
very narrow upper airway in combination with a highly sensitive chemore
ex could be the causes of OSA,
whereas in a dierent OSA patient, OSA can result from a markedly collapsible upper airway and a high
arousability from sleep. While these two hypothetical cases would result in unstable breathing patterns, the
mechanisms that are responsible for such ventilatory instabilities are completely dierent. In the former
case, breathing instabilities are mediated by the chemore
ex and could potentially be xed by putting this
subject to supplemental oxygen. While in the latter case, the unstable ventilatory patterns are governed by
the sleep-wake controller and could perhaps be xed by the administration of a non myorelaxant sedative.
This simple example illustrated the need for the transition from the one-size-ts-all treatment of OSA to a
more individualized one (Malhotra et al., 2015). This idea of switching to a targeted treatment of OSA has
been developing and evolving over the past decade and shows very promising results (Eckert, 2016; Edwards
et al., 2016a). Among the multiple advantages of this ideology, we have the development of alternative
and innovative therapeutic strategies. We strongly believe that switching to a personalized and targeted
treatment of OSA will bring us one step closer to completely eradicating it.
1.2 Specic aims and objectives
The primary goal of this study was to better understand the pathophysiology of OSA in a population of
overweight adolescents and ultimately nd what is/are the underlying mechanism/s predisposing to this
respiratory disorder. As we previously discussed, there are multiple potential mechanisms behind pediatric
OSA and it would be of critical importance to objectively measure them. Therefore, our rst objective
was to develop noninvasive respiratory bedside tests to allow the study of such mechanisms. Along with
5
the development of the experimental interventions, we wanted to implement a data acquisition system for
physiological data monitoring and recording. Once the experimental setup was tested and nalized, the next
objective was to apply it to a population of overweight adolescents with OSA and record data from them.
Following this step, we aimed at developing the appropriate tools for physiological signal processing and
cleaning. In addition, we wanted to develop the analytical tools that allow the quantication of the traits
that predispose to OSA from the experimental recordings. Lastly, we aimed at integrating the quantied
traits from our population in order to design patient specic therapies.
1.3 Document organization
This work is separated into ve main chapters. In Chapter 1 we introduce the motivations behind this
research and describe the specic aims and objectives that we intended to accomplish.
Chapter 2 presents an overwiew on the physiology behind two processes that are essential for life: res-
piration and sleep; as well as on the complex interactions between them that could result in pathological
conditions. More specically, it focuses on the description of the most popular manifestation of these sleep-
related breathing disorders known as obstructive sleep apnea. We also describe the implications of the disease
as well as the current diagnostic and treatment strategies.
Chapter 3 focuses on the quantication of ventilatory control stability via mathematical modeling. It
contains a detailed description of the population under study, as well as of the experimental setup. In
addition, it also shows the steps that were followed for the preparation and preprocessing of the signals of
interest. It presents a comprehensive description of the methodology utilized for modeling purposes and the
denition of the features extracted from the derived models. It also evaluates the validity of the proposed
modeling methodology with synthetic data generated with a parametric model under various circumstances.
Lastly, it summarizes the main experimental results obtained from a population of overweight adolescents.
Chapter 4 discusses the methodology that was used in order to extract the phenotypes of our subjects with
OSA with the purpose of identifying the causes behind the disease and ultimately provide each individual
with a specic treatments. It describes the multiple experimental interventions that were used for the study
6
of the multiple OSA traits. In addition, it covers the analytical tools that were used for feature extraction.
It also presents a method that combines the extracted OSA traits from our overweight adolescent cohort
for the selection of patient-specic treatments. Lastly, it describes the cross-validation procedure that was
carried out to the predictive power and the generalizability of our methodology to an independent data set.
Chapter 5 presents a concluding summary of the key overall ndings of our study after the analysis of
the experimental data.
Chapter 6 describes the future directions that this work could take that we believe could nicely comple-
ment our ndings. For instance, the inclusion of other features such as muscle responsivennes that could
greatly improve our therapy selection method is discussed. Moreover, the idea of evaluating the eects of
sleep state transitioning on the OSA traits via adaptive algorithms is also introduced. In addition, the con .
Lastly, it introduces what we believe is the next step of the OSA phenotyping models like ours. This would
involve the administration of the patient-specic therapies predicted by the model in our cohort of obese
adolescents and evaluate their eectiveness at eliminating OSA.
7
Chapter 2
Literature review. Anatomy, physiology and
pathophysiology of the respiratory and sleep
regulation systems.
This chapter presents an overview on two systems that are ubiquitous in animal life: respiration and sleep.
The overview consists of the description of the anatomy as well as the physiology behind these two processes.
In addition, it presents the eects that both systems have on each other and the complex interactions
occurring between them that might lead to pathological conditions. In particular, it focuses on the description
of some factors leading to the most popular manifestation of sleep-related breathing disorders known as
obstructive sleep apnea; its current diagnostic techniques, the major healthcare and economical implications,
as well as the main therapeutic strategies.
8
2.1 Respiratory system
2.1.1 Anatomy and morphology
Respiration is the act of inhaling air that is rich in oxygen from the atmosphere and exhaling the carbon
dioxide that results as a product of metabolism. The organ where the gas exchange process takes place is
the lung, which is located inside the thoracic chamber and thus it is protected by the bones and muscles of
the rib cage. In order to pump air in and out of the lungs, the volume of the thoracic cavity is constantly
being increased and decreased by the contraction (inspiration) and relaxation (expiration) of the intercostal
and diaphragm muscles (Ionescu, 2013). These cyclic changes in intrathoracic volume create a dierence in
pressure around the lungs making the air to
ow inside and out of them (West, 2012). Figure 2.1 illustrates
the anatomical and physiological changes inside the thoracic cavity that promote respiration.
Figure 2.1: Anatomical changes occurring in the thoracic cavity associated with the inspiratory and expira-
tory phases of respiration. Adopted from Britannica (2016).
The path that the incoming air has to go through before it reaches the gas exchanging portion is known
as the airway. The airways are divided into an upper and a lower part. The upper part starts at the nose and
mouth and continues down to the pharynx, which then connects to the larynx and ends at a windpipe known
as the trachea. While the pharynx is a soft tissue conduit, the larynx and the trachea are both surrounded
by bony and cartilaginous structures (Thiriet, 2014). Such structural dierence makes the pharynx the site
9
that is more prone to collapse during sleep (Wu et al., 2015). The lower airways start at the left and right
bronchi, which are subdivisions of the trachea that go into the left and right lung, respectively. Within each
lung, these dichotomous bifurcations will continue to generate a bronchial tree that will again be subdivided.
This self-repeating pattern was reported to go on for a total of 23 generations with the branching tubes
becoming narrower and shorter as they go deeper into the lung until they nally reach the sites for oxygen
and carbon dioxide exchange (Weibel, 1963; Mandelbrot, 1983; Sauret et al., 1999).
2.1.2 Gas exchange
The gas exchanging portions of the respiratory tract are known as the alveoli, which are grape-like clusters
of microscopic air sacs known as the alveolus. This alveolated region of the lung is the actual respiratory
zone, while the rest of the airway mainly serves as a transport duct. The alveoli are wrapped in a ne
mesh of capillaries and it is at the interface (respiratory membrane) between these two systems that the
gas exchange process takes place (See Figure 2.2A.). Such process occurs through a transport phenomenon
known as diusion that is characterized by the gradual mixing of molecules between two compartments,
with dierent initial concentrations, occurring in the absence of bulk motion until an equilibrium is achieved
(Bird, 2002; Truskey et al., 2004). Diusion in the lungs is possible due to the dierence in gas concentrations
existing between the alveolar region (high oxygen and low carbon dioxide) and the pulmonary capillaries
(low oxygen and high carbon dioxide). Fick's diusion law establishes that the amount of gas moving across
a tissue is proportional to the area of the tissue and inversely proportional to its thickness. With a total area
for gas exchange ranging between 50 and 100 square meters and an average alveolar membrane thickness of
0.3 micrometers (West, 2012), the conditions are optimal for gas transfers (Gheorghiu et al., 2005). Thus, as
a result of the diusion process, the capillaries transform deoxygenated blood into oxygenated blood and the
alveoli are left with a high concentration of carbon dioxide that is expelled out of the body during exhalation.
As one can see from Figure 2.2B., the respiratory and the cardiovascular systems are tightly coupled.
Once the gas exchange process is terminated, the oxygenated blood is returned to the left atrium in the
heart via the pulmonary veins and then passed to the left ventricle to ultimately be pumped out of the
10
heart and distributed to the entire body through the systemic circulation. These highly complex circulatory
networks supply the amount of oxygen that all the cells forming organ and muscle tissue require for proper
functioning (Krogh, 1919). Under normal resting conditions, cells in the human body consume approximately
250 milliliters per minute of oxygen and produce around 200 milliliters per minute of waste carbon dioxide as
a result of metabolism. These quantities yield a respiratory quotient (ratio of oxygen consumption to carbon
dioxide production) of approximately 0.8 which lies within the ranges found in mammals (0.72 - 0.97) in
the early studies conducted by Krogh (1916). The blood with low oxygen and high carbon dioxide contents
travels from the dierent tissues back to the right atrium through the systemic veins, where it is then passed
to the right ventricle which nally pumps it back into the lungs through the pulmonary artery. The whole
circulatory cycle, lasting approximately 20 seconds (Meier and Zierler, 1954), is then nalized and would be
continuously repeated.
2.1.3 Ventilatory control
Respiration is a cyclic process that under normal resting conditions has a frequency of approximately twelve
breaths per minute (0.2 Hz) (Mead, 1960). This rate is sucient to maintain the optimal gas composition
of arterial blood gases for normal conditions; however, the respiratory frequency can be adjusted to operate
optimally depending on the environmental and behavioral conditions of the body such as the exposure to
extreme altitude and exercise, respectively. Such compensatory action is a result of a highly sophisticated
feedback system that is able to modify both the depth and the frequency of breathing to ensure the generation
of proper ventilation patterns. Due to its fascinating and overly complex structure this feedback mechanism
has been and continues to be extensively studied by respiratory physiologists and neuroscientists. This
compensatory mechanism has a hierarchical organization that is comprised of neural structures of the spinal
cord, medulla oblongata, and higher parts of the central nervous system (Safonov and Lebedeva, 2003).
The spinal cord is considered the output tract that is in charge of sending the command signals coming
from the brain to the respiratory pump muscles that drive respiration. For instance, phrenic motoneurons
innervate the diaphragm (Berger, 1979), motoneurons innervate the intercostal (Larnicol et al., 1982) and
11
A. Oxygen and carbon dioxide exchange between the alve-
oli and blood capillaries across the respiratory membrane.
B. Flow diagram of oxygen and carbon dioxide transporta-
tion through the circulatory system.
Figure 2.2: Schematic of the cardiovascular and respiratory interactions that allow the oxygen to reach the
cells and tissues and the carbon dioxide to be expelled out of the body. Figures extracted from Germann
and Staneld (2002).
the abdominal muscles (Holstege et al., 1987). In addition, the brainstem contains motoneurons that inner-
vate muscles controlling the dimensions and patency of the upper airway such as the pharyngeal and the
hypoglossal muscles (Bianchi et al., 1995; Barnett et al., 2016).
The medulla oblongata serves like a connection between the spinal cord and higher centers of the brain
and is responsible for controlling several autonomic functions of the human body like breathing, heart
rate, vasomotor activity, among others (Loewy and Spyer, 1990). It is relevant to this work to have an
understanding of the dierent elements of the medulla that play a role in respiration, as well as to know
their individual contributions to the generation of the breathing pattern. Respiratory pattern has been
proposed to have a rhythmic component, associated with the synchronous activity of pacemaker-type of cells
12
(Butera et al., 1999); and aerent components that are sensitive to external in
uences such as the activity of
other cerebral regions, environmental, humoral and/or re
ex factors (Hey et al., 1966; Taylor et al., 1999).
The rhythmic activity has been attributed to a group of neurons located in the ventral respiratory column
(VRC) within the medulla denominated the pre-B otzinger complex (Pre-B otC), which has been deemed
crucial for respiratory eort generation because experimental studies showed that disruption of synaptic
transmission in this region causes respiratory arrest (Rekling and Feldman, 1998). Some people refer to
this component as the respiratory pattern generator (RPG); however, as most of the regions of the brain,
it does not operate in complete isolation. Before being sent out to the eector muscles, the commanded
respiratory pattern is modulated by a population of excitatory neurons that are located in the rostral part
of the medulla known as the retrotrapezoid nucleus (RTN) (Guyenet et al., 2012). RTN is known as the
central chemoreceptor site and has been proposed to have the properties of a chemosensory integrating
center, where information coming from the carotid body aerents, being relayed through the nucleus tractus
solitarii (NTS), gets also processed (Guyenet, 2008). These aerent neurons are known as the peripheral
chemoreceptors and are supposed to send information to the central nervous system associated with the
gas tensions present in the systemic circulation. Therefore, the output of the RTN re
ects both brain and
systemic blood partial pressure of carbon dioxide levels as well as blood oxygenation. The nature of the
interactions between the central and the peripheral chemoreceptors remains controversial. The simplest of
the interactions and the most widely used is a pure summation of contributions from both chemoreceptors
(Heeringa et al., 1979; St Croix et al., 1996). There are, however, other groups that have suggested more
complex forms of interaction such as hyperadditive (Dempsey et al., 2012), hypoadditive (Day and Wilson,
2009) and even a hybrid form of interaction where all of the aforementioned possibilities are feasible and
dependent upon behavior and/or metabolism (Wilson and Day, 2013). Independently of the nature of the
interactions between the chemoreceptors, the output of the RTN region was found to encode levels of arterial
pressure of carbon dioxide (hypercapnia) and were found to have a linear increase in ring discharge rate that
ranged between 0-10 Hz for changes in PaCO2 between 35 and 76 mmHg in experiments performed in rats
(Mulkey et al., 2004). These animal experiments agree with the seminal study performed by Haldane and
13
Figure 2.3: Parasagital slice of the lower brainstem of a rodent showing the location and projection of the
RTN neurons and the regions participating in the breathing pattern generation. Adapted from Guyenet
et al. (2012).
Priestley (1905) on the impact that the partial pressure of carbon dioxide had on the control of ventilation
in the early nineteen hundreds. With the advance in experimental techniques we have gained some insight
into the anatomical and functional connectivity of the medulla and now recognize the RTN as a convergence
site that is a common central pathway connecting the chemosensors with the RPG to nally yield a motor
output to the respiratory muscles. Figure 2.3 shows a schematic of the brainstem of a rodent highlighting
the main regions that are interconnected with the RTN to produce the breathing pattern.
The previously described interconnections of the medullary and spinal cord circuitries are the most
relevant to the generation of the breathing pattern; however, there are several other excitatory and inhibitory
connections of less importance that were not mentioned herein. For a more detailed explanation of the
anatomical and functional connectivity of the medulla and the mutliple spinal cord terminals, the reader is
referred to the schematics presented in the manuscripts by Bianchi et al. (1995) and Barnett et al. (2016).
Finally, an important component of ventilatory control is the voluntary action provided by higher centers
of the brain located in the cerebral cortex (Bucy and Case, 1936). This type of respiratory control is
particularly important when performing activities such as speaking, singing, etc. Despite the fact that
voluntary control is the most powerful among the neural mechanisms regulating the respiratory pattern
(Pitts, 1946), its study lies outside of the scope of this work and is not further discussed.
In summary, respiration involves the interplay of several mechanisms that must operate in harmony to
14
achieve stable ventilatory patterns that would enable proper body function. Figure 2.4 shows a cartoon of
the interconnection between these dierent mechanisms.
Figure 2.4: Schematic of the elements that participate in the control of respiration during sleep.
2.2 Sleep system
Sleep is a universal need of most animals that is characterized by a reduced response to exogenous and
endogenous stimuli; minimal movement; and species-specic posture, diurnal timing and duration (Roehrs,
2000). This consciousness state diers from other non awake states such as comma and anesthesia in that it
counts with responsiveness and reversibility characteristics (Cirelli and Tononi, 2008). Contrary to the latter
states, during sleep, responsiveness to perturbations is not fully absent and the sleeping state can always be
interrupted and reversed back to an awake state provided a suciently strong stimulus.
The function of sleep is still not fully understood and many theories based on experimental observations
15
have been proposed to explain the reasons why sleep is required (Barone and Krieger, 2015). Among the
main theories of sleep function we nd some that are based on concepts such as energy conservation and
optimal allocation (Berger and Phillips, 1995; Schmidt, 2014); neurotoxic clearance resulting in a restorative
and recuperative function (Reimund, 1994; Xie et al., 2013); and neuronal connectivity reorganization and
plasticity leading to the consolidation of newly acquired information in memory(Diekelmann and Born, 2010;
Krueger et al., 2016). Independently of the intrinsic function of sleep, its importance has been evidenced by
the eects of deprivation. Sleep deprivation consists of a complete lack of sleep during a certain period of
time or a reduction of the time spent in sleep that signicantly deviates from the optimal sleep time required
by the dierent animal species(Orze l-Gryglewska, 2010). Experimental studies performed in humans have
shown that progressive sleep loss results in increased distractednes and irritability; impaired cognition and
motor function; and diculty in memorizing new information (Durmer and Dinges, 2005). In addition,
animal experiments revealed that sleep deprivation eventually lead to death (after 2-3 weeks) independently
of whether the rats were completely deprived from sleep or selectively deprived from having a specic sleep
stage (Rechtschaen and Bergmann, 1995).
2.2.1 Sleep architecture and associated physiological changes
Sleep is separated into two dierent types, non-rapid eye movement (NREM) and rapid eye movement sleep
(REM). NREM is further subdivided into two main components depending on the relative depth: A transition
period from wakefulness to sleep is considered to occur during sleep stages 1 and 2; and a deeper sleep state
that is noticed in sleep stages 3 and 4 and that is also known as slow-wave sleep due the characteristics seen
in the electroencephalogram. Just as in the case of slow-wave sleep, each of the sleep stages are associated
with distinctive brain activities and physiological behaviors. Table 2.1 summarizes the main behavioral and
physiological characteristics (measured through electrography) of the two main sleep stages and compares
them with the wakefulness state.
In addition to these dierences, sleep state transitioning has also been associated with changes in multiple
systems. For instance, heart rate and blood pressure are known to decrease when transitioning from wake-
16
Table 2.1: Behavioral and physiological characteristics of the main sleep-wake states. Note that NREM
encompasses all of the 4 sleep stages. Adopted from Phillipson (1978) and Asyali (1998).
Phenomenon Wakefulness NREM REM
Behavioral
Eyes Open Closed Closed
Mentation Purposeful Absent or reduced Dreaming
Responsiveness Appropriate simple or Simple re
ex responses Inhibition of sensori-
complex responses to to external stimuli with motor responses to
external stimuli elevated response thresholds external stimuli
Electrographic
EEG Low amplitude, High amplitude, Low amplitude,
high frequency low frequency high frequency
EMG High tonic activity Low tonic activity Abolition of tonic activity
EOG Slow or rapid movements Slow movements if any Rapid movements
fulness to deep NREM sleep and become chaotic during REM sleep (Snyder et al., 1964). Sympathetic nerve
activity also changes with sleep showing a marked decrease as NREM sleep deepens and an increase during
REM sleep (Somers et al., 1993). Moreover, cerebral blood
ow and metabolism during NREM sleep are
signicantly reduced as compared to wakefulness, which surprisingly exhibits comparable values with REM
sleep (Madsen et al., 1991b,a). Furthermore, renal and endocrine functions have also been found to depend
on sleep state showing changes in glomerular ltration (Koopman et al., 1989) and hormone secretion rates
(Van Cauter et al., 2008), respectively. Evidently, respiration is also aected by sleep changes; however,
these eects will be explained more in detail in section 2.3.
2.2.2 Sleep-wake regulation
Sleep is thought to be regulated by the interaction of two processes, one promoting sleep (process S) and
one that maintains wakefulness (process C) (Colten et al., 2006). Process S is associated with a homeostatic
build up of sleep debt throughout the day, and process C is associated with the circadian rhythm and is able
to counteract the rise on process S during the daytime (Gillette and Abbott, 2005). Proper synchronization
of these two processes and environmental light-dark cycles contributes to good health.
Wakefulness generates by an ascending arousal system that initiates at the brainstem and propagates to
dierent structures of the forebrain (Moruzzi and Magoun, 1949). As can be seen from Figure 2.5A., there
17
A. Wake-generating system. B. Sleep-generating system.
Figure 2.5: Schematics showing the key components and neuronal projections of the sleep and wake-
generating systems. Adopted from Saper et al. (2005).
are two main pathways related to the arousal mechanism. The rst pathway (yellow arrows) originates from
the upper pons and relays the information to the cerebral cortex through the thalamus. The second pathway
(red arrows) originates in the upper brainstem which in turn activates the hypothalamus to nally reach the
forebrain region.
Sleep is generated by neurons that inhibit the arousal mechanism thus allowing the brain to fall asleep.
It can be noted from Figure 2.5B. that this inhibitory action (purple arrows) has its origin in the ventrolat-
eral preoptic (VLPO) area of the hypothalamus and propagates downstream until it reaches the neuronal
populations that are responsible for arousal genesis. This sleep-generating system also has some specialized
neurons located in the pons that intermittently switch between NREM and REM states throughout the
night (Colten et al., 2006). These neurons send outputs to the lower parts of the brainstem and spinal cord
re
ecting the physiological characteristics associated with each sleep state like the muscle tone reduction and
chaoticity in autonomic control of heart rate and respiration found during REM sleep.
18
2.3 Eects of sleep on respiration
We have previously described the anatomy and physiology of both the respiratory and the sleep systems.
In this section we will focus on the bidirectional interactions between these two systems. It has long being
recognized that there are multiple changes in respiratory neurophysiology as a result of sleep. For instance,
the retirement of the tonic input from the wakefulness stimulus to the respiratory center leaves ventilation
being critically dependent on aerent input from chemical stimuli and thus operating under metabolic control
only (Xie, 2012). Moreover, steady state minute ventilation has been reported to decrease from wakefulness
to sleep by as much as 20% (Gothe et al., 1981), despite the marked increase (3 to 9 mmHg) observed
in resting alveolar PaCO2 occurring during NREM sleep (Dempsey and Skatrud, 1986). Such unexpected
behavior discards the possibility of the decreased ventilation being a consequence of a reduced metabolic
rate associated with sleep and, on the contrary, suggests that the operating points of ventilation and CO2
change during the sleeping states (Colrain et al., 1987). These changes in operating points produce a shift
in CO2 buering, allowing higher values of CO2 as sleep deepens (Berry et al., 1998) without the presence
of an arousal (Longobardo et al., 2009). Additionally, the emergence of sleep could lead to brief periods of
breathing cessation (apnea) in the presence of hypocapnia. This pause in breathing is triggered when CO2
values are below the apneic threshold. Such hypocapnic apneas are a characteristic of the sleeping state and
are rarely seen during wakefulness, even under severe hypocapnic conditions (Dempsey, 2005). Furthermore,
the sensitivity of the chemoreceptors detecting hypercapnia and/or hypoxia is also diminished during NREM
sleep, reducing the compensation ability for these type of chemical loads that occur spontaneously throughout
the multiple sleep stages (Phillipson, 1978).
In addition to the neurophyisiological consequences of sleep, there other anatomical and mechanical
changes that are also associated with sleep. For example, as a result of sleeping in the supine position,
the lung volume is reduced, especially in overweight and asthmatic subjects (Ballard et al., 1990). This
postural eect on lung volume could aect the way air and blood are distributed within the lungs making
ventilation not uniform and less ecient. Additionally, as sleep progresses into deeper stages, the tone of
19
the musculoskeletal system declines becoming completely atonic during REM sleep (Peever, 2011). This
reduction in muscular activity, in particular from the genioglossus and the pharyngeal muscles, results in
an increase in upper airway resistance that rises with sleep deepening making it prone to collapse (Worsnop
et al., 1998).
So far we have discussed the main eects that sleep has on respiratory physiology. Interactions occurring
on the opposite direction are also present, though they are not as numerous. As has been previously
stated, the goal of respiration is to maintain homeostasis of blood gas contents to assure proper body
functioning. During sleep, there could be spontaneous hypercapnic and/or hypoxic instances that can not
be appropriately compensated for by the chemore
ex due to a decreased sensitivity. In those cases, the need
of a stronger compensatory action is required and the sleep state is disrupted and an arousal is triggered.
In response to the change in alertness, the sensitivity of the chemore
ex is increased and the eects of
the respiratory disturbances are diminished. This hypercapnic/hypoxic-induced arousal could be seen as a
protective mechanism that our body uses to maintain respiratory homeostasis (Berry and Gleeson, 1997).
2.4 Sleep-related breathing disorders
As it was described in Section 2.3, the interactions between the respiratory and the sleep system are very
complex. They involve the interdependence of several mechanisms that must operate in harmony in order
to achieve a stable breathing pattern. The malfunctioning of one of the many mechanisms that participate
in respiration during sleep could have deleterious eects and lead to a pathological state. These disorders
are denominated sleep-related breathing disorders (SRBD) and they expand through a wide spectrum en-
compassing from primary snoring with no gas exchange abnormalities, to obstructive hypoventilation with
hypercapnia and/or hypoxemia with normal sleep patterns, to the cases involving upper airway resistance
syndrome and OSA (Roux et al., 2000). The focus of this section will be centered around the most com-
mon and severe type of SRBD, OSA. This disorder is characterized by repetitive episodes of upper airway
narrowing or collapsing, with persistence of respiratory eorts, that result in air
ow obstruction for periods
longer than ten seconds (McCoy et al., 1981).
20
In the United States, the prevalence of the disease ranges between 3% and 7% in adults (Punjabi, 2008),
and from 1% to 4% in children, depending of the diagnostic criteria utilized to dene OSA (Lumeng and
Chervin, 2008). Among the factors that increase the risk of developing OSA in both children and adults
we have age, male sex, obesity, history of asthma, African American and Hispanic races, menopause; and
certain health behaviors such as smoking and alcohol consumption (Redline et al., 1999; Young et al., 2004).
2.5 Diagnostics
Despite the importance of recognizing and treating OSA, it still remains underdiagnosed (Hallowell et al.,
2007). Screening tools to identify patients at risk for developing OSA have been designed in the form of
questionnaires. For example, the STOP is a simple self-report questionnaire consisting of four yes/no type
of questions that evaluates for loud snoring, tiredness, apnea and high blood pressure (Chung et al., 2008a).
Another popular screening tool for sleep apnea is the Berlin questionnaire, which is slightly more complex
than the STOP questionnaire because it consists of eleven multiple choice questions separated in three
dierent categories related to the risk of having OSA. As a result of answering the questionnaire, the subject
is categorized as being at high or low risk for OSA depending on the overall scores and symptoms (Netzer
et al., 1999). These two screening tools have shown to provide a moderately high level of sensitivity for OSA
assessment (Chung et al., 2008b); however, given the self-report nature of the questionnaires, the results are
quite variable and dier across dierent populations. In order to increase the questionnaires' sensitivity and
specicity, they can be used in combination with the Epworth (Johns, 1991) and Stanford (Hoddes et al.,
1973) sleepiness scales. While questionnaires and sleepiness scales are quite simple and easy to administer,
their widespread use as a diagnostic tool remains limited by their subjectivity.
A more objective way of diagnosing OSA is through a continuous overnight polysomnography (PSG)
performed in a sleep laboratory. During a full night PSG, several body physiological functions are measured
including; breathing, heart rate, body movements, brain activity and eye movements. All these measurements
are collected completely noninvasively with the use of surface electrodes to monitor the electrical activity of
the brain, the heart, muscles and the eyes; a nasal cannula to record air
ow patterns and sample the inspired
21
and expired gas concentrations; a pulse oxymeter positioned at the nger tip to track the oxygen saturation
of the blood; and inductance belts placed on the abdominal and chest regions to measure respiratory eort.
The PSG recordings are then used by clinicians to detect the presence of adverse respiratory events such as
oxygen desaturations, hypoventilation, hypercapnia and/or obstructive hypopneas/apneas. The amount and
kind of the respiratory events per hour of sleep provides clinicians with markers that indicate the nature and
the severity of the SRBD, and potentially helps them guiding therapeutic strategies. In order to diagnose
OSA specically, clinicians usually look at the obstructive apnea/hypopnea index (OAHI) which measures
the incidence of obstructive respiratory events per hour spent in sleep. This marker is used to measure the
severity of the disease and for diagnostic purposes. In adults, an OAHI of ve events/hour are considered
as mild OSA (Force et al., 2009), while in young children an OAHI of 1.5 events/hour is already considered
abnormal (Marcus et al., 1996). While, PSG is the current gold standard diagnosis tool for OSA, issues like
inaccessibility as well as high cost restricts its widespread application (Subramanian et al., 2011).
2.6 Implications
The most tangible eect of OSA is sleep fragmentation due to the constant episodes of arousal that are
elicited to terminate the obstructive apneic events. The exposure to sleep deprivation has been shown to
have a negative impact on alertness, mood, cognitive performance and motor function (Durmer and Dinges,
2005). The excessive daytime sleepiness and impaired vigilance has been even associated with motor vehicle
crashes and occupational injuries.
OSA has also been associated with cardiovascular abnormalities. There are three key components of
OSA that result in adverse implications on the cardiovascular system (Leung and Douglas Bradley, 2001).
First, the exaggerated negative intrathoracic pressure that is generated as the body exerts a breathing eort
against a blocked airway, results in an impairment of the left ventricular relaxation which could in turn
lead to a reduced ventricular lling and thus decreasing stroke volume (Virolainen et al., 1995). Second,
the arousal mechanism, thought to be a defense method that terminates the apnea preventing asphyxiation
(Horner et al., 1995), has also some negative eects on the cardiovascular system associated with the abrupt
22
surges in sympathetic neural trac, heart rate and blood pressure (Somers et al., 1995; Peled et al., 1998).
Third, the repetitive apneic events result in cycles of hypoxia and reoxygenation, which are known to promote
atherosclerosis through the activation of in
ammatory mechanisms causing endothelial dysfunction (Garvey
et al., 2009). Atherosclerosis is known to be associated with hypertension, hence hypoxia could be seen as
an indirect cause of hypertension (Fletcher, 1995).
The metabolic system has also been shown to be aected by OSA. For instance, some studies performed
in adults showed that OSA was associated with glucose intolerance, decreased insulin sensitivity, glucose
eectiveness and pancreatic cell function (Punjabi et al., 2003). While the pathways through which
OSA leads to metabolic dysfunction remain unclear, there are two lines of thought that could explain
such eects. The rst one relates to the sympathetic neural hyperactivity resulting from the frequent
arousals that accompany OSA. The increased sympathetic out
ow can in
uence glucose homeostasis by
increasing glycogen breakdown and glucogenesis (Punjabi and Beamer, 2009). The second potential pathway
is associated with the aforementioned in
ammatory response resulting from the recurrent episodes of hypoxia
that are characteristic of OSA. Cyclical hypoxic events could lead to glucose intolerance and decreased insulin
sensitivity by promoting the release of proin
ammatory cytokines (interlukin-6 and TNF-). The work by
Vgontzas et al. (2000) and Huiguo et al. (2000) found that these specic cytokines were elevated in patients
with sleep-disordered breathing and were correlated with measurements of insulin resistance and an increased
risk of developing type 2 diabetes mellitus.
As can be seen, OSA is an important health problem that is associated with multiple adverse behavioral
and health outcomes that could translate into societal consequences and costs (Knauert et al., 2015). For
instance, an interesting study by Vishesh Kapur et al. (1999) showed that the mean annual medical costs
for undiagnosed OSA were signicantly higher when compared to matched age and gender controls; and
OSA severity was positively correlated with the magnitude of medical costs. Moreover, a study performed
in Australia by Hillman et al. (2006) looked at the costs associated with sleep disorders (mostly OSA) in
a more comprehensive way considering multiple factors. Table 2.2 presents a summary of their ndings.
Interestingly, this study found that only the 6% of the total economic burden that OSA represents to society
23
Table 2.2: Summary of costs related to sleep disorders in Australia. Note that costs are presented in 2004
US dollars. Adopted from AlGhanim et al. (2008).
Direct health costs:
Diagnosis and treatment of sleep disorders $146 million
Associated conditions (e.g., cardiovascular disease, $313 million
diabetes, depression, work-related injuries, motor vehicle crashes)
Indirect costs:
Work-related injuries, production disturbance, legal investigation, $1,956 million
human capital, travel, funerals
Motor vehicle crashes, including long-term care, labor disruption, $808 million
quality of life, legal costs, repairs, towing, travel delays,
administration, police, property damage
Other costs: $1,301 million
Net cost of suering $2,970 million
Total $7,494 million
is associated with diagnostics, treatment and diseases and/or accidents caused by OSA. The most substantial
economic impact comes from indirect causes that are a consequence of the direct ones contributing with the
remaining 94%. Among the many indirect sources of cost we have the long-term medical care as a result
of a vehicle or a work-related injury, legal assistance, damage repair, loss of productivity, etc. The total
sum of direct and indirect costs of OSA adds to approximately $4.5 billion, which, when extrapolated to the
U.S. population (more than ten times the population of Australia), would surpass the economic burden that
other respiratory disorders like asthma (Beasley, 2002; Nurmagambetov et al., 2018) and chronic obstructive
pulmonary disease (Mannino and Braman, 2007) represent.
2.7 Treatment
Given the association between OSA and overweight/obesity, the rst-line treatments, for both adults and
children, would be behavioral modications including weight loss and avoiding sleeping on the supine position
(Loube et al., 1994; Tuomilehto et al., 2009). In addition, some lifestyle changes such as quitting smoking
and avoiding the alcohol consumption are suggested to the adult population to alleviate their OSA.
Given the major role that upper airway anatomy and collapsibility play in the development of OSA,
there are more specialized treatments that would target to x the abnormal upper airway. While surgical
24
Figure 2.6: Schematic showing how the neural implant provides a stimulation pattern to the hypoglossal
nerve based on the respiratory activity measured at the intercoastal muscles. Adapted from Strollo Jr et al.
(2014).
intervention like adenotonsillectomy is used in the majority of the pediatric cases (American Academy of
Pediatrics, 2002), continuous positive airway pressure (CPAP) is mostly used in the adult population (Loube
et al., 1999). Despite the relatively high eectiveness of these two methods at alleviating the symptoms of
OSA, there are also problems associated with OSA recurrence after surgical interventions (Spilsbury et al.,
2015) and low adherence to CPAP (Weaver and Grunstein, 2008), that make clinicians think of alternative
therapeutic strategies. For instance, oral appliances, such as tongue repositioning or restraining devices
and mandibular advancement devices, have both shown to signicantly reduce OSA severity (Deane et al.,
2009). Moreover, a more innovative treatment, proposed by Strollo Jr et al. (2014), suggests the use of
electrical stimulation of the hypoglossal muscle to maintain upper airway pattency. Figure 2.6 shows how the
neurostimulator delivers the electrical stimulating patterns to the hypoglossal nerve through the stimulation
lead, based on the respiratory activity measured at the intercoastal muscles. This treatment has already
been proven to be eective in humans and led to signicant improvements in OSA severity and quality of
life after implantation (Eastwood et al., 2011; Van de Heyning et al., 2012; Kezirian et al., 2014). Although
this therapy seems to have a very promising future, its invasiveness, surgical associated costs, and the report
of some adverse events related to the implantation procedure, are still restraining its widespread use.
25
So far we have described the therapeutic strategies that aim at xing the anatomical and collapsible char-
acteristics of the upper airway; however, there are other therapeutic strategies that target the nonanatomical
traits that predispose to OSA. For example, the application of supplemental oxygen and acetazolamide ther-
apies have been found to reduce the overall respiratory control gain, a parameter that determines propensity
towards respiratory instability (Wellman et al., 2008; Edwards et al., 2012). Moreover, a low arousal thresh-
old has also been associated with unstable breathing during sleep and thus it can be increased with the use
of medications such as eszopiclone and trazodone (Eckert et al., 2011; Heinzer et al., 2008). Furthermore, the
use of drug therapies targeting the upper airway muscle tone and responsiveness have also been proposed to
reduce the amount of respiratory events. Finally, for those subjects who suer from REM related OSA, the
administration of some antidrepressants could reduce the proportion of sleep spent in REM and ultimately
alleviate OSA (Pagel and Parnes, 2001). Although all of these pharmacologic agents show potential at re-
ducing OSA severity, their use is still under investigation due to the side eects that may result from their
administration.
Combination therapy using two or more of all of the aforementioned interventions, targeting the multiple
traits (anatomical and nonanatomical) that predispose to OSA, has also been experimentally tested in
humans and has proven to be more eective at reducing OSA severity than utilizing a single therapy alone
(Owens et al., 2015).
26
Chapter 3
Model-based stability assessment of ventilatory
control in overweight adolescents with obstruc-
tive sleep apnea during NREM sleep
3.1 Introduction
Obstructive sleep apnea (OSA) is one of the most common sleep-related breathing disorders (SRBD) (Ade-
gunsoye and Ramachandran, 2012; Erler and Paditz, 2004) and is characterized by recurrent episodes of
upper airway narrowing or collapse during sleep (Strollo Jr et al., 2014). These apneic events are often
accompanied by hypoxia and arousal which might lead, in the long term, to hypertension and other cardio-
vascular and cerebrovascular diseases (Leung and Douglas Bradley, 2001), as well as to metabolic dysfunction
(Khoo, 2010; Khoo et al., 2013), neurocognitive impairment (Durmer and Dinges, 2005; Goel et al., 2009)
and poor professional performance (Orze l-Gryglewska, 2010). In the United States, OSA is more prevalent
in adults (3%) (Punjabi, 2008) compared to the 1.6% found in children and adolescents with ages ranging
between 2-18 years (Lumeng and Chervin, 2008). However, the prevalence of OSA in children could be
increased due in large part to the growing prevalence of childhood overweight (Ogden et al., 2012), which is
27
a known risk factor (Redline et al., 1999).
Although there are similarities in the diverse forms of SRBD between adults and children, there are also
important dierences in treatment and diagnosis (Messner and Pelayo, 2000). Table 1.1 summarizes the
main discrepancies found in OSA between these two populations. For instance, while OSA aects males and
females equally in the pediatric population (Redline et al., 1999), in the adult case it is more predominant
in males with an increased incidence in postmenopausal females only (Young et al., 2002a). It is also of note
that although OSA is mostly associated with anatomical and structural abnormalities in both populations,
in children it is attributed to adenotonsillar hypertrophy (Jain and Sahni, 2002), whereas in adults is largely
associated with obesity. This is why, when it comes to treatment strategies, adenoids and tonsils removal
through surgical intervention is frequently used in children (American Academy of Pediatrics, 2002); whereas,
continuous positive airway pressure (CPAP) is a more common therapy in adults (Loube et al., 1999). Lastly,
in terms of diagnostics there are also dierences that should be pointed out. Polysomnography (PSG) is the
gold standard for both adults and children; nevertheless, there are dierences in the way OSA is dened
based on the number of obstructive respiratory events per hour of sleep. In adults, ve events/hour are
considered as mild OSA (Force et al., 2009); while in young children, 1.5 events/hour are already considered
abnormal (Marcus et al., 1996).
It is known that upper airway anatomy and collapsibility play an important role in the development of
childhood OSA (Arens et al., 2011). However, there is compelling evidence from adult studies suggesting that
this type of breathing disorder is a rather complex phenomenon involving other nonanatomical mechanisms
as well (Eckert et al., 2013; Onal and Lopata, 1982). Other factors include a low arousal threshold, depressed
genioglossus muscle responsiveness and instability of the ventilatory control system (Dempsey et al., 2014;
Wellman et al., 2013). Recently, there has been growing interest in developing experimental and analytic
methods that quantify the traits that predispose to OSA in order to help clinicians design patient-specic
treatment strategies that target a particular mechanism (Wellman et al., 2011).
Special attention has been focused on studying the ventilatory control system using mathematical models
and employing control theory to extract the stability characteristics of the system. Loop gain (LG), has been
28
used as an index of the propensity towards feedback instability, mediated through ventilatory disturbances
that aect CO
2
and/or O
2
. A ventilatory system with a high LG would tend to magnify disturbances and
could potentially develop self-sustained oscillations in ventilation known as periodic breathing; whereas a
low LG would diminish such perturbations and exhibit a more stable ventilation. It is generally accepted
that a respiratory system with an elevated LG accompanied by a highly collapsible upper airway is prone
to exhibit cyclical episodes of upper airway obstruction (Dempsey et al., 2014). Therefore, it is of extreme
importance to quantify LG in the context of OSA.
The term \loop gain", initially employed by the engineering community, is currently being applied in
the clinical environment as it provides clinicians with a concise representation of the overall performance of
ventilatory control and its principal components i.e. gas exchange, circulatory delay, chemoreception and
respiratory muscles activation. LG is a frequency dependent parameter (Khoo et al., 1982) that can be
accurately estimated from data driven dynamic mathematical models.
Throughout the years, dierent groups have developed novel stimulation techniques along with the an-
alytical tools to analyze the experimental data and, ultimately, extract ventilatory stability features. For
instance, static models using linear regression associating ventilation and end-tidal CO
2
(P
ET
CO
2
) steady-
state values following hypercapnic stimulation have been previously proposed (Benlloch et al., 1995; Marcus
et al., 1998b). Although such studies provide important and well founded results, by analyzing the ventilatory
control system, known to be dynamic (Grodins et al., 1954), under steady or quasi steady state conditions,
the transient temporal responses to stimulation are discarded. On the other hand, dynamic models such
as autorregressive models have been used to estimate ventilatory stability parameters from responses to
dierent inhaled mixtures ofCO
2
(Ghazanshahi and Khoo, 1997; Modarreszadeh et al., 1995). Furthermore,
proportional-assist ventilation has been utilized to induce periodic breathing and experimentally quantify
relative respiratory stability assuming a dynamic behavior of the system (Wellman et al., 2003; Younes et al.,
2001). In addition, changes in ventilatory control stability in response to drug administration have also been
evaluated by means of dynamic modeling (Mitsis et al., 2009; Nemati et al., 2011). Evidently, all of the
aforementioned methods involve the application of strong stimuli or maneuvers that could alter LG from
29
baseline conditions.
There are other groups that have quantied stability through dynamic models from data collected under
more \natural" sleeping conditions, in which less intrusive interventions were applied. Notable is the work
developed by Asyali et al. (2002), where hyperventilation due to an acoustically induced transient arousal
from sleep was employed as the driving stimulus to the system; and that of Gederi et al. (2014), where
spontaneous variations in ventilation and P
ET
CO
2
during non-rapid eye movement (NREM) sleep proved
to be sucient to provide accurate model estimations. The application of CPAP to minimize the resistance
of the upper airway was a common denominator in these two studies and key to the implementation of
their nonparametric modeling techniques. A more recent study takes the concept of minimal intervention
one step further and uses spontaneous breathing data collected during routine diagnostic PSG (without the
application of CPAP) to quantify stability in response to obstructive apneas/hypopneas occuring naturally
during sleep (Terrill et al., 2014). In order to quantify ventilatory stability they t the data to a structured
model of ventilatory drive composed of a rst order dierential equation to represent the chemical drive and
an additive drive associated with arousal.
Similar to these eorts of quantifying ventilatory control stability under natural conditions, our work
also exploits the spontaneous variations in ventilation and P
ET
CO
2
to identify the gas exchange process
and subsequently derive the plant gain (PG). Moreover, our group designed a novel experimental technique
to perturb the ventilatory control system by inducing sighs with a bilevel positive pressure ventilator, and
estimating LG from the ensuing ventilatory responses. This protocol emulates the spontaneous sighs that
are present in natural sleep, allowing us to study ventilatory control dynamics in response to typical sleep
perturbations. Similar to what was done by Asyali et al. (2002) and Gederi et al. (2014), our experimental
interventions also utilized CPAP as a means to stabilize the upper airway and therefore enabled us to study
the neurochemical response only. Our proposed models are dynamic and are estimated using a nonparametric
identication technique that will be introduced in section 3.3.1.
30
3.2 Experimental methods and data preparation
This chapter contains a detailed description of the population that participated in our experimental study.
It also presents a careful explanation of the three stages that conformed our experimental protocol, as well
as of the indicators that we extracted from each stage. The experimental instrumentation in addition to
the data acquisition system that were utilized for the application of the protocols and data recording are
also described. It then guides the reader through the steps that were followed for data preparation and
processing.
3.2.1 Experimental methods
3.2.1.1 Subjects
A total of 45 adolescents (24 women and 21 men; age range, 13 - 21) with a history of snoring and a body
mass index (BMI) greater than the 85
th
percentile, after adjusting for age and gender, were recruited to
participate in the study. Each subject underwent a standard diagnostic PSG to detect the presence of OSA;
a pulmonary function test (PFT) to evaluate for pulmonary disease; and a research PSG during which
experiments were performed to obtain information about the stability of ventilatory control. The study
was approved by the Institutional Review Board at Children's Hospital Los Angeles and all parents and
participants gave written informed consent prior to their participation in the experiment.
Subjects taking medications that could aect breathing, or who were using supplemental oxygen or who
were on positive pressure treatments (CPAP or BiPAP) were excluded. Additionally, diabetes, cardiac dis-
ease, chronic lung disease, persistent asthma, syndromic conditions, mental illness, neuromuscular disorders
and craniofacial malformations were also considered exclusion criteria.
3.2.1.2 Standard polysomnography
A baseline overnight PSG was carried out to classify the population into non-OSA and OSA subjects, using
an OAHI of 5 events/hour of sleep as the cuto value. Surface electrodes were used to record electroen-
31
cephalogram (EEG), electrocardiogram (ECG), electrooculogram (EOG), and chin and leg electromyogram
(EMG). In addition, chest and abdominal displacements, pulse oximetry and end-tidal carbon dioxide tension
(P
ET
CO
2
) were also monitored. Data were recorded with the SomnoStar z4 Sleep System (Carefusion, San
Diego, CA) and respiratory events were scored according to the American Academy of Sleep Medicine criteria
(Berry et al., 2012). Table 3.1 summarizes the characteristics of the subjects that participated in the study
after categorizing them as non-OSA and OSA based on the obstructive apnea hypopnea index (OAHI) calcu-
lated from the baseline PSG. It should be noted that besides dierences found in neck circumference, OAHI
and males to females ratio, both groups are comparable in other anthropometric measurements and even
therapeutic pressures. The surprising similarity in the latter parameter can be attributed to the persistent
snoring and
ow limitation episodes exhibited by the non-OSA group.
Table 3.1: Subject pool anthropometric and polysomnographic characteristics. BMI, body mass index;
OAHI, obstructive apnea hypopnea index; CPAP, continuous positive airway pressure. * indicates that
there is one missing value. ** indicates that there are two missing values. Values are presented as mean
SD.
Variable non-OSA OSA Signicance
(n = 22) (n = 23)
Subject Characteristics
Gender (M:F) 6:16 15:8 p <0.05
Age (years) 15.545 0.504 14.913 0.350 ns
BMI (kg/m
2
)* 35.011 1.598 37.507 1.230 ns
Neck Circumference (cm)** 39.718 1.147 42.995 0.979 p <0.05
Polysomnography
OAHI (events/hour) 2.173 0.294 30.974 5.328 p <0.001
Therapeutic CPAP (cmH2O) 10.455 0.650 11.130 0.459 ns
3.2.1.3 Pulmonary function test
On a dierent night, within three months after being diagnosed (72 13 days), subjects returned to the
hospital for pulmonary function testing. This test was performed immediately before the experimental PSG
to evaluate for pulmonary disease as a contributor to hypoxia or hypercapnia during the diagnostic PSG.
The PFT was conformed by: a body plethysmography, to measure various lung capacities; a spirometry, to
assess airway obstruction; and a single breath nitrogen washout to look for abnormalities in the distribution
32
of ventilation (Crapo, 1994). Figure 3.1 presents a schematic of the equipment that was used to perform the
full body plethysmography along with the spirometry tests. In addition, sample recordings of lung volumes
and expiratory
ow measurements are also shown. Table 3.2 summarizes the measurements collected from
the PFT procedures.
Figure 3.1: Schematic of the full body plethysmography and spirometry tests that are part of the pulmonary
function test along with sample measurements that are obtained from various maneuvers. Figure adapted
from Siberry and Iannone (2000).
3.2.1.4 Experimental polysomnography
On a dierent night, subjects returned to the sleep laboratory for the overnight research PSG. Subjects were
asked to sleep in supine position and were tted with a full face mask (Mirage Quattro, ResMed, San Diego,
CA), which was attached to a unique breathing circuit. The circuit consisted of a two-way t-shape non-
rebreathing valve (Model 1400, Hans Rudolph, Kansas City, MO) with a whisper swivel valve (Respironics,
Pittsburgh, PA) connected at the expiratory port to remove exhaled CO
2
from the circuit. An 18-inch
long,
exible CPAP tube was appended to the swivel valve and was fed back to the inspiratory limb, in
order to maintain pressure during inspiration and expiration constant. Positive pressure was provided via a
bilevel pressure ventilator (S/T-D 30, Respironics, Pittsburgh, PA) operating in CPAP mode. In addition
to the standard polysomnography measurements, mask pressure was monitored by means of a dierential
pressure transducer (Validyne, Northridge, CA) referenced to atmospheric pressure. Respiratory air
ow
33
Table 3.2: Subject pool pulmonary function test measurements. FRC, functional residual capacity; FVC,
forced vital capacity; FEV1, forced expired volume in one second; FEF 25/75, forced expiratory
ow between
25% and 75% of FVC; PEF, peak expiratory
ow; Vmax 80%, percentage of FVC remaining. Values are
presented as means SEM. * Missing data from six subjects. ** Missing data from seven subjects. yy
indicates that the results are statistically signicantly dierent between the groups at p 0.05.
Variable non-OSA OSA P-Value
(n = 22) (n = 23)
Body Plethysmography
FRC (% pred) 100.1 16.5 96.8 19.5 p = 0.537
FVC (% pred) 115.5 14.3 114.3 18.7 p = 0.805
Spirometry
FEV1 (% pred) 111.2 14.3 104.6 14.4 p = 0.135
FEV1/FVC 85.2 3.8 80.5 6.9 p = 0.008yy
FEF 25/75 (% pred) 110.5 19.9 93.8 21.7 p = 0.010yy
PEF (% pred) 100.5 13.1 93.9 15.1 p = 0.125
Vmax 80% (% pred)* 98.8 13.8 91.0 16.2 p = 0.125
Nitrogen Washout
FRC Upright (% pred)** 91.9 17.9 109.7 37.9 p = 0.128
FRC Supine (% pred)** 83.3 18.7 107.2 81.0 p = 0.459
was measured by a second Validyne pressure transducer in conjunction with a pneuomotachometer (Model
4813, Hans Rudolph, Kansas City, MO) connected to the ventilator. Arterial blood pressure was assessed
using a peripheral arterial tonometer placed on the index nger (Itamar Medical, Caesarea, Israel) and was
used concomitantly with EEG signals to detect arousals (Davies et al., 1993). All physiological signals were
sampled atf
s
= 200Hz and recorded with a digital acquisition system (NI USB-6218, National Instruments,
Austin, TX), which was also used to send pressure command signals from the computer to the ventilator.
Figure 3.2 (A) illustrates the schematic of our experimental setup that included the respiratory circuit and its
interconnection with the command computer. Figure 3.2 (B) depicts one of the study participants wearing
the respiratory circuit along with the noninvasive sensors used for physiological measurements monitoring.
After sleep onset, CPAP was gradually increased starting at a baseline value of 3 cmH
2
O pressure and
until respiratory events (snoring, hypopneas, apneas) and
ow limitation, dened as a
attening in the
inspiratory portion of the air
ow signal (Clark et al., 1998), were eliminated. When the therapeutic level
was reached, and once a stable Non Rapid Eye Movement (NREM) sleep stage was achieved, inspiratory
pressure was abruptly increased by 5 cmH
2
O for two consecutive breaths, keeping the expiratory pressure
34
Figure 3.2: A. Schematic of the breathing circuit and the integrated control and data acquisition system
utilized for protocol execution. B. Picture of the experimental setup taken on a subject who participated in
the study.
at therapeutic level. The response to these "induced sighs" was recorded for 50 breaths and used for further
analysis. This intervention lasted 4-5 minutes in average and was carried out multiple times throughout
the night, discarding from our analysis those segments that resulted in arousal. In addition, segments of
spontaneous breathing at therapeutic pressure during quiet NREM sleep lasting approximately 10 minutes
were also recorded and utilized for analysis.
3.2.2 Data preparation
3.2.2.1 Sleep state monitoring
As has been previously stated, we are interested in assessing ventilatory control stability during NREM
sleep. Therefore, in order to assure that the segments that were included in our analysis corresponded to
the sleeping consciousness state, we monitored the electrical activity of the brain by means of an EEG.
The
uctuations in frequency content as well as the amplitude of the EEG measurements depend upon the
alertness state of the brain. While high amplitude EEG and slow oscillations correspond to a sleeping state,
low amplitude EEG potentials with fast oscillations are associated with a more alert consciousness state
35
(Campbell, 2009; Phillipson, 1978). Table 3.3 presents a summary of the relevant EEG frequency bands and
their corresponding interpretation in sleep analysis.
In order to obtain a time-frequency map of the EEG activity, we employed a procedure similar to what
was previously proposed by Asyali et al. (2007). They suggest the tting of autoregressive models (AR)
to the EEG signal, segmented into multiple windows, to obtain estimations of the power spectral density
(PSD) (Akaike, 1969; Kay and Marple, 1981). AR-PSD estimation of the EEG segments is a powerful
technique that also exploits the stationarity concept provided by the short term Fourier transform (STFT),
while overcoming the time and frequency trade o and the nite frequency resolution that are limitations
associated with the STFT (Cohen, 1995).
We rst partitioned the EEG recording into multiple consecutive segments of ve seconds each with an
eighty percent overlap. For each data portion, we found AR models of increasing orderq (up toQ = 15) and
computed the Akaike's nal prediction error (FPE) for all of the candidate models selecting the one that
minimized FPE as the optimal model. We then used the optimal model parameters corresponding to each
individual data chunk to compute the PSD using the following expression:
P
EEG
(f) =

