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Principal dynamic mode analysis of cerebral hemodynamics for assisting diagnosis of cerebrovascular and neurodegenerative diseases
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Principal dynamic mode analysis of cerebral hemodynamics for assisting diagnosis of cerebrovascular and neurodegenerative diseases
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Content
Principal Dynamic Mode Analysis of Cerebral Hemodynamics for
Assisting Diagnosis
of Cerebrovascular and Neurodegenerative diseases
By
Yue Kang
A Dissertation Presented to the
Faculty of the Graduate School
University of Southern California
In Partial Fulfillment of the
Requirement of the Degree
Doctor of Philosophy
(Biomedical Engineering)
August 2017
Dedication
To my parents.
Acknowledgements
First and foremost, I would like to express my sincere gratitude to my advisor Professor Vasilis Z.
Marmarelis. You have been a tremendous mentor and a treasured friend to me and it has been an
honor to be your Ph.D. student for the past four years. I would like to thank you for your continuous
support, encouragement, guidance and inspiration for my research that allow me to grow as a
research scientist. I am also thankful for the excellent example you have provided as a successful
scientist and professor. I would like to thank Dr. Michael C.K. Khoo, Dr. Mara Mather, to serve
on my quanlifying and/or defense comittees, and I am very grateful to them for their valuable
comments and suggestions. I would also like to thank Dr. Vera Novak and Dr. Ihab Hajjar for
providing the human cerebral hemodyanmic data for my research. I would like to thank Dr. Dae
Shin for his scientific advice and knowledge and many insightful discussions and suggestions. I
thank all my friends, collegues and labmates at USC for their support and help during this four
years’ journey.
Contents
LIST OF FIGURES: ..................................................................................................................... 1
LIST OF TABLES: ....................................................................................................................... 4
CHAPTER 1: INTRODUCTION ................................................................................................ 6
1.1 BACKGROUND, INTRODUCTION AND RESULT SUMMARY ..................................................... 6
CHAPTER 2 PHYSIOLOGY, CLINICAL AND RESEARCH REVIEW ............................ 11
2.1 ALZHEIMER’S DISEASE: ....................................................................................................... 11
2.1.1 Overview: ..................................................................................................................... 11
2.1.2 Clinical Diagnostic Guidelines: .................................................................................... 11
2.1.3 Clinical Diagnostic Assisting Tool: Brain Imaging Techniques ............................... 12
2.1.4 Medications and Clinical Treatments: .......................................................................... 12
2.2 TYPE 2 DIABETES ................................................................................................................. 13
2.2.1 Overview ...................................................................................................................... 13
2.2.2 Symptoms and Clinical Diagnosis:............................................................................... 13
2.2.3 Clinical Interventions and Medications: ....................................................................... 14
2.3 MILD COGNITIVE IMPAIRMENT: .......................................................................................... 15
2.3.1 Overview ...................................................................................................................... 15
2.3.2 Diagnosis: ..................................................................................................................... 15
2.3.3 Medications and Treatment: ......................................................................................... 16
CHAPTER 3: INTRODUCTION OF PDM-BASED MODELING ANALYSIS ................. 17
CHAPTER 4: PRINCIPAL DYNAMIC MODE (PDM) ANALYSIS OF EEG DATA FOR
ASSISTING THE DIAGNOSIS OF ALZHEIMER’S DISEASES ......................................... 20
4.1 ABSTRACT: .......................................................................................................................... 20
4.2 INTRODUCTION AND OVERVIEW:......................................................................................... 20
4.3 METHODOLOGY ................................................................................................................... 23
4.3.1 Data Collection and Pre-processing ............................................................................ 23
4.3.2 Nonlinear Modeling Methodology ............................................................................... 25
4.4 RESULTS .............................................................................................................................. 30
4.5 DISCUSSIONS AND CONCLUSIONS ........................................................................................ 36
CHAPTER 5: PRINCIPAL DYNAMIC MODE (PDM) ANALYSIS OF HEMODYNAMIC
SIGNAL FOR ASSISTING THE DIAGNOSIS OF ALZHEIMER’S DISEASE ................. 40
5.1 INTRODUCTION AND OVERVIEW:......................................................................................... 40
5.2 METHODOLOGY ................................................................................................................... 41
5.2.1 Data Collection and Pre-processing ............................................................................. 41
5.2.2 Linear Modeling Methodology ..................................................................................... 42
5.3 RESULTS .............................................................................................................................. 46