2

j1
P
Q
q=1

q
e
2ifqT
j
2
; (3.1)
where
2

represents the variance of the residuals, Q is the optimal model order for the specic data portion
of interest,
q
are the AR optimal model coecients, f is the frequency in Hertz and T is the sampling
Table 3.3: Description of frequency content of the EEG signal and its interpretation in sleep analysis. The
frequency ranges that are dened herein are not standard and could be slightly dierent to some other
conventions found in the literature. N1-N3 denote the multiple sleep stages in accordance with the notation
proposed by the American Academy of Sleep Medicine (Iber, 2007). Table adapted from Asyali et al. (2007).
Frequency band Frequency Range (Hz) Interpretation
(delta) 1.0 - 4.0 Deep sleep
(theta) 4.0 - 7.5 Transition from light (N1, N2) into deep (N3) sleep
(alpha) 7.5 - 12.0 Alertness or awake state
(sigma) 12.0 - 16.0 Sleep spindles occurring during N2 sleep
(beta) 16.0 - 25.0 Fully alert or awake state
36
period. After nding estimations of P
EEG
(f) for each of the overlapping time windows, we concatenated
them all to nally yield the time-frequency mapping of the EEG signal with a time resolution of 1 second
to identify the presence of cortical arousals.
A recorded segment whose EEG frequency spectrum had the power concentrated in the lower frequency
bands (i.e., below 7.5 Hz) with no abrupt changes into the higher frequency bands was considered to be fully
in sleep and was used for further analysis. However, if an arousal was noted during the recording, then the
signals were truncated eliminating the portion that followed the arousal and the remainder was used in the
subsequent steps of our analysis. If the arousal occurred early into the recording, then the complete data
set was discarded and not included in our analysis. The episodes of arousal contained in our recorded data
segments were also identied and scored by a certied sleep technician and used to cross validate the results
obtained with our AR-PSD estimation technique. Figure 3.3 shows a sample recording of our induced sighs
protocol that resulted in arousal after approximately thirty breaths. It can be seen from the heat map,
presented in the second panel, that the power of the EEG signal is concentrated in the delta frequency band
for the rst fty seconds indicating a period of deep sleep. Then, while the sighs are being induced by the
CPAP machine, the EEG activity shows a transition into a more light sleep state that manifests with the
appearance of theta oscillations. The EEG frequency power remains stable within the sleeping frequency
bands until an abrupt change into the beta band (fully alert) is detected at approximately 180 seconds. This
change in EEG activity is then followed by other transitions into the alpha frequency band until the sleeping
state resumes at approximately 210 seconds. Such changes in the frequency content of the EEG signal are
accurately detected by our time-varying spectral estimation technique and are associated with an episode
of arousal. Thus, the signals that were recorded after the arousal started were discarded and not utilized in
the subsequent steps of our analysis.
3.2.2.2 Data processing
Once the segments had been cleaned from the presence of arousal, they underwent further processing steps
to derive breath-by-breath measurements. First, time of inspiration and expiration, T
I
andT
E
respectively,
37
Figure 3.3: Sample induced sighs recording that resulted in arousal. The top panel shows a forty second
window of the continuous recording of EEG activity that includes the region were the arousal was detected.
The second panel depicts, in the form of a heat map, the normalized power spectrum of the EEG recording
as a function of time. Note that the frequency axis has been limited to the frequencies that are relevant in
sleep analysis. The lower three panels show the continuous measurements of pressure, air
ow and PCO
2
,
respectively. The arrow indicates the portions of these measurements that are discarded from our analysis.
were automatically detected from the air
ow signal crossings by zero. Then, tidal volume at the k
th
breath
V
T
(k) was obtained by integrating the continuous air
ow signal
_
V (t) over T
I
, and kept constant for the
38
entire breath duration (T
I
+T
E
).
V
T
(k) =
Z
T
I
(k)
T
E
(k1)
_
V (t) dt (3.2)
From the spontaneous breathing recordings, ventilation at the k
th
breath was dened as the air volume
entering the lungs during the total breath duration
_
V
E
(k) =
V
T
(k)
T
I
(k) +T
E
(k)
(3.3)
Conversely, for the induced sighs data, we dened ventilatory drive at the k
th
breath as the air volume
entering the lungs only during the inspiratory period. By excludingT
e
from the computation, we suppressed
the eects of the long expiratory times produced by the provoked sighs
_
V
D
(k) =
V
T
(k)
T
I
(k)
(3.4)
Figure 3.4 shows how the breath-by-breath measurements of tidal volume, ventilation and ventilatory
drive were derived from the continuous recording of air
ow.
We were also interested in having a measurement of the breath-to-breath variability in CO
2
concentra-
tion at the arterial sites (P
a
CO
2
). Since our measurements are completely noninvasive, we were not able
to directly measure P
a
CO
2
. We instead utilized the PCO
2
signal measured via a nasal cannula to extract
breath-by-breath values of end-tidal CO
2
(P
ET
CO
2
). This signal has been proven to accurately approxi-
mate P
a
CO
2
under normal conditions in populations of adults and children (McNulty et al., 1990; Friesen
and Alswang, 1996). We followed the procedure described below to derive the breath-by-breath P
ET
CO
2
measurements.
First, the PCO
2
signal was low-pass ltered digitally using a Finite Impulse Response (FIR) lter with
Kaiser windowing. The cuto frequency was set to 5 Hz and, in order to keep the amplitude of the original
measurement unaected, the lter order was set to 30. Second, in order to automatically derive a breath-
by-breathP
ET
CO
2
value, we had to overcome a challenge attributed to the presence of a delay in thePCO
2
39
−50
0
50
100
Airflow
(L/min)

0
0.5
1
Tidal Volume
(L)
0
10
20
Ventilation
(L/min)
170 175 180 185 190 195 200 205 210
0
20
40
Ventilatory Drive
(L/min)
Time (sec)
Start of Inspiration
Start of Expiration
Figure 3.4: Breath-by-breath derivation of ventilatory time series from the continuous recording of air
ow.
recording that was associated with the sampling time of the device that was used for gas analysis, and also
with the subjects' anatomical dead space. Such delay had to be properly identied and accounted for, so that
we could have a one-to-one correspondence between the breath-by-breath ventilation and P
ET
CO
2
signals.
In order to do so, our team developed an adaptive algorithm that estimated the delay existing between the
air
ow and thePCO
2
signal in each breath and shifted the latter signal to properly align both measurements.
Once this was achieved, the nal step was to nd the PCO
2
values at the end of the expiratory phase by
simply nding the maximum PCO
2
value corresponding to the k
th
breath and keeping it constant for the
entire breath to nally yield the measurement of P
ET
CO
2
:
P
ET
CO
2
(k) = max
t2[T
I
(k);T
E
(k)]
PCO
2
(t): (3.5)
The process through which the breath-by-breath P
ET
CO
2
measurements were obtained is illustrated in
Figure 3.5.
40
−50
0
50
100
Airflow
(L/min)
0
20
40
60
PCO
2
(mmHg)
170 175 180 185 190 195 200 205 210
40
45
50
Time (sec)
P
ET
CO
2
(mmHg)
SD
(k−1)
th
k
th
(k+1)
th
(k−1)
th
k
th
(k−1)
th
k
th
(k+1)
th
(k+1)
th
Start of Inspiration
Start of Expiration
Figure 3.5: Breath-by-breath derivation of P
ET
CO
2
time series from the continuous recordings of air
ow
and PCO
2
.
Once the breath-by-breath ventilatory andP
ET
CO
2
measurements were obtained, the linear trends were
removed. Furthermore, these time series were downsampled to 1 Hz by averaging in order to produce
uniformly sampled sequences for subsequent analyses.
3.3 Mathematical modeling and stability feature extraction
This chapter introduces the mathematical framework under which our computational models are built upon.
It also shows the exhaustive validation process of our mathematical models using synthetic data representing
a wide variety of circumstances. Some concepts of linear systems stability theory are then invoked and used
for stability feature extraction from the estimated models. It nally discusses the statistical tests that will
be employed for comparing the stability features extracted from the experimental data collected in our
population of pediatric overweight subjects.
41
3.3.1 Mathematical modeling
3.3.1.1 Volterra series and basis expansion technique
The mathematical framework utilized to characterize the dynamics of the systems under study, is commonly
known as nonparametric modeling. Such denomination is attributed to those models whose underlying
structure is not based upon any prior knowledge of the physics of the system, but in the contrary, it is
directly estimated from observable input-output data.
The goal of nonparametric modeling is to nd a mathematical representation of how the functional, F [],
maps the input function x (t
0
);t
0
t into an output signal y(t) (Marmarelis, 2004):
y(t) =F [x (t
0
);t
0
t] (3.6)
The Volterra series, rst introduced by the late Vito Volterra in the 1930s (Volterra, 1930), is a general
method for expanding a continuous functional. It describes the nonlinear dynamic relationship between
input and output variables x(t) andy(t), respectively, for stable time-invariant systems (Marmarelis, 1997).
For the continuous case takes the form:
y(t) =
Z
1
0
k
1
()x(t) +
Z
1
0
Z
1
0
k
2
(
1
;
2
)x(t
1
)x(t
2
) +::: +
Z
1
0
:::
Z
1
0
k
q
(
1
;:::2) +::: (3.7)
Since data are collected at regular sampling intervals T , it is more convenient to express the Volterra
series with its discrete representation:
y(n) =k
o
+T
M1
X
m=0
k
1
(m)x(nm) +T
2
M1
X
m1=0
M1
X
m2=0
k
2
(m
1
;m
2
)x(nm
1
)x(nm
2
) +::: +; (3.8)
whereM represents the amount of previous values of the input aecting the current output, and k
i
is thei
th
42
order kernel associated with the degree of nonlinearity of the system. Since the signals show small variations
around an operating point close to zero after being detrended, the discrete Volterra series reduces to a
discrete linear convolution:
y(n) =
M1
X
m=0
k
1
(m)x(nm): (3.9)
In order to make the impulse response more compact and improve model estimations, we assume that k
1
can be expanded using a properly selected set of causal basis functionsb
q
(m) (see Equation 3.10) dened over
the dynamic range of the system [0;M] (Marmarelis, 2004). We utilized the set of Meixner basis functions
(MBF), which has a built-in exponential term suitable for modeling the relaxation characteristics exhibited
by various physiological systems. This set of orthonormal functions represents a generalization of the widely
used discrete Laguerre functions (Den Brinker, 1995), and has proven to be suitable for modeling systems
with sluggish dynamics such as the ones that we aim to study (Asyali and Juusola, 2005). The dierent slow
onsets can be captured by varying the order of generalization, which is an MBF parameter that controls the
time at which the basis functions will start to
uctuate. A detailed explanation of the MBF is presented in
section 3.3.1.2.
k
1
(m) =
Q1
X
q=0
c
q
b
q
(m); (3.10)
where Q is the total number of basis functions utilized to describe the system, b
q
represents the q
th
order
MBF and c
q
f0 q Q 1g are the expansion coecients. Figure 3.6 illustrates, using matrix notation,
the impulse response expansion technique with Meixner basis functions.
By combining equations 3.9 and 3.10 we obtained:
y(n) =
M1
X
m=0
Q1
X
q=0
c
q
b
q
(m)x(nm); (3.11)
from which the expansion coecientsc
q
can be estimated by least squares minimization. This procedure was
applied to the spontaneous breathing data to nd estimations of the gas exchange process, and the induced
43
Figure 3.6: Graphical representation of the expansion of the impulse response function as a weighted sum
of Meixner basis functions. In this example the memory of impulse response of the system M was selected
to be 100 seconds and was expanded using a total of basis functions Q = 4.
sighs recordings to estimate the dynamics of the chemore
ex as a whole.
3.3.1.2 Meixner basis functions
As stated before, the set of Meixner functions are a generalization of the Laguerre basis and can be easily
constructed using the latter as illustrated in gure 3.7. It can be seen that the discrete Laguerre functions
are generated by passing an impulse, denoted by the Kronecker delta function, through a cascaded lter
structure composed by one low-pass lter and a set of all-pass lters. The Meixner functions are nally
obtained by applying a transformation to the Laguerre functions. This scheme for Laguerre and Meixner
functions generation is more practical than their recursive implementation (Asyali and Juusola, 2005). For
a detailed explanation on the explicit derivation of the Laguerre and Meixner analytical expressions, the
reader is referred to the monograph by Den Brinker (1995).
A formal mathematical representation of how the Laguerre functions are transformed to yield the Meixner
basis is given by the following expression:
G
(n)
q
(z) =A
(n)
(z); (3.12)
whereG
(n)
q
(z) and (z) are matrices containing the z-transforms of the Meixner and Laguerre basis functions
respectively; A
(n)
is an orthogonal transformation matrix that needs to be estimated; and n = 0; 1; 2;::: is
44
Figure 3.7: Cascaded lter structure used to generate the Laguerre and the Meixner set of basis functions.
Figure was adopted from Asyali and Juusola (2005).
known as the order of generalization. The latter parameter is an additional degree of freedom that the
Meixner basis functions posses controlling the time at which the functions start to
uctuate. Note that
a particular case is presented when n = 0. This makes the transformation matrix A
(n)
= I and hence,
according to equation 3.12, the Meixner and Laguerre sets of basis functions are equivalent.
According to the study performed by Den Brinker (1995) the transformation matrix can be obtained by:
A
(n)
=L
(n)
U
n
; (3.13)
where L
(n)
is an unknown lower triangular matrix that has to be derived; and U
n
is an upper band matrix
of dimensions QQ as follows:
U
n
=
2
6
6
6
6
6
6
6
6
6
6
4
1 p 0 ::: 0
0 1 p ::: 0
.
.
.
.
.
.
.
.
.
.
.
. 0
0 0 0 ::: 1
3
7
7
7
7
7
7
7
7
7
7
5
;
the dimensions of matrix U
n
are given by the total number of functions to be generated. The parameter
p(0 < p < 1) is repeated along the second principal diagonal and corresponds to the pole of the cascaded
lters shown in gure 3.7, and it will determine the decaying time of the Laguerre of Meixner basis functions.
Given the orthogonality characteristics of matrix A
(n)
we have that:
45
A
(n)
n
A
(n)
o
T
=L
(n)
U
n
fU
n
g
T
n
L
(n)
o
T
=I (3.14)
The matrix U
n
fU
n
g
T
is a positive denite band matrix with bandwidth w = 2n + 1 (Strang and Press,
1993). The inverse of the Cholesky factorization ofU
n
fU
n
g
T
was then computed to nd the lower triangular
matrix L
(n)
. By using this matrix on equation 3.13, we can nally obtain the transformation matrix A
(n)
.
Then, the derivation of the Meixner basis functions from the Laguerre set follows from equation 3.12.
Figure 3.8 illustrates the generated Meixner basis functions for various orders of generalization n and
number of basis functions Q. The left most column depicts the cases when n = 0, or in other words, when
the Meixner basis functions are identical to the Laguerre set. It can be seen that as the parametern increases,
the time at which the functions start to
uctuate also increases.
0 50 100
−0.5
0
0.5
m = 3 ; n = 0
0 50 100
−0.5
0
0.5
m = 3 ; n = 2
0 50 100
−0.5
0
0.5
m = 3 ; n = 4
0 50 100
−0.5
0
0.5
m = 3 ; n = 6
0 50 100
−0.5
0
0.5
m = 4 ; n = 0
0 50 100
−0.5
0
0.5
m = 4 ; n = 2
0 50 100
−0.5
0
0.5
m = 4 ; n = 4
0 50 100
−0.5
0
0.5
m = 4 ; n = 6
0 50 100
−0.5
0
0.5
m = 5 ; n = 0
0 50 100
−0.5
0
0.5
m = 5 ; n = 2
0 50 100
−0.5
0
0.5
m = 5 ; n = 4
0 50 100
−0.5
0
0.5
m = 5 ; n = 6
0 50 100
−0.5
0
0.5
m = 6 ; n = 0
0 50 100
−0.5
0
0.5
m = 6 ; n = 2
0 50 100
−0.5
0
0.5
m = 6 ; n = 4
0 50 100
−0.5
0
0.5
m = 6 ; n = 6
Increasing Number of Basis Functions
Lags (Number of Samples)
Incresing Order of Generalization
Figure 3.8: Generated Meixner basis functions of memory M = 100 lags and for n = 0; 2; 4; 6 and Q =
3; 4; 5; 6.
46
3.3.1.3 Model formulations
3.3.1.3.1 Gas exchange
The dynamic input-output relationship between the current value of end-tidal P
CO2
and the present and
past values of ventilation was formulated by:
P
ET
CO
2
(n) =
Mp1
X
m=0
k
p
(m)
_
V
E
(nm) +
p
(n); (3.15)
where the operator implies variations around the mean values of P
ET
CO
2
and
_
V
E
; k
p
(m) is the plant
impulse response;
p
(n) represents the changes in P
ET
CO
2
that are not due to changes in ventilation; and
M
p
is the memory of the gas exchange process. Given that this phenomenon has been found to exhibit
fast dynamics with eects lasting for only a few breaths (Mitsis et al., 2009; Nemati et al., 2011), M
p
was
assumed to be 30 seconds long.
3.3.1.3.2 Chemore
ex loop
The chemore
ex loop model characterizes the combined dynamics of several mechanisms: the gas exchange
occurring in the lungs and tissues; the transport delay through circulation; the process of chemoreception
by the peripheral and central chemoreceptors; and the activation of the respiratory muscles. After imposing
causality by inserting the time delay D, the chemically-mediated changes in ventilation are modeled as the
output of an autoregressive linear process (Akaike, 1968; Gustavsson et al., 1977):

_
V
D
(n) =
Mc1
X
m=0
k
c
(m)
_
V
D
(nmD) +
c
(n); (3.16)
where the operator indicates variations around the mean value of
_
V
D
;k
c
(m) is the loop impulse response
(LIR) and combines the eects of all the processes that conform it;M
c
denotes the memory of the chemore
ex
loop and it was assumed to be 100 seconds;
c
(n) represents the changes in
_
V
D
that are not mediated
by the chemore
ex; and D is a pure time delay representing the time it takes for a change in alveolar
P
CO2
to be transmitted through the circulatory system to the chemoreceptors loci, signal transduction and
47
processing within the medullary circuitry (Ben-Tal and Smith, 2010; Feldman et al., 2003). Based on previous
experimentally derived models (Asyali et al., 2002; Bellville et al., 1979),D was assumed to lie within a range
between 6 and 12 seconds.
Note that equation 3.16 would not hold during the application of the external perturbation (induced
sighs), thus we excluded this portion of the data when tting the model and considered only the part that
immediately followed the sighs.
3.3.1.4 Model selection criterion
A common way to evaluate model performance is by examining the dierence between the measured output
y(n) and the one predicted by the estimated model ^ y(n). The dierence between these two time series is
known as the prediction residual in modeling jargon and is computed as follows:
e(n) =y(n) ^ y(n): (3.17)
Given that the data sets utilized for modeling purposes are recorded from multiple subjects, the variability
in the data can be quite dierent between them. Therefore, there is a need to incorporate a normalization
factor to equation 3.17 that would account for this sources of variability. We now dene the normalized mean
squared error as the ratio between the variance of the residuals and the variance of the output as described
by equation 3.18. This parameter takes values between 0 and 1 and indicates how much of the variability
of the output is explained by the estimated model. In other words, a high NMSE indicates that the model
explains few of the variability of the output data, while a low NMSE indicates that the model has accounted
for most of the variance present in the output measurement.
NMSE =
P
N
n=1
(e(n) e)
2
P
N
n=1
(y(n) y)
2
(3.18)
where N denotes the length of the time series, e(n) is the dierence between the model prediction and the
measured output y(n), and e and y are the mean values of the residuals and the output, respectively.
48
Although, NMSE is widely employed for optimal model selection, it could sometimes be misleading and
thus it should be used carefully. For instance, a low signal to noise ratio at the output would yield very
high NMSE, independently of the accuracy of the estimated model (Marmarelis, 2004). Moreover, by only
considering the NMSE in the optimization problem for model selection, the model could end up having more
parameters than needed and thus could lead to overtting the data. Overtting results from a model that
not only captures the underlying system dynamics, but also the noise dynamics, which is undesired (de Sousa
Aranha Oliveira, 2011).
In order to avoid the problem of over tting the data and to obtain the most parsimonious model
that represented the system accurately, we employed the concept of Minimum Description Length (MDL).
This model selection criterion, rst introduced by Rissanen (Rissanen, 1978), includes the normalized mean
squared error as well as a penalizing factor for increasing model complexity by adding parameters that have
to be estimated (Ljung, 1987) :
MDL = ln (NMSE) +
Q ln(N)
N
; (3.19)
whereQ is the total number of MBF. A global search for the minimum of the MDL function was performed
for dierent combinations of number of MBF, orders of generalization and, in the case of the CIR estimation,
time delays.
3.3.2 Simulation
A discrete linear feedback model of the chemore
ex implemented in Simulink (The MathWorks, Inc., Natick,
MA) was used to produce articial breeath-by-breath data sets that emulated our experimental interventions
(see gure 3.9). The model consisted of three main components: a) a feedforward branch representing the
gas exchange occurring in the lungs; b) a pure time delay to account for the latency in signal transmission
from the lungs to the chemoreceptors location sites; and c) a feedback component constituting the sensing
function provided by the chemoreceptors which ultimately command a ventilatory compensation through
the activation of the respiratory muscles. The gas exchanger was approximated by a single compartment
49
model with a negative gain so that an increase in ventilation would cause a decrease in P
ET
CO
2
(Ben-Tal,
2006; Khoo et al., 1991). The feedback portion of the model, conformed by the central and the peripheral
chemore
exes, was represented by two parallel compartments (Bellville et al., 1979) with additive ventilatory
contributions (Clement et al., 1995; St Croix et al., 1996).
-Gl/Tl
1-exp(-1/Tl)z
-1
Gas Exchange
in the Lungs
Z
-d Circulatory
Delay
Gp/Tp
1-exp(-1/Tp)z
-1
Peripheral
Chemoreflex
Gc/Tc
1-exp(-1/Tc)z
-1
Central
Chemoreflex
\
Noise
Disturbance
Figure 3.9: Simulation discrete model used to emulate the experimental interventions and generate the
articial data segments.
Spontaneous breathing was simulated for 10 minutes by the addition of a normally distributed random
signal to the system without any other external disturbance. Random variations of Ventilation andP
ET
CO
2
were then utilized as input and output to the rst order Volterra model in order to estimate the dynamics
of the gas exchange process.
On the other hand, the Induced Sighs protocol was simulated by injecting a disturbance that took the form
of a pulse with amplitude 15 Lmin
1
and a duration of two breaths, in addition to a stochastic component
with the same characteristics as the ones used to simulate spontaneous breathing. The ventilatory response
to the perturbation was simulated for 50 breaths and used in the autoregressive rst order Volterra model
to recover the Chemore
ex Loop dynamics.
One-at-a-time, Two-at-a-time and All-at-a-time sensitivity analyses were performed in order to test the
accuracy of our identication technique for multiple combinations of parameter values (Saltelli et al., 2008).
50
In addition, the precision in our estimations was also evaluated for variations in the amount of noise added
to the system. A total of 100 data sets were generated for each of the various scenarios and used to produce
a family of estimated models. Subsequently, the estimated models and the model-derived stability features
were compared to the theoretical ones and the performance of the stability quantication technique was
evaluated by means of the relative percent error.
Table 3.4 shows the parameters that were used as mean values to produce the articial data sets and
were adapted from other respiratory control models (Bellville et al., 1979; Khoo, 2000b).
Table 3.4: Nominal values of the parameters used for data generation. Values were adopted from previous
studies (Bellville et al., 1979; Khoo, 2000b).
Parameter Symbol Value
Lung Sensitivity (min mmHg
-1
L
-1
) G
l
1
Lung Time Constant (sec) T
l
6.5
Peripheral Chemore
ex Sensitivity (L min
-1
mmHg
-1
) G
p
1
Peripheral Chemore
ex Time Constant (sec) T
p
15
Central Chemore
ex Sensitivity (L min
-1
mmHg
-1
) G
c
2
Central Chemore
ex Time Constant (sec) T
c
150
Circulatory Time Delay (sec) D 8
Breath Duration (sec) T
t
4
Noise Variance (L
2
min
-2
)
2
1.05
3.3.2.1 Sensitivity analysis
Sensitivity analyses were carried out to evaluate the accuracy of the estimations provided by our algorithms
for variations in the multiple parameters conforming the simulation model introduced in Section 3.3.2 that
was used to generate the synthetic data sets. A one-at-a-time sensitivity analysis is performed by changing
one parameter of a model (
i
) within a predened range (around its nominal value) while xing the rest
of the parameters to their nominal values (shown in Table 3.4) to nally evaluate a certain aspect of the
model. In our case, we were interested in evaluating how sensitive our stability quantiers (extracted from
a nonparametric model) were to changes in the parametric model. Similarly, a two-at-a-time sensitivity
analysis is carried out by varying two parameters of a model (
i
;
j
) while keeping the rest xed at nominal
values. The sensitvity of the variable of interest to the variations of the two parameters S(
i
;
j
) would be a
51
surface that could still be visually presented and analyzed. However, the visualization of sensitivity analyses
on models containing more than two variables becomes challenging. Since the parametric model that we
proposed for synthetic data generation contains seven variables, we had to employ the concept of parallel
coordinates for result visualization.
3.3.2.1.1 Parallel coordinates
Parallel coordinates is a widely utilized framework that allows visualization and exploration of multivariate
data in a two-dimensional plane. In its origins, this type of framework was applied to air trac control
(Inselberg and Dimsdale, 1987) and automobile (Wegman, 1990) problems. Since then, the theory and
applications of parallel coordinates has continued to evolve and it is now being applied to evaluate the
behavior of dynamic biological systems (Nguyen et al., 2015). Although the principles behind the concept
of parallel coordinates are relatively simple, it involves several steps that must be carefully explained.
It starts with the selection of a dynamic system whose behavior is governed by a set of ordinary dierential
equations (model) describing its temporal behavior. Next, we must dene the parameters of interest (
1
:::
n
)
and the ranges within which they can vary (frequently spanning physiologically plausible values). Then, a
random and unbiased sampling algorithm (typically Monte Carlo sampling) must be selected to draw dierent
sample sets from the uniform parameter distributions. The parameter set sampling step is suggested to be
applied more than 10,000 times such that the parameter space is fully explored. Next, an evaluation of
the system dynamical behavior for each of the sampled parameter sets is carried out based on a predened
criterion or outcome, providing a categorization of the results. Lastly, the outcome is plotted as a function
of the parameter set that produced such outcome. The parameters (corresponding to a specic set) are
interconnected by a line whose color is used to distinguish the diverse behaviors of the system or categories.
Figure 3.10 illustrates the aforementioned steps.
The assessment of the system's behavior can be dened in multiple manners and depends entirely on the
characteristics that we are interested in evaluating. The simplest way of evaluating the behavior of a system
is by using a dichotomous variable. Examples of this type of categorization include the study of whether
a dynamic system exhibits oscillations or not, or even to assess whether a system is stable or unstable. A
52
Figure 3.10: Data characterization and visualization framework for multi-dimensional sensitivity analysis
using parallel coordinates. Values of each parameter are represented on the corresponding vertical axes and
each line connecting the n parameter values represent a single parameter set. Note that all of the sampling
parameter ranges have been normalized to the [0,1] range to facilitate visualization and system's behavior
comparison for the multiple parameter sets. Adapted from Nguyen et al. (2015).
sample of a dichotomous stability assessment of the dynamical model presented in Section 3.3.2 is depicted in
Figure 3.11 (top panel). The red lines correspond to the parameter sets that resulted in an unstable behavior
of the respiratory control system. It can be observed that the combinations that resulted in such unstable
patterns are low peripheral and lung time constants, in combination with elevated circulatory time delays
and peripheral and lung gains. The parameters associated with the central chemore
ex (T
c
and G
c
) do not
appear to play a major role in the development of the unstable respiratory patterns. While the dichotomous
way of categorizing the outcome variable could provide good qualitative assessment in some cases, when it
comes to quantifying system's stability it could fall short at depicting the various degrees of stability. The
utilization of more than two categories to evaluate the system's behavior could be of great help when trying
to quantify stability. The addition of the other categories can be incorporated into the parallel coordinates
53
plot by introducing color gradients. This feature adds another dimension to the plot and allows for a more
continuous evaluation of a variable as a function of the model parameters. Figure 3.11 (bottom panel) shows
a more gradual quantication of stability of the system. Loop gain is a quantier of the degree of stability
of a system. The closer LG is to zero (blue), the more stable the system is, and on the contrary, the closer
LG is to one (red), the more unstable the system is. Note that the ner resolution, resulting from including
more categories, allows to detect those combinations of parameters that yielded responses that are on the
verge of becoming unstable.
Tc Tp Tl D Gc Gp Gl
0
0.2
0.4
0.6
0.8
1
Normalized Parameter Values
[75,225] [7.5,22.5] [3.25,9.75] [4,12] [1,3] [0.5,1.5] [0.5,1.5]
0
0.2
0.4
0.6
0.8
1
Stable
Unstable
Tc Tp Tl D Gc Gp Gl
0
0.2
0.4
0.6
0.8
1
Normalized Parameter Values

[75,225] [7.5,22.5] [3.25,9.75] [4,12] [1,3] [0.5,1.5] [0.5,1.5]
0
0.2
0.4
0.6
0.8
1
Loop Gain
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Figure 3.11: Parallel coordinates used to summarize an all-at-a-time sensitivity analysis of the stability
characteristics of the feedback dynamic system presented in Section 3.3.2. Note that while in the top panel
the outcome variable is dichotomous, in the bottom panel the outcome variable is given by a continuous
variable.
For a more detailed review on the several things that must be considered when utilizing the parallel
coordinates visualization framework, the reader is referred to the review paper by Heinrich and Weiskopf
54
(2013).
3.3.3 Stability feature extraction
3.3.3.1 Plant, controller and loop gain
Once the optimal models were determined, the impulse responses k
p
(m) and k
c
(m) were transformed into
the frequency domain using the discrete Fourier transform. These frequency dependent complex variables,
K
p
(e
j!
) and K
c
(e
j!
), represent the plant gain (PG) and the loop gain (LG), respectively, and were used to
assess ventilatory stability. Subsequently, the average magnitude within the range 2=100! 2=20 was
computed. This frequency range corresponds to ventilatory oscillations cycling between 20 and 100 seconds
(0.01 - 0.05 Hz), and has been associated with the phenomenon known as periodic breathing that could
potentially lead to apnea (Carley and Shannon, 1988; Khoo et al., 1991).
One measurement of PG was obtained per subject, since the no intervention protocol was only performed
once. On the other hand, several estimations of LG were calculated per subject from the induced sighs
segments that did not result in arousal. The LG value that represented each subject was found by computing
the median from the successful segments only.
Theoretically, the overall LG is the product of PG and the controller gain (CG); thus, we utilized our
estimated LG and PG to nd representations of CG as follows:
CG(e
j!
) =
LG(e
j!
)
PG(e
j!
)
: (3.20)
CG estimations were found under the assumption that there were no signicant changes in PG throughout
the night during NREM sleep, i.e. the one PG estimate was kept the same for the dierent LG. Similar to
the LG case, the average gain over the periodic breathing frequency range was computed and the median
CG value was used to represent each subject.
55
3.3.3.2 Relative stability
Up to this point, we have only considered the magnitude of the frequency response of the estimated models
as a means to quantify the predisposition to respiratory instability. As stated in section 3.3.3.1, LG is a
complex variable and, as such, it possesses magnitude and phase characteristics. Geometrically, the phase
represents the angle formed by the real and the imaginary components of a complex variable (Goluzin, 1969).
In the context of systems engineering, it refers to the amount by which the output of a system temporally
lags the input. Large phase shifts between input and output in a feedback system, in combination with an
increased transfer function magnitude, might lead to instabilities (Bode, 1940); thus, the quantication of
the phase, in addition to the magnitude, of our ventilatory control models is of critical importance for a
full assessment of respiratory stability. Linear control theory provides us with tools that help us visualize
and analyze the stability characteristics of a feedback system (Dorf and Bishop, 1998; Franklin et al., 1994).
These analytical tools are known as Bode diagrams, Nichols charts and Nyquist plots, which combine the
magnitude and phase information of the open loop transfer function to assess the proximity to an unstable
behavior, or in other words, the degree of relative stability (Kuo, 1987; Ogata, 2001). The mathematical
foundations to these tools were developed by Nyquist (1932), who proposed to analyze the shape of the
open loop frequency response rather than simply looking at the roots of the characteristic equation as was
traditionally done. Such a modication made the stability analysis amenable to systems that did not count
with an analytical rational expression for their frequency responses, and instead were experimentally derived,
just like the models derived in this work.
The Nyquist criterion determines stability by assessing whether there are any singularities within a
contour enclosing the unstable region of the z-plane, i.e. the space outside the unit circle (Franklin et al.,
1998). This principle establishes that the number of closed loop unstable roots Z will be given by:
Z =N +P (3.21)
where N is the number of clockwise encirclements of the -1 point and P is the number of the open loop
56
unstable poles. Given that all of our LG models are stable, closed loop stability would be achieved if there
are no encirclements of the -1 point for a contour evaluation of LG(z) with z = e
j!T
for 0 !T . A
graphic representation of the Nyquist stability criterion is shown in Figure 3.12:
Figure 3.12: Schematic of the Nyquist stability criterion and relative stability parameter denition. The
dashed circle with a unity radius delimits the stability boundaries on the complex plane with Im and Re
representing the imaginary and real axes. LG(e
j!T
), loop gain taking values of up to half of the sampling
frequency; T , sampling period; PM, phase margin; GM, gain margin; !
pc
, phase crossover frequency; !
gc
,
phase crossover gain.
It can be seen that there are some parameters that can be extracted from the Nyquist plot that can be
used to evaluate the relative stability characteristics of the system under study. For instance, the frequency
at which the function LG crosses by the real axis of the complex plane is known as the phase crossover
frequency!
pc
. The amplication gain that needs to be added to LG, evaluated at!
p
, in order for it to cross
the -1 point is known as the gain margin GM. Additionally, the frequency at which the magnitude of LG
equals to one is known as the gain crossover frequency !
gc
; and the amount of phase shift required for LG,
evaluated at !
gc
, to intersect the real axis of the complex plane is dened as the phase margin PM. The
Nyquist diagram shows graphically how these parameters are obtained; however, there are also mathematical
ways to derive them as it will be further discussed.
Assume that we have successfully identied LG and we set it in a feedback conguration with a constant
gain dened as k connected in series as shown in Figure 3.13A..
57
A. Schematic of the feedback conguration implemented
for gain margin GM and phase crossover frequency !pc
estimations. k, represents the constant gain that is being
injected to the open loop frequency response.
B. Schematic of the feedback conguration implemented
for phase margin PM and gain crossover frequency !gc
estimations. z

, represents the phase shift that is being
injected to the open loop frequency response.
The closed loop conguration assuming a negative feedback has a transfer function dened by Equation
3.22:
H
cl
(z) =
w(n)
u(n)
=
kLG(z)
1 +kLG(z)
; (3.22)
where the denominator is known as the characteristic polynomial and whose roots would determine the
overall stability characteristics of the closed loop system (Hurwitz, 1964; Routh, 1877). Thus, we must nd
the roots that make the closed loop transfer function become innitely large. In order to do so, we solve the
characteristic equation by separating it into its magnitude and phase components. Equation 3.23 represents
the argument equation associated with the phase.
\k +\LG(e
j!
) =\ 1 (3.23)
The phase crossover frequency can be easily obtained by solving Equation 3.24:
\LG(e
j!pc
) =; (3.24)
where represents the phase of the complex number -1. Once !
pc
has been identied, and based on 3.12,
we can derive GM as follows:
GM =k =
1
jLG(e
j!pc
)j
: (3.25)
Note that in order for GM to exist, the Nyquist diagram must intersect the negative real axis. In other
58
words, there must exist a frequency !
pc
that is a solution for Equation 3.24.
We can now proceed to estimate the rest of the relative stability parameters. Following a similar procedure
of setting our previously estimated LG in a feedback conguration, but this time with a constant phase shift
dened as connected in series, as shown in Figure 3.13B.. If we dene the phase marginPM as the rotation
e
j
necessary such that:
LG(e
j!
)e
j
=1: (3.26)
By solving the Equation 3.26 by looking at the magnitude property, we have that the gain crossover
frequency can be obtained from the following expression:
jLG(e
j!gc
)j = 1: (3.27)
Once !
gc
has been identied, we again utilize the aid of the Nyquist diagram shown in Figure 3.12 to
nally derive the phase margin as follows:
PM = = +\LG(e
j!gc
): (3.28)
Note that in order for PM to exist, there must exist a frequency !
gc
for which the Nyquist diagram
crosses the unit circle.
Given the lack of a mathematical rational expression for the open loop model LG, we are left with a
numerical approach that utilizes both the time and frequency domains to determine the relative stability
characteristics of ventilatory control. We rst drew Nyquist diagrams like the one shown in Figure 3.12
for each of the estimated LG (including the circulatory time delay information). Following the theoretical
denition of the relative stability parameters previously presented, we looked for the crossings by the negative
real axis, the associated frequencies and gains to have a set of candidate phase crossover frequencies and gain
margins. Similarly, we searched for the intersections of LG with the unit circle to nd sets of gain crossover
frequencies and phase margins. Nevertheless, we found that none of the LG analyzed so far has a magnitude
59
greater or equal to 1 for 0 !T ; thus, suggesting that PM is innitely large. Consequently, we only
have to investigate the eects of increasing the gain in the closed-loop system to evaluate relative stability.
Therefore, we implemented the feedback system presented in Figure 3.14 and simulated the response w(n)
of the closed-loop system to an input u(n) that took the form of a pulse with unit amplitude and one
second duration. The time course of the response w(n) was simulated for 1000 seconds while monitoring its
behavior for the multiple candidate gains k that were tested iteratively in increasing order. The search for
the stability parameters was stopped when w(n) exhibited self-sustained oscillations as shown in the right
panel of Figure 3.14. In this particular example, the self-sustained oscillatory behavior was obtained for
a gain k = GM = 3:81. After careful inspection of the closed loop impulse response, it can be observed
that there are a total of 33 cycles occurring within a 1000 seconds simulation period. Therefore, the phase
crossover frequency !
pc
is approximately 0.033 Hz. This procedure was carried out multiple times in all of
the LG that we estimated per individual. Median LG(e
j!pc
), GM and !
pc
values were computed and used
to represent relative stability in each subject.
Figure 3.14: Schematic showing the feedback conguration that was utilized iteratively to search for the
relative stability parametersGM and!
pc
. The open loop impulse response functionLG(mD) is an actual
estimation from a subject from the induced sighs protocol.
3.3.4 Statistical analyses
All variables were rst tested for normality using the Kolmogorov-Smirnov test. Comparisons between groups
were performed using independent samples Student's t-test for those variables that passed the normality test.
Whereas, for the variables that failed normality, the comparisons between the groups were performed via
60
the Mann-Whitney Rank Sum test. Linear correlations between the model derived parameters and various
measurements, obtained during pulmonary function testing and the diagnostic PSG, were evaluated by
means of the correlation coecient. Selection between Pearson and Spearman rank order correlation tests
depended of whether the variable passed the normality test or not. Two-way analysis of variance (ANOVA)
was utilized to investigate the eects of gender and the presence of OSA in our stability quantiers. Lastly, a
two-way repeated measures ANOVA was carried out to investigate how our stability features changed within
two NREM sleep stages (NREM2 and NREM3). All tests used p < 0.05 to determine signicance and were
performed with SigmaPlot (version 12.0, Systat Software, San Jose, CA).
3.4 Results
This chapter presents a summary of the results and has beeen separated into two main sections: simulation
and experimental. The rst section shows the results obtained from the simulation study that was carried
out to test the performance of the proposed models with articially generated data. We utilized the closed-
loop parametric model described in section 3.3.2 to simulate our experimental interventions and evaluate the
performance of our estimation algorithm recovering the theoretical models under dierent circumstances.
After our techniques were validated with synthetic data, we proceeded to apply them on experimental
measurements. The second section presents the results that have been obtained using experimental data
collected from a cohort of overweight adolescents up to this point. We present a comparison of the extracted
models and the model-derived stability quantiers between subjects with and without OSA. We nally show
the results obtained after testing for associations between our stability markers and OSA severity.
3.4.1 Simulation
3.4.1.1 Robustness to noise
We rst evaluated the accuracy in the estimations of the overall loop model for dierent levels of noise
present in the data that emulated the induced sighs protocol. As previously described, the sigh is simulated
61
by the addition of an external ventilatory drive of 15 L/min that is independent of the chemore
ex. The
external drive, in addition to the added Gaussian white noise are the driving stimuli of the closed-loop system.
Figure 3.15 shows examples of the simulated induced sighs data and compares it with the prediction produced
by the estimated model (left panels) for diverse noise amplitudes ranging from low (50%) to high (150%)
around a nominal value obtained from the experimental data; as well as a comparison between the mean
of the estimated chemore
ex loop models and the ground truth, in the time (middle panel) and frequency
domains (right panel). The identication algorithm was able to capture the negative onset of the impulse
response fairly accurately for the dierent noise magnitudes; however, the latter part was underestimated in
all cases, becoming more prominent as noise increased. Despite the inaccuracies found in the time domain,
the estimated dynamic gain resembled the true gain in the frequency range of interest (0.01 - 0.05 Hz) as
noise varied. As expected, after computing the average percent error in estimated LG for the three dierent
scenarios, we observed an increased error as the variance of the noise also increased; however, the results
showed that the average percent error were below 15% for the three cases.
We then proceeded to evaluate the performance of our estimation algorithm of the feedforward branch
(plant) of the closed-loop model representing the gas exchange process occurring in the lungs. In order to
do so, we simulated the no intervention protocol by just driving the model with Gaussian white noise and
without any other added external disturbance, emulating quiet breathing during sleep. A slight modica-
tion to the induced sigh model that was implemented for the no intervention model, was the addition of
measurement noise to the simulated P
ET
CO
2
. It should be noted that this measurement noise is not used
as a driving stimulus to the system, but it is rather used as a way to simulate errors that could be present
in the measurement of end-tidal CO
2
. Figure 3.16 shows examples of the simulated data for dierent noise
variances, which ranged between 50% and 150% around the nominal value of both the driving stimulus and
the measurement noise. The left-most columns show representative tracings of the simulated ventilation
and P
ET
CO
2
, respectively, for the dierent levels of noise. The third column depicts a comparison of the
impulse response between the theoretical model and the average of the estimated models. It can be noted
that while the estimated models are able to capture the latter part of the simulated impulse response, they
62
Figure 3.15: Simulation example of the induced sigh protocol for dierent levels of noise around a nominal
value. The noise realizations followed a gaussian distribution with zero mean. Results are shown for dierent
noise variances: 0.5 L
2
min
-2
(A), 1 L
2
min
-2
(B) and 1.5 L
2
min
-2
(C). The estimated impulse response and
dynamic loop gain are presented as mean SD over 100 trials with dierent noise realizations.
failed to accurately capture the system's rapid onset. This slight discrepancy in the time domain remains
consistent as the levels of noise present in the data increase. The analysis in the frequency domain shows
that even though there are discrepancies in the time domain, the frequency response of the estimated models
accurately approximate the theoretical ones for the three noise levels that were tested. The stability feature
extraction procedure yielded an average percent error that was below 10% for the three dierent scenarios.
These results indicate that the accuracy of our estimations are not considerably aected by the amount of
noise contained in the data.
3.4.1.2 Sensitivity analysis
A similar exercise was carried out to examine the estimation performance for dierent combinations of the
seven parameters conforming the theoretical model shown in Figure 3.9. Parameter values ranged between
63
Figure 3.16: Sample of the simulated no intervention protocol for three dierent levels of noise present in
the data. Noise realizations followed a Gaussian distribution with zero mean. Results are shown for dierent
noise variances in ventilation and P
ET
CO
2
: 0.5 L
2
min
-2
, 0.25 mmHg
2
(A); 1 L
2
min
-2
, 0.5 mmHg
2
(B);
and 1.5 L
2
min
-2
, 0.75 mmHg
2
(C). The estimated impulse response and dynamic plant gain are presented
as mean SD over 100 trials with dierent noise realizations.
50% and 150% around the mean values shown in table 3.4, after xing the variance of the added noise to a
nominal value. Figure 3.17 depicts the multiple sensitivity analyses that were carried out on the estimation
error in LG within the periodic breathing region with respect to the ground truth. The One-at-a-time
analysis (Figure 3.17A.) showed that our estimation error is not very sensitive to variations in the central
chemore
ex parameters nor it is to changes in circulatory transport times. Conversely, variations in the
peripheral chemore
ex and lung gains appear to impact our LG estimations showing an increased error for
low gains and lower errors for elevated gains. These results were conrmed by the Two-at-a-time analysis
shown in Figure 3.17B., where it can be seen, based on the color gradient, that the estimation accuracy
is mostly sensitive to changes in lung and peripheral chemore
ex gains (elements inside the box). After
allowing for all the parameters to take dierent values and fully exploring the parameter space within the
physiological range, we found that the estimation error increased for parameter sets with long circulatory
delays, high peripheral and lung time constants and low gains. These inaccuracies in LG estimation are
64
attributed to a low overall system gain for that combination of parameters, which resulted in low signal to
noise ratio present in the simulated data used to t the nonparametric model. Note from Figure 3.17C. that
there are also few cases where the estimation error is elevated for parameter sets including low peripheral
and lung time constants and high peripheral and lung gains. This particular behavior is not caused by a
low overall system gain as discussed before, it is rather attributed to the complete opposite case; i.e. an
extremely high overall system gain. Such characteristics make the closed loop ventilatory response to be
highly oscillatory or even unstable making our nonparametric model, which is estimated upon the ensuing
oscillatory data, to fail given that its structure assumes a nite system's memory. Independently of the source
of inaccuracy, our All-at-a-time sensitivity analysis revealed that our nonparametric model approximates the
theoretical LG quite accurately, yielding relative errors in estimated LG that were lower than 30% in 95%
of the 10,000 dierent simulated cases.
Just as for LG, we also performed a sensitivity analysis of the accuracy of the estimations of PG for
variations in parameters conforming the theoretical model. Such analysis was also carried out by varying one,
two and all parameters at a time. Results from the One-at-a-time and the Two-at-a-time sensitivity analyses
showed that the relative error in PG estimations was always below 7%, independently of the parameter/s
that were being varied (data not shown). On the other hand, the All-at-a-time sensitivity analysis showed
that our feedforward nonparametric model yielded relative errors in the estimated PG that were below 30%
for approximately 700 times out of the 10,000 dierent parameter sets that were tested (93%). These results
suggest that PG estimations are very robust to parameter variations and that there needs to be at least
three parameters that are altered in the system in order for estimation errors to start becoming appreciable.
The All-at-a-time sensitivity analysis revealed that the accuracy of our estimations is particularly sensitive
to variations in the peripheral chemore
ex time constant and gain, central chemore
ex and lung gains
and circulatory time delays (see Figure 3.18). The percent error was increased for elevated peripheral and
central chemore
exes gains, indicating that there are inaccuracies for systems with a strong feedback action.
These miscalculations are associated with the recycling eect, characteristic of feedback systems, aecting
the estimations that were done in open loop. In addition, low peripheral chemore
ex time constant and
65
50 100 150
0
10
20
30
40
50
Percent Tc (%)
Percent Error (%)
50 100 150
Percent Tp (%)
50 100 150
Percent Tl (%)
50 100 150
Percent D (%)
50 100 150
Percent Gc (%)
50 100 150
Percent Gp (%)
50 100 150
Percent Gl (%)
A.
50 100 150
50
100
150
S
Error
Tp,Tc
Percent Tc (%)
Percent Tp (%)
50 100 150
50
100
150
S
Error
Tl,Tc
Percent Tc (%)
Percent Tl (%)
50 100 150
50
100
150
S
Error
Tl,Tp
Percent Tp (%)
Percent Tl (%)
50 100 150
50
100
150
S
Error
D ,Tc
Percent Tc (%)
Percent D (%)
50 100 150
50
100
150
S
Error
D ,Tp
Percent Tp (%)
Percent D (%)
50 100 150
50
100
150
S
Error
D ,Tl
Percent Tl (%)
Percent D (%)
50 100 150
50
100
150
S
Error
Gc,Tc
Percent Tc (%)
Percent Gc (%)
50 100 150
50
100
150
S
Error
Gc,Tp
Percent Tp (%)

Percent Error (%)

Percent Gc (%)
50 100 150
50
100
150
S
Error
Gc,Tl
Percent Tl (%)
Percent Gc (%)
50 100 150
50
100
150
S
Error
Gc,D
Percent D (%)
Percent Gc (%)
50 100 150
50
100
150
S
Error
Gp,Tc
Percent Tc (%)
Percent Gp (%)
50 100 150
50
100
150
S
Error
Gp,Tp
Percent Tp (%)
Percent Gp (%)
50 100 150
50
100
150
S
Error
Gp,Tl
Percent Tl (%)
Percent Gp (%)
50 100 150
50
100
150
S
Error
Gp,D
Percent D (%)
Percent Gp (%)
50 100 150
50
100
150
S
Error
Gp,Gc
Percent Gc (%)
Percent Gp (%)
50 100 150
50
100
150
S
Error
Gl,Tc
Percent Tc (%)
Percent Gl (%)
50 100 150
50
100
150
S
Error
Gl,Tp
Percent Tp (%)
Percent Gl (%)
50 100 150
50
100
150
S
Error
Gl,Tl
Percent Tl (%)
Percent Gl (%)
50 100 150
50
100
150
S
Error
Gl,D
Percent D (%)
Percent Gl (%)
50 100 150
50
100
150
S
Error
Gl,Gc
Percent Gc (%)
Percent Gl (%)
50 100 150
50
100
150
S
Error
Gl,Gp
Percent Gp (%)
Percent Gl (%)
0
5
10
15
20
25
30
35
40
45
50
B.
Tc Tp Tl D Gc Gp Gl
0
0.2
0.4
0.6
0.8
1
Normalized Parameter Values