5.4 DISCUSSION AND CONCLUSION .......................................................................................... 48
CHAPTER 6: MODEL-BASED INDICES OF CEREBRAL HEMODYNAMICS AS
DIAGNOSTIC MARKERS IN TYPE 2 DIABETES MELLITUS ...................................... 51
6.1 INTRODUCTION AND OVERVIEW:......................................................................................... 51
6.2 DATA COLLECTION AND PRE-PROCESSING ......................................................................... 54
6.3 MODELING METHODOLOGY AND RESULTS: ....................................................................... 61
6.4 RESULTS .............................................................................................................................. 63
6.5 CONCLUSIONS AND DISCUSSIONS ........................................................................................ 71
6.6 TYPE 2 DIABETES: GENDER DIFFERENCES AND MEDICATION ASSESSMENT ......................... 74
CHAPTER 7: MODEL-BASED INDICES OF CEREBRAL HEMODYNAMICS AS
DIAGNOSTIC MARKERS FOR MCI PATIENTS WITH EXECUTIVE DYSFUNCTION
....................................................................................................................................................... 80
7.1 INTRODUCTION ................................................................................................................... 80
7.2 METHODS ............................................................................................................................. 82
A. Data Collection and Pre-processing.................................................................................. 82
B. Modeling Methodology: ................................................................................................... 83
7.3 RESULTS: ............................................................................................................................. 84
7.4 CONCLUSION AND DISCUSSIONS ......................................................................................... 90
7.5 T2DM, MILD COGNITIVE DISEASE AND NEURODEGENERATIVE DISEASES: ....................... 93
REFERENCES: ......................................................................................................................... 100
1
List of Figures:
Figure 3.1 Block-diagram of the PDM-based model of the single-input and single-output
system with 4 global PDMs…………………………………………………………...19
Figure 4.1 Illustrative EEG signal for representative AD patient………………………………...25
Figure 4.2 Block-diagram of the PDM-based model of the O1-F3 system………………………30
Figure 4.3 Global PDMs of O1-to-F3 system…………………………………………………….31
Figure 4.4 Average ANFs of O1-to-F3 system…………………………………………………...32
Figure 4.5 Global PDMs of O2-to-F3 system…………………………………………………….33
Figure 4.6 Scatter-plot classification result of O2-to-F3 system with ROC…...............................33
Figure 4.7 Scatter-plot classification result of O1-to-F3 system with ROC…...............................35
Figure 5.1 Illustrative hemodynamic signal for representative subjects………………………….42
Figure 5.2 NMSE-based parameter selection (alpha value)……………………………………….44
Figure 5.3 Block-diagram of the PDM-based model of ABP-to-MCAL system………………....45
Figure 5.4 Global PDMs of ABP-to-MCAL system……………………………………………...47
Figure 5.5 Scatter-plot classification result with global PDM frequency representation…............48
Figure 6.1 Hemodynamic signal raw data for representative subjects…………………………….54
Figure 6.2 Representative example of data pre-processing………………………………………..55
Figure 6.3 Representative example of signal artifacts…………………………………………..…56
Figure 6.4 Illustrative example of GWN Input and simulated output signal ……………………...57
Figure 6.5 Signal interpolation simulations with two interpolation techniques………………..….59
Figure 6.6 Impulse response function estimations with two interpolation techniques………….....60
Figure 6.7 Pre-processed hemodynamic signal for representative subjects…………………….…61
Figure 6.8: Illustrative pre-processed time-series data for a representative control subject……….62
Figure 6.9: Block-diagram of the linear PDM-based model of the ABP/ETCO2-CBFV
system with 4 global PDMs for each input…………………………………………...63
Figure 6.10: Illustrative traces of the model prediction and its two components generated
by the ABP and the ETCO2 input…………………………………………………...64
2
Figure 6.11: Time-domain and frequency-domain representations of the four global PDMs
for the ABP-to-CBFV dynamic relationship …………………………………..……65
Figure 6.12: Time-domain and frequency-domain representations of the four global PDMs
for the ETCO2-to-CBFV dynamic relationship………………………………….…66
Figure 6.13: Scatter-plots of obtained Gains for the contributions to the model-predicted
CBFV output along with separation/classification line ……………………………..67
Figure 6.14: The average kernel estimates of the ABP-to-CBFV dynamic relationship for
the T2DM patients and controls, as well as the model-predicted average response
to an ABP input pulse…………………………………………………………….....69
Figure 6.15: The average kernel estimates of the ETCO2-to-CBFV dynamic relationship for
the T2DM patients and controls, as well as the model-predicted average response
to an ETCO2 input pulse………………………………………………………….....70
Figure 6.16: Gender differences in scatter-plots of obtained Gains for the contributions to
the model predicted CBFV output of the 1st ETCO2-PDM versus the 3rd
ABP-PDM (left) and versus the 4th ABP-PDM (right)…………………………......76
Figure 6.17: Gender difference in model-predicted average response to an ETCO2 input
pulse over 5 sec for the 12 T2DM patients and the 5 control subjects……………...77
Figure 6.18: Metformin treatment in scatter-plots of obtained Gains for the contributions to
the model-predicted CBFV output of control subjects (blue), T2DM patients
with metformin treatment (pink) and T2DM patients without
metformin treatment(red)…………………………………………………………...78
Figure 6.19: Model-predicted average response to an ETCO2 input pulse over 5 sec for the