[75,225] [7.5,22.5] [3.25,9.75] [4,12] [1,3] [0.5,1.5] [0.5,1.5]
0
0.2
0.4
0.6
0.8
1
Percent Error (%)
5
10
15
20
25
30
35
40
45
>50
C.
Figure 3.17: One-at-a-time (A), Two-at-a-time (B) and All-at-a-time (C) sensitivity analyses of the percent
error between the estimated and the theoretical loop gain within the periodic breathing frequency band. In
A and B, each data point represents the ensemble average over 100 trials with dierent noise realizations
but with constant statistics. In C, each line connects all the elements of the parameter set that was used
to generate the multiple data sets with color representing the average percent error over 100 trials as well.
Note that the ranges over which the parameters were varied are presented on top of the gure.
66
Tc Tp Tl D Gc Gp Gl
0
0.2
0.4
0.6
0.8
1
Normalized Parameter Values

Percent Error (%)
[75,225] [7.5,22.5] [3.25,9.75] [4,12] [1,3] [0.5,1.5] [0.5,1.5]
0
0.2
0.4
0.6
0.8
1
5
10
15
20
25
30
35
40
45
>50
Figure 3.18: All-at-a-time sensitivity analysis performed on the percent error of the estimated plant gain
from the simulated spontaneous breathing protocol. Each line connects all the elements of the parameter
set that was used to generate the multiple data sets with color representing the average percent error over
100 trials with dierent noise realizations. Note that the ranges over which the parameters were varied are
presented on top of the gure.
increased lung gain also yielded high estimation errors. These parameter values are associated with feedback
instabilities and potentially produced errors related to highly oscillatory data that were used to perform the
model estimation. Interestingly, low circulatory time delays also yielded considerable errors implying that
the faster the feedback action was provided by the chemore
exes, the more dicult it was for the open loop
model to separate that eect from the plant dynamics.
It is of note the similarity found in the percentage of parameter sets that resulted in relative errors below
30% with a 95% for the loop gain case and 93% for the plant gain. Such similarities are striking considering
the fact that in the case of plant dynamics estimation, data were generated solely as a response to random
stimulation and the additional impulsive stimulus (sighs) was absent.
3.4.2 Experimental
3.4.2.1 Induced sighs
Figure 3.19 shows representative data recorded from the induced sighs protocol. As can be seen, this
particular subject was initially provided with therapeutic pressure (8cmH
2
O) for ten baseline breaths. Stable
breathing is noted during baseline recording with a mean tidal volume of approximately half a liter and a
mean ventilatiry drive of about 20 liters per minute. Following the baseline recording, inspiratory pressure
67
was abruptly increased by 5 cmH
2
O for two consecutive breaths and brought back to the therapeutic level
afterwards. The increase in inspiratory pressure roughly doubled tidal volume and consequently ventilatory
drive, which led to a corresponding drop in P
ET
CO
2
levels. This drop stimulated the chemoreceptors,
which in turn responded with a decrease in ventilatory drive. The diminished respiratory activity elevated
P
ET
CO
2
, stimulating the chemoreceptors again, but in the opposite direction, causing an activation of the
respiratory muscles and a raise in ventilatory drive. The eects of the perturbation continued to propagate
around the chemore
ex loop until P
ET
CO
2
was restored back at its homeostatic state.
5
10
15
Pressure
(cmH2O)

−50
0
50
Airflow
(L/min)
0.5
1
Tidal Volume
(L)
20
30
40
Ventilatory Drive
(L/min)
0 20 40 60 80 100 120 140
0
20
40
60
PCO
2
(mmHg)
Time (sec)

Inspiratory
Mask
P
ET
CO
2
PCO
2
Figure 3.19: Sample induced sighs recording. The top two panels represent the continuous recordings of
pressure and air
ow. The bottom three panels depict the derived breath by breath measurements of tidal
volume, ventilatory drive and P
ET
CO
2
, respectively. Note that the bottom-most panel also shows the
continuous recording of PCO
2
from which the end-tidal values were derived.
Sample recordings of ventilatory drive (A) and the corresponding estimated models in the time (B) and
frequency domains (C) of a subject from each category are presented in gure 3.20. It can be noted that
the non-OSA subject (top panels) exhibited larger and longer
uctuations of ventilatory drive following the
68
induced sighs, compared to the OSA subject (bottom panels). Moreover, the left panels also show that the
predictions provided by the estimated models resemble accurately the ventilatory responses to the induced
sighs quantied by an NMSE of approximately 75% for both cases. By looking at the characteristics of the
impulse response functions (B), it can be noted that the long lasting ventilatory
uctuations exhibited by the
non-OSA subject were captured by a model with an impulse response that oscillates before reaching steady
state. The optimal model structure for this particular example is comprised of a total of four basis functions,
an order of generalization of ve and a time delay of nine seconds. On the other hand, the short duration
ventilatory response observed in the OSA subject was better characterized by a less oscillatory model with
a smaller negative peak value and a shorter settling time. In this case the optimal model consisted of a
total of four basis functions, an order of generalization of four and a time delay of twelve seconds. Lastly,
by inspecting the frequency response of the estimated models (C), it can be observed that the oscillatory
nature of the non-OSA subject's model expressed in the form of two resonant peaks in the frequency domain.
Interestingly, both of these resonant frequencies lie within the frequency band of interest at approximately
0.015 and 0.045 Hz, which correspond to ventilatory oscillations of 67 and 22 seconds, respectively. On the
other hand, the frequency response of the OSA subject's model appears to have less prominent resonant
frequencies resulting in a lower dynamic loop gain as compared to the non-OSA subject. The resonances for
this subject are located approximately at 0.011 and 0.033 Hz, which correspond to oscillations with periods
of 90 and 30 seconds, respectively.
The induced sighs protocol was repeated several times in each individual during the experimental polysomnog-
raphy, although the model estimation procedure was only carried out on those segments that did not result
in arousal as a response to the ventilatory disturbance. After a careful examination of the recordings, we
selected a total of 142 segments that were considered successful measurements and were included in our
analysis. Out of these 142 segments, 77 were recorded from 21 non-OSA subjects and 65 segments came
from a total of 21 OSA subjects. This yields an average of three analyzed segments per subject; however,
this number varied quite signicantly among the 42 subjects with some subjects having as low as two ana-
lyzed segments and some others as high as six. In order to represent each subject from the total analyzed
69
40 60 80 100 120
0
10
20
30
non−OSA
A. ΔVentilatory Drive
(L/min)

0 50 100
−0.03
−0.02
−0.01
0
0.01
0.02
B. Loop Impulse Response
(Dimensionless)
0 0.05 0.1
0
0.1
0.2
0.3
C. Dynamic Loop Gain
(Dimensionless)
40 60 80 100 120
0
10
20
30
Time (sec)
OSA
0 50 100
−0.03
−0.02
−0.01
0
0.01
0.02
Time (sec)
0 0.05 0.1
0
0.1
0.2
Frequency (Hz)
Experimental Data
Model Prediction
Figure 3.20: Sample results obtained from the induced sighs protocol on a non-OSA subject (top panels)
and an OSA patient (bottom panels). Column A shows the measured responses to the sighs in addition to
the predictions provided by the estimated models. Column B shows the corresponding estimated impulse
responses. Column C depicts the associated frequency responses.
segments, we computed the median of the estimated model in the time and frequency domains. Once we
found the individuals' representative responses, we proceeded to look for the overall characteristics of the
two populations under study. Figure 3.21 shows the mean impulse and frequency responses of the non-OSA
and OSA populations. It can be seen from Figure 3.21A. that the average impulse responses in both groups
have a biphasic behavior that transition from inhibitory to excitatory characteristics. There are however
some dierences in the proles of the average impulse responses that should be pointed out. For instance,
the negative onset of the impulse responses of both groups peak between ten and fteen seconds but the
drop is more abrupt in the OSA population. The average recovery period, immediately following the peak,
within the OSA population is much faster and crosses by zero after 30 seconds, while the average non-OSA
response crosses by zero approximately 20 seconds later at 50 seconds. The relaxation period back to steady
state is almost identical in the two groups, as can be seen by the complete overlap of the average responses
as well as the error bars. Note that the jagged impulse response plots are due to the within and between
subjects' variability.
70
A similar procedure was carried out to obtain representative frequency responses from both of our sub-
groups; i.e. median values were used to represent each individual and the average between subjects of the
same phenotype were used to represent the group. Figure 3.21B. shows a comparison of the magnitude of the
frequency response between the non-OSA and the OSA groups. It can be easily noted that the dynamic loop
gain shows a resonant peak at approximately 0.015 Hz that is common in the two groups. Nonetheless, the
estimated dynamic loop gain in the periodic breathing region appeared to be slightly higher in the non-OSA
group, due to the presence of a second resonant peak around 0.04 Hz that is not particularly dominant
in the OSA group. This second resonant frequency observed in the non-OSA group is associated with the
undulation of the loop impulse response occurring at around 35 seconds that is absent in the average OSA
model. The potential mechanisms responsible for the dierences found in the time and frequency responses
between the groups are further discussed in section 3.5.2.
A. Average loop impulse response functions for both
groups.
B. Average dynamic loop gains for both groups.
Figure 3.21: Average loop impulse responses (A) and dynamic loop gains (B) of the non-OSA and OSA
groups. Median responses in the time and frequency domains were used to represent each individual and
were obtained from the multiple induced sighs that were performed per experimental sleep study. The mean
and variability of both responses were computed at each point to obtain a representation of the group.
Results are displayed as mean SEM.
71
3.4.2.2 No intervention
A sample of a representative recording of the no intervention protocol is shown in Figure 3.22. For this
protocol, the inspiratory and expiratory pressures of the BiPAP ventilator were both set at the therapeutic
level; thus, the ventilator was set to operate in CPAP mode and respiratory measurements were done during
spontaneous breathing. In this sample recording, it can be seen that the subject required a therapeutic
pressure of 9 cmH
2
O in order to stabilize the upper airway and minimize air
ow limitations. Although,
the respiratory pattern appears to be very stable (based on the continuous measurements of mask pressure,
air
ow and PCO
2
), variability in the breath-by-breath time series is quite noticeable. For instance, tidal
volume shows a mean that is slightly above 300 milliliters with a range of 150 milliliters. Moreover, the
ventilation measurement exhibits values ranging between 4 and 5.5 liters per minute with a mean laying just
below 5 liters per minute. Furthermore, the end-tidalCO
2
time series presents values that range around the
mean of 45mmHg, with values between 43 and 46 mmHg. The variability present in the breath-by-breath
data re
ects a wide dynamic range, which is advantageous in input-output time-series modeling due to the
coverage of a large range of possible responses to incoming stimuli (Garrett et al., 2013; Jacono and Dick,
2011).
Representative recordings and associated estimated models, obtained from a subject of each category, are
presented in Figure 3.23. Samples of ventilation (A),P
ET
CO
2
and the corresponding prediction provided by
the model (B), the estimated models in the time (C) and frequency domains (D). It can be noted that the non-
OSA subject (top panels) has ventilation andP
ET
CO
2
measurements that are more variable as compared to
the OSA subject (low panels). Independently of the variability in the signals, the estimated models are able
to accurately predict the changes inP
ET
CO
2
as indicated by an NMSE of approximately 80% in both cases.
Note that these values are not considerably dierent from those obtained from the induced sighs protocol
(NMSE of 70%) even though here the estimation was carried out with spontaneous breathing measurements
only. The estimated impulse response shows a negative onset in both cases capturing the negative association
between ventilation and P
ET
CO
2
; however, a slower dynamic response of lower amplitude is noted in the
non-OSA subject. This type of response is given by a model structure consisting of one basis function and
72
5
10
15
Pressure
(cmH
2
O)

−50
0
50
Airflow
(L/min)
0.2
0.3
0.4
Tidal Volume
(L)
4
5
6
Ventilation
(L/min)
0 20 40 60 80 100 120 140
0
20
40
60
Time (sec)
PCO
2
(mmHg)

Inspiratory
Mask
P
ET
CO
2
PCO
2
Figure 3.22: Sample no intervention recording. The top two panels represent the continuous recordings of
pressure and air
ow. The bottom three panels depict the derived breath by breath measurements of tidal
volume, ventilation and P
ET
CO
2
, respectively. Note that the bottom-most panel also shows the continuous
recording of PCO
2
from which the end-tidal values were derived.
an order of generalization of three, being the latter parameter the one that determined the sluggish response
onset. On the other hand, the selected optimal model structure for the OSA subject was composed of two
basis functions and an order of generalization of zero, which in turn resulted in a faster system's response.
The characteristics of the impulse responses translate into the frequency domain exhibiting responses that
resemble that of a low pass lter, with the magnitude within the periodic breathing region being lower in
the non-OSA subject when compared to its OSA counterpart.
This pair of examples perfectly picture the dierence between variability and instability that Khoo (2000a)
discusses in his manuscript. The author cleverly illustrates, with the aid of a numerical simulation model,
the underlying dierences between these two terms that are of great importance in time series and systems
analysis. In contrast with that purely simulation study, our results are completely obtained from experimental
73
data. While the recordings from the non-OSA subject have a greater variability, the model linking the two
measurements has a low gain and thus could be seen as being more stable. On the other hand, the OSA
subject exhibits breath-to-breath variations that are smaller in both of the physiological measurements and
yet the estimated model has a higher gain and could be seen as having a more unstable behavior.
0 200 400
−3
−2
−1
0
1
2
3
Time (sec)
0 200 400
−2
−1
0
1
2
Time (sec)
0 10 20 30
−0.2
−0.15
−0.1
−0.05
0
Time (sec)
0 0.05 0.1
0
0.2
0.4
0.6
Frequency (Hz)
0 200 400
−3
−2
−1
0
1
2
3
A. ΔVentilation
(L/min)
0 200 400
−2
−1
0
1
2
B. ΔP
ET
CO
2
(mmHg)

0 10 20 30
−0.2
−0.15
−0.1
−0.05
0
C. Plant Impulse Response
(mmHg min/L)
0 0.05 0.1
0
0.2
0.4
0.6
D. Dynamic Plant Gain
(mmHg min/L)
Experimental data
Model prediction
non−OSA
OSA
Figure 3.23: Sample results obtained from the no intervention protocol on a non-OSA subject (top panels)
and an OSA patient (bottom panels). Columns A and B show breath-to-breath ventilation and P
ET
CO
2
with the corresponding model predictions, respectively. Column C depicts the estimated impulse responses
and D the associated frequency responses of the estimated models.
Figure 3.24 displays and compares the average estimated plant impulse response (left panel) and dynamic
plant gains (right panel) from the two cohorts of subjects. These results include the analysis performed on a
total of 45 individuals (22 non-OSA and 23 and OSA subjects). It can be noted from Figure 3.24A. that the
average impulse responses for both groups have a very similar overall dynamic behavior. They both show
an instantaneous negative peak and a relaxation period that brings the system back to homeostasis after
approximately 20 seconds or equivalently ve breaths. While the overall dynamics is similar in both groups,
there are also a couple of discrepancies that must be mentioned. First, the negative peak at the zero lag is
slightly increased in the OSA response. This indicates that if subjects from both groups are subjected to
a sudden increase in ventilation of one liter per minute, there would be an instantaneous decrease in end-
74
tidal CO
2
that would be, in average, slightly more pronounced in the OSA population. Second, the OSA
average impulse response decays slower ans exhibits some minor oscillations before returning to homeostatic
conditions. The non-OSA average impulse response, on the other hand, possesses a smaller time constant
and thus it decays faster toward zero without exhibiting oscillations. Figure 3.24B. shows the plant impulse
responses following a transformation into the frequency domain. It can be seen that the average plant gain
in both groups follow a similar prole; however, the OSA group exhibits a slightly higher gain for frequencies
that are lower than 0.01 Hz as compared to its non-OSA counterpart. A more detailed explanation of the
potential mechanisms behind the observed temporal and frequency patterns will be presented in Section
3.5.2.
A. Average impulse response functions for both groups rep-
resenting the gas exchange dynamics in the lungs.
B. Average dynamic plant gains for both groups.
Figure 3.24: Average plant impulse responses (A) and dynamic plant gains (B) of the non-OSA and OSA
groups. The mean and variability of both responses were computed at each point to obtain a representation
of the group. Results are displayed as mean SEM.
3.4.2.3 Relative stability
Figure 3.25 illustrates the process of relative stability quantication described in Section 3.3.3.2. It compares
the results of the analysis that was carried out using the sample estimated models from the non-OSA and OSA
individuals shown in Figure 3.20. As it has been previously discussed, this process consisted of monitoring
the response (in the frequency and time domains) of the feedback system by increasing the feedback gain k
75
until self sustained oscillations in the closed loop impulse response were achieved. The search of the value of
k was carried out using numerical simulations and were performed using Simulink. Figure 3.25I. depicts the
frequency response of the impulse response functions in the form of a Nyquist diagram of a non-OSA subject
(top) and an OSA (bottom) individual for increasing values of the feedback gain k. The left most panels
represent the cases where both the non-OSA and the OSA subjects' models have a unit feedback gain. By
comparing these two panels, we can observe that the OSA Nyquist plot has an overall smaller amplitude as
compared to the non-OSA plot and it is farther away from the Nyquist critical point (represented by the
red star). This would indicate that the addition of a larger gain k would be required in order to reach the
critical point. After gradually increasing the feedback gain, shown from left to right, in both the non-OSA
and OSA cases, we can observe that the frequency responses expand and grow in amplitude until they reach
the critical Nyquist point. The OSA case required the addition of a gain k = 10.21 before it reached the
critical point, which, as we had anticipated, is approximately 2.7 times greater than what it was required in
the non-OSA case (k = 3.82). In the context of stability, these results would indicate that the OSA subject
has a ventilatory control system that is 2.7 times more stable as compared to the non-OSA individual.
The time responses associated with the aforementioned Nyquist diagrams are presented in 3.25II.. It
can be observed that as the feedback gain is increased, the oscillatory behavior of the closed loop impulse
responses becomes more prominent in both the non-OSA and the OSA cases. Note that for low values of k,
the oscillations exhibit exponentially decaying time proles until the oscillations become self-sustained when
k =GM. At this point, the system is on the verge of becoming unstable. In other words, if the feedback gain
k were to be increased even further (beyond GM), then the oscillations would start to grow in magnitude.
3.4.2.4 Stability feature extraction
Four model derived stability features were dened to facilitate statistical comparisons between the two
phenotypes: (a,b) the average magnitudes of the dynamic PG and LG within the periodic breathing region
(0.01 - 0.05 Hz); (c) estimates of CG in the same frequency band were derived by simply dividing LG
by PG; and (d) median circulatory time delay was extracted from the various CIR estimations obtained
76
−1 0 1
−1.5
−1
−0.5
0
0.5
1
1.5
Nyquist Diagram

Imaginary Axis
k = 1
−1 0 1
−1.5
−1
−0.5
0
0.5
1
1.5
Nyquist Diagram

k = 1.5238
−1 0 1
−1.5
−1
−0.5
0
0.5
1
1.5
Nyquist Diagram

k = 2.2857
−1 0 1
−1.5
−1
−0.5
0
0.5
1
1.5
Nyquist Diagram

k = 3.0476
−1 0 1
−1.5
−1
−0.5
0
0.5
1
1.5
Nyquist Diagram

k = 3.8094
−1 0 1
−1.5
−1
−0.5
0
0.5
1
1.5
Real Axis

Imaginary Axis
non−OSA
−1 0 1
−1.5
−1
−0.5
0
0.5
1
1.5
Real Axis

−1 0 1
−1.5
−1
−0.5
0
0.5
1
1.5
Real Axis

−1 0 1
−1.5
−1
−0.5
0
0.5
1
1.5
Real Axis

−1 0 1
−1.5
−1
−0.5
0
0.5
1
1.5
Real Axis

OSA
k = 1 k = 4.0874 k = 6.1311 k = 8.1748 k = 10.2186
I. Representative Nyquist diagrams from a non-OSA subject (top panel) and an OSA subject (bottom panel) for
increasing values of the feedback gain k. Note that the black circle is the unit circle and that the red star represents
the point at which self-sustained oscillations would be attained by the system.
0 500 1000
−0.2
−0.1
0
0.1
0.2
Closed Loop Impulse Response
Amplitude (L/min)

k = 1
0 500 1000
−0.2
−0.1
0
0.1
0.2
Closed Loop Impulse Response

k = 1.5238
0 500 1000
−0.2
−0.1
0
0.1
0.2
Closed Loop Impulse Response

k = 2.2857
0 500 1000
−0.2
−0.1
0
0.1
0.2
Closed Loop Impulse Response

k = 3.0476
0 500 1000
−0.2
−0.1
0
0.1
0.2
Closed Loop Impulse Response

k = 3.8094
0 500 1000
−0.2
−0.1
0
0.1
0.2
Time (sec)
Amplitude (L/min)

0 500 1000
−0.2
−0.1
0
0.1
0.2
Time (sec)

0 500 1000
−0.2
−0.1
0
0.1
0.2
Time (sec)

OSA non−OSA
0 500 1000
−0.2
−0.1
0
0.1
0.2
Time (sec)

0 500 1000
−0.2
−0.1
0
0.1
0.2
Time (sec)

k = 1 k = 4.0874 k = 6.1311 k = 8.1748 k = 10.2186
II. Closed loop impulse responses corresponding to the dierent scenarios presented above. Note the appearance of
oscillations as the parameter k is increased. Such oscillations become self-sustained as k approaches the gain margin.
Figure 3.25: Relative stability analysis comparison between a non-OSA and an OSA individual. Simulation
results show that the OSA subject requires the incorporation of more feedback gain k in order to exhibit
self-sustained oscillations as compared to its OSA counterpart.
from the responses to the induced sighs protocol. Figure 3.26I. illustrates the comparison of the stability
markers between the two phenotypes. Statistical analyses revealed a signicantly lower controller gain in
OSA compared to its non-OSA counterpart (p = 0.05). Although, loop gain was lower in OSA because of
the presence of an additional resonant peak, it failed to reach statistical signicance (p = 0.19). Similarly,
77
plant gain showed a trend to be increased in the OSA population, but it failed to reach statistical signicance
(p = 0.30). Circulatory time delay was found to be marginally statistically signicantly lower in OSA (p =
0.08).
In addition to the aforementioned features, we then dened three relative stability markers by combining
the gain and phase information of the overall loop responses following the methodology presented in Section
3.3.3.2: (a) LG evaluated at the phase-crossover frequency; (b) the phase-crossover frequency; and (c) the
gain margin, which measures how prone the system is to instability. Figure 3.26II. shows a statistical
comparison of the relative stability parameters between the two populations under study. Interestingly,
LG when evaluated at the phase-crossover frequency re
ects a marginally signicant dierence between the
groups (p = 0.09) that was not detected when computing the average over the periodic breathing frequency
band. The inverse of the previously described parameter denes the gain margin and was also found to be
marginally signicantly dierent between the groups (p = 0.07). The phase-crossover frequency was found
to lie within the periodic breathing frequency band for the vast majority of the subjects with a trend for
OSA subjects' frequencies to be slightly elevated; however, this was not found to be statistically signicantly
dierent between the two groups (p = 0.36). All variables were compared via the Mann-Whitney Rank Sum
test, except for the loop gain, the circulatory time delay and the loop gain evaluated at the phase-crossover
frequency, which were found to be normally distributed and thus required testing with the independent
sample t-tests.
Table 3.5 summarizes the results of the statistical comparison of our model-derived stability quantiers
between the non-OSA and the OSA populations.
3.4.2.5 Correlation of stability parameters with OSA severity
In order to test for linear dependence between our model derived stability descriptors and OSA severity
(represented by OAHI), we computed the Pearson correlation coecient after proper data transformation
to pass the normality test. Table 3.6 summarizes the results of the multiple comparisons that were tested.
It can be noted that none of the gains, computed as the average within the periodic breathing range, were
78
I. Dynamic plant (A), overall loop (B), and controller (C) gains represent the average magnitude of the transfer
functions within the periodic breathing frequency band; (D) represents the circulatory time delay.
II. Overall loop gain evaluated at the phase-crossover frequency (A), phase-crossover frequency (B) and gain margin
(C).
Figure 3.26: Model-derived stability markers comparison between the non-OSA and OSA groups. Variables
are presented as mean SEM.y indicates that the results are marginally signicantly dierent between the
groups with 0.1 > p > 0.05.yy indicates that the results are statistically signicantly dierent between the
groups at p 0.05.
79
Table 3.5: Summary of the model-derived stability markers comparison between the non-OSA and OSA
groups. Variables are presented as mean SEM. * indicates that for Plant Gain the sample size was dierent
(non-OSA = 22 and OSA = 23). x is used to highlight the variables that did not pass the normality test
and required the application of a nonparametric statistical test. y indicates that the results are marginally
signicantly dierent between the groups with 0.1 > p > 0.05.yy indicates that the results are statistically
signicantly dierent between the groups at p 0.05.
Stability parameter non-OSA OSA P-value
(n = 21) (n = 21)
Loop Gain (0.01-0.05 Hz) 0.195 0.012 0.169 0.015 0.19
Plant Gain (0.01-0.05 Hz)*x 0.310 0.046 0.327 0.030 0.30
Controller Gain (0.01-0.05 Hz)x 1.056 0.211 0.651 0.113 0.05yy
Circulatory Time Delay 9.476 0.351 8.452 0.448 0.08y
Loop Gain (!
p
) 0.225 0.015 0.186 0.016 0.09y
Phase-crossover Frequencyx 0.037 0.003 0.043 0.004 0.36
Gain Marginx 5.052 0.388 6.693 0.779 0.07y
signicantly associated with the OAHI. While controller gain just failed to reach signicance with p = 0.06,
both the loop and plant gains were far from reaching signicance with p = 0.12 and p = 0.40, respectively.
Conversely, all the dened relative stability parameters were found to be moderately though signicantly
associated with OSA severity. For instance, a negative correlation between LG, evaluated at the phase-
crossover frequency, and OAHI was detected. Furthermore, the phase-crossover frequency and gain margin
were both found to be positively correlated with OAHI, with the latter correlation being statistically highly
signicant (p = 0.01). Figure 3.27 displays the scatter plots showing the relationships between the stability
parameters and the OAHI of the correlation analyses that were found to be statistically signicant. The
dierence found in the directionality of the trends shown in panels A and C is not surprising since the two
independent variables (LG(!
pc
) andGM) have a reciprocal relationship. Contrary to what has been reported
in previous studies, these results combined indicate that the frequency of the apneic/hypopneic events
occurring during sleep increases for ventilatory control systems that are overly stable. Equally important
is the positive relationship found between OAHI and the phase-crossover frequency shown in panel B. Just
as GM, the phase-crossover frequency is also inversely related to LG(!
pc
). Given the overall resemblance
of LG with the frequency response of a low-pass lter, the higher the gains would be associated with a
lower phase-crossover frequency and vice versa. A more detailed explanation to these interesting ndings is
80
Table 3.6: Correlation analysis between the model-derived stability markers and OSA severity measured by
the amount of obstructive apnea/hypopnea vents per hour of sleep. The symbolx indicates that the variable
was log-transformed to pass normality prior to the correlation analysis. y indicates that the variables were
marginally signicantly associated with 0.1 > p > 0.05. yy indicates that the variables were signicantly
associated at p 0.05.
Stability parameter OAHI (events/hour) x
r P-Value
Loop Gain (0.01-0.05 Hz) -0.243 0.12
Plant Gain (0.01-0.05 Hz)x 0.126 0.40
Controller Gain (0.01-0.05 Hz)x -0.286 0.06y
Circulatory Time Delay -0.145 0.35
Loop Gain (!
pc
) -0.350 0.02yy
Phase-crossover Frequencyx 0.300 0.05yy
Gain Marginx 0.384 0.01yy
presented in Section 3.5.4.
0.1 1 10 100
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
OAHI (events/hour)
Loop Gain(ω
p
) (Dimensionless)
A. OAHI vs. LG( ω
pc
)

0.1 1 10 100
−1.9
−1.8
−1.7
−1.6
−1.5
−1.4
−1.3
−1.2
−1.1
−1
−0.9
OAHI (events/hour)
log
10
(Phase−crossover Frequency (Hz))
B. OAHI vs. log
10
(ω
pc
)

0.1 1 10 100
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
OAHI (events/hour)
log
10
(Gain Margin (Dimensionless))
C. OAHI vs. log
10
(GM)

non−OSA
OSA
r = −0.350
p = 0.02
r = 0.300
p = 0.05
r = 0.384
p = 0.01
Figure 3.27: Correlation plots of the signicant associations between the model-derived stability parameters
and OSA severity represented by the OAHI. Note that the OAHI was log-transformed prior to the correlation
analysis and is plotted in logarithmic scale.
3.4.2.6 Eects of gender and NREM sleep stage on ventilatory control stability
Thus far, we have investigated the dierences in ventilatory control stability that exist between subjects
with and without OSA. In this section we investigated the eect that some other factors such as gender and
81
changes in sleep stage had on our model-derived ventilatory control stability features independently.
3.4.2.6.1 Gender
As a rst step we sought to study whether gender and the presence of OSA were linked together. Table
3.7 summarizes the proportion of males and females in our population of OSA and non-OSA individuals. A
Chi-squared test of independence was calculated to compare the prevalence of OSA in males and females.
Note that a statistically signicant interaction was found between gender and the presence of OSA in our
sample pool of adolescents (
2
(1) = 4.677 ; p = 0.031). Our ndings could indicate that adolescent OSA
is more likely to occur in males as compared to females, which agrees with what has been reported in the
adult population (Young et al., 2002b, 2004; Punjabi, 2008).
Table 3.7: Contingency table showing the distribution of males and females within our non-OSA and OSA
groups. A statistically signicant interaction was found between gender and the presence of OSA (
2
(1) =
4.677 ; p = 0.031).
Females Males Total
non-OSA 15 6 21
OSA 7 14 21
Total 22 20 42
After nding a signicant interaction between gender and the presence of OSA, we then reevaluated the
comparisons between non-OSA and OSA that we showed in Figure 3.26 after accounting for the eects of
gender. A two factor analysis of variance (ANOVA) on our model-extracted stability features with gender
and presence of OSA as the independent variables was carried out. We observed that the dierence in
mean values of all of our stability features among the dierent genders was not statistically signicantly
dierent after allowing for phenotypic dierences. Furthermore, we also found that there were no signicant
interactions between the presence of OSA and gender in none of our seven model stability quantiers. There
were, however, some statistically signicant dierences in mean values among the dierent phenotypes after
allowing for dierences in gender. For instance, dierences in mean controller gain were signicant (p = 0.04),
as well as loop gain evaluated at the phase crossover frequency (p = 0.04) and gain margin (p = 0.05). Figure
82
3.28 shows the aforementioned variables that showed a signicant dierence across the dierent phenotypes.
The rest of the stability variables did not show a signicant dierence across the two dierent phenotypes. In
general, we found that after allowing for the eects of gender, our results did not show a dramatic change in
trends from our previous analyses where gender dierences were not taken into account. However, by allowing
for the eects of gender, we were able to detect statistically signicant dierences in those parameters that
showed borderline signicance with the utilization of simple t-tests (comparing non-OSA vs. OSA only).
Figure 3.28: Two way analysis of variance results that permit the interaction between phenotype and gender.
Controller gain (A), loop gain evaluated at the phase crossover frequency (B) and gain margin (C). Results are
presented as mean SEM. Note that controller gain and gain margin were log-transformed prior to statistical
testing.yy indicates that the mean values of the variables were found to be statistically signicantly dierent
among the two phenotypes after allowing for the gender dierences at p 0.05.
3.4.2.6.2 NREM Sleep stages
Our analysis of ventilatory control stability has so far been carried out by considering NREM sleep, or quiet
sleep, as a whole; however, it is known that within the NREM sleep state, there are certain physiological
variations that may aect the ventilatory control mechanisms. In order to investigate the eects that changes
occurring within the quiet sleep state (NREM2 and NREM3, specically), we rst had to get the segments
scored by a sleep clinician. The sleep stage scoring for our induced sighs segments was determined by the
dominant stage (< 50%) over the recording period. Segments recorded during the transition from wake
to sleep (NREM1) were scarce, and were lumped together with NREM2. Table 3.8 shows the frequency
83
distribution of the sleep stages on a total of 127 induced sighs segments that were measured from 19 subjects
with OSA and 19 subjects without OSA. Note that each induced sighs segment was considered to be coming
from a dierent non-OSA and OSA subject in the table. It is also of note that we are missing the staged
segments of four subjects (15 segments) whose polysomnographic data could not be found. A Chi-squared
test of independence was calculated to compare the frequency of NREM2 and NREM3 in the induced sighs
segments recorded from our non-OSA and OSA subjects. Statistical testing revealed that the proportion of
analyzed segments in NREM2 and NREM3 does not depend on whether the subject suers from OSA or
not (
2
(1) = 0.132 ; p = 0.715). These results indicate that in our population there was not a particular
predominance of analyzed segments in a certain sleep stage across the non-OSA and OSA individuals.
Table 3.8: Contingency table showing the frequency distribution of the sleep stages of the induced sighs
segments measured on a total of 38 subjects (19 non-OSA and 19 OSA). Note that each induced sighs
segment was considered to be coming from a dierent non-OSA and OSA subject in this case. No signicant
interaction was found between the frequency of NREM2 and NREM3 and the presence of OSA (
2
(1) =
0.132 ; p = 0.715).
NREM2 NREM3 Total
non-OSA 31 37 68
OSA 25 34 59
Total 56 71 127
Once we found that we had a similar distribution of NREM2 and NREM3 analyzed segments in our non-
OSA and OSA groups, we proceeded to investigate their eects on our stability quantiers. In order to do
this, we identied those subjects from which we successfully quantied stability in both NREM2 and NREM3
sleep stages. If multiple measurements were obtained within a certain sleep stage, the median was used to
represent the subject's parameter at that sleep stage. A total of 19 subjects (14 non-OSA and 5 OSA) had
measurements of our stability features in the two sleep stages. In terms of statistical analysis, a two-factor
repeated measures analysis of variance (ANOVA) was utilized to compare the mean dierences that exist
in our model-derived stability features between the non-OSA and the OSA population within sleep stages
NREM2 and NREM3. Following a log-transformation of loop gain, we found that there is a statistically
signicant interaction between the presence of OSA and sleep stage (p = 0.036). Post-hoc comparisons using
the Holm-Sidak method revealed a marginally signicant dierence in mean loop gain between the non-OSA
84
and OSA populations within NREM2 (p = 0.066). It can be seen from Figure 3.29 (left panel) that loop
gain in the OSA population tends to be higher within NREM2; however, such dierences vanish within
NREM3. Similarly, after log-transforming the phase crossover frequency, we found that the dierence in the
mean values among the dierent sleep stages is greater than would be expected by chance after allowing
for the eects of the presence of OSA. There is a statistically signicant dierence (p = 0.008). By looking
at Figure3.29 (right panel) it becomes apparent that phase crossover frequency is increased in NREM3 as
compared to NREM2 in both the non-OSA and the OSA groups. In this case no statistically signicant
interaction between phenotype and sleep stage was found (p = 0.717), which can be visually detected by
the similar slopes in both curves. After applying the same analysis to the rest of the stability markers, no
signicant results were found.
NREM2 NREM3
−1.15
−1.1
−1.05
−1
−0.95
−0.9
−0.85
−0.8
−0.75
−0.7
−0.65
log
10
(Loop Gain(0.01 − 0.05 Hz))
NREM Sleep Stages

non−OSA
OSA
NREM2 NREM3
−1.75
−1.7
−1.65
−1.6
−1.55
−1.5
−1.45
−1.4
−1.35
−1.3
−1.25
log
10
(Phase Crossover Frequency)
NREM Sleep Stages

non−OSA
OSA
**
††
Figure 3.29: Two-way repeated measures ANOVA results for the log-transformed loop gain and phase
crossover frequency. Results are presented as mean SEM. ** indicates that the interaction term of sleep-
stagephenotype is statistically signicant. yy indicates that the main eect of sleep stage was found to
be statistically signicantly dierent after allowing for phentotypic dierences. In both cases statistical
signicance was set at p 0.05.
85
3.5 Discussion
The main purpose of this study was to develop the methodology that would enable us to accurately quan-
tify ventilatory control stability under natural NREM sleep circumstances (quiet sleep and sighing) after
bypassing the mechanical properties of the upper airway with the application of CPAP. This work involved
the design and implementation of the experimental setup that allowed us to replicate quiet sleep and sighing
episodes during NREM sleep and collect data completely noninvasively. Furthermore, it also involved the
development of the model estimation techniques that facilitated stability features extraction. This study
was carried out in a group of obese adolescents with and without OSA to help us better understand the
contributions of instabilities in the ventilatory control system to the development of OSA.
3.5.1 Simulated data
Our simulation study revealed that the proposed models adequately recovered the dynamics of the systems
under study; nonetheless, it also helped us recognize some of their potential limitations. First, there are
inaccuracies in the estimates of the circulatory time delay since they were obtained from breath-by-breath
data, which have a coarser temporal resolution compared to events occurring on a beat-by-beat scale. Second,
the LIR long lasting eects and, in the frequency domain, the very low frequency components, which are
attributed to the central chemore
ex, were underestimated (see Figure 3.15). This systematic error occurred
mainly due to two factors: a) xing the memoryM
c
of the autoregressive model to 100 seconds neglected the
eects of the central chemoreceptor, which has a more sluggish response; however, experimental results have
demonstrated that the contributions to LG from the peripheral chemoreceptors are more substantial than
the ones from the medullary chemoreceptor (Khoo et al., 1995; Younes, 1989); b) keeping the length of the
response to the induced sighs used for the estimations short enough (50 breaths) so that the stationarity
property would hold (Kaplan, 1997).
The application of this methodology to the simulated spontaneous breathing data exhibited a better
estimate of the long lasting eects of the impulse response and a very accurate representation in the fre-
86
quency domain, even at the very low frequencies. This accuracy was achieved by the analysis of considerably
longer (threefold) data segments, compared to the induced sighs. As discussed previously, the presence of
nonstationarity is evident in long data sets (Popivanov and Mineva, 1999) even when there is no transition
from NREM to REM sleep or wakefulness. There are likely to be subtle time-varying changes in ventila-
tory control even within the same NREM sleep stage (Berry et al., 1998) that we are not accounting for.
Gederi et al. (2014) proposed an adaptive autoregressive algorithm that circumvents this problem and could
potentially be used to track changes in ventilatory control within the various NREM sleep stages.
3.5.2 Physiological interpretation of experimental models
The application of our estimation technique to experimental quiet sleep and induced sighs data yielded
interesting results. The dynamic loop and plant estimated models from the cohort of subjects with and
without OSA and revealed features that can be related to physiology. The chemore
ex loop as a whole
exhibited impulse responses that were oscillatory in both groups which appeared in the form of resonant
peaks in the frequency domain (See Figure 3.21B.). The presence of resonant peaks in ventilatory control
has been reported previously from experimental studies based on other nonparametric techniques such as
spectral analysis (Van den Aardweg and Karemaker, 2002) and dynamic modeling (Mitsis et al., 2009); and
has been attributed mainly to the feedback action of the chemoreceptors. The low resonant frequency that is
centered around 0.015 Hz and that is common in both groups is likely to be associated with the ventilatory
modulation provided by the central chemoreceptors, while the higher resonant frequency (centered between
0.03 and 0.04 Hz) might be related to the faster response of the peripheral chemore
ex. Thus, the absence of
a resonant peak in the 0.03 to 0.04 Hz region in the OSA group might indicate that there is an impairment
of the peripheral chemoreceptor that makes the overall loop gain to be lower when compared to the loop
gain of the non-OSA group. Despite the marked dierences found in the impulse and frequency responses
between the two population groups, statistical testing revealed no dierence in the number of basis functions
that were used to t the data (p = 0.72). On the other hand, the order of generalization tended to be higher
in the non-OSA population (mean sem, 2.90 0.32) as compared to the OSA group (2.09 0.36) but this
87
dierence did not reach statistical signicance (p = 0.10). If we recall that higher orders of generalization
result in longer onsets of the impulse response functions, the trend toward a higher order of generalization
in the non-OSA group could explain the observable dierences found in the time to peak of the loop impulse
response functions.
On the other hand, the plant exhibited impulse responses that had in general faster dynamics, with
a quicker return to steady state, in the non-OSA group as compared to OSA. We evaluated for potential
dierences in model structures between the groups and found a trend toward a lower order of generalization in
the OSA population models (mean sem, 1.04 1.89) as compared to their non-OSA counterparts (1.95
0.43), however this trend did not reach statistical signicance (p = 0.129). This nding suggests that changes
in ventilation have a faster impact on CO
2
tensions in non-OSA subjects, while the OSA patients exhibit a
more gradual eect on gas tension in response to ventilatory
uctuations. Despite the aforementioned timing
discrepancies in the impulse response functions, the frequency responses are similar to that of a low pass lter
in the periodic breathing region in both populations with no apparent dierences between them (See Figure
3.24B.). This characteristic might indicate that the gas exchange process occurring in the lungs during quiet
sleep and under normoxic conditions behaves just like a rst order linear system, at least at the very low
frequencies. While this may be true, the dierential equations relating ventilation and CO
2
tensions that
are commonly used, might need to be modied to also re
ect the behavior that was found experimentally at
higher frequencies in some subjects. Of particular interest to us would be the modication to the simplied
analytical models proposed by Carley and Shannon (1988) and Khoo et al. (1982) to accommodate for
the resonant frequency centered around 0.1 Hz that was commonly found in the frequency responses in
both groups. The appearance of this oscillatory frequency has been previously reported in the context of
ventilatory control (Preiss et al., 1975) and has been associated to metabolic-hemodynamic
uctuations in
blood gas tensions related to tissue metabolism or cardiac output (Francis et al., 1999). While some studies
claim that the occurrence of these
uctuations can be attributable to the feedback action of the peripheral
chemoreceptor (Anderson et al., 1950; Lahiri et al., 1985), there is compelling evidence showing that this
type of cardiorespiratory rhythm develops in the respiratory center, more specically in the retrotrapezoid
88
nucleus, with no need of sensory feedback information (Preiss and Polosa, 1974; Preiss et al., 1975; Ott
et al., 2011). If the former hypothesis were to be true, our results could indicate that our feedforward model
is capturing some of the undesired feedback eect provided by the peripheral chemore
ex. If the second
hypothesis were to be true, then our results could indicate that there is an intrinsic dierence at the level of
the respiratory pattern generator in the brain across subjects.
Pathology has been previously associated with changes in the qualitative dynamics of physiological control
systems (Glass and Mackey, 1979). As a matter of fact, Mackey and Milton (1987) and Glass (2015) suggest
that such changes in systems' dynamics can be manifested in three dierent forms: the development of a
regular oscillation when rhythmic behaviors are not expected; the appearance of a rhythm with a dierent
oscillatory frequency; and lastly the reduction or even complete disappearance of a rhythmic process. Our
ndings to date seem to match the latter scenario, suggesting that the pathophysiology of OSA is associated
with the diminution of oscillatory frequencies associated with the peripheral chemore
ex. Whether these
impairments are causes or consequences of the disease still remains unclear, and further research is needed
to determine the directionality and causality of these relationships.
3.5.3 Stability markers
The model extracted stability parameters (see Figure 3.26I.) revealed no signicant dierence in PG between
the groups, however we observed a trend toward an increase in the OSA group compared to its non-OSA
counterpart. The trend toward an increased PG in the OSA group might be due to multiple factors including
a lower cardiac output, a decreased lung storage volume for CO
2
or to the inability of the gas exchanger to
eliminate CO
2
adequately due to a ventilation/perfusion mismatch (Burgess, 2012; Khoo, 2000a). Cardiac
output was not measured during the experiment, but it is unlikely that there was a systematic dierence
between the two subject groups given their young age. Any change in cardiac output resulting from CPAP
was likely to be comparable in both groups, considering that therapeutic CPAP was similar in both groups
(see Table 3.1) (Digby et al., 2011; Johnson et al., 2008). Pulmonary function tests revealed that there was
no signicant dierence in forced vital capacity (FVC) nor in functional residual capacity (FRC), measured
89
by a full body plethysmography, between the groups (p = 0.805 and p = 0.537) (see Table 3.2). Even though
these results might appear to suggest that the trend of increased PG is not associated with low lung volumes,
one should be careful when drawing denite conclusions. The measurement of FRC by a plethysmography
might be misleading when there is obstruction in the lower airways just as in the case of pathological
conditions such as asthma and chronic obstructive pulmonary disease (ODonnell et al., 2010; Woolcock
et al., 1971). The inaccurate lung volume measurements are obtained because by using this technique, one
sees all of the lung gas volume, even behind the closed airways that do not participate in exchanging gas.
As an alternative, FRC could be measured using the nitrogen washout technique which, when performed
correctly, would provide a more accurate estimation of the actual lung volume that is being used for gas
exchange purposes. Fortunately, FRC measurements via the washout test were also carried out as part of
the pulmonary function test and they were performed in the upright and supine positions. Statistical testing
comparing these measurements between the non-OSA and the OSA populations both, in the upright and
supine positions, revealed a signicant dierence between the groups when they were expressed in absolute
units (p = 0.003 and p = 0.032, respectively); however, the signicance did not hold with the parameters
expressed as percent predicted (p = 0.103 and p = 0.459, respectively). We performed a correlation analysis
between the measurements of lung volume, obtained from the full body plethysmography and the nitrogen
washout test, and our PG estimations and found no apparent linear association between them.
Forced expired volume after 1 second, normalized by the forced vital capacity (FEV1/FVC) and forced
expired volume between the 25% and 75% of forced vital capacity (FEF25/75) were found to be signicantly
lower in the OSA group (p = 0.008 and p = 0.010), although these measurements were not suciently
low to imply clinically abnormal lung mechanics as mean values were still within the normal range. These
reductions in forced expiratory
ows may be attributed to in
ammation and/or constriction in the small
airways (Pellegrino et al., 2005; Zerah-Lancner et al., 1997), and has been previously reported in children
and adolescents with OSA (Van Eyck et al., 2014; Verhulst et al., 2008). No evident trend was detected
when performing a correlation analysis between PG and FEV1/FVC and PG and FEF25/75 (r = 0.019, p =
0.89; r = -0.043, p = 0.77). Note that these correlation analyses required the utilization of a nonparametric
90
Spearman rank order test due to the non normal distribution of the variables. Despite the inability to detect
a linear correlation between PG and the expiratory
ows, the signicantly lower
ows found in OSA might
still be associated with a decreased eective lung volume and perhaps more indirectly with an increased PG.
Hence, we speculate that the slight dierences found in PG between the groups are mainly due to a reduced
eective pulmonary CO
2
exchange. This reduction is likely due to changes in the ventilation/perfusion
matching relationship, as a result of obstruction in the small airways.
Overall LG was found to be considerably low in both groups, implying highly stable neurochemical control
of ventilation. This could be in part due to an increase in lung volumes produced by the high therapeutic
CPAP levels required by the subjects to maintain upper airway patency. Given that there was no signicant
dierence in therapeutic values between the groups, we believe that the eect of CPAP on lung volume was
comparable in the two populations. However, it should not be completely discarded the idea that the same
amount of CPAP may have preferentially lowered loop gain in the OSA group by reopening small airways
that could cause more severe gas trapping and V/Q mismatch o CPAP.
Figure 3.26I. shows a lower LG in the OSA group compared to the non-OSA group. Even though these
results did not reach statistical signicance, the observed trend contradicts what has been proposed by some
recent studies in adults, which have suggested that one phenotype of OSA may be associated with increased
loop gain that lead to chemical control instabilities (Hudgel et al., 1998; Younes et al., 2001). Furthermore,
CG was found to be signicantly lower in the OSA group, indicating a lower sensitivity in the chemorecep-
tors to changes in CO
2
levels. These results agree with the decreased ventilatory response to hypercapnic
stimulation found in awake adult OSA subjects by Benlloch et al. (1995), McNicholas et al. (1984) and Gold
et al. (1993). Osanai et al. (1999) also found a diminished ventilatory response to both hypercapnia and
hypoxia in awake adult OSA subjects when compared to healthy controls. Experimental interventions were
performed before and after administration of a dopaminergic receptor antagonist (domperidone) and the
eects on the ventilatory responses were compared between the two groups. The study reported that the
application of the pharmacological agent increased peripheral chemosensitivity in the OSA patients only and
appeared to have no eect on the control group. They suggested that patients with OSA have an abnormal-
91
ity of dopaminergic mechanisms in the peripheral chemoreceptors making them more sensitive to dopamine
receptor antagonists; however, more experimental research is needed to test this hypothesis. Independently
of the source of abnormality in the peripheral chemoreceptor, these ndings might indicate that OSA pa-
tients are unable to exhibit a normal increase in respiratory drive to compensate for changes in gas tensions
associated with inspiratory
ow-resistive loading and/or apnea (McNicholas et al., 1984; Patil et al., 2007;
Rajagopal et al., 1984).
Note that all of the aforementioned studies were performed in populations of adults and while the subjects
were in the awake state, therefore it remains unclear whether these results also hold true for our population
of overweight adolescents. To our knowledge, Yuan et al. (2012) performed some pioneering work in the
quantication of chemore
ex sensitivity in a population of obese adolescents with and without OSA during
the awake and sleeping (quiet and active) states in response to a hypercapnic challenge. They found that
ventilatory responses to hypercapnia during wakefulness were elevated in both obese groups, with and without
OSA, as compared to a lean control group. When comparing the ventilatory responses to hypercapnia
between quiet and active sleep within the three groups, they found no signicant dierences. Interestingly,
however, when they performed the comparison across the three groups, they found a statistically signicant
blunted response in minute ventilation, tidal volume, inspiratory
ow, among other respiratory variables; to
hypercapnic stimulation during quiet sleep in the obese OSA group, as compared to the obese non-OSA and
the healthy lean groups. Our results of a blunted chemore
ex sensitivity in the obese OSA group during
quiet sleep seem to support their ndings and could suggest that central ventilatory drive abnormalities play
a role in the pathophysiology of OSA in obese adolescent individuals.
As it becomes apparent from Figure 3.26II., the inclusion of the phase-crossover information in the
evaluation of loop gain leads to a marginal statistical dierence between the groups (p = 0.09) that was
not detected when only considering the magnitude of the loop gain. This result showcases the importance
of incorporating the phase information when quantifying the stability of a feedback system. Rather than
LG(e
j!pc
), perhaps gain margin is more accepted by the clinical community as a quantier of the propensity
towards ventilatory control instabilities. Given the reciprocal relationship between these two parameters, it
92
was not surprising the fact that there was also a marginally statistically signicant dierence in gain margin
between the groups (p = 0.07). The results obtained from the relative stability analysis conrm that OSA
subjects, after stabilizing the upper airway, have a ventilatory control system that is less prone to instabilities
as compared to their non-OSA counterparts.
Our overall results suggest that OSA in pediatric overweight adolescents is unlikely to be the consequence
of ventilatory control instability via a hypersensitive chemore
ex to external perturbations. On the contrary,
our results indicate that a hyporesponsive chemore
ex, that is unable to provide the correct compensatory
reaction to the diverse respiratory events, is what leads to ventilatory instabilities. The unstable breathing
patterns in the adolescent OSA population might ensue due to an enhanced ventilatory response to arousal
from an apnea. The lack of an appropriate respiratory compensation could result in a reduction of CO
2
beyond the apneic threshold, and therefore inducing an apnea as sleep is restored. These self-sustained
episodes of apnea and arousal would propagate and continue to occur until a resetting mechanism brings
the system to a normal and steady state. Further research is required to investigate the interactions existing
between the chemical control of respiration, the arousal mechanisms and the neuromotor characteristics of
upper airway.
3.5.4 Correlation analysis
We found a moderate negative correlation between the severity of OSA and the LG evaluated at the phase-
crossover frequency (see Figure 3.27). Associations between LG and OAHI have been reported in recent
studies. In Wellman et al. (2004), a signicant and strongly positive correlation between LG and OAHI was
found in subjects with a moderately collapsible upper airway. Interestingly, a negative correlation between
these variables was found in subjects with a less collapsible airway; however, this result was not found to be
signicant, due primarily to the lack of statistical power. Although Wellman's study was conducted on adults,
their results could well be applicable to the pediatric population, since children tend to have an increased
upper airway caliber (Martin et al., 1997), and augmented upper airway muscle function (Worsnop et al.,
2000), making it less collapsible compared to adults. Terrill et al. (2014) found a strong positive correlation
93
between NREM OAHI and LG and, conversely, a moderate though signicant negative correlation between
LG and the relative predominance of NREM over REM OSA. In gure 3.27, the reported OAHI encompassed
those events occurring during both NREM and REM sleep; thus, our correlation might have been confounded
by those subjects with REM predominant OSA, which has been reported to be common among the pediatric
population (Goh et al., 2000).
Interestingly, a positive correlation was found between the phase-crossover frequency and OAHI. A possi-
ble interpretation to these results could be given if we recall that OAHI is a measure of the rate of occurrence
of an adverse respiratory event (apnea or hypopnea), or in other words it is a measure of how frequent these
episodes are throughout the night. The phase-crossover frequency, on the other hand, would be the frequency
at which the ventilatory control system would resonate if the open loop gain were to be increased by a factor
equivalent to the gain margin. Thus, as the resonant frequency increases, the likelihood of the occurrence of
apneic/hypopneic events per hour of sleep would tend to increase as well.
Finally, we found a statistically signicant positive correlation between OAHI and gain margin. To
the best of our knowledge a correlation between OSA severity and gain margin has not been presented
explicitly to date; although, the study by Wellman et al. (2004) reported a positive correlation between
AHI and LG(e
j!pc
). Given the reciprocal relationship between the latter variable and gain margin, we can
condently expect a negative association between AHI and their measurement of relative stability, dened
as the tidal volume amplication factor (VTAF). The VTAF parameter is homologous to our gain margin
and was experimentally derived following the technique proposed by Younes et al. (2001), whereby periodic
breathing was induced through the augmentation of the level of proportional assist ventilation (Younes,
1992). VTAF was dened as the amount of pressure support provided by the ventilator immediately before
periodic breathing was induced. While the expected negative correlation between AHI and VTAF that could
be drawn from the study performed by Wellman et al. (2004) are consistent with the theory of ventilatory
instability contributing to OSA severity, our results contradict that theory and suggest that it is an overly
stable ventilatory control system that promotes the occurrence of respiratory events.
94
3.5.5 Eects of gender and NREM sleep stages on stability quantiers
3.5.5.1 Gender
Our adolescent sample exhibited a statistically signicant interaction between gender and the presence of
OSA, which was more prevalent in the male population. Similar results have been found in the adult
population, where OSA has been found to be three times more prevalent in men than in women (Young
et al., 1993; Redline et al., 1994; Bixler et al., 2001). Although the reasons for this remain unclear, there
are two factors that may be critical: dierences in fat distribution patterns as well as hormonal dierences.
In males, fat is preferentially distributed in the abdominal area, upper body, and neck. Such centripetal fat
distribution pattern is more closely linked to OSA as compared to a peripheral pattern of obesity, which is
more commonly observed in the female population. Such obesity distribution pattern is characterized by
a fat localization in the subcutaneous tissues of the hips and thighs (Vgontzas et al., 2000; Young et al.,
2002b). The hormonal contribution to an increased OSA prevalence in the male population is less apparent,
however it is believed to be associated with the contribution of testosterone to the fat deposition in the
neck region that may cause OSA via a reduction in the size of the upper airway. In addition, it has also
been hypothesized that progesterone, a respiratory stimulant, has a stabilizing eect on the respiratory
control system protecting women against OSA (Bixler et al., 2001). Further, the onset of menopause, which
is accompanied by a reduction of the estrogen and progesterone production levels, is considered by some
studies as a major factor triggering the increase in OSA in adult women (Jordan and McEvoy, 2003; Resta
et al., 2003, 2004).
The increased risk of males developing OSA has also been reported in studies performed in adolescents
(Baker et al., 2017; Redline et al., 2007). In addition to the predisposition of males to OSA, some studies
have also reported obesity and adenotonsillar hypertrophy as risk factors for adolescent OSA (Kohler et al.,
2009; Baker et al., 2017). It remains unclear whether the dierences in sex hormones, that were previously
described for the adult population, are applicable to prepubertal girls and adolescents, in whom sex hormones
are signicantly dierent. One potential way in which sex hormones can promote OSA is through dierences
95
in neural control of respiration. It has been demonstrated that sex steroid hormones, namely testosterone,
estrogen and progesterone; have eects on the brain, and the neural control of breathing in a rat model
(Holley et al., 2012). Therefore, we sought to investigate whether our respiratory control stability features
were dierent across males and females. A two-way ANOVA with gender and presence of OSA as the
independent variables, revealed that there is no signicant dierences across gender in none of our stability
quantiers after allowing for the factor of presence of OSA. Moreover, there was no signicant interaction
between gender and the presence of OSA at predicting our stability features. Interestingly, by allowing for
the dierences in gender, we were able to nd a statistically signicant dierence between non-OSA and
OSA in three of our stability parameters. It can be observed from Figure 3.28 that within the female group
the dierences in mean values across non-OSA and OSA subjects are not as notorious as within the male
group.
Respiratory stability has been previously compared between adult males and females with no observed
dierences across the groups either (Wellman et al., 2003; Jordan et al., 2005). Moreover, van Klaveren
and Demedts (1998) noted that the ventilatory responses to both hypercapnic and hypoxic stimulation were
independent of gender and that men and women had similar respiratory drives. This evidence might indicate
that the neural control of respiration in both adults and adolescents does not depend on gender; however,
more studies that assess the role that sex hormone factors play in ventilatory control and the development
of OSA are needed.
For a detailed review on the gender dierences in the pathophysiology of OSA, the reader is referred to
the literature reviews performed by Lin et al. (2008) in the adult population and by Brockmann et al. (2016)
in the pediatric population.
3.5.5.2 NREM sleep stages
The eect that changes in sleep stage has on the predisposition toward OSA has been widely studied.
It is well accepted that the severity of OSA increases during active sleep (REM) as compared to quiet
sleep (NREM) (Ratnavadivel et al., 2009). Such dependence could be attributed in part to the loss of
96
muscular tone and responsiveness that is characteristic of REM that makes the upper airway more prone to
collapse (Carberry et al., 2016). Other factors could also include sleep-stage-dependent variations in arousal
threshold and ventilatory control stability. While the eects of sleep state on the arousal threshold has been
extensively studied (Berry et al., 1998; Edwards et al., 2014), their eects on ventilatory control stability
remain unexplored. To our knowledge, there are a few studies performed in adults that showed that the
chemore
ex sensitivity to hypoxia and hypercapnia progressively decreases from wake to NREM sleep and
reaches its minimum during REM sleep (Douglas et al., 1982b,a). In the adolescent population, Yuan et al.
(2012) studied the dierences in ventilatory responses to hypercapnia that exist between quiet and active sleep
across obese subjects with and without OSA in addition to a lean control group. They reported no signicant
dierences between NREM and REM sleep states in any of their sensitivity quantiers. While these results
might indicate that there are no changes in ventilatory control parameters with sleep stage variations in
the adolescent population, there are still some analyses that must be done before drawing any denitive
conclusion. Accordingly, we proposed to study the dierences in ventilatory control stability parameters
that occur within NREM sleep, namely NREM2 (light sleep) and NREM3 (deep or slow wave sleep). A
two-way repeated measures ANOVA analysis, with the log-transformed loop gain as the dependent variable,
revealed that there are signicant interactions between sleep state and the presence of OSA (p = 0.036).
Post-hoc comparisons showed that within NREM2 there is a marginally signicantly decreased loop gain
in the OSA group as compared to its non-OSA counterpart. Further, when looking at the log-transformed
phase crossover frequency, a two-way repeated measures ANOVA showed a statistically signicant dierence
between NREM2 and NREM3 (p = 0.008). These results indicate that the mean oscillatory frequency of
the ventilatory control system is more elevated in slow wave sleep as compared to light sleep.
A major limitation to this analysis is the lack of a balanced proportion of non-OSA and OSA individuals
from which ventilatory stability was quantied within the two sleep stages (non-OSA = 14 ; OSA = 5). Such
low proportion of OSA subjects' with complete measurements can perhaps be explained by their irregular
sleeping patterns that are composed primarily by either light or deep sleep with a lack of an even distribution
of both. Further studies with a larger and more balanced sample size are therefore needed to fully understand
97
the eects of the subtle changes that occur within NREM sleep. Our analyses were focused on quiet sleep
only, however future studies could investigate the stability features during active sleep (REM sleep) and
compare those results to the multiple NREM sleep stages.
3.5.6 Methodological considerations
Among the advantages of our proposed modeling technique is the lack of required a priori assumptions in
the model structure, i.e. the model is entirely data driven (Marmarelis, 1993). Furthermore, the number
of free parameters was considerably reduced by expanding the impulse response in a set of basis functions.
This approach allowed us to obtain more accurate model parameter estimates from short data recordings
(Marmarelis, 2004). Moreover, the utilization of MBF for impulse response estimation helped improve
the estimation of slow systems dynamics. Despite the aforementioned advantages of the kernel expansion
technique, it has not yet been widely exploited in the context of respiratory control to quantify stability.
Previous eorts that utilized this technique with the Laguerre set of basis functions include the study by
Asyali et al. (2002), where a linear autoregressive model was implemented to measure LG. In this case,
esophageal pressure was assumed to represent ventilatory drive, making their model extendable to the case
where an airway obstruction occurs. However, this necessitated a slightly more invasive regimen of instru-
mentation. In contrast, both of our models were estimated with variables derived from tidal volume which
was measured completely noninvasively. Mitsis et al. (2009) also employed Laguerre-based Volterra models
to nd estimations of the feedforward and feedback pathways of the ventilatory control loop, and subse-
quently multiplied their frequency responses to nally obtain estimations of LG. Our autoregressive model,
on the other hand, combined the feedforward and feedback eects in one single model, which simplied the
manner for estimating LG.
There are however some constraints of our model formulations that must be considered. First, we per-
formed direct estimation of the plant impulse response, disregarding the eects of the feedback branch. This
procedure could lead to biased estimations due to the correlations existing between the input and the dis-
turbance signals that are inevitable in systems operating under closed loop conditions (Baselli and Bolzern,
98
2006; Van den Hof, 1998). In order to reduce the eects of the disturbance, we excluded from the analysis
those data segments containing large breaths that were unlikely to be generated by changes in P
ET
CO
2
as
proposed by Mitsis et al. (2009). Second, our autoregressive model, could be formulated given the existence
of a suciently strong driving stimulus (sighs) and the imposition of a time delay in the time series to assure
causality (Akaike, 1968). This model structure yielded estimations that were accurate in a limited frequency
range.
One limitation to our approach is the fact that PG and LG were estimated from data recorded at dierent
points of the night, under the assumption that the plant remained unchanged within the various NREM sleep
stages. Ideally, both PG and LG should have been estimated from the induced sighs segments; however, we
detected thatPCO
2
measurements (sampled noninvasively by a nasal cannula) were not suciently reliable
to approximate P
ET
CO
2
during and after the sighs. These inaccuracies could be attributed to the
ushing
eect on expired PCO
2
caused by the changes in air pressure used to provoke the sighs. This led us to
analyze more stable segments for PG computations where P
ET
CO
2
estimations were more trustworthy.
Finally, it should also be noted that the results presented herein are based on the underlying assumption
that the ventilatory control system behaves as a linear system after stabilizing the upper airway. Although
it is known that the rest of its components are nonlinear (Grodins et al., 1954; Khoo, 2000a), linear ap-
proximations are often used (Khoo, 2000b). In this case, the assumption of linearity is valid because, aside
from the perturbation, there were no large
uctuations present in the signals. In addition, by assuming the
feedback system to be linear, the problem of stability quantication was greatly simplied by the application
of classical control theory.
3.5.7 Conclusion
In summary, we have developed a novel experimental setup and the computational methodology for quanti-
fying stability in the chemore
ex control of respiration. Our ndings to date suggest that OSA in pediatric
overweight is unlikely to result primarily from increased chemical loop gain. These results appear to con-
tradict the theory that, besides an unfavorable anatomy and a collapsible upper airway, a highly unstable
99
ventilatory control system predisposes to OSA. On the contrary, the present study suggests that upper air-
way collapsibility, in addition to a blunted neurochemical response to blood gas concentrations are the main
factors leading to the development of OSA. The design of therapeutic strategies targeting one or more of
these mechanisms might help alleviate OSA severity in this cohort of subjects. For instance, the application
of supplemental oxygen could help increase the chemore
ex sensitivity and ultimately increase loop gain to
normal values. Although these results are still preliminary, they still show the potential of using mathe-
matical modeling as a means for guiding clinicians in selecting the optimal therapy to treat OSA. However,
to better understand the pathophysiology of this sleep-related respiratory disorder in overweight children
and potentially personalize treatment, future studies should explore alternative mechanisms of ventilatory
instability that involve the complex interactions among other factors such as upper airway dynamics, arousal
threshold and wakefulness drive.
100
Chapter 4
Model-based phenotyping of obstructive sleep
apnea in overweight adolescents for personal-
ized theranostics
4.1 Introduction
Obstructive sleep apnea (OSA) is a breathing disorder characterized by repetitive episodes of upper airway
(UA) collapse occurring during sleep. In the United States, OSA is prevalent in 1.6% of children and
adolescents with ages ranging between 2 and 18 yrs Lumeng and Chervin (2008). However, this number is
expected to increase because of the growing prevalence of pediatric obesity, which is a known risk factor
for OSA Redline et al. (1999). From the pediatric population, we are specically studying a cohort of
adolescents. Adolescence marks the transition from child to adult, and is characterized by changes in sexual
development in addition to somatic growth and cortical processing (Chugani, 1998). Moreover, adolescence
has been associated with an increase in upper airway collapsibility, with attenuation of important protective
upper airway re
exes (Bandla et al., 2008). Despite these anatomical and physiological changes, little is
know about the pathophysiology in adolescent OSA.
101
In order to reduce the deleterious long term eects of OSA, such as hypertension and cardiovascular
disease, it is necessary to eectively diagnose and treat the disorder at an early age. While the current
gold standard diagnostic method (i.e. polysomnography) is eective at detecting the presence of OSA, it is
not specic enough to identify the causes of the breathing disorder. For this reason, treatment selection is
challenging considering that OSA involves the interplay of anatomical mechanisms, such as an unfavorable
UA structure and/or a collapsible UA; as well as non-anatomical mechanisms, including an unstable respi-
ratory control system, a low arousal threshold, and an overly strong arousal respiratory response Wellman
et al. (2013). Current treatment strategies in the pediatric population mostly target the anatomical char-
acteristics of the UA through the surgical removal of the adenoids and tonsils or through the application of
continuous positive airway pressure (CPAP). While these treatments are in general eective at reducing the
severity of OSA, they do not completely resolve the problem Brietzke and Gallagher (2006); Marcus et al.
(2006). The failure to eliminate OSA could be in part attributed to an inappropriate treatment selection.
Therefore, there is a need for clinicians to have access to physiological measurements of both the anatomical
and non-anatomical traits that predispose to OSA in order to better diagnose and improve the treatment
outcomes.
Previous phenotyping studies that aimed at measuring the OSA traits include those carried out by Well-
man et al. (2011, 2013). This work demonstrated that the quantication of upper airway collapsibility,
ventilatory control stability, arousal threshold and muscle responsiveness was achievable using a single ex-
perimental intervention by manipulating CPAP levels. Additionally, they proposed a model that integrated
all of the extracted traits that graphically represented the relative contribution of each trait to each individ-
ual's OSA. This type of OSA phenotyping approaches could be useful in the identication of patients who
are likely to respond to existing therapies; the development of new therapies targeted at each of the specic
physiological traits; and the improvement of treatment success rates by tailoring therapies to the specic
needs of each patient (Edwards and White, 2016; Eckert, 2016). This will ultimately lead to a transition
from the current one-size-ts-all management of OSA to a precision medicine model (Malhotra et al., 2015;
Pack, 2016; Edwards et al., 2016a).
102
The transition to a more personalized treatment of OSA implies the development of alternative thera-
peutic strategies that not only focus on xing the upper airway anatomy and/or collapsibility. There have
been numerous groups who investigated the eects of therapies that do not target the upper airway. For
instance, the stability of the ventilatory control system has been proven to be increased by the application
of supplemental oxygen and acetazolamide (Wellman et al., 2008; Edwards et al., 2012). In addition, the
administration of sedatives such as eszopiclone and trazodone demonstrated the capability to signicantly
increase the arousal threshold (Eckert et al., 2011; Heinzer et al., 2008; Eckert et al., 2014). More recently,
the combination of these non-anatomical therapies has been studied and demonstrated a reduction in the
severity of OSA by 50% (Edwards et al., 2013, 2016b). While this represents a signicant drop in OSA
severity, in very severe patients this does not represent the complete resolution of the problem. Therefore,
we believe that the combination of two or more anatomical and non-anatomical therapies will be required
to eliminate OSA in some patients.
Currently, there is a strong interest in the development of methods and models that integrate the physio-
logical traits that predispose to OSA and fully exploit their potential. For example, Eckert (2016) proposed
the utilization of the PALM scale as a means to divide OSA patients into those with pure anatomical compro-
mise; those with anatomical predisposition with other contributing traits; and those with a mild anatomical
predisposition but with other abnormal traits being largely responsible for their OSA. The PALM scale was
then used to evaluate which subjects would or would not respond to therapies that do not target the upper
airway deciencies. Also, notable is the work of Owens et al. (2015) who developed a graphical model that
combined the physiological traits in order to predict whether an individual would benet from anatomical
or non-anatomical therapies or a combination thereof. They used their model to simulate the eects of
diverse treatments on the OSA traits and predicted whether OSA would be eliminated by using single or
combination therapy. The aforementioned studies have focused in the adult population. To the best of our
knowledge, only Marcus et al. (2017) has carried out a phenotypic approach in the adolescent population.
They proposed a mathematical model that integrated the underlying traits in order to quantify their relative
contributions to the risk for OSA in a group of obese adolescents. Even though this study provides great
103
insight into the overall pahtophysiology of adolescent OSA, it does not provide information of how the traits
interact with each other to cause OSA in a specic individual. Our study, on the other hand, integrates the
physiological traits in order to examine the causes of OSA at an individual level to ultimately suggest a line
of treatment.
This work presents a series of experimental maneuvers along with the modeling techniques that were used
in order to extract the traits that predispose to OSA in a population of obese adolescents. In addition, we
present a model that enables the accurate classication into non-OSA and OSA groups based on the extracted
physiological traits. Moreover, we present a visual tool that allows the examination of the contribution of
each of the traits to each of the individual's OSA. We believe that our methodology can be used to guide
clinicians in the phenotyping of OSA and thus in the design of personalized treatment strategies that could
potentially help to completely eradicate OSA in the pediatric population.
4.2 Materials and methods
4.2.1 Subjects
A total of 235 adolescents (13 - 21 years old) with a history of snoring and a Body Mass Index (BMI) greater
than the 85
th
percentile, after adjusting for age and gender, were screened to participate in the study.
We excluded from further tests those subjects who were taking medications that could aect breathing,
or who were using supplemental oxygen or who were on positive pressure treatments (CPAP or BiPAP).
Additionally, diabetes, cardiac disease, chronic lung disease, persistent asthma, syndromic conditions, mental
illness, neuromuscular disorders and craniofacial malformations were also considered exclusion criteria. The
inclusion criteria was met by 64 subjects who underwent a standard diagnostic polysomnography (PSG)
to detect the presence of OSA. We lost to follow up with eleven subjects, therefore only 53 returned for
a Pulmonary Function Test (PFT) to evaluate for pulmonary disease and a research PSG. Seven subjects
were not able to tolerate the instrumentation and were unable to fall asleep. This left us with a total of 46
subjects on which we were able to perform our experimental interventions during NREM sleep. Table 4.1
104
shows the characteristics of the 46 subjects who completed the experimental sleep study.
The study was approved by the Institutional Review Board at Children's Hospital Los Angeles and all
parents and participants gave written informed consent prior to their participation in the experiment.
4.2.2 Standard polysomnography
A baseline overnight PSG was carried out to detect the presence of OSA. We used an OAHI of 5 events/hour
of sleep as the cuto value to diagnose OSA. From the 46 subjects, the proportion of those who were
diagnosed with OSA and as non-OSA was equal (23 OSA and 23 non-OSA). Surface electrodes were used
to record electroencephalogram (EEG), electrocardiogram (ECG), electrooculogram (EOG), and chin and
leg electromyogram (EMG). In addition, chest and abdominal displacements, pulse oxymetry and expired
carbon dioxide tension (P
ET
CO
2
) were also monitored. Data were recorded with the SomnoStar z4 sleep
system (VIASYS Healthcare Inc.) and respiratory events were scored according to the American Academy
of Sleep Medicine criteria Berry et al. (2012).
4.2.3 Pulmonary function test
On a dierent night, subjects returned to the hospital for pulmonary function testing (PFT). This was carried
out immediately before the experimental sleep study to evaluate for potential pulmonary abnormalities
contributing to hypoxia or hypercapnia detected during the diagnostic PSG. The PFT consisted of a full
body plethysmography, to measure lung capacities; a spirometry test, to evaluate for airway obstruction;
and a single breath nitrogen washout, to look for an abnormal distribution of ventilation. Table 4.1 shows a
summary of the PFT measurements that we obtained from our cohort of adolescents after being stratied as
non-OSA and OSA. It can be observed that some of the variables collected from the spirometry test, namely
FEV1/FVC and FEF27/75, showed a statistically signicant dierence between the non-OSA and the OSA
groups.
105
4.2.4 Experimental polysomnography
In addition to the equipment used during the baseline PSG, subjects were tted with a full face mask (Mirage
Quattro, ResMed, San Diego, CA). Attached to the face mask, we placed a two way shuto in
atable balloon
valve that was activated with a controller unit (9340 Series, Hans Rudolph, Kansas City, MO) to generate
upper airway occlusions when activated. Connected to the balloon valve, we had a two-way t-shape non-
rebreathing valve (Model 1400, Hans Rudolph, Kansas City, MO) with a whisper swivel exhalation valve
(Respironics, Pittsburgh, PA) connected at the expiratory port. These two pieces helped remove the waste
gas resulting from respiration. An 18 inch
exible CPAP tube was appended to the swivel valve and was fed
back to the inspiratory limb, in order to maintain pressure during inspiration and expiration constant.
Subjects were asked to sleep in the supine position and were provided with positive pressure using a
bilevel pressure ventilator (S/T-D 30, Respironics, Pittsburgh, PA) operating in CPAP mode. Mask pressure
was monitored by means of a pressure transducer (Validyne, Northridge, CA), which sampled from a port
located at the face mask and was referenced to atmospheric pressure. Respiratory air
ow was measured by a
second Validyne pressure transducer in conjunction with a pneuomotachometer (Model 4813, Hans Rudolph,
Kansas City, MO) connected at the expiratory port of the ventilator. Arterial blood pressure was assessed
by a nger plethysmograph (Nexn, BMEYE, Amsterdam, The Netherlands) and used in combination with
EEG signals to detect arousals Davies et al. (1993). All physiological signals were recorded with a digital
acquisition system (NI USB-6218, National Instruments, Austin, TX), which was also used to send pressure
command signals to the ventilator and to activate the in
atable balloon valve from a computer. Figure 4.1
shows a schematic of the experimental setup that was implemented.
We utilized CPAP to individually titrate all of our subjects. After sleep onset, CPAP was gradually
increased starting at a baseline value of 3cmH
2
O pressure and until respiratory events (snoring, hypopneas,
apneas) and
ow limitation, dened as a
attening in the inspiratory portion of the air
ow signal Clark et al.
(1998), were eliminated. The CPAP pressure that minimized upper airway resistance and eliminated all of
the respiratory events was deemed the holding or therapeutic pressure and was used as a starting pressure
106
Figure 4.1: Left. Schematic of the breathing circuit and the integrated control and data acquisition system
that was utilized for protocol execution. Right. Sample recordings of the main physiological measurements
that were used for the extraction of the physiological traits.
for our experimental interventions. All of our recordings were performed after a stable period of NREM of
more than ve minutes was noticed and multiple repetitions of each intervention were carried out throughout
the night. Each of our experimental interventions will be described in the following sections.
Table 4.1 summarizes the demographic and polysomnography characteristics of the non-OSA and OSA
groups. It should be noted that besides signicant dierences found in males to females ratio, OAHI and
neck circumference, both groups are comparable in other antropometric measurements and even therapeutic
CPAP pressures. The surprising similarity in the latter parameter can be attributed to the persistent snoring
episodes exhibited by the non-OSA group.
4.2.5 Upper airway collapsibility determination
In order to measure the collapsibility of the upper airway, we made an adaptation to the experimental
maneuver rst introduced by Smith et al. (1988). Pressure sequences consisting of four abrupt drops in
CPAP level of increasing amplitudes and ve breaths duration were delivered to the subjects. The four
levels to which the pressure was dropped lay within the range of the individuals' therapeutic pressure and
the minimal CPAP pressure of 3 cmH
2
O. Each pressure drop was followed by a rapid return to therapeutic
107
pressure lasting ve breaths as well. Figure 4.2.A shows representative recordings of mask pressure (top
panel) and air
ow (bottom panel) during the intermittent pressure drops protocol. It can be observed that
for this subject in particular, the holding pressure is of 10cmH
2
O and drops in multiples of 1.4cmH
2
O until
it reaches a minimum of 4.4 cmH
2
O. It can also be noted that the progressive decrease in mask pressure
results in a reduction in the amplitude of the air
ow signal. Such eects were quantied by performing
a linear regression on the peak inspiratory
ow and mask pressure values of those
ow limited breaths
occurring at subtherapeutic CPAP pressures. Only breaths 2-4 of each pressure drop were included in the
regression analysis. We excluded the rst breath following the drop to allow lung volume and maximum
ow
to stabilize (Owens et al., 2010; Boudewyns et al., 2000); as well as the fth breath post drop to avoid the
inclusion of non-
ow limited breaths (Marcus et al., 2005; Katz et al., 2006). In addition, breaths occurring
after an arousal were also discarded from the computation of the regression coecients. The estimation of
the regression coecients was carried out using an iteratively reweighted least squares algorithm because
it is more robust than the ordinary least squares method to the presence of outliers in the measurements
(Holland and Welsch, 1977; Huber, 2011).
Figure 4.2.B depicts the corresponding linear regression analysis performed on the data shown in gure
4.2.A. Two parameters that are associated with the collapsibility of the upper airway were extracted from
the regression analysis: 1) the slope of the regression line (Slope
pf
), which represents the ratio between
changes in air
ow and changes in mask pressure. A higher value of the slope parameter would indicate that
the drops in CPAP pressure have a greater impact on the amplitude of the air
ow signal. 2) the projection
of the tted line to the point of zero air
ow (x-intercept), which is also known as the hypotonic critical
closing pressure (P
crit
) in the clinical world. It refers to the luminal pressure at which the upper airway
would collapse if there were no nueromuscular compensation (Schwartz et al., 1998) and it is calculated as
follows.
P
crit
=
_
V
0
=Slope
pf
(4.1)
where
_
V
0
denotes the air
ow at zero pressure and Slope
pf
is the slope of the pressure-air
ow plot.
108
A very negative P
crit
value, using atmospheric pressure as a reference, indicates that the upper airway
requires the application of an extremely negative pressure in order for it to collapse. Thus, it follows that
the more positive the P
crit
value is, the more prone the upper airway is to collapse. In OSA subjects, the
slope of the pressure-air
ow regression has been found to be elevated as compared to non-OSA individuals.
In addition, P
crit
in OSA subjects has been reported to take values that are close to or even above zero,
indicating that the upper airway is susceptible to collapse even under pressure conditions that are close to
atmospheric (Gleadhill et al., 1991).
Figure 4.2: A. Sample continuous recordings of pressure and air
ow during the intermittent CPAP drops
protocol. Shaded areas correspond to the instances where CPAP pressure was lowered to the various sub-
therapeutic levels. B. Scatter plot of peak inspiratory
ow and mask pressure for the
ow limited breaths
along with the results from the linear regression analysis that lead to the extraction of the upper airway
collapsibility features.
4.2.6 Ventilatory control stability quantication
The quantication of ventilatory control stability was possible by the application of a novel experimental
technique that uses changes in inspiratory pressure to create a ventilatory disturbance in the form of sighs.
This novel approach, developed by our group, has proven to ecaciously perturb the ventilatory control
system and has been previously described (Nava-Guerra et al., 2016). Brie
y, after ten baseline breaths at
109
therapeutic pressure, inspiratory pressure was abruptly increased by 5 cmH2O for two consecutive breaths,
keeping the expiratory pressure at therapeutic level. After the hyperventilatory sighs, inspiratory pressure
was returned to therapeutic pressure. Responses to the induced sighs were recorded and used for further
analysis, discarding those leading to an EEG arousal.
Figure 4.3.A shows a typical recording of pressure (top panel) and air
ow (bottom panel) in response
to the induced sighs intervention. Note that for this subject the protocol starts at a holding pressure of
8 cmH
2
O and it is raised up to 13 cmH
2
O to induce the two sighs. It can be seen that the increase in
CPAP pressure roughly doubles the amplitude of the air
ow signal. Moreover, the appearance of oscilla-
tions modulating the air
ow amplitude that arise from the intervention can be observed. We assume that
these oscillations result from a compensatory action provided by the chemore
ex. In order to quantify the
propensity toward this oscillatory behavior (ventilatory control instability), we utilized the breath-by-breath
ventilatory measurements to t a linear autoregressive model. The modeling technique employed herein
required an input-output formulation (Marmarelis, 1997); therefore, we considered the sigh as an exogenous
disturbance or "input" to the ventilatory control system and the ensuing response to the sigh as an "output".
We then used this input-output data to estimate the model that best predicted the ventilatory response to
the sighs. The optimal model was subsequently used to quantify ventilatory control stability by means of the
concept of loop gain. A ventilatory system with an elevated loop gain would tend to magnify disturbances,
such as a sigh, and could potentially develop self-sustained oscillations. On the other hand, a system with
a low loop gain would diminish such perturbations and exhibit a more stable ventilatory pattern. A sample
of the breath-by-breath ventilatory response to the induced sighs along with the model-predicted response
are illustrated in gure 4.3.B. Note that the model accurately captures the damped oscillatory ventilatory
response exhibited by this subject.
In addition, spontaneous breath-by-breath measurements of ventilation (input) were used concomitantly
with the breath-by-breath end-tidal CO2 signal (output) to t a feedforward linear dynamic model that
allowed us to quantify the direct eects that ventilation had on CO2 concentrations (plant gain). Given
the assumption of linearity in our models, controller gain could be simply derived by dividing loop gain
110
by the plant gain. The main advantage of the employed modeling methodology over parametric modeling
techniques, is that it requires minimal a priori assumptions on the biophysics governing the system and
the models are entirely driven by the data (Marmarelis, 1993). For a more detailed explanation on the
application of this modeling technique in the context of respiratory control, the reader is referred to the
original manuscript (Nava-Guerra et al., 2016).
Figure 4.3: A. Sample measurements of pressure (top) and air
ow (bottom) throughout the induced sighs
intervention. The shaded area indicates the time during which the hyperventilatory sighs are being provoked.
B. Corresponding breath-by-breath ventilatory drive measurement (solid) and prediction provided by the
optimal model (dashed).
4.2.7 Arousal components extraction
We performed an experimental protocol that elicited an arousal from sleep by completely blocking the pass
of air coming from the CPAP machine and going into the mask. The goal of performing this protocol was
to understand how these subjects would respond to an apneic episode. In particular, we were interested in
having estimates of the breathing eort against a blocked airway that is required to disturb the sleeping
state and elicit an arousal. In addition, it was of interest for us to measure the compensatory respiratory
drive, associated with the arousal, that is commanded by the brain to compensate for the hypercapnic
111
and/or hypoxic events that might result from the apnea. The quantication of these arousal mechanisms
is of particular importance because recent studies indicate that a subphenotype of OSA could include a
low arousal threshold (sensitive to small changes in negative intrathoracic pressures) (Eckert, 2016); and an
increased ventilatory response to arousal (Iber et al., 1986; Younes, 2004; Eckert and Younes, 2014).
The experimental protocol is again started at therapeutic pressure and with the subject in a stable NREM
sleep stage for at least ve minutes. After ten baseline breaths, the air
ow is completely blocked with the
help of an in
atable balloon valve. The balloon valve is activated automatically by the investigator through
an automated valve controller (see the diagram shown in Section 4.2.4). The valve remains active for as
many breathing eorts as the subject can exert without showing a sleep state change from NREM sleep to
awake (monitored in real-time from EEG activity and scored according to the AASM standards (Berry et al.,
2012)). The air
ow occlusion is nally released one or two breathing eorts after arousal is rst noticed, and
subjects are put back to their therapeutic CPAP pressure. In order to avoid premature arousals, the air
ow
occlusion is precisely timed to occur toward the end of the expiratory phase of the respiratory cycle.
Figure 4.4 shows a sample recording of the inspiratory occlusion protocol. The gure shows three base-
line breaths at therapeutic pressure (15 cmH
2
O for this subject), before the occlusion valve is activated,
followed by three occluded breaths before arousal is noticed in the EEG measurement (dashed vertical line).
Following the arousal, the occlusion valve remains activated for three extra breaths before being released
and breathing is resumed at therapeutic pressure. The arousal threshold can be directly extracted from
the peak inspiratory pressure of the breath immediately preceding the arousal. The dierence between the
peak inspiratory pressure of the breath following the arousal and the previously derived arousal threshold,
is deemed to represent the respiratory drive that is associated with arousal. Note that these parameters
are not measured by their absolute values, but rather by the relative pressure dierence existing between
them and the therapeutic pressure (black arrows). Thus, the units of these parameters are given in cmH
2
O
instead of L=min.
112
Figure 4.4: A. Sample continuous recording of brain activity by means of the EEG (top panel), pressure
(middle panel) and air
ow. B. Zoom in to the pressure panel during the application of the occlusion. The
time of arousal is represented by the vertical dashed line and is used as a reference to extract the two
components of the arousal mechanism. Note that both the arousal threshold and the arousal drive are
referenced to the therapeutic pressure.
4.2.8 Classication model incorporating all traits
Once we completed the extraction of the traits that predispose to OSA from our cohort of obese adolescents,
we proceeded to develop a methodology that allowed us to assess the cause of the disorder at an individual
level with the ultimate goal of suggesting a personalized treatment. Figure 4.5 shows a schematic of the
procedure that we implemented in order to achieve this goal. In this case we are showing the example of
an OSA individual whose extracted traits are plotted in a spider plot with predened normal (green) and
abnormal (red) regions. It can be observed that this subject has two traits that lie in the abnormal area,
namely the upper airway anatomy as well as the ventilatory control stability. On the right hand side we are
showing the corresponding treatments that could be used to target each of the traits to help bring them to
113
Figure 4.5: Schematic of the diagnostic and therapy suggestion methodology for a subject with OSA. The
abnormal upper airway anatomy in combination with an abnormal ventilatory control stability leads to a
therapeutic strategy that combines weight loss and the application of supplemental oxygen.
the normal range. Based on this scheme for this particular subject, we can therefore suggest a therapy that
would involve a combination of weight loss and the application of supplemental oxygen to target those traits
specically and potentially help eradicate OSA from this individual.
For us to be certain that our methodology would only suggest a treatment to those subjects who have
OSA and not to those without OSA, we rst needed to evaluate whether by using our traits we can correctly
diagnose OSA. In order to so, we implemented a classication model that utilized our model-extracted
OSA traits and compared its performance against the diagnosis provided by the polysomnography. In order
to do so, we rst identied those traits that were highly associated with OSA. For this, we performed a
correlation analysis between the model-derived traits and measurements we obtained from our subjects and
their severity of OSA quantied by the OAHI. We also performed a correlation analysis between the traits to
test for colinearity among them. When a statistically signicant association between two traits was detected,
we selected the one that best correlated with OAHI and discarded the other one from our classication model.
In the end we kept those traits that best represented the mechanisms that play a role in the development
of OSA, which are UA anatomy, UA collapsibility, ventilatory control stability, arousal mechanisms and
pulmonary function.
114
Subsequently, we ranked the selected traits and normalized them to range between zero and one by
diving them by the number of total observations of each particular trait. It should be noted that there are
only nineteen subjects with complete measurements of the ve selected traits; however, the normalization
process was carried out including also those subjects with incomplete measurements. Having selected and
normalized the variables that would be included in our classication model, the question remains as to how
many traits must be abnormal to diagnose OSA and, more importantly, what would be an ideal threshold
or cut-o point that separates the normal from the abnormal values of our extracted OSA traits. In order
to solve for these two unknowns, we implemented the algorithm that is shown in Figure 4.6.
Brie
y, we initialized our search with one abnormal trait considered in the diagnostic and a threshold set
at zero. The latter parameter was iteratively increased until it spanned the whole range between zero and one.
Once a complete cycle of the threshold was completed, we increased the number of traits considered to be
abnormal and reset the threshold to zero to perform another span from zero to one. For a particular subject,
when the number of traits that exceeded the threshold was greater or equal than the predened number of
abnormal traits considered in the diagnostic, our classication model would categorize that subject as OSA
and as non-OSA otherwise. We evaluated the diagnostic performance for each combination of number of
variables considered in the diagnosis and discrimination threshold by comparing it to the diagnosis provided
by the PSG in the nineteen subjects. For every possible combination, there are some cases where the disease
is correctly classied as positive (TP = true positive), but some cases where the disease is classied as
negative (FN = false negative). On the other hand, some cases without the disease are correctly classied
as negative (TN = true negative), but some cases without the disease will be classied as positive (FP =
false positive). By combining these four metrics, we can compute the probability that the results of our
classication model will be positive when the disease is actually present (sensitivity or true positive rate).
And also the probability that our diagnosis will be negative when the disease is not present (specicity or
true negative rate). The ideal classier would be the one that is 100% sensitive and 100% specic; however,
there is always a trade o between the these two statistics as the threshold changes. In order to assess
such changes in both sensitivity and specicity, we utilized Receiver Operating Characteristic (ROC) curves.
115
Figure 4.6: Flow chart describing the procedure that was followed to nd the optimal parameters of our
classication model.
This type of curves plots the sensitivity as a function of the false positive rate (100-specicity) for every
possible value of the threshold. Since we are interested in maximizing both the sensitivity and specicity
simultaneously, we utilized the following cost function to search for the optimal threshold.
J(threshold) =
p
(1Sensitivity)
2
+ (1Specificity)
2
(4.2)
116
This cost function is essentially the distance from the top left corner with coordinates (0,1) to the ROC
curve and we aim to search for the value of the threshold that minimizes it. Therefore, by nding the
minimal distance from the ROC curve to the upper left corner, we would nd the optimal threshold, which
will provide the highest overall accuracy of our diagnostic scheme (Metz, 1978; Zweig and Campbell, 1993).
For those subjects that were diagnosed as having OSA by our methodology, we would then suggest a
personalized treatment that would be designed to target only those abnormal traits. We employed spider
plots in order to visually present the results of this analysis and evaluate which traits exceeded the optimal
threshold and would require a targeted therapy for the nineteen subjects. This type of plots is a graphical
method of displaying multivariate data in the form of a two-dimensional chart of various quantitative variables
(in our case ve variables or traits) represented on axes starting from the same point. In our case, the axes
of all variables span the range from zero to one, which is the values our variables take after the rank
normalization. This graphical tool dates back to 1877 (Von Mayr, 1877; Friendly and Denis, 2001) and is
equivalent to the parallel coordinates technique that was discussed in Section 3.3.2.1.1, but this representation
is given in polar coordinates. This type of representation has been used in the biomedical eld to assess the
risk for metabolic syndrome (Jeong et al., 2014) and to explore the heterogeneity of the clinical presentations
in sleep apnea (Ye et al., 2014).
4.2.8.1 Cross-validation
In order to assess the variability of our estimated optimal thresholds and the accuracy of our diagnostic
scheme with unseen data, we performed a Leave-M-Out cross-validation procedure (Shao, 1993; Zhang,
1993). This concept refers to the process of partitioning a data set of N subjects, who have been previously
labeled as OSA and non-OSA, into two, a training and a testing set. The training set would consist of the
measurements collected from all subjects except for M, therefore the length of the training set would be of
N-M. The estimation of the model parameters (threshold and number of traits considered in classication)
is carried out using only the data from N-M subjects. Then the estimated rules learned during this process
are applied to the data from the M subjects that were left out of the training step, for validation. This
117
procedure of splitting the data, training and testing the model is repeated a total of