5 controls, 5 T2DM patients without metformin treatment as well as 7
T2DM patients under metformin treatment……………………………………….....79
Figure 7.1: Illustrative pre-processed time-series data over 4 min for representative control
subjects…………………………………………………………………....................83
Figure 7.2: Block-diagram of the PDM-based model of the ABP/ETCO2-CBFV system with
4 global PDMs for ABP and 4 global PDMs for ETCO2…………………………...85
Figure 7.3: Time-domain (left) and frequency-domain (right) representations of the global
PDMs for the ABP input when the output is CBFV measured via TCD…………....86
Figure 7.4 : Time-domain (left) and frequency-domain (right) representations of the global
PDMs for the ETCO2 input (bottom) when the output is CBFV measured via
TCD………………………………………………………………………………....87
Figure 7.5 : Scatter-plots of computed Gains for the contributions to the CBFV output the
1st ETCO2-PDM and 4th ETCO2-PDM versus the 4th ABP-PDM………………...89
3
Figure 7.6 : The average kernel estimates of the ABP-to-CBFV dynamic relationship for the
43 MCI-ED patients and the 5 control subjects, as well as the model-predicted
average response to an ABP input pulse over 5sec……………………………..……89
Figure 7.7 : Average model-predicted CBFV response to a positive ETCO2 5-sec RMS-pulse
change for the 43 MCI-ED patients and the 5 controls ……………………………...90
Figure 7.8 : Time-domain and frequency-domain representations of the global PDMs for the
ABP input and for the ETCO2 input when the output is CBFV measured via
TCD………………………………………………………………………………….96
Figure 7.9: Time-domain and frequency-domain representations of the global PDMs for the
ABP input when the output is CBFV……………………………………….………..98
Figure 7.10: Scatter-plots of computed Gains for the contributions to the CBFV output of MCI
and T2DM patients…………………………………………………………………..99
4
List of Tables:
Table 4.1: Statistic Results of PDM 4 Gain Values of O2-to-F3 System……………………....34
Table 4.2: Statistic Results of PDM 4 Gain Values of O1-to-F3 System……………………....36
Table 5.1: Statistic Results of PDM Gain Values of ABP-to-MCAL System…………………48
Table 6.1: Average Square Deviation and Normalized Mean Square Error (NMSE) for
Simulation Model……………………………………………………………………...60
Table 6.2: Mean (SD) values of ABP-PDM Gains for T2DM patients and controls,
and corresponding p-values……………………………………………………….…..65
Table 6.3: Mean (SD) values of ETCO2-PDM Gains for T2DM patients and controls,
and corresponding p-values…………………………………………………………....67
Table 6.4: Mean (SD) values of estimated Composite Gains (ABP-PDM3, ETCO2-PDM1)
for T2DM patients and controls, and corresponding p-values………………………....68
Table 6.5: Mean (SD) values of estimated Composite Gains (ABP-PDM4, ETCO2-PDM1)
for T2DM patients and controls, and corresponding p-values………………………....69
Table 6.6: Mean (SD) values of DVR indices for T2DM patients and controls, and
corresponding p-value…………………………………………………………………71
Table 6.7: Mean (SD) values of DCA indices for T2DM patients and controls, and
corresponding p-value…………………………………………………………………71
Table 6.8: Mean (SD) values of DVR indices for T2DM female and male patients,
and corresponding p-value…………………………………………………………….77
Table 6.9: Mean (SD) values of DVR indices for T2DM patients with and without metformin,
and corresponding p-value……………………………………………………………..79
Table 7.1: Mean (SD) values of ABP-PDM Gains for MCI patients and controls, and
corresponding p-values.................................................................................................. 86
Table 7.2: Mean (SD) values of ETCO2-PDM Gains for MCI patients and controls, and
corresponding p-values………………………………………………………………..88
Table 7.3: Mean (SD) values of DCA indices for MCI-ED patients and controls, and
corresponding p-value…………………………………………………………………90
Table 7.4: Mean (SD) values of peak CBFV response to unit-step ETCO2 change for MCI-ED
patients and controls, and corresponding p-value………………………………….…..91
Table 7.5: Mean (SD) values of DVR indices for MCI-ED patients and controls, and
corresponding p-value…………………………………………………………………91
5
Table 7.6: Mean (SD) values of ABP-PDM4 Gains for T2DM patients, MCI-ED patients and
controls, and corresponding p-values……………………………………………….…96
Table 7.7: Mean (SD) values of ETCO2-PDM1 Gains for T2DM patients, MCI-ED patients
and controls, and corresponding p-values………………………………………….…..97
Table 7.8: Mean (SD) values of DVR index for T2DM patients, MCI-ED patients and controls,
and corresponding p-values…………………………………………………………....98
Table 7.9: Mean (SD) values of ABP-PDM3 Gains for T2DM patients and MCI-ED patients,
and corresponding p-values……………………………………………………….…...99
6
Chapter 1: Introduction
1.1 Background, Introduction and Result Summary
As humans, it’s in our nature to want to improve our health and minimize our suffering. The need
for effective and accurate detection of diseases has been dramatically grows in clinical significance,
quality of life and health-care cost. One of the key issues in the clinical management of cognitive
disease, such as Alzheimer’s disease (AD), is the challenge of performing reliable and noninvasive
diagnosis at early stages. For example, a definite diagnosis of AD can only be made by autopsy,
although the pathology itself is hypothesized to start years before the first symptoms appear, which
means that the patient’s quality of life is already affected significantly by the time symptoms are
observed and the efficacy of medication is limited. For this reason, numerous diagnostic techniques
during the early stages of Alzheimer’s disease have been explored (e.g. PET imaging and analysis
of cerebral spinal fluid). These currently available techniques have not demonstrated adequate
sensitivity and specificity yet, although they tend to be very expensive and onerous for the elderly
patients. The critical need for reliable, non-invasive and affordable means to support clinicians in
the diagnosis of neurodegenerative diseases including Alzheimer’s disease provides the motivation
for my research work.
Led by Dr. Marmarelis, our group focuses on the use of advanced methods of physiological system
modeling to improve clinical diagnosis and minimally-invasive treatment in various clinical
domains. The proposed modeling approach examines the causal relationship between cerebral
hemodynamic signals. This input-output modeling approach utilizes the concept of Principal
Dynamic Modes (PDM) which has been pioneered by our group and applied successfully over the
last 10 years to various physiological systems [V.Z.Marmarelis, 2004].
7
We start with the analysis of EEG signal for the assisting the diagnosis of Alzheimer’s disease in
Chapter 4. In this study, we employ the nonlinear input-output modeling approach to examine the
causal dynamic relationships between EEG signals by taking the occipital recordings (O1/O2) as
input and frontal recordings (F3/F4) as output. The proposed approach utilizes the concept of PDM
and their associated nonlinear functions (ANFs) for the classification between AD patients and
control subjects. The preliminary results to data collected from 17 AD patients and 24 control
subjects offer considerable promise. Specifically, the resulting global PDMs exhibit spectral
characteristics that correspond to the neural rhythm bands that are commonly reported in research
and clinical studies. More importantly, when the effective gain coefficients of the 2nd and 4th
PDMs are used as classifiers for the O2-F3 system, we have one false-positive and two false-
negatives - i.e. 88.2% sensitivity and 95.8% specificity. Likewise, when the effective gain
coefficients of the 2nd and 4th PDMs are used as classifiers for the O1-F3 system, we have two
false-negatives and two false-positves - i.e. 82.3% sensitivity and 91.7% specificity. The best
classifiers for both O1-F3 and O2-F3 systems corresponded to the PDMs with theta-delta spectral
characteristics, and are consistent with previously reported observations of increased theta and delta
activity in the left hemispheric frontal region in AD patients compared to control subjects, as well
as decreased alpha activity in AD patients (Sankari et al, 2011; Ponomareva et al, 2008; Adler et
al, 2003).
The concept of PDM and PDM-based modeling approach were then investigated for the study of
cerebral hemodynamic signals. In Chapter 5 we review the input-output linear modeling
methodology and preliminary results for the hemodynamic study of Alzheimer’s disease. The close
relationship between cerebral vascular modulations with cerebrovascular and neurodegenerative
diseases has been widely explored, and the study aims to explore the cerebral autoregulation
activity via linear input-output modeling approach, where the arterial blood pressure (ABP) is taken
as the input and cerebral blood flow velocity (CBFV) is taken as the output. The featured dynamics
8
of ABP-to-CBFV relationship were represented by the Principal Dynamic Modes (PDM). The
linear ABP-to-MCAL modeling approach limits the number of free parameters with reliable
estimation under the low SNR condition, and yields diagnostic indices with reduced computational
complexity as compared to their counterparts in nonlinear modeling. The preliminary result shows
the difference between AD patients and control subject by using classification features that concern
the causal relation between blood pressure and cerebral blood flow velocity. Specifically, for the
dataset of 17 AD patients and 13 control subjects, the effective gain coefficients of the 1st and 2nd
PDMs (i.e. the linear coefficients) are used as classifiers and yield 82.3% sensitivity and 84.6%
specificity. The classifiers correspond to the PDMs with resonance peaks at 0.1Hz and 0.18Hz
respetively, which are consistent with the resonance rhythms agreed by the current view for
sympathetic and vagal modulation rhythms(Amiya et al, 2014; Furlan et al ,2000; Julien, 2006;
Algotsson et al, 1995; Perini et al, 2003). Moreover, we observe that the Alzheimer’s patients
possess lower values in both PDM 2 (0.1Hz) and PDM 1(0.18Hz) gains in the classification plots
(Fig. 4.5). This indicates that possible impairment of autonomic nervous system, characterized by
the attenuation in both sympathetic and vagal modulations, might associate with the Alzheimer’s
disease pathology. However, due to the data quality and lack of demographic information of the
recruited dataset, this study was not proceeded with further analysis and investigation.
The previous hemodynamic analysis of Alzheimer’s disease reveal potential of using linear PDM-
based model for the study the cerebral vascular system. In Chapter 6, we present the dual-
inputs/single-output modeling approach to the study of Type 2 diabetes mellitus, where the end-
tidal CO2 is taken as the second input. Due to the damage to blood vessel, long-term health
complications including cardiovascular disease and small vessel diseases, such as hypertension,
stroke and neuropathy, have been widely and consistently observed and eventually become the
leading lethal factors for the diabetic population. These clinical observations therefore offer an
alternative perspective to explore the pathophysiology of Type 2 diabetes. The study seeks to
9
quantify two key aspects of cerebral hemodynamics – viz. Dynamic Cerebral Autoregulation
(DCA) to blood pressure changes, and Dynamic Vasomotor Reactivity (DVR) to blood CO2
changes -- in 12 patients with Type-2 Diabetes Mellitus (T2DM), without cognitive impairment,
and 5 age-matched controls. Our approach utilizes data-based predictive dynamic models to explain
changes in beat-to-beat cerebral blood flow velocity (CBFV), measured via Transcranial Doppler
(TCD) at the middle cerebral arteries, in terms of spontaneous beat-to-beat changes of arterial blood
pressure (ABP) and breath-to-breath end-tidal CO2 (ETCO2), under resting conditions. The model
is estimated from 5-min data for each subject and subsequently used to compute subject-specific
indices of DCA and DVR that may serve as diagnostic markers. The results indicate a statistically
significant decrease of the DVR marker in T2DM patients relative to controls (p=0.003), suggesting
impairment of dynamic CO2 vasomotor reactivity in T2DM (in fact the average DVR index in
T2DM patients becomes negative). The average DCA value was higher in the T2DM patients, but
not in a statistically significant manner (p=0.352). This would be consistent with the hypotheses of
sympathetic hyperactivity causing “overregulation” and impairment of the baroreflex, which are
corroborated by statistically significant changes in the contributions of the 3rd and 4th PDMs for
the ABP input. Following our preliminary result of Type 2 diabetes hemodynamic analysis, we
proceed with the study on gender differences using model-based analysis, and examine whether the
model-based biomarkers reveal gender differences with respect to the diabetic pathology. We also
relate our hemodynamic analysis with the pharmaceutical information of recruited diabetic patients
and examine the “biomarkers” of two specific groups: 7 T2DM patients are under medication
(metformin) treatment and 5 T2DM patients without medication (metformin) to investigate the
medication effectiveness on type 2 diabetes mellitus.