N
M

times, which allows
to exhaustively explore all the possible combinations of training and testing data splits (Arlot et al., 2010). It
can be observed that since the number of times this procedures are carried out grow factorially, the number
of instances can become intractable and therefore are usually recommended for problems with low sample
sizes (Breiman et al., 1984). Given the small amount of subjects with complete measurements, our problem
was a good candidate for the Leave-M-Out cross-validation technique. In our case, we implemented it for
low values of M ranging from one to four.
4.2.9 Statistical analyses
All variables were rst tested for normality using the Kolmogorov-Smirnov test. Comparisons between groups
were performed using independent samples Student's t-test for those variables that passed the normality test.
Whereas, for the variables that failed normality, the comparisons between the groups were performed via the
Mann-Whitney Rank Sum test. Linear correlations between the model derived parameters and the severity
of OSA were evaluated with the nonparametric Spearman correlation on the ranks. Cohen's kappa coecient
was calculated to evaluate the agreement between our classication model and the diagnostic provided by
the polysomnography. All tests used p < 0.05 to determine signicance.
4.3 Results
4.3.1 Upper airway collapsibility
Figure 4.7 shows the peak inspiratory air
ow and pressure values that were extracted from the intermittent
pressure drops protocol in three dierent subjects. Along with the data, we show the estimated linear models
that resulted from the regression analyses and that were used to nd the slope of the pressure-air
ow plot, as
well as the projection to the zero air
ow point (P
crit
). By comparing the results from these three individuals,
we can observe that there are some similarities that must be pointed out. First, the three data sets start
with very similar air
ow amplitudes that are slightly above 20 L=min. Second, the intermittent pressure
118
drops spanned a similar range of pressure values. Such similarities can be attributed to the fact that all
three subjects had similar therapeutic pressures (left panel @ 8 cmH
2
O ; middle panel @ 10 cmH
2
O ; right
panel @ 8 cmH
2
O). Despite the similarities found in the initial conditions of the experimental intervention
across the three subjects, we can observe that the responses are markedly dierent. For instance, the left
panel shows air
ow amplitudes that span within a small range of approximately 5 L=min in response to the
intermittent drops. On the other hand, the middle panel sows a response that exhibits a slightly higher range
of air
ow values of approximately 8.5 L=min. Lastly, the most notorious eect of the intermittent pressure
drops on the air
ow amplitude is presented in the right panel, where the air
ow measurements spans within
a range of 12 L=min.
Having in mind that the slope of the pressure-air
ow regression line (Slope
pf
) can be estimated as

_
V=P , we can therefore expect that a subject with a smaller change in air
ow will have a lower slope and
thus a less collapsible UA. On the contrary, a subject with a larger eect on the air
ow amplitude will have
a higher slope and thus a more collapsible UA, provided that the change in pressure is comparable in the two
cases. The subject on the left possesses a slope of 0.95 LcmH
2
O
1
min
1
, indicating that the air
ow would
decrease at a rate of almost 1 L=min per each drop in pressure of 1 cmH
O
. This rate is roughly doubled
by the subject in the middle panel (1.99 LcmH
2
O
1
min
1
) and tripled by the subject shown in the right
panel (3.25 LcmH
2
O
1
min
1
).
It can be observed from Equation 4.1 that when the y-intercept (i.e. the intersection between the regres-
sion and theP
atm
lines) is positive, then theP
crit
parameter is negative. Conversely, when the y-intercept is
negative, then P
crit
becomes positive. While the data from the left and middle panels represent the former
case, the right panel represents the latter.
Considering these two parameters (P
crit
and Slope
pf
) we can quantify the static characteristics of the
upper airway collapsibility and identify those subjects with non-collapsible, mildly collapsible, or highly
collapsible upper airways.
119
−10 0 10
0
5
10
15
20
25
A. Non collapsible UA
Pressure (cmH
2
O)
Airflow (L/min)
−10 0 10
0
5
10
15
20
25
B. Mildly collapsible UA
Pressure (cmH
2
O)
−10 0 10
0
5
10
15
20
25
Pressure (cmH
2
O)
C. Highly collapsible UA