In the following section of Chapter 7, the cerebral autoregulation and CO2 vasomotor reactivity
were analyzed using hemodynamic signals (arterial blood pressure, end-tidal CO2 and cerebral
blood flow velocity) collected noninvasively from Mild Cognitive Impairment (MCI) patients with
10
executive dysfunction (ED) due to chronic hypertension, and from normotensive controls. Dynamic
analysis was employed to examine the concurrent variations of these physiological signals based
on the concept of Principal Dynamic Modes (PDMs) to obtain predictive dynamic models of the
relationships between these variables. The modeled dynamics are used to generate subject-specific
markers that we posit to be able to delineate MCI-ED patients from normotensive controls. Since
the model was extracted from spontaneous beat-to-beat data under resting conditions, the computed
markers quantify the dynamic cerebral autoregulation (DCA) and dynamic cerebral vasomotor
reactivity (DVR). To further address the issue of the association between T2DM and cognitive
impairment and neurodegenerative disease from a diagnosis standpoint, group differences between
T2DM patients, MCI patient and healthy controls were then observed with respect to model-based
“biomarkers”. This PDM-based analysis on different patients offer important implications for
disease pathology and may prove to be beneficial for clinical and diagnosis applications. The
connection between PDM model-based analysis and physiology systems and mechanisms remains
a challenge and ought to be carefully examined and validated to assess the PDM-based
methodology, as a practical, robust and reliable diagnostic tool in clinical environment.
11
Chapter 2 Physiology, Clinical and Research Review
2.1 Alzheimer’s Disease:
2.1.1 Overview:
Alzheimer’s disease (AD) is the most common neurodegenerative disorder in the worldwide range
and the most common cause for dementia diseases which accounts for 60% to 80% of the estimated
cases (Charles, 2011). The number of AD patients is expected to double approximately every 20
years because of the aging population (Wimo and Prince, 2010), making AD a major burden on
health and health-cost in the western world. Though it is commonly believed that AD majorly
affects populations over 65 year old, evidences have shown that in 2% to 10% of Alzheimer’s cases
the onset of disease starts before the age of 65 years (Prince et al, 2014). The pathophysiology
associated with AD is characterized by the accumulation of amyloid plaques and neurofibrillary
tangles in the patient’s brain and loss of cortical neurons and synapses (Blennow et al, 2006). These
pathological changes cause loss in memory and language ability, decline in problem-solving skills
and other cognitive and behavioral impairments that progressively affect the patient’s ability to live
independently (Blennow et al, 2006).
2.1.2 Clinical Diagnostic Guidelines:
Unfortunately, currently there is no single test proven to be effective for the diagnosis of
Alzheimer’s disease. A thorough medical evaluation on AD patients are usually conducted by
doctors through various types of studies and measurements, including medical history study ,
memory and attention tests, and imaging techniques such as computed tomography(CT) and
magnetic resonance imaging(MRI). However, a definite diagnosis of AD can only be made by
autopsy, through medical measurement on brain tissues (Blennow et al, 2006). In fact, AD
pathology is hypothesized to start years before the first symptoms appear, which means that the
12
patient’s quality of life already affected by the time clinical diagnosis is made and the efficacy of
medication is limited (Blennow et al, 2006). Thus, there is critical need for reliable and non-
invasive means to support clinicians for accurate diagnosis the AD pathology, especially at its early
stages.
In 2011, the National Institute of Aging and Alzheimer’s Association have jointly issued the revised
criteria and guidelines of Alzheimer’s disease diagnosis, and for the first time defined the
conditions in which Alzheimer’s patients do not show any clear symptoms such as memory loss or
inability in performing daily tasks as the first stage of Alzheimer’s disease: the ‘preclinical’ stage
(Alzheimer’s, 2015). This further addresses the clinical significance of early-stage Alzheimer’s
disease, a condition in which the symptoms are not noticeable yet the physiological changes are
already under way in the body.
2.1.3 Clinical Diagnostic Assisting Tool: Brain Imaging Techniques
Because of the critical need in performing early diagnosis of Alzheimer’s disease, numerous
diagnostic techniques have been explored by researchers and clinicians. These currently available
techniques include structural imaging with magnetic resonance imaging (MRI) or computed
tomography (CT), and also functional imaging with positron emission tomography (PET).