Data
Regression
P
atm
Slope
p−f
= 3.25 LcmH
2
O
−1
min
−1
P
crit
= +1.9 cmH
2
O
Slope
p−f
= 1.99 LcmH
2
O
−1
min
−1
P
crit
= −2.8 cmH
2
O
Slope
p−f
= 0.95 LcmH
2
O
−1
min
−1
P
crit
= −15.2 cmH
2
O
Figure 4.7: Sample regression results for three subjects with dierent critical pressures as well as with dierent
slopes. Note that the air
ow and pressure data correspond to those breaths that were
ow limited during
the CPAP pressure drops. Critical pressures are referenced to aptmospheric pressure which is represented
by the dashed line.
4.3.2 Ventilatory control stability
A comparison between three subjects with dierent levels of ventilatory control stability is presented in
Figure 4.8. It can be observed that the increase in ventilatory drive during the application of the sighs is
comparable in the three cases with values ranging between 15 and 17.5 L=min. Despite the similar size of
the respiratory disturbance, the ensuing responses are markedly dierent among the three individuals. The
response shown in the left panel exhibits low amplitude and short duration oscillations of approximately of
30 seconds before relaxing back to steady state. On the other hand, the response that is presented in the
middle panel shows oscillations that are larger in amplitude and longer in duration with a settling time that
is close to 50 seconds. Lastly, the panel on the right shows a response with larger swings and oscillations
with a faster cycling period of approximately 20 seconds that decay after approximately 60 seconds. The
increased ventilatory eects, in both amplitude and duration, of the stimulating sighs are attributed to an
increased sensitivity of the ventilatory control system. We quantied such sensitivity by means of the loop
gain, which was extracted from dynamic models that were estimated from the ventilatory data. It can be
seen that the eects of the disturbance tend to propagate more in those cases where loop gain is higher.
120
While the response from the rst panel is due to a ventilatory control system whose loop gain is of 0.13,
the second response corresponds to a ventilatory control system that is twice as sensitive with a loop gain of
0.26. Lastly, the response presented in the right panel comes from a ventilatory control system with a loop
gain of 0.31, which makes it almost three times more sensitive to external disturbances than the case shown
in the left panel and therefore the oscillatory behavior is more prominent.
Figure 4.8: Sample breath-by-breath measurements of the induced sighs protocol in three subjects with
dierent degrees of oscillatory responses. The dashed line represents the prediction provided by the dynamics
model from which respiratory stability was quantied.
4.3.3 Arousal components
Similar to what we have done for the upper airway collapsibility and the ventilatory control stability, Figure
4.9 presents a comparison of the measurements of the arousal components between two dierent subjects
from the inspiratory occlusion protocol. The subject on the left started from a therapeutic pressure of 15
cmH
2
O and tolerated the occlusion for a total of three breathing eorts before arousing from sleep. After
calculating the dierence between the peak inspiratory pressure of the breath preceding arousal and the
therapeutic pressure we found that the arousal threshold for this subject was of 17.9 cmH
2
O. Additionally,
we measured the restoration of the respiratory drive after arousal by nding the dierence between the
breaths that preceded and followed the arousal. For this subject, we found that such ventilatory response
to arousal is not very strong with an arousal drive of 6.35 cmH
2
O. On the other hand, the subject on the
121
right starts at a therapeutic pressure of 12cmH
2
O. While the occlusion is being applied, it can be observed
that the subject makes ve respiratory eorts before transitioning from sleep to an arousal state. Despite
the fact that this subject showed a couple of extra breathing eorts, there was not a gradual decrease in
peak inspiratory pressure providing an arousal threshold of 16.8 cmH
2
O, which is even lower than the one
from the subject on the left. The ventilatory response to arousal in this subject was found to be of 40.3
L=min, which is roughly ve times larger when compared to the subject on the left. Such strong ventilatory
response to arousal could produce large swings in blood gases which can then in turn lead to an apneic
episode. These cyclic episodes of arousal followed and apnea can be another form of breathing instability
that is not mediated by the chemore
ex.
75 80 85
−50
−40
−30
−20
−10
0
10
20
A. Higher arousal threshold
Lower arousal drive
Time (sec)
Mask pressure (cmH
2
O)
55 60 65
−50
−40
−30
−20
−10
0
10
20
B. Lower arousal threshold
Higher arousal drive
Time (sec)
AT = 17.9 cmH
2
O
AD = 6.35 cmH
2
O
AT = 16.86 cmH
2
O
AD = 40.3 cmH
2
O
Figure 4.9: Sample continuous recordings of mask pressure during the application of the inspiratory occlusion
in two dierent individuals. The solid line marks the therapeutic pressure. The broken vertical line indicates
the time at which cortical arousal was detected. The horizontal dashed line marks the pressure of the
respiratory measurement following arousal.
4.3.4 Classication model incorporating all traits
Table 4.1 summarizes the measurements that we made and estimated from our population of obese adoles-
cents. It presents the mean values of the dierent parameters for both the non-OSA and OSA populations
and the results of the statistical tests that were performed to compare them. It should be noted that there
122
was a signicant dierence in the males to females ratio within the non-OSA and the OSA populations (p =
0.017). Not surprisingly, neck circumference was found to be signicantly elevated in the OSA population (p
= 0.035). Interestingly, the therapeutic pressure was not signicantly dierent between the groups. This can
be due to the fact that the subjects in both groups were obese and had a history of snoring. The pulmonary
function test revealed that FEV1 and FEF25/75 were both signicantly decreased in the OSA population (p
= 0.008 and p = 0.010, respectively). From our upper airway collapsibility estimated parameters we found
that the slope of the pressure
ow curve tended to be more elevated in the OSA population, however it failed
to reach signicance (p = 0.157). On the other hand, the critical pressure P
crit
was found to be comparable
between the groups. Ventilatory control stability parameters showed that controller gain was signicantly
decreased in the OSA population as compared to non-OSA subjects (p = 0.05). Circulatory time delay, loop
gain evaluated at the phase crossover frequency and gain margin were all marginally signicantly dierent
between the groups (p = 0.08 , p = 0.09 and p = 0.07, respectively). Lastly, both the arousal threshold
and arousal drive were found to be comparable between the two populations (p = 0.540 and p = 0.635,
respectively).
The correlation analyses between OSA severity, quantied by means of the OAHI, and the multiple
measurements and traits also yielded very interesting results. We observed moderately signicant correlations
between OAHI and body mass index, FEF25/75, peak expiratory
ow, forced residual capacity measured
in the upright position with the nitrogen washout test, the critical pressure and gain margin. On the other
hand, neck circumference showed a highly signicant positive association with OAHI. The slope of the
pressure-
ow plot was also found to be signicantly positively correlated with a OSA severity. In addition,
the ratio between FEV1 and FVC and loop gain evaluated at the phase-crossover frequency were found to
be signicantly negatively associated with OAHI.
We based the selection of the traits that we included in our classication model on the results from the
correlation analysis. We included those variables that showed a statistically signicant association with the
severity of OSA i.e. neck circumference, FEV1/FVC, slope of the pressure-
ow plot and loop gain. These
variables represented the anatomy of the upper airway, the pulmonary function, upper airway collapsibility,
123
Table 4.1: Summary of population demographics and OSA traits. BMI, body mass index; OAHI, obstructive apnea hypopnea index; FRC,
functional residual capacity; FVC, forced vital capacity; FRC Pleth, forced residual capacity measured by plethysmography; FEV1, forced
expired volume in one second; FEF 25/75, forced expiratory
ow between 25% and 75% of FVC; PEF, peak expiratory
ow; Vmax 80%,
percentage of FVC remaining; FRC Upright N2 and FRC Supine N2, functional residual capacity measured in the upright and positions using
the nitrogen washout technique. x is used to highlight the variables that did not pass the normality test and required the application of a
nonparametric statistical test. y indicates that the results are marginally signicantly dierent between the groups with 0.1 > p > 0.05. yy
indicates that the results are statistically signicantly dierent between the groups at p 0.05. Correlation analyses using the nonparametric
Spearman correlation on ranks were carried out between the variables and OAHI. * indicates that there is a marginally signicant association.
** indicates that there is a statistically signicant association between the variables.
non-OSA OSA Correlation w/ OAHI
Type Variable N Mean SEM N Mean SEM P-value R P-value
Subject Characteristics Gender (M:F) (6:17) - (15:8) - 0.017yy - -
Age (years)x 23 15.609 0.486 23 14.913 0.350 0.414 -0.0522 0.729
BMI (kgm
2
) 23 34.757 1.548 22 37.507 1.230 0.174 0.284 0.0585 *
Neck Circumference (cm) 21 39.718 1.147 22 42.995 0.979 0.035yy 0.413 0.00607 **
Polysomnography OAHI (events/hour)x 23 2.143 0.282 23 30.974 5.328 < 0.001yy - -
Therapeutic CPAP (cmH
2
O)x 23 10.304 0.639 23 11.130 0.459 0.118 0.189 0.206
Pulmonary Function Test FVC (%pred) 22 115.5 14.3 23 114.3 18.7 0.805 0.0199 0.896
FRC Pleth (%pred) 22 100.136 3.520 23 96.783 4.061 0.537 -0.0931 0.542
FEV1 (% pred) 22 111.2 14.3 23 104.6 14.4 0.135 -0.118 0.439
FEV1/FVC 22 85.2 3.8 23 80.5 6.9 0.008yy -0.408 0.00562 **
FEF 25/75 (% pred) 22 110.5 19.9 23 93.8 21.7 0.010yy -0.328 0.0279 *
PEF (% pred) 22 100.5 13.1 23 93.9 15.1 0.125 -0.268 0.0745 *
Vmax 80% (% pred) 18 98.8 13.8 21 91.0 16.2 0.125 -0.323 0.0452 **
FRC Upright N2 (% pred) 16 91.9 17.9 22 109.7 37.9 0.128 0.274 0.0959 *
FRC Supine N2 (% pred) 16 83.3 18.7 22 107.2 81.0 0.459 0.159 0.339
Upper Airway Collapsibility P
crit
(cmH
2
O) 12 -14.210 3.563 16 -11.668 3.161 0.599 0.336 0.0802 *
Slope
pf
(Lmin
1
cmH
2
O
1
)x 12 1.046 0.203 16 1.843 0.377 0.157 0.450 0.0165 **
Ventilatory Control Stability Loop Gain (dimensionless) 21 0.195 0.012 21 0.169 0.015 0.19 -0.237 0.130
Plant Gain (mmHgL
1
min)x 22 0.310 0.046 23 0.327 0.030 0.30 0.105 0.491
Controller Gain (LmmHg
1
min
1
)x 21 1.056 0.211 21 0.651 0.113 0.05yy -0.247 0.115
Circulatory Time Delay (sec) 21 9.476 0.351 21 8.452 0.448 0.08y -0.150 0.340
Loop Gain(!
pc
) (dimensionless) 21 0.225 0.015 21 0.186 0.016 0.09y -0.311 0.0449 **
Phase-crossover Frequency (Hz)x 21 0.037 0.003 21 0.043 0.004 0.36 0.224 0.153
Gain Margin (dimensionless)x 21 5.052 0.388 21 6.693 0.779 0.07y 0.289 0.0636 *
Arousal Mechanisms Arousal Threshold (cmH
2
O)x 16 16.916 1.118 15 18.655 3.654 0.540 -0.0252 0.891
Arousal Drive (cmH
2
O)x 16 11.599 1.956 15 16.022 3.930 0.635 0.0545 0.769
124
and ventilatory control stability, respectively. Although none of the arousal mechanisms was found to be
signicantly associated with the severity of OSA, we decided to incorporate them into the model so that
we could have an idea of how the arousal component aected these subjects. However, we found that there
was an association between the arousal threshold and the arousal drive and therefore we had to leave one of
the two traits out of the model for compactness. We dropped the wakefulness drive out because it was also
found to be associated with loop gain.
Prior to performing the classication using our extracted OSA traits, we normalized them to range
between zero and one following the steps shown in Figure 4.10. It can be noted that all ve traits have
dierent number of measurements because some of the interventions were better tolerated by our subjects
than others. From the total of 46 subjects who were enrolled to participate in the experimental sleep study,
only nineteen tolerated all of our interventions and thus we were able to extract measurements of the ve
OSA traits from them. The rest of the data was not discarded and the rank transformation was carried out
using all of the available measurements. We believe that this ranking would better represent the position of
these measurements with respect to the overall population.
Once the traits were all normalized, we proceeded to search for the optimal cut-o percentile that would
provide the best classication accuracy. Figure 4.11 depicts the receiver operating curves that resulted from
the comparison between the classication performed using our model extracted features and the diagnosis
provided by the polysomnography. We carried out this analysis using dierent number of features considered
in the classication process and evaluated their performances by means of the area under the receiver
operating curve, sensitivity and specicity for the various cases. We can observe that the these three
parameters reach their maximum values when two features are considered in the classication process and
they decline as the number of features increases, reaching its lowest when the classication is done using
the ve features. Another parameter that we monitored for the dierent scenarios was the threshold, which
was dened as the cut-o percentile above which a certain parameter was considered to be abnormal. The
optimal threshold was selected by maximizing both the sensitivity and the specicity simultaneously. Not
surprisingly, we found that the threshold decreased as the number features considered in the classication
125
Figure 4.10: Schematic of the rank normalization procedure that was used to transform all of the OSA traits
to range between zero and one. Note that the normalization was carried out using all of the available data
from all subjects including those with incomplete measurements.
process increased. From this analysis we found that the classier that performs the best is the one that
considers two features in the classication process and that having a cut-o at the 62
nd
percentile provided
the maximal sensitivity and specicity of 83.33% and 85.71%, respectively. Statistical testing using Cohen's
kappa coecient to evaluate the agreement between our classication model and the polysomnography
revealed a substantial agreement ( = 0.67 ; p = 0.004) according to the scale suggested by Landis and Koch
(1977); Watson and Petrie (2010). Following this same scale, we found a moderate agreement between our
method and the polysomnography diagnosis when one or three abnormal traits were considered to perform
the classication ( = 0.54 ; p = 0.017 and = 0.57 ; p = 0.019). No signicant agreement was found
when four or ve traits were included in the classication model. A summary of the inter-rater agreement
statistical test comparing our results with the PSG diagnosis for the dierent number of traits considered in
the classication process is presented in Table 4.2.
Spider plots showing the features of the nineteen subjects with complete measurements are presented in
Figure 4.12. Note that all of the parameters were normalized using the percentile rank based on the complete
126
0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
# of features for classification = 1
False−positive rate (1 − Specificity)

True−positive rate (Sensitivity)
AUROC = 0.845
Opt. Thresh. = 76
th
Sens. = 83.33%
Spec. = 71.42%
0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
# of features for classification = 2
False−positive rate (1 − Specificity)

AUROC = 0.892
Opt. Thresh. = 62
nd
Sens. = 83.33%
Spec. = 85.71%
0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False−positive rate (1 − Specificity)
# of features for classification = 3

AUROC = 0.785
Opt. Thresh. = 47
th
Sens. = 75%
Spec. = 85.71%
0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False−positive rate (1 − Specificity)
# of features for classification = 4

AUROC = 0.678
Opt. Thresh. = 27
th
Sens. = 83.33%
Spec. = 57.14%
0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False−positive rate (1 − Specificity)
# of features for classification = 5

AUROC = 0.500
Opt. Thresh. = 20
th
Sens. = 41.66%
Spec. = 85.71%
Figure 4.11: Receiver operating curves for the dierent number of features considered in the classica-
tion process. The red line represents the optimal threshold that simultaneously maximized sensitivity and
specicity.
population cohort i.e. including those subjects with incomplete measurements. The bottom table represents
the confusion matrix, which summarizes the performance of our classication model with the best classier
(i.e. considering two abnormal features to perform the classication and with the threshold set at the 62
nd
percentile). In other words, our classication algorithm would diagnose a subject as having OSA if at least
two out of the ve features are above the 62
nd
percentile. It can be observed that the seven subjects on the
top row are those who were diagnosed by the polysomnography as not having OSA, while the subjects in
the bottom two rows were diagnosed with OSA using an OAHI 5 events/hour as a cut-o. Among the
twelve patients in whom OSA was clinically diagnosed, the model correctly identied ten of them (83.3%
sensitivity). While out of the seven non-OSA individuals, our model correctly predicted their OSA status in
six of them (85.7% specicity).
Table 4.2: Inter-rater agreement statistical test summary for the dierent number of traits considered in
the classication process. yy indicates that the classication agreement between our methodology and the
polysomnography is statistically signicant at p 0.05.
Number of features Optimal threshold Cohen's Kappa Agreement P-value
1 75
th
prc. 0.547 Moderate 0.017yy
2 62
nd
prc. 0.670 Substantial 0.004yy
3 46
th
prc. 0.573 Moderate 0.019yy
4 26
th
prc. 0.321 Fair 0.161
5 17
th
prc. 0.232 Fair 0.473
127
Among the non-OSA individuals, SRBD034 and SRBD063 have all ve traits below the 62
nd
percentile
and therefore they all lie within the green or normal region. Conversely, SRBD008, SRBD041, SRBD048
and SRBD036 have one trait that is abnormally elevated. While the latter three non-OSA subjects have an
abnormal trait related to the upper airway (either increased neck circumference or slope of the pressure-
ow
diagram), SRBD008 has an abnormal arousal threshold, which is not related to the upper airway. Note that
the classier results in a false positive for subject SRBD050 whose traits were all abnormally elevated except
for the arousal threshold parameter that lied within the normal region and was therefore incorrectly classied
as OSA by our methodology. Additionally, our classier failed to detect the presence of OSA (false negative)
in two subjects SRBD055 and SRBD056. Both subjects had an abnormal arousal threshold, however their
upper airway related traits were found to lie within the normal range. Although the upper airway traits
were normal, they were close to exceed the cut-o point, thus making them borderline OSA according to our
classication model. Among the accurately classied OSA subjects, there are interesting combinations of
abnormal traits that are the cause of the disease and should be further discussed. For instance, in SRBD031,
SRBD059 and SRBD067 their OSA appears not to be due to upper airway abnormalities but instead could
be attributed to a neurochemical factor, an obstruction in the lower airways or a combination thereof. On
the other hand, SRBD017, SRBD0039 and SRBD065 are on the other extreme, where both the anatomy and
collapsibility of the upper airway are abnormal. Lastly, SRBD035, SRBD045, SRBD053 and SRBD066 show
only one trait associated with the upper airway that is altered. These cases are interesting because they
show that even subjects with a non-compromised upper airway anatomy or a non-collapsible upper airway
are prone to have OSA, provided that another non-upper airway related trait is abnormal.
Figure 4.13 presents, in the form of pie charts, a summary of our ndings in the OSA population. The left
panel shows the proportion of OSA subjects with a determined number of abnormal OSA traits. It can be
observed that with the threshold set at the 62
nd
percentile, 2/12 OSA subjects have only one abnormal trait
and were therefore misclassied by our method as not having OSA. On the other hand, approximately 40%
(5/12) of the OSA individuals have two abnormal traits. Additionally, 3/12 subjects had three abnormal OSA
traits. Lastly, 2/12 of the OSA cases could be attributed to either four or ve abnormal traits. It is of critical
128
importance to know these proportions, since the therapeutic strategies will be designed accordingly to target
those traits that are abnormal. The middle panel illustrates the proportion of subjects who would benet
from therapies that target the upper airway and those who would require the application of an alternative
treatment that does not involve agents to x the upper airway. It can be noted that approximately 60%
(7/12) of the OSA individuals would require at least one therapy that focuses on xing some aspect of the
upper airway, either anatomically or physiologically. Interestingly, one quarter of our OSA population would
require interventions that target non-upper-airway-related mechanisms only. The right panel, illustrates
the distribution of the 28 dierent treatments that were suggested to the ten subjects who were correctly
diagnosed as having OSA by our methodology. Surprisingly, the therapies targeting the upper airway (weight
loss and CPAP combined) only account for approximately one third of the total prescribed treatments. By
contrast, supplemental oxygen, sedatives and bronchodilators account for the remaining 64% of the total
suggested treatments.
4.3.4.1 Cross-validation
Results from the Leave-M-Out (LMO) cross-validation procedure that was carried out to test the variability
in the selected optimal threshold and classier performance metrics are shown in Figure 4.14 for M = 1, 2,
3 and 4. Figure 4.14I. presents the receiver operating curves that were calculated for all the possible

N
M

training subsamples. It can be observed that as we leave more samples out of our training session (increase
in the M parameter), there is a greater variability in the shape of the ROC curve, however the mean ROC
curve is identical in the four cases. Figure 4.14II. shows the variation of the area under the curve (top panel),
the estimated optimal threshold (middle panel) and the sensitivity and specicity of our classier using the
optimal threshold (bottom panel) in all of the

N
M

possible training subsamples. It can be seen that despite
the great variability found in the area under the receiving operating curve, the sensitivity and the specicity,
the estimated optimal threshold remains virtually unchanged at a value of 62%, which corresponds to the
62
nd
percentile that we also estimated by using the full sample of N = 19. These results indicate that the
estimation of the cut-o value is quite robust and does not depend on the data we used for the training
129
Figure 4.12: Spider plot representations of the model-extracted features of the nineteen subjects with complete measurements. Subjects are
ordered from lower to higher OAHI with the seven subjects on the top row having an OAHI 5 (non-OSA), while the twelve subjects in the
bottom two rows had an OAHI 5 (OSA). The green area in the pentagons indicates the region that is considered as normal, while the red
represents the abnormal region. Note that the loop gain, arousal threshold and FEV1/FVC parameters were inverted in order to have the
abnormal region on the upper part of the pentagon. The red broken boxes highlight the three erroneous classications performed by our model.
130
Figure 4.13: Summary of the abnormal traits found in the OSA group with the threshold set at the 62
nd
percentile along with the summary of the therapeutic strategies that are suggested by our methodology. A.
Proportion of subjects with a determined number of traits exceeding the cut-o point. B. Proportion of
subjects whose therapeutic strategies target the upper airway. C. Distribution of the 28 dierent treatments
that were suggested to the ten subjects who were correctly diagnosed as having OSA by our methodology.
process.
All of the aforementioned results correspond to in-sample variations of our parameters, however in order to
determine the predictive capabilities of our classication method, we estimated its accuracy when presented
unseen data. Table 4.3 summarizes the out-of-sample accuracy for the four dierent sampling schemes. It
can be observed that the accuracy of our classier is very consistent between the four dierent sampling
schemes which is roughly of 80%. These indicate that our experimental techniques in combination with our
mathematical models provide an accurate classication in most of the cases and can potentially be used with
condence by clinicians in order to suggest treatment strategies.
Table 4.3: Out-of-sample predictive accuracy of the classier with the for the four dierent cross-validation
schemes.
Leave-M-Out CV Predictive Accuracy Number of Predictions
Leave-1-Out 0.78947 19
Leave-2-Out 0.78947 342
Leave-3-Out 0.78947 2907
Leave-4-Out 0.78625 15504
131
0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Leaving−Out−1−Samples for X−val
False−positive rate (1 − Specificity)

True−positive rate (Sensitivity)
AUROC = 0.89286 ± 0.020284
Opt. Thresh. = 61.8947 ± 0.45883
Sens. = 83.7719 ± 3.3626
Spec. = 85.7143 ± 3.637
0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False−positive rate (1 − Specificity)
Leaving−Out−2−Samples for X−val

True−positive rate (Sensitivity)
AUROC = 0.89286 ± 0.024249
Opt. Thresh. = 61.7544 ± 0.84604
Sens. = 84.2593 ± 4.7778
Spec. = 85.7143 ± 5.1856
0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False−positive rate (1 − Specificity)
Leaving−Out−3−Samples for X−val

True−positive rate (Sensitivity)
AUROC = 0.89286 ± 0.028323
Opt. Thresh. = 61.4809 ± 1.3079
Sens. = 85.2597 ± 5.9865
Spec. = 84.9403 ± 5.7616
0 0.5 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False−positive rate (1 − Specificity)
Leaving−Out−4−Samples for X−val

True−positive rate (Sensitivity)
AUROC = 0.89286 ± 0.050394
Opt. Thresh. = 61.1976 ± 1.9248
Sens. = 85.9563 ± 7.0998
Spec. = 84.9698 ± 7.2888
I. Receiver operating curves generated by the Leave-M-out sampling algorithm. The gray lines represent all of the
possible ROC curves that were found with all the possible training subsamples. The blue line represents the average
ROC curve.
0 5 10 15
0.75
0.8
0.85
0.9
0.95
1
AUROC
Leaving−Out−1−Samples for X−val
0 5 10 15
0.5
0.6
0.7
0.8
Threshold
0 5 10 15
0.75
0.8
0.85
0.9
0.95
1
Sensitivity
Training Instances
0 5 10 15
0.6
0.7
0.8
0.9
1
0 50 100 150
0.75
0.8
0.85
0.9
0.95
1
Leaving−Out−2−Samples for X−val
0 50 100 150
0.5
0.6
0.7
0.8
0 50 100 150
0.75
0.8
0.85
0.9
0.95
1
Training Instances
0 50 100 150
0.6
0.7
0.8
0.9
1
0 200 400 600 800
0.75
0.8
0.85
0.9
0.95
1
Leaving−Out−3−Samples for X−val
0 200 400 600 800
0.5
0.6
0.7
0.8
0 200 400 600 800
0.75
0.8
0.85
0.9
0.95
1
Training Instances
0 200 400 600 800
0.6
0.7
0.8
0.9
1
0 1000 2000 3000
0.75
0.8
0.85
0.9
0.95
1
Leaving−Out−4−Samples for X−val
0 1000 2000 3000
0.5
0.6
0.7
0.8
0 1000 2000 3000
0.75
0.8
0.85
0.9
0.95
1
Training Instances
0 1000 2000 3000
0.6
0.7
0.8
0.9
1
Specificity
II. Area under the receiver operating curve (top row), estimated optimal threshold (middle row) and sensitivity and
specicity of the classier using the estimated optimal threshold (bottom row).
Figure 4.14: Variability of the receiver operating curves, optimal threshold and the classier performance
metrics using the Leave-M-Out sampling technique for M = 1, 2, 3 and 4. The results are shown for all of
the

N
M

possible training subsamples.
132
4.4 Discussion
The main purpose of this study was to develop and implement the experimental and mathematical modeling
techniques to allow the measurement and quantication of several traits that predispose to OSA. This type of
work has been previously done but mostly in the adult population (Eckert, 2016; Wellman et al., 2011, 2013),
perhaps motivated by the increased prevalence of OSA in that population. To the best of our knowledge,
only Marcus et al. (2017) have quantied the traits predisposing to OSA in a population of adolescents.
What this study adds to the eld, is the demonstration that our measurements could provide clinicians
with valuable information that could be used to assess the cause of the disease at an individualized level. We
believe that understanding the pathophysiology of OSA and treating it ecaciously at an early age could
help prevent its adverse eects.
4.4.1 Upper airway anatomy and collapsibility
In our study, we used neck circumference as an indicator of how compromised the anatomy of the upper
airway is due to the deposition of fat in the neck area. Although neck circumference has been reported to be
a predictor for OSA in adults (Davies et al., 1992) and also in children (Katz et al., 2015; Vora et al., 2017),
more accurate anatomical measurements, such as the ones provided by imaging techniques, are required to
properly assess the structure of the upper airway. Notable is the work carried out by (Arens et al., 2011) who
utilized magnetic resonance (MR) imaging to assess body fat composition in obese children (ages ranging
between 8 and 17 years). They reported that the OSA subjects had a signicantly smaller oropharynx and
larger adenoid, tonsils and retropharyngeal nodes as compared to the obese control group. Moreover, they
reported a positive correlation between the size of the lymphoid tissues and the severity of OSA. In addition,
a very comprehensive study carried out in a cohort of adolescents, Schwab et al. (2015) also utilized MR
images to assess the anatomic risk factors in obese subjects with OSA and compared them to an obese and
a lean control groups. Similar to the aforementioned results, they also found that the adenotonsillar tissue
was increased in the obese subjects with OSA. In addition, this study also reported a signicantly reduced
133
nasopharyngeal airway in the OSA group as compared to the control subjects. Although our nding of a
statistically signicantly increased neck circumference in the OSA population agrees with these results, the
neck circumference measurement should be used with caution as it does not represent the internal structural
composition of the upper airway.
In addition to these anatomical constrains in the upper airway, there could also be an increased collapsi-
bility that could be causing the episodes of sleep disordered breathing. Among the studies that quantied
upper airway collapsibility in children with OSA, there are a few that have focused in the prepubertal
population. The interest in this specic group is attributed to the increased prevalence of sleep disordered
breathing reported to be as high as 11% in children with ages ranging between 2-8 years (Gislason and
Benediktsdottir, 1995; OBrien et al., 2003; Anuntaseree et al., 2001). The reason for this is that during
this age, the tonsils and adenoids are the largest in relation to the underlying airway (Jeans et al., 1981).
It is also common at this age the presence of adenotonsillar hypertrophy, which results in a narrow upper
airway anatomy (Marcus, 2001). There have been some eorts that aimed at measuring the collapsibility
of the upper airway in prepubertal children. For example, Marcus et al. (1994) compared P
crit
estimations
between primary snorers and children with OSA during sleep. They reported a highly statistically signicant
dierence inP
crit
between the two groups, with the OSA children having an average value above atmospheric
pressure of approximately 1 cmH
2
O. In addition, Gozal and Burnside (2004) quantied upper airway col-
lapsibility in children with OSA during wake
uness and found that following the application of a topical
airway anesthetic, children with OSA showed an increased reduction in upper airway cross-sectional area as
compared to controls. Although the application of anesthesia might have altered the characteristics of the
upper airway, this study demonstrates the propensity of the upper airway to collapse in OSA subjects.
More recently, upper airway collapsibility was quantied from cohorts of adolescents. For instance, Huang
et al. (2012) estimated the hypotonic upper airway collapsibility through pressure-
ow measurements during
sleep in a relatively large group of teenagers stratied in three dierent groups: obese with OSA, obese
controls and lean controls. They reported that P
crit
was signicantly more positive in the group of obese
subjects with OSA as compared to the two control groups. No signicant dierence was reported between
134
the obese and the lean control groups. The slope of the pressure-
ow plot was signicantly
atter in the
lean controls when compared to the two obese groups. No signicant dierence was found in the slope
parameter between the obese populations. In our population of obese adolescents, none of the upper airway
collapsibility quantiers was found to be signicantly dierent between the OSA and the non-OSA groups.
Although, a trend toward a more positive P
crit
and an increased Slope
pf
in the OSA population were
observed. The average P
crit
values that we obtained from our adolescent cohort without OSA compare to
those reported by Yuan et al. (2013) (-14.2 cmH
2
O vs. -14.3 cmH
2
O), however our OSA group showed a
more negative average value as compared to what was reported in this study (-11.6cmH
2
O vs. -7.8cmH
2
O).
In terms of theSlope
pf
, the average values that we found in our non-OSA population appear to agree with
what was reported by Huang et al. (2012) (1.04 L=mincmH
2
O vs. 0.99 L=mincmH
2
O). Whereas,
our OSA population showed a slightly increased average value of Slope
pf
as compared to that study (1.84
L=mincmH
2
O vs. 1.38 L=mincmH
2
O) (Bandla et al., 2008). From what is reported in the literature
and also based on our experience, many adolescents are able to maintain the upper airway open even at
markedly negative pressures, suggesting low upper airway compliance (Katz and D'ambrosio, 2008). In such
cases,P
crit
could not be determined without extreme extrapolation (Marcus et al., 2004; Huang et al., 2011).
In these cases,P
crit
results in extremely negative values which could be deemed as being not physiologically
feasible. In order to deal with the presence of these unfeasible estimations, some groups have opted for
saturating theP
crit
values to the lowest pressure that can be provided by the ventilator that is used in their
experiments (Marcus et al., 1999, 2005). On the other hand, there are groups that evaluate upper airway
collapsibility solely based on the slope of the pressure-
ow curve (Marcus et al., 1999; Katz and D'ambrosio,
2008). We agree with the latter ideology, since the Slope
pf
is extracted directly from the pressure and
air
ow measurements without the need of extrapolating the data. We utilized this same reasoning in order
to select the upper airway quantier that was included in the classication model.
The application of MR imaging has recently focused on better understanding the contribution of up-
per airway collapsibility to OSA. This transition from mainly structural to functional imaging has lead to
tremendous advancements including the improvement of spatial and temporal resolutions, which has enabled
135
the visualization of the behavior of the complex upper airway structure during tidal breathing and at multi-
ple locations. When using MR images in combination with physiological measurements such as air
ow and
pressure, one can have a better picture of how the structure of the upper airway impacts the respiratory
proles (Kim et al., 2014). This approach has been adopted by several groups in recent years. For instance,
Wu et al. (2015) estimated the projected closing pressure P
close
and upper airway compliance (slope of
pressure vs. area plots) from occlusion protocols in adolescents with OSA and found that both parameters
were signicantly dierent as compared to an adult control group. On the other hand, a combination of MR
imaging, physiological signal monitoring and computational
uid dynamics was used to quantify upper air-
way collapsibility in a population of adolescent females with and without OSA(Wootton et al., 2016). They
report a signicant dierence in pharyngeal compliance (estimated from two locations: nasopharynx and
velopharynx) between the two populations, with OSA having a lower and even negative average compliance
as compared to the healthy controls. They also report a marginally signicant dierence in P
crit
between
the two populations, with OSA having a more positive average value that lies close to atmospheric pressure.
Lastly, Chen et al. (2017) implemented sudden pressure drops from therapeutic to dierent subtherapeutic
levels to measure the passive collapsibility of the upper airway in OSA subjects during sleep while they were
scanned using real-time MR imaging. They reported that OSA subjects had greater
uctuations of airway
area in response to the pressure drops as compared to healthy controls. Despite the low sample size in this
study, these results can be used as a proof of concept that the intermittent pressure drops protocol could
be implemented inside an MR scanner to better quantify upper airway collapsibility. We believe that these
approaches that combine imaging and physiological monitoring tools hold promise since they can be used to
simultaneously study anatomical and physiological changes that occur during the night and should continue
to be exploited in the context of OSA.
4.4.2 Pulmonary function test
It is relevant to note that the pulmonary functions test yielded very interesting results. More specically,
the results from the spirometry showed a marked dierence between the groups. For instance FEV1 after
136
being normalized by the forced vital capacity was highly statistically signicantly decreased in the OSA
population. Similarly, FEF25/75 followed the same trend and was found to be signicantly decreased in
the OSA individuals. Despite these values being lower in the OSA group, the measurements were not
suciently low to imply clinically abnormal lung mechanics as mean values were still within the normal
range. Moreover, moderate though statistically signicant correlations were found between the ranks of
these two PFT parameters and the severity of OSA quantied by the OAHI.
Thee reductions in forced expiratory
ows may be attributed to in
ammation and/or constriction in
the small airways (Pellegrino et al., 2005; Zerah-Lancner et al., 1997), and has been previously reported in
children and adolescents with OSA (Van Eyck et al., 2014; Verhulst et al., 2008). Furthermore, Verhulst
et al. (2008) by the inclusion of a control group of obese children with normal sleep studies, demonstrated
that obesity in the absence of sleep-disordered breathing was not associated with decreased spirometry
values indicating increased airway in
ammation. This nding is important, because it has been suggested
that sleep-disordered breathing could be one of the mechanisms linking obesity with asthma. Although this
evidence might appear conclusive, the linking mechanisms between OSA, abesity and asthma are still no well
understood. For instance, there have been other studies that reported no associations between pulmonary
function measurements and polysomnography metrics in obese children and adolescents (Marcus et al., 1996;
Dubern et al., 2006). Another potential question that remains unanswered is whether the in
ammation of the
smaller airways is a cause or a result of OSA. Therefore, there is a need for further studies that help unravel
the possible mechanisms linking OSA and in
ammation in the lower airways and the causal relationship that
exists between them.
4.4.3 Ventilatory control stability
Ventilatory control stability has been widely studied in infants because the process of maturation of the
chemoreceptors, which starts in utero and continues for weeks to months after birth, is associated with
increased ventilatory instability until they reach adult levels (Fleming et al., 1984; Barrington et al., 1987).
Such chemoreceptor maturation gets interrupted if the child is born prematurely leading to periodic breathing
137
and OSA (Rigatto and Brady, 1972; Barrington and Finer, 1990; Gauda et al., 2004). The increased likelihood
of children born prematurely to develop OSA has attracted a lot of attention to the infant population (Katz
et al., 2012). However, less attention has been paid to the study of ventilatory control stability in older
children. Marcus et al. (1998b) studied ventilatory responses to chemical stimulation in children with ages
ranging between six and eleven years with and without OSA. They reported no dierence in chemore
ex
sensitivity between the groups in response to hypercapnic and hypoxic stimulation.
To the best of our knowledge, we are one of the rst groups that quanties ventilatory control stability
in a population of adolescents. One of the key ndings of this study was the depressed sensitivity of
the ventilatory control system in the OSA subjects as compared to their non-OSA counterparts. After
separating loop gain into its two components we were able to recognize that the decreased sensitivity was
attributed to the chemore
ex, which was signicantly lower in the OSA population. Our results appear
to agree with what was found by Yuan et al. (2012) in a dierent cohort of obese adolescents with OSA.
They reported blunted ventilatory responses to hypercapnic stimulation during both quiet and active sleep
in obese subjects with OSA when compared to an obese without OSA and a lean control groups. These
ndings, in combination with ours, would suggest that OSA in adolescents does not initiate as a result of
an overly sensitive chemore
ex but, on the contrary, could result from an inappropriate compensation to
ventilatory stimulation. An increased hyperventilatory response upon arousal, in combination with such a
blunted compensatory action from the chemore
ex, could lead to a reduction of CO
2
beyond the apneic
threshold and thus inducing an apnea when sleep is resumed. These cyclic transitions between arousal and
apnea lead to a dierent type of ventilatory instability, which is not mediated by the chemore
ex.
4.4.4 Arousal components
The arousal response in the pediatric population has been extensively studied in infants (ward1992hypoxic)
and prepubertal children (Marcus et al., 1998b). These studies demonstrated that in both age groups,
moderate hypoxemia is a weak stimulus to arousal with a proportion of subjects who aroused from the quiet
sleep state that ranged between 0 and 50%. This proportion varied depending on whether the subjects were in
138
NREM2 or NREM3, with a lower arousing rate exhibited within the latter sleep stage. This evidence suggests
that in children, the major stimuli for arousal are respiratory load, hypercapnia and hypoxic hypercapnia
(Alsubie and BaHammam, 2017). Based on this evidence, and in order to test the arousal response under
more natural conditions, we avoided the use of chemical stimulation and instead implemented the inspiratory
occlusion protocol. This protocol allowed us to elicit arousal through the application of a respiratory load
without the application of a gas mixture, that could perhaps alter the natural arousal response. Other groups
have also used non chemical sources of stimulation such as the application of loud sounds to induce arousal
(Badr et al., 1997; Asyali et al., 2002).
To the best of our knowledge there are no data available regarding the quantication of the arousal
mechanism in adolescents with and without OSA. Marcus et al. (1998b) compared the arousal responses to
hypercapnic stimulation in a prepubertal children population with and without OSA. Patients with OSA
aroused at signicantly higherPCO
2
levels, which indicates the presence of an elevated arousal threshold in
this population as compared to the control group. In addition, a moderate though statistically signicant
positive correlation between OSA severity and arousal threshold was detected. We did not nd a trend in
particular in the arousal threshold parameter in our cohort of obese adolescents; nor did we nd a trend
toward a correlation with the severity of OSA. Our results appear to indicate that the arousal threshold
is comparable between obese adolescents with and without OSA. However, it should be noted that we
dened arousal threshold as the respiratory eort occurring immediately before an arousal occurs, under
the assumption that the breathing eort is proportional to the CO
2
concentrations in the blood. Such
assumption had to be made due to the lack of a reliable measurement ofPCO
2
, provided by a nasal cannula,
during the application of the occlusion. Other noninvasive means of measuringPCO
2
such as transcutaneous
monitoring could be implemented in order to obtain reliable measures during the occlusive episodes (L