However, these techniques are mainly used to rule out other dementia conditions that are not caused
by Alzheimer’s disease and have not demonstrated adequate sensitivity and specificity, although
they tend to be very expensive and onerous for the elderly patients.
2.1.4 Medications and Clinical Treatments:
Due to the non-reversible neuropathology impairment occurred in the brain, currently there is no
cure for Alzheimer’s disease. Medications and clinical treatments are mainly employed to slow
13
down or stop the progress of cognitive dysfunctions and associated behavioral symptoms. U.S.
Food and Drug Administration (FDA) have approved six medications that temporarily relieve the
Alzheimer’s disease symptoms by increasing the amount of neurotransmitters in the brain (Prince
et al, 2014; Alzheimer’s, 2015). However, the effectiveness of medications is inevitably subject to
individual patients and none of the treatments or medications is able to alter the abnormal
neurodegeneration and dysfunctions occurred in the brain.
2.2 Type 2 Diabetes
2.2.1 Overview
Type 2 Diabetes Mellitus, also called the “noninsulin-dependent diabetes”, is the most common
form of diabetes (accounting for 90% of the cases of diabetes mellitus). In 1985, 30 million people
were diagnosed with Type 2 diabetes, while in 2010 the number of patients reaches to
approximately 285 million (Melmed et al, 2011; Smyth and Heron,2006). The prevalence of Type
2 diabetes has been increased markedly in worldwide range with growing clinical significance.
While the Type 1 diabetes are due to the pancreas failure to produce enough insulin for blood
glucose regulation, the Type 2 diabetes occur under the specific condition called “insulin
resistance”, in which the patient’s body does not respond to the insulin properly, or little insulin is
produced by the pancreas, and eventually leads to abnormal high blood glucose level. However, a
comprehensive understanding of the etiology of the disease is still needed.
2.2.2 Symptoms and Clinical Diagnosis:
Common symptoms associated with Type 2 diabetes include polyuria (frequent
urination), polydipsia (increased thirst), polyphagia (increased hunger), and weight loss (Weyer et
14
al, 2001). By affecting the major organs including hearts, blood vessels and nerves, Type 2 diabetes
dramatically increase the risk of serious health complications, such as heart attack, stroke,
hypertension and neuropathy that eventually become fatal to the diabetes patients.
Clinical diagnoses of Type 2 diabetes are based on measurements of blood sugar level. The World
Health Organization defined the blood glucose level of diabetes patients as with fasting glucose
level reaches beyond 7.0 mmol/l, or with glucose tolerance test (two hours after the oral dose
plasma glucose) reaches beyond 11.1 mmol/l (Alberti,1998). After the subjects is diagnosed with
diabetes, further blood test is performed to check for autoantibodies that are commonly seen in
Type 1 diabetes and help clinicians to distinguish between Type 1and Type 2 diabetes patients.
2.2.3 Clinical Interventions and Medications:
For Type 2 diabetes patients, the first-line management starts with healthy eating, regular physical
exercises and weight control, as these steps have been proven to keep the blood sugar level close
to normal level. It is important for diabetic patients to center their diet on high-fiber and low-fat
food (e.g. fruits, vegetables and whole grains). Aerobic exercises such as walking or dancing also
help to lower the blood sugar level.
Despite the daily life-style measures, medications are advised for patients with remaining high
blood glucose level. Metformin is one of the most prescribed medications for type 2 diabetes
patients. It works by suppressing the glucose production by the liver while improving the body’s
sensitivity to efficiently react to insulin.
15
2.3 Mild Cognitive Impairment:
2.3.1 Overview
Mild cognitive impairment (MCI) refers to the brain functioning with cognitive impairment beyond
the expected age and education of the individual. Memories, language functions as well as
executive functions are affected but not to the extent to be defined as “dementia”. MCI is therefore
viewed as the transitional stage between normal aging and dementia and the onset stage of
Alzheimer’s disease. Two major sub-types are sometimes defined based on presence or absence
of memory difficulties (amnestic vs. non-amnestic MCI).
Executive dysfunction is frequently found in aMCI, and it offers important information for
prognosis. Executive dysfunction involves disruption to the efficacy of the cognitive processes that
regulate, control, and manage other cognitive processes. It is reported that MCI patient with
executive dysfunction have high tendency to develop Alzheimer’s disease. [Huntley, J. D,
2010;Albert, M et al, 2007; Chen, P et al 2000] Predictive accuracy for transition from MCI to AD
for one set of cognitive variables (composed of episodic memory and processing speed measures)
has been found to be as high as 0.86 (sensitivity, 0.76; specificity, 0.90) [Tabert, M. H. et al, 2006]
2.3.2 Diagnosis:
Mild cognitive impairment is diagnosed by doctor's best professional judgment and confirmed with
biomarker tests such as brain imaging and cerebrospinal fluid tests if the individual has MCI due
to Alzheimer's. Other tests include blood tests, MRI scan of the brain, neurological examination,
neuropsychological testing and a review of how symptoms are affecting every day functioning.
16
2.3.3 Medications and Treatment:
Currently, no drugs or other treatments are proved to be effective for Mild Cognitive Impairment.