Ubbers,
1981; Tremper et al., 1981).
Similarly, our measurement of arousal drive did not show a dierence between our non-OSA and OSA
groups. In addition, no apparent correlation exists between the response to the arousal and the severity of
OSA. The extraction of other features, such as the time to arousal following the onset of the occlusion, could
139
have been carried out to provide another quantier of the tolerance of these subjects to breathing cessation.
Our results, based on the two arousal mechanisms' quantiers, could indicate that the arousal mechanism
operates similarly in both groups of obese adolescents. In turn, the dierences between the groups could be
attributed to the way these arousal mechanisms interact with the upper airway anatomy/collapsibility and
the respiratory control components (Malhotra and Jordan, 2016).
4.4.5 Classication model incorporating all traits
The diagnostics provided by our classication model, using two features considered as abnormal and a cut-o
value of 62
nd
percentile, substantially agreed with the gold standard polysomnography as indicated by the
Cohen's Kappa statistic ( = 0.67 ; p = 0.004). This means that by using our model-derived features, in
addition to neck circumference and an indicator of pulmonary function, we can reliably diagnose OSA. The
fact that our model performs better at classifying the disease by considering two altered traits, as opposed to
only one, agrees with the nowadays well accepted idea that OSA is a multifactorial phenomenon that could
result from a combination of two or more malfunctioning mechanisms (Wellman et al., 2011; Eckert et al.,
2013). In fact, Figure 4.13.A shows that approximately 40% of the OSA subjects have at least three traits
above the cut-o point. In addition to the diagnostic capabilities of our methodology, we can also utilize
the maps shown in Figure 4.12 to pinpoint the causes of OSA at an individualized level and can be used
to design patient-specic therapies. This type of approach could help transition treatment selection from
the so-called one size ts all approach to an individualized approach (Malhotra et al., 2015). This ideology
of targeted treatment of OSA has been developing and evolving over the past decade and shows promising
results (Eckert, 2016; Edwards et al., 2016a).
4.4.6 Design of therapeutic strategies
Given the association between OSA and obesity, the rst-line treatments in our population of obese adoles-
cents would be behavioral modications including weight loss and avoiding sleeping on the supine position
(Loube et al., 1994; Tuomilehto et al., 2009). As secondary approaches to x the anatomy of the upper airway
140
we could suggest the utilization of oral appliances (Morgan, 2016), such as tongue repositioning or restraining
devices and mandibular advancement devices, which have shown to signicantly reduce OSA severity (Deane
et al., 2009). In addition, surgical interventions like adenotonsillectomy could also be recommended to x
the anatomy in some cases (American Academy of Pediatrics, 2002). In order to x the collapsibility of the
upper airway we could suggest the utilization of CPAP, which is considered the gold standard. Furthermore,
the use of drug therapies targeting the upper airway muscle tone and responsiveness have also been proposed
to reduce the collapsibility of the upper airway and therefore the amount of respiratory events.
If we assume that the in
ammation and/or constriction of the smaller airways is a cause for OSA, we
can potentially suggest a therapy that could help x this problem. Bronchodillators are mostly employed in
patients who suer from asthma, however they can be administered in those subjects in which measurements
of PFT spirometry were found to be low. In a study performed in adults with OSA who were otherwise
healthy, Rasche et al. (1998) studied the eects of a bronchodialtor (salmeterol) in polysomnography metrics.
While they found no signicant eect of the drug on the apnea-hypopnea index, these results may not apply
to the younger populations. After performing a literature survey, we found that there is a lack of studies
investigating the eects that asthma treatment has on OSA in the pediatric population (S anchez et al.,
2016). We believe that there is great potential in the utilization of bronchodilators to improve pediatric
OSA; however, the side eects that result from the treatment, such as the increase in upper collapsibility,
should be further investigated (Taussig and Landau, 2008).
Regarding the therapeutic strategy that we sought to apply in our population of obese adolescents with
OSA, rst it is important to note that our ndings contradict what has been previously found in the adult
population. Adult subjects with OSA have been found to have an overly sensitive ventilatory control system
(Hudgel et al., 1998; Salloum et al., 2010) and, moreover, the sensitivity is more pronounced in subjects
with severe OSA (Younes et al., 2001). This poses a challenge in terms of the development of alternative
therapeutic strategies, because the treatments that have been suggested to date are meant to reduce the
sensitivity of ventilatory control. For example, Wellman et al. (2008) showed that the application of sup-
plemental oxygen (values ranging between 3 and 5 L/min) resulted in a signicant decrease in ventilatory
141
control sensitivity, which in turn reduced the severity of OSA by 50%, approximately. Moreover, the uti-
lization of acetazolamide, a pharmacological agent that produces metabolic acidosis yielding an increase
in baseline ventilation, has been shown to help improve the severity of OSA in some individuals (Whyte
et al., 1988; Sakamoto et al., 1995). Recently, Edwards et al. (2012) found that following the application
of acetazolamide, the apnea hypopnea index was signicantly reduced by half as a result of a reduction in
ventilatory sensitivity. The advantage of the latter study is that in addition to quantifying loop gain, they
also measured upper airway collapsibility, arousal threshold and upper airway muscle responsiveness and
found that they remained unaltered, thus indicating that the reduction in OSA severity was solely due to a
stabilization in ventilatory control. In our population of obese adolescents, we would seek to design therapies
that achieve the opposite eects i.e. an increase in chemore
ex sensitivity. One potential treatment could
be to subject those patients with OSA to acute controlled episodes of intermittent hypoxia. These episodes
of hypoxia have been reported to induce long term facilitation in the phrenic, hypoglossal and glossopharyn-
geal nerves in rat models (Bach and Mitchell, 1996; Fuller, 2005; Cao et al., 2010). Phrenic nerve long term
facilitation has been extensively studied and has been found to result in increased minute ventilation either
by an increase in tidal volume or increase in breathing frequency (Ryan and Nolan, 2009). The mechanism
behind this is thought to be the activation of the peripheral chemoreceptor which stimulates serotonergic
or adrenergic release from medullary raphe or locus coeruleus neurons (Kinkead et al., 2001), respectively,
onto respiratory motor neuron pools (Deacon and Catcheside, 2015). Another alternative therapy could
be through the application of pharmacological agents that increase the sensitivity of the chemoreceptors
directly. The utilization of domperidone, a dopamine D
2
-receptor antagonist that increases the senstivity
of the peripheral chemoreceptors, has shown to increase ventilatory drive in animals (Tomares et al., 1994)
and in human adults (Walsh et al., 1998). In a recent study, Edwards et al. (2008) utilized this drug in
a lamb model to increase the sensitivity of the chemore
ex to ultimately induce respiratory instabilities or
periodic breathing. Therefore, we speculate that controlled dosages of this drug can be used in our popula-
tion of obese adolescents with OSA to increase the sensitivity of their ventilatory control system to normal
ranges. While we believe that some of our obese OSA patients could benet from these proposed alternative
142
therapies, further testing in animals is required before actually administering them in humans.
On the other hand, a low arousal threshold has also been associated with unstable breathing during
sleep and thus some pharmacological agents have been tested in order to elevate this trait. The use of
sedatives such as eszopiclone and trazodone have been proven ecacious at increasing the arousal threshold
and reducing the apnea hypopnea index in adults (Eckert et al., 2011; Heinzer et al., 2008; Eckert et al.,
2014). Although these pharmacological agents show potential at reducing OSA severity, their prescription
to the adolescent population should be carefully investigated due to the side eects that may result from
their administration.
If we select weight loss, CPAP, oxygen, sedatives and bronchodilators as means to manipulate neck circum-
ference, Slope
pf
, loop gain, arousal threshold and FEV1/FVC, respectively, we can use our methodology
to suggest targeted treatment. Figure 4.13.A shows that 10/12 OSA subjects would require the combination
of two or more of the aforementioned therapies to treat their OSA. These ndings seem to agree with recent
studies suggesting that combination therapy for the treatment of OSA is more appropriate in some cases.
This approach has proven to be ecacious in simulation models (Owens et al., 2015) and has started to be
tested experimentally (Deacon et al., 2016). Based on the individual eect that some treatments have on the
specic OSA traits, Owens et al. (2015) created a simulation model that was used to predict whether OSA
could be resolved by manipulating one or more traits at a time. This simulation model demonstrated that
combination therapy using two or more of all of the aforementioned interventions, targeting the multiple
OSA traits (anatomical and non-anatomical), could be more ecacious than using a single intervention. An-
other interesting nding from our therapy recommendation methodology was that 3/12 of the OSA subjects
would require a therapy that does not target the upper airway neither anatomically nor physiologically (See
Figure 4.13.B). This nding appears to contradict what was suggested by Eckert (2016), who claimed that
all OSA patients must have a certain degree of upper airway impairment. The fact that non-upper-airway
related therapeutic strategies could be used in several of the OSA patients implicates that there is a need
for the development of alternative treatments that can be used concomitantly with the ones that target the
upper airway.
143
The need for the development of novel combination therapies has recently attracted the attention of
various research groups who are currently experimentally testing their ecacy. For instance, a combination
of oral appliances and CPAP therapy was implemented by El-Solh et al. (2011). They reported that by
treating the upper airway anatomy and collapsibility, a signicant decrease in apnea-hypopnea index, oxy-
gen desaturations and daytime sleepiness can be achieved. Additionally, a combination therapy including
supplemental oxygen and hypnotics were implemented in Edwards et al. (2013, 2016b). They reported a
signicant reduction in apnea-hypopnea index of approximately 50% through the manipulation of loop gain
and arousal threshold. However, in more than 50% of the subjects, the reduction in AHI did not entirely
resolve OSA. The failure to completely eliminate OSA in the whole population could be attributed to the
inclusion of subjects whose ventilatory control system and arousal mechanisms are operating normally in the
sample pool. Just like these eorts, other studies should explore other alternatives of combination therapy
such as CPAP plus oxygen therapy and/or the administration of hypnotic drugs.
4.4.7 Methodological considerations
One of the main advantages of our proposed experimental interventions is that given the few pieces of
instrumentation that need to be added to a standard polysomnography, they can be incorporated as part
of a CPAP titration study that is usually prescribed after OSA has been diagnosed. This would provide
clinicians with more information about the potential causes of OSA and could detect even if CPAP is
necessary or not. By having more of these studies done in OSA patients, our data base could grow and
our model could be trained with a richer data set. A second advantage of our methodology is that all
traits can be reliably extracted in a single night. Achieving this is of critical importance in order to avoid
the night-to-night variability of the traits that could be causing the night-to-night variability observed in
OAHI (St oberl et al., 2017). We accomplished this by running our three dierent protocols multiple times
throughout the night. By contrast, (Wellman et al., 2011) demonstrated that the extraction of all of the
OSA traits is possible by utilizing a single experimental maneuver. This is desirable in order to quantify
all measurements within the same sleep stage and also increases the chances of performing more of these
144
recordings.
There are also some methodological limitations that should be pointed out to the reader. For instance,
all of our interventions were performed during NREM sleep and therefore our ndings are constrained to
quiet sleep stages. It would be very interesting to run our experiments during REM sleep and see whether
our ndings remain unchanged. Another potential weakness of our methodology is the lack of quantication
of upper airway muscle responsiveness, which is one of the key traits predisposing to OSA according to
(Eckert et al., 2013). Highly responsive upper airway muscles have been found to be critical to avoid OSA
in overweight and obese subjects (Sands et al., 2014). In addition, we are also missing the inclusion of the
activated upper airway collapsibility parameters. Although we carried out the estimation of the activated
P
crit
and Slope
pf
, we are not including that analysis in this work. (Marcus et al., 2017) found that
activatedP
crit
was an independent predictor of the risk for OSA in adolescents. Therefore, our classication
model could have been greatly beneted from an estimation of muscle responsiveness and the inclusion of
the activated upper airway quantiers.
There is also a limitation in the experimental technique that we are using to estimate our upper airway
collapsibility traits, namely the critical pressure and the slope of the pressure-
ow plot. The CPAP machine
that we used to provide the intermittent drops in pressure was unable to provide negative sucking pressures;
therefore, our estimations of P
crit
required extreme extrapolation in some cases. Some other studies have
used modied CPAP machines that could provide pressure drops to subatmospheric levels and thus their
estimations of the collapsibility features of the upper airway could be considered as more reliable (Marcus
et al., 2004; Jordan et al., 2005; Yuan et al., 2013). There are also some limitations related to the way we are
quantifying collapsibility. First, we are assuming that the upper airway reduces size linearly as a function
of the applied CPAP pressure. While this may be true at high CPAP pressures, at low values of pressure
there may be some nonlinear behavior that our linear model is not able to capture. Second, given that we
were constrained to apply positive values of CPAP pressure, the amount of intermittent drops was limited to
four in our case. While these many drops could be sucient for performing the regression analysis, for those
segments where an arousal was observed at an early stage of the protocol, the computation was performed
145
with data coming from less than four drops. This could yield inaccurate estimations ofP
crit
and slope of the
pressure-
ow plot; however, we believe that by using the median values over the multiple trials to represent
each subject, we eliminated the potential presence of outliers in the data. Despite these experimental and
methodological limitations, our estimations of P
crit
and Slope
pf
are similar to what has been previously
reported in a population of obese adolescents (Huang et al., 2012; Marcus et al., 2017).
On the other hand, the experimental intervention that was utilized to induce sighs is supposed to re
ect a
spontaneous sigh that occurs naturally during sleep; nevertheless, the application of a positive pressure is far
from representing the negative pressure that is created by the contraction of the diaphragm. A more natural
way to induce a sigh could be achieved by stimulating the diaphragm muscle but this would require the
insertion of stimulating electrodes which would be highly invasive. We believe that despite the dierence in
the mechanism used to create the increase in tidal volume, the eect of such disturbance would be the same.
Moreover, our induced sighs protocol started at the therapeutic pressure, which in turn caused an increase
in lung volume and therefore an overall reduction in the measurements of ventilatory control stability in our
subjects. The application of CPAP at therapeutic levels was necessary to minimize the resistance of the
upper airway and avoid any obstructive event. By setting the ventilatory control system's steady state value
away from the saturation region we can be more condent at saying that the respiratory system behaves
in a linear fashion and thus apply linear control theory to quantify its stability characteristics. Another
underlying assumption of our methodology, besides linearity, is that the response to the induce sighs is solely
mediated by the chemore
ex; however, there could be a mechanical response from the stretch receptors due
to the hyperin
ation of the lungs that our model is not accounting for (Porges et al., 2000; West, 2012).
The inspiratory occlusion protocol was sometimes not very well tolerated by some subjects. In a good
amount of them, the application of the occlusion elicited an immediate arousal which sometimes was ac-
companied by strong movements and resulted in a complete disconnection of the respiratory circuit and
loss of some of our respiratory measurements. This response left us with fewer recordings to analyze per
subject as compared to the intermittent drops and the induced sighs protocols. Moreover, the quantication
of the arousal mechanisms required the manual and visual detection of the exact time where an episode of
146
arousal occurred by a sleep expert, which makes our results subject to error. One potential way of minimiz-
ing the subjectivity of the arousal detection could be to present the same measurements to two (or more)
sleep experts and have them identify the time of arousal, which could be cumbersome. The application
of automatic sleep-stage scoring algorithms could make our estimations and measurements of the arousal
mechanisms more objective and accurate. The automatic scoring of sleep has been recognized as a highly
complex problem since the 1980s (Haustein et al., 1986), however recent advances in time-frequency anal-
ysis and articial intelligence, namely neural networks and deep learning hold promise to solve this issue
(Krakovsk a and Mezeiov a, 2011; Peker, 2016; Supratak et al., 2017).
The spider plot, which was the visual tool that we utilized to display the multiple traits for all of our
subjects has also some limitations. For instance, it is hard to visually compare the dierence in length between
spokes unless there are very marked dierences. Also, the ordering in which the variables are presented is
completely arbitrary and could therefore create spurious connections between variables. Additionally, these
representations are helpful in visualizing small to moderately sized data sets and can become overwhelming
for large data sets (Robbins, 2012).
One potential limitation of our classication model and therapy suggestion method is the low number of
subjects with complete measurements. A model with access to a larger data set would be subject to a greater
source of variability and would therefore be more representative of the entire population of obese adolescents.
Our cross-validation procedure showed that despite the low sample size, the estimated parameters remained
relatively unchanged after allowing for multiple resampling instances. A second limitation of our methodology
is the lack of the incorporation of the eect of gender, which has been proven to be an important predictor
of OSA (Young et al., 1993; Bixler et al., 2001) and a source of variability in some of the OSA traits (Bandla
et al., 2008; Schwab et al., 2015). We carried out a two way repeated measures ANOVA to test for dierences
on the physiological traits after allowing for the dierent genders. We found that only neck circumference
showed a signicant dierence between males and females, with the former group showing more elevated
values for this parameter. However, the rest of the OSA traits did not show such dependency on gender
(data not shown). Alternative methods to predict OAHI or OSA, such as multiple linear regression or
147
logistic regression, respectively, can include the categorical eect of gender in combination with the rest of
the continuous OSA traits. Marcus et al. (2017) performed a multivariate logistic regression analysis using
the OSA traits to predict OSA status with data from a population of obese adolescents with and without
OSA. Their ndings suggest that only anatomical factors such as adenotonsillar and nasopharyngeal airway
volumes in addition to a neuromotor component mediate OSA in adolescents after adjusting for gender,
age, BMI and race. The key factor the allowed the estimation of multinomial logistic regression models in
this study was the relatively larger number of subjects with complete measurements, which is a requirement
for accurate logistic regression model estimation (Bewick et al., 2005; Vittingho et al., 2007; Vittingho
and McCulloch, 2007). A third limitation of our classication model is that the cut-o point that was used
to perform the diagnosis was shared by the ve traits that were included in the model. By linking all of
the variables with the same threshold we could be limiting the classication capabilities of our approach. A
scenario where each of the traits has its own cut-o point could yield better results. Therefore, we investigated
the eects of having independent cut-o points for the dierent traits and conrmed that the classication
accuracy improved by correctly identifying two subjects who were misclassied when all the traits shared
the same cut-o point. These results showed an almost perfect agreement with the gold standard and were
statistically signicant as indicated by the Cohen's Kappa statistic ( = 0.89 ; p = 0.0001). Despite the
great results obtained with this alternative methodology, the drawback is that the thresholds for the ve
traits were not found to be as stable as for the case where the threshold was shared by all traits. In fact,
we found that various combinations of cut-o points in the ve traits could yield the same classication
accuracy and thus making dicult the selection of the optimal set of cut-o points. An interesting nding
of this alternative methodology was that the optimal cut-os for the variables associated with the upper
airway (neck circumference andSlope
pf
) spanned values from the entire range from zero to one. The lower
variability in the estimated optimal cut-o point that was found with the shared threshold scheme made the
selection of treatment much easier and was therefore preferred by our group.
A limitation to our therapy suggestion scheme is that we are assuming that each of the potential treat-
ments only aects one trait with no signicant positive or negative impact on the rest. Such assumption
148
does not hold for all of the suggested treatments. For instance, weight loss has been found to reduce the
upper airway collapsibility as quantied by P
crit
(Schwartz et al., 1991). In addition, the application of
CPAP was reported to reduce loop gain via an increase in lung volume (Edwards et al., 2009). Moreover,
bronchodilators can also lead to an increase in the collapsibility of the upper airway (Taussig and Landau,
2008). By considering the positive eects that one treatment could have on multiple traits at the same time,
we could potentially prescribe our OSA subjects with less therapeutic agents than what our methodology is
currently suggesting. On the other hand, by taking into account the indirect negative eects that a particular
treatment could have on some trait, clinicians could prevent the undesired worsening of OSA.
4.4.8 Conclusion
In summary, we have developed a methodology that combines experimental interventions along with the
analytical tools that allowed the quantication of traits that predispose to OSA in a population of obese
adolescents. In addition, we developed a classication method that can be used as a diagnostic tool that
can reliably detect the cause of OSA at an individualized level. We believe that our methodology can be
generalized to younger children and the adult populations and could be used to aid clinicians in the selection
of therapy that can be targeted to improve a specic trait and could perhaps resolve OSA completely. Future
studies could involve the application of the therapies that are suggested by our model to our OSA patients
and test the eciency of the treatment with a follow up polysomnography.
149
Chapter 5
Conclusions
This work presents a methodology that combines experimental measurements along with mathematical
modeling tools in order to extract and quantify the physiological traits that predispose to OSA in a population
of overweight adolescents. In addition, we introduce a scheme for combining the aforementioned traits in
order to diagnose OSA and recommend a therapeutic strategy that would be patient-specic and that would
target the abnormal traits only.
Our team designed an experimental setup composed by a computer, a breathing circuit, a CPAP machine,
an occlusion valve controller and a data acquisition system that altogether allowed the monitoring and study
of the respiratory system under natural NREM sleeping conditions. The breathing circuit consisted of various
components with dierent functions and its main purpose was to serve as the interface between the subjects
and the CPAP machine. The latter was used to provide the subjects with sucient pressure to stabilize the
upper airway and eliminate all respiratory events. In addition, the CPAP machine was also utilized to create
dierent pressure sequences that served as stimuli to the respiratory system. In addition, the occlusion valve
controller was used to apply a dierent stimulus to the subjects. The data acquisition system allowed for
simultaneous monitoring of physiological measurements and control of external devices, such as the CPAP
machine and the occlusion valve controller, which were used for the application of our interventions. Our
acquisition system also permits the interaction with sleep monitoring devices used clinically allowing for the
150
synchronized acquisition of physiological variables that are typically recorded during a polysomnography.
Our team designed dierent experimental interventions that were applied to our group of overweight
adolescents. A novel intervention was developed by our team, which perturbed the respiratory system by
manipulating the inspiratory pressure, provided by the CPAP machine operating in the bilevel pressure mode,
to increase tidal volume and induce sighs. These sudden changes in tidal volume created changes in blood gas
tensions, which in turn stimulated the chemore
exes. We utilized this intervention to quantify how well the
ventilatory control system rejected disturbances or in other words its stability characteristics. In addition,
we implemented two previously proposed experimental interventions that facilitated the quantication of
the collapsibility of the upper airway and the propensity to arousal as well as the intensity of the arousal.
Moreover, to quantify the collapsibility of the upper airway, four abrupt drops in CPAP level of increasing
amplitudes and ve breaths duration were delivered to the subjects. Each pressure drop was followed by a
rapid return to therapeutic pressure lasting ve breaths as well. The application of the rapid and intermittent
pressure drops allowed us to estimate the static characteristics of the upper airway, which do not include the
neuromuscular compensation provided by the upper airway muscles. Lastly, we utilized the aforementioned
occlusion valve to elicit an arousal from sleep by completely blocking the pass of air coming from the CPAP
machine and going into the mask. The goal of performing this protocol was to understand how these subjects
would respond to an apneic episode. In particular, we were interested in measuring how easy it was for the
subjects to arouse from the sleeping state, as well as in having estimates of the compensatory respiratory
drive that is associated with the arousal.
We believe that clinicians would nd great value in having access to measurements of the physiological
traits predisposing to OSA, therefore there is a need to translate the experimental maneuvers described
above to the clinical setting. We speculate that our experimental interventions, at least in part, could be
easily translatable to the clinical setting and could be incorporated as part of a regular CPAP titration
study. The reasons that support this idea are the following: 1) The experimental setup developed by our
team was designed and built using components that are commercially available. 2) All of the physiological
measurements that were used for trait quantication were collected in a completely noninvasive manner. 3)
151
The experimental maneuvers that were implemented in order to perturb the respiratory system were short
in duration and were in general well tolerated by the subjects. We strongly believe that the results obtained
from these experimental interventions would be very informative and would nicely complement the results
that are currently extracted from clinical sleep studies.
Furthermore, this work presents a detailed explanation of the modeling strategies and theoretical con-
cepts that were used to analyze the noninvasively measured ventilatory responses to our various stimulation
protocols. For instance, linear dynamic modeling techniques were used to analyze the induced sighs and
spontaneous breathing recordings to obtain representations of the processes involved in the chemical regu-
lation of respiration and ultimately extract their stability characteristics. Moreover, a linear static model
was used to t the progressive decrease in air
ow amplitude that resulted from the increasing intermittent
drops in mask pressure. The results from this analysis provided us with estimations of the collapsibility of
the upper airway in our cohort. Lastly, the extraction of the arousal components was carried out directly
from the measurements of the elicited arousals without the need of tting a model. After careful valida-
tion with simulated data, our modeling and traits quantication techniques were applied to data collected
experimentally from a total of 46 overweight adolescents (23 non-OSA and 23 OSA). The experimentally-
extracted traits were compared between the two populations to nd the underlying physiological dierences
that characterize the disease. In addition, we combined our experimentally-derived traits along with neck
circumference and pulmonary mechanics measurements to create a classication model that was used as a
diagnostic tool. After comparing our results with those provided by the diagnostic polysomnography, we
found that our methodology was reliable at detecting the presence of OSA. Our technique was also successful
at indicating the cause for OSA at an individualized level. We think that these analytical tools could be
used to aid clinicians in the selection of therapy that can be targeted to improve a specic trait and could
perhaps help resolve OSA completely.
The results from our study indicate that adolescent OSA shares some commonalities with adult OSA.
For example, we found that having a compromised upper airway anatomy and a highly collapsible upper
airway are predisposing factors for OSA and were both predictors for OSA severity. On the other hand, we
152
found that there also exist some discrepancies between adolescent and adult OSA. The fact that chemore
ex
sensitivity was signicantly decreased in the OSA population contradict the recent ndings of a hypersensitive
chemore
ex in some adult OSA cases. The explanation for such dierences between both groups remains
unknown and should continue to be explored. Moreover, we found no dierences in any of the arousal
components between our two populations. This also opposes to some recent ndings in the adult population
that suggested a greater degree of arousability in the OSA population as well as an increased ventilatory
responses to arousal.
The population results discussed above provide good insights about the overall trends of the traits in the
OSA group, however we are more interested in observing how these traits interacted with each other at an
individualized level to produce dierent OSA phenotypes. Therefore, we developed a data visualization and
classication scheme that enabled the detection of the causes of OSA in each of the OSA individuals. One of
the key ndings of our classication model was that, in addition to upper airway abnormalities, non-upper
airway related traits importantly contribute to the development of adolescent OSA. We strongly believe that
with the development of novel and personalized therapeutic strategies that aim at xing both the anatomical
and the non-anatomical traits would help to improve the outcomes of treatment and will ultimately lead to
completely eradicate OSA.
153
Chapter 6
Future Work
6.1 Estimation of other OSA traits
As has been recognized, OSA is a multifactorial phenomenon that could be attributed to the malfunctioning
of one or more mechanisms. In the rst part of this work we focused our attention on quantifying the
stability of the ventilatory control system. For the second part we integrated the ventilatory stability com-
ponents with measurements of upper airway anatomy and collapsibility, arousal threshold and PFT results
in order to provide an assessment of the underlying cause of OSA at an individualized level. As compared
to other studies, our analysis is missing the incorporation of a measurement of the upper airway muscles'
responsiveness, which has been demonstrated to be a protective mechanism against OSA by preventing the
airway from collapse (Sands et al., 2014). Muscle responsiveness could be extracted from the genioglossus
electromyogram data that was recorded during the experimental PSG. Based on previous studies, the inter-
mittent pressure drops protocol is adequate for the quantication of the upper airway muscles' activation.
The
ow limitation that occurs at subtherapeutic CPAP pressure creates an increase in the concentration
of carbon dioxide levels, which in turn stimulates the upper airway muscles to become activated to increase
their tone (Loewen et al., 2011).
154
6.2 Sleep-state eects on OSA traits
All of our OSA traits were extracted while the subjects were in NREM sleep only. It would be interesting to
perform the same measurements during episodes of active or REM sleep. Moreover, our analysis considers
quiet sleeping state as a whole and does not dierentiate between the multiple stages of NREM sleep.
Future studies could also investigate the eects that sleep transitioning into the deeper sleep stages and
even switching to the active sleeping state have on the physiological traits predisposing to OSA. Recent
experimental studies performed in adults and other computational studies have suggested that chemore
ex
sensitivity declines as sleep deepens and reaches the lowest sensitivity during REM sleep (Douglas et al.,
1982b,a; Krimsky and Leiter, 2005). Moreover, plant gain is also known to be in
uenced by the sleep stage
mainly because of the changes in pulmonary blood
ow that are associated with changes in metabolism. In
addition, it is known that muscle tone is signicantly diminished during REM sleep, which makes the upper
airway more collapsible and therefore more prone to suer from a collapse. Lastly, the arousal threshold
has also been found to show within night variations with a trend to increase and reach its peak at the
middle of the NREM cycle (Berry et al., 1998). It would be of interest to us to investigate this sleep-induced
physiological changes in our cohort of overweight adolescents.
6.3 Adaptive estimation of OSA traits
The quantication of the OSA traits so far has been performed under the assumption that there are no drastic
changes in the systems' parameters with time. While this assumption might be valid for short periods of
time, it seldom holds for time lapses that span over the course of hours or even several minutes. Therefore,
the time invariant assumption limits our trait extraction methodologies to be performed on data recordings
of short duration and the analysis to be performed oine. The implementation of an adaptive algorithm
that is able to quantify the OSA traits could help analyze data recordings of longer duration. Additionally,
it could also be used to track the changes in OSA traits over the entire sleeping period. This is of great
importance because it has been demonstrated that there are variations in some of the traits depending on
155
the time of the day and are likely to depend on the circadian rythm (Spengler et al., 2000; Stephenson
et al., 2000; Siekierka et al., 2007; El-Chami et al., 2014). The access of the OSA traits in real time could
potentially be used to administer on demand therapy to help prevent episodes of OSA.
6.4 Experimentally-derived personalized models
For those subjects who successfully completed our four experimental protocols and thus have accurate esti-
mations of the traits that predispose to OSA, a model just as the one presented in Figure 6.1 can be built.
Such personalized models of respiratory control during sleep could be implemented and simulated to study
the complex interactions existing between the dierent mechanisms. Figure 6.2 shows sample simulated res-
piratory and sleeping patterns of the model run with dierent experimentally-derived parameters in response
to a transition from wakefulness to sleep. The two cases that are presented in the gure illustrate the tem-
poral dierences in respiratory measurements that could result from subjects with dierent degrees of upper
airway collapsibility and gas exchange and chemore
ex sensitivities. The example on the left represents the
case where the upper airway is not collapsible and therefore not susceptible to changes in sleep state. This
results in stable patterns of ventilation and arterial PCO
2
, which in turn lead to a smooth transition from
wakefulness to the deeper stages of sleep. On the other hand, the example shown on the right, represents the
opposite case in which the upper airway is highly susceptible to changes in sleep stage, which leads to repeti-
tive episodes of obstruction. These obstructive events translate into drops in ventilation which produce large
increases in the arterial concentrations of CO
2
(due to an increased gas exchange sensitivity) surpassing the
arousal threshold and ultimately inducing arousals from sleep. The cyclic transitions between wakefulness
and sleep result in unstable breathing patterns which are undesired.
In addition to simulating the eects of sleep state transitioning, these type of experimentally-derived
models can be used by clinicians to investigate the eect of dierent treatments targeting one or more of
the OSA traits. This idea would be similar to the graphical model that was rst described by Owens et al.
(2015); however, our model would have the advantage that it would include the dynamic part associated with
the chemore
ex. This would enable the assessment of the transient eects that a disturbance would have on
156
Figure 6.1: Minimal feedback model of respiratory control during sleep that combines the anatomical with
the nonatanomical traits predisposing to OSA.
the respiratory pattern after a specic trait has been manipulated to simulate the application of a therapy.
Thus, this type of models could be used by clinicians to design optimal and patient-specic treatments and
potentially help eradicate completely the disease.
I. Simulated sleeping and respiratory patterns exhibited
by a subject with a non-collapsible upper airway whose
patency is independent of the sleep state.
II. Simulated sleeping and respiratory patterns exhibited
by a subject with a collapsible upper airway whose size
depends on sleep state.
Figure 6.2: Simulation results of the model shown in Figure 6.1 after incorporating the experimentally
derived parameters from two subjects with dierent degrees of upper airway collapsibility.
157
6.5 Prescribing the subjects with the therapies predicted by the
model
With the development of more simulation models that could inform about the potential benet that a specic
subject would get from a treatment, we believe we are one step closer to their actual prescription in OSA
patients. In order to evaluate the validity and ecacy of the methodologies that we employed to perform the
phenotyping and ultimately to suggest treatment, we propose to administer the patient-specic therapies
predicted by the model in our cohort of obese adolescents. After some time on treatment, we could carry
out follow-up sleep studies to evaluate the eects of the targeted treatment in OSA severity. An interesting
study could compare the ecacy at resolving OSA of these targeted therapeutic methods to conventional
ones that target the anatomy only.
158
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Abstract (if available)

Abstract Obstructive sleep apnea (OSA) is one of the most common sleep-related breathing disorders and is characterized by recurrent episodes of upper airway narrowing or collapse occurring during sleep. These apneic events are often accompanied by hypoxia and arousal which might lead, in the long term, to hypertension and other cardiovascular and cerebrovascular diseases, as well as to metabolic dysfunction, neurocognitive impairment and poor professional performance. There are also importnat short term implications of OSA. For instance, the constant episodes of arousal throughout the night have shown to have a negative impact on mood and alertness. The excessive daytime sleepiness and impaired vigilance have been even associated with motor vehicle crashes and occupational injuries. As can be seen, OSA is an important health problem that is associated with multiple adverse behavioral and health outcomes that could translate into major societal consequences and costs. The sum of direct and indirect annual costs associated with OSA have been estimated to range between 70 and 160 billion dollars. Such economic burden surpasses other common respiratory disorders such as asthma and chronic obstructive pulmonary disease. The problem is that less than 5% of the estimated cost of OSA is associated with the diagnostic and treatment of the disease itself and the rest corresponds to the indirect expenses such as long-term medical care as a result of a vehicle or a work-related injury, legal assistance, damage repair, loss of productivity, etc. We believe that in order to prevent the health and economic effects that OSA represents, there is a need to develop more accurate diagnostic tools as well as better therapeutic strategies. ❧ The current gold standard diagnostic tool for OSA (i.e. polysomnography) is highly effective at detecting the presence of OSA

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Asset Metadata

Creator Nava-Guerra, Leonardo (author)

Core Title Model-based phenotyping of obstructive sleep apnea in overweight adolescents for personalized theranostics

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 02/14/2018

Defense Date 01/10/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag biomedical signal processing,chemoreflex stability,diagnostic,experimental sleep study,mathematical modeling,OAI-PMH Harvest,obstructive sleep apnea,physiological signal monitoring,therapy,upper airway collapsibility

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Khoo, Michael (committee chair), Keens, Thomas (committee member), Marmarelis, Vasilis (committee member), Nayak, Krishna (committee member), Ward, Sally (committee member)

Creator Email nava.leo1@gmail.com,navaguer@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-475259

Unique identifier UC11267347

Identifier etd-NavaGuerra-6035.pdf (filename),usctheses-c40-475259 (legacy record id)

Legacy Identifier etd-NavaGuerra-6035.pdf

Dmrecord 475259

Document Type Dissertation

Rights Nava-Guerra, Leonardo

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