For MCI patients whose main syndrome is memery loss, doctors sometimes prescribe
cholinesterase inhibitors , which is a type of medications for Alzheimer’s disease. However,
cholinesterase inhibitors aren't recommended for routine treatment of MCI. Clinical studies are
underway to shed more light on the disorder and find treatments that may improve symptoms or
prevent or delay progression to dementia.
17
Chapter 3: Introduction of PDM-based Modeling Analysis
The PDM modeling approach relies on an efficient methodology for the estimation of Volterra
kernels using Laguerre expansions. For a given system, a set of “global” PDMs are extracted from
the estimated kernels of control subjects cohort. The resulting PDMs yield with concise PDM-
based models, and should inform the featured dynamics of the causal relationships between input
and output signal. Therefore they are used as a common frame of reference for the comparison
between different cohorts (controls and patients). Specifically, the global PDMs are generated
through singular value decomposition (SVD) of a rectangular matrix containing all the 1
st
order
kernel estimates from control subjects. It is posited that the computation of the global PDMs should
be based on the controls kernels only because they represent the dynamics of given system without
pathological abnormality, and therefore are expected to represent a standardized and stable
common frame for all subjects. The “significance” of each singular vector is then assessed by the
respective singular value, and these “significant” singular vectors constitute the global PDMs.
We summarize below the PDM-based modeling methodology using Laguerre expansions of the
kernels for linear dynamic modeling of the single-input and single-output system s. The 1
st
order
(linear) Volterra-type model is given by:
(3.1)
where 𝑥 and 𝑦 denote the input and output, respectively. We first seek to estimate the unknown
kernels 𝑘 0
, 𝑘 1
, 𝑘 2
using input-output data by minimizing the mean-square value of the prediction
error 𝜀 (𝑛 ). The system “memory” (i.e. the extent of the kernels) is represented by M. In order to
reduce the number of free parameters that must be estimated, the kernels are expanded onto a basis
1
0
1 0
M
m
) m n ( x ) m ( k k ) n ( y
18
of orthonormal discrete Laguerre functions {𝑏 𝑗 } (𝑗 = 1,2 … 𝐿 ) . The Laguerre parameters are
determined through a search procedure that minimizes the normalized mean square error (NMSE)
of the model prediction for all subjects. The linear model based on Laguerre expansion technique
is expressed as follows:
(3.2)
where:
(3.3)
The linear expansion coefficients (c 0, c 1, c 2) are estimated via the ordinary least-squares method
and the 1
st
order kernel estimates are given by the expression:
(3.4)
The global PDMs are generated through Singular Value Decomposition (SVD) of a matrix
composed of all the 1
st
order kernel estimates in the cohort of control subjects, as the singular
vectors corresponding to the “significant” singular values (i.e. those >1% of the maximum singular
value). These global PDMs enable concise PDM-based modeling of the dual-input system through
data-based estimation of “Gain coefficients” for each input via linear regression, according to Eq.
(3.5)
L
j
j
n V j c c ) n ( y
1
1 0
1
0
M
m
j j
m n x m b n V
m b ) j ( c m k
j
L
j 1
1
1
1 1 1
19
𝑦 (𝑛 ) = ∑ 𝑐 𝑖 𝐻 𝑖 =1
{∑ 𝑝 𝑖 (𝑚 )𝑥 (𝑛 − 𝑚 )
𝑀 −1
𝑚 =0
} (3.5)
where 𝑝 𝑗 1
is the 𝑗 1
th global PDM of ABP-to-CBFV and 𝑝 𝑗 2
is the 𝑗 2
th global PDM of ETCO2-to-
CBFV, and * denotes convolution. The regression estimates {c 1 and c 2} are the Gain coefficients
for each subject. Figure 3.1 shows a block diagram of the PDM-based model example of the dual-
input system. The 1
st
order kernel estimate for ABP can be computed as:
𝑘 𝑖 (𝑚 𝑖 ) = ∑ 𝑐 𝑖 (𝑗 𝑖 ) 𝑝 𝑗 𝑖 (𝑚 𝑖 )
4
𝑗 𝑖 =1
(3.6)
Figure 3.1: Block-diagram of the PDM-based model of the single-input and single-output system with 4
global PDMs. 𝑐 𝑗 is the least square estimation of linear coefficient of the jth PDM j.
20
Chapter 4: Principal Dynamic Mode (PDM) Analysis of EEG Data for
Assisting the Diagnosis of Alzheimer’s Diseases
4.1 Abstract:
We examine whether modeling of the causal dynamic relationships between frontal and occipital
electroencephalogram (EEG) time-series recordings reveal reliable differentiating characteristics
of Alzheimer's patients versus control subjects in a manner that may assist clinical diagnosis of
Alzheimer's disease (AD). The proposed modeling approach utilizes the concept of Principal
Dynamic Modes (PDM) and their associated nonlinear functions (ANF) and hypothesizes that the
ANFs of some PDMs for the AD patients will be distinct from their counterparts in control subjects.
To this purpose, "global" PDMs are extracted from 1-min EEG signals of 17 AD patients and 24
control subjects at rest using Volterra models estimated via Laguerre expansions, whereby the O1
or O2 recording is viewed as the "input" signal and the F3 or F4 recording as the "output" signal.
Subsequent singular value decomposition (SVD) of the estimated Volterra kernels yields the global
PDMs that represent an efficient basis of functions for the representation of the EEG dynamics in
all subjects. The respective ANFs are computed for each subject and characterize the specific
dynamics of each subject. For comparison, signal features traditionally used in the analysis of EEG
signals in AD are computed as benchmark. . The results indicate that the ANFs of two specific
PDMs, corresponding to the delta-theta and alpha bands, can delineate the two groups well.
4.2 Introduction and Overview:
Alzheimer’s disease (AD) is the most common neurodegenerative disorder in the western world
and the number of patients is expected to double approximately every 20 years because of the aging
population (Wimo and Prince, 2010). AD is characterized by the accumulation of amyloid plaques
and neurofibrillary tangles in the patient’s brain and loss of cortical neurons and synapses (Blennow
21
et al, 2006). These pathological changes cause memory loss and other cognitive and behavioral
impairments that progressively affect the patient’s ability to live independently (Blennow et al,
2006).
The guidelines for clinical diagnosis of AD (McKhann et al, 2011) are based on the exclusion of
other causes for the symptoms. However, a definite diagnosis of AD can only be made by autopsy
(Blennow et al, 2006) and AD pathology is hypothesized to start years before the first symptoms
appear. The patient’s quality of life already affected by the time clinical diagnosis is made
(Blennow et al, 2006). Thus, there is a need for objective, non-invasive and affordable means to
support clinicians in the detection and monitoring of AD. One of such potential means is the
analysis of electroencephalogram (EEG) recordings (Sanei and Chamber, 2008).
The analysis of EEG time series has been explored previously for its diagnostic potential in AD,
based on the notion that the EEG signals represent fluctuations of aggregate brain activity in the
respective brain regions and, therefore, may be able to reveal differences in brain function under
different clinical conditions (Jeong, 2004; Hornera et al, 2009). Many previous studies have
explored this question through the computation of diverse signal features from EEG recordings
(Jeong, 2004; Hornera et al, 2009). Spectral features, including both spectral indices such as median
frequency and relative power values, have revealed a spectral slowdown of the brain activity in AD
(Sanei and Chamber, 2008; Jeong, 2004; Hornera et al, 2009; Henderson et al, 2006). Nonlinear
features provide additional points of view in the inspection of the EEG signals. Features such as
Sample Entropy have been applied to the EEG recordings of patients (Hornera et al, 2009). The
results indicate that AD affects the nonlinear characteristics of the EEG signals, making them more
regular and predictable (Jeong, 2004; Hornera et al, 2009).
AD is hypothesized to be a disconnection syndrome (Jeong, 2004;Stam et al, 2009). Therefore,
22
there is increasing interest in the inspection of the connectivity of EEG recordings (Jeong, 2004;
Stam et al, 2009; Dauwels et al, 2010; Escudero et al, 2011; Greenblatt et al, 2012).This is often
evaluated by measuring the (linear or nonlinear) dependencies between two signals in different
spectral bands (Jeong, 2004 ; Dauwels et al, 2010;Greenblatt et al, 2012). This is particularly
important in AD as the disease may cause opposing changes in different frequency ranges (Jeong,
2004; Stam et al, 2009; Escudero et al, 2011).
Traditional approaches to measure the connectivity between EEG signals are limited by a number
of factors. To start with, spurious results could appear due to the volume conduction effects (Stam
et al, 2009; Escudero et al, 2011; Greenblatt et al, 2012), because nearby channels are likely to
record activity from identical sources. Ideally, the connectivity evaluation should also inform about
the causality of the interactions between signals (Greenblatt et al, 2012). While some techniques
have been recently developed to address these issues (e.g., phase lag index in Stam et al, 2009),
their use is limited perhaps due to a less straightforward interpretation than other techniques.
As an alternative, the present study focuses on the modeling and analysis of the possible causal
relationship between occipital recordings (viewed as the "input" signal) and frontal recordings
(viewed as the "output" signal) in order to generate model-based indices to characterize the EEGs
of AD patients. To this purpose, we apply the Volterra modeling approach using Laguerre
expansions of the kernels and employ the concept of Principal Dynamic Modes (PDM), which our
group has pioneered (V.Z.Marmarelis, 2004). This reduces significantly the required number of
free parameters in the model and enables estimation of reliable linear or nonlinear dynamic models
under conditions of low SNR. This modeling methodology has been recently applied to many
different physiological domains, including the cerebral hemodynamics in AD patients (Marmarelis
et al, 2013). The results to date corroborate the potential and efficacy of this modeling approach.
The proposed diagnostic indices in this study are generated through the use of the Associated
23
Nonlinear Functions (ANFs) that correspond to each PDM of each subject.
Our aim is to examine whether the estimated PDMs exhibit spectral characteristics in line with the
neural rhythms naturally occurring in the brain (delta, theta, alpha and beta, and gamma) and
whether the ANFs obtained for each subject can be used as descriptors of disease. It is posited that
these ANFs may constitute useful "features" for the classification and differentiation of overall
cognitive function in AD patients versus controls.
4.3 Methodology
4.3.1 Data Collection and Pre-processing
This study involves 24 control subjects (42% male; average age: 69.4±11.5 years, mean±standard
deviation, SD) and 17 AD patients (53% male; average age: 77.6±10.0 years) who voluntarily
participated and signed the Informed Consent Form according to institutional guidelines. The EEG
recordings were obtained for patients at rest and with their eyes closed, using the traditional 10–20
system in a Common Reference montage using a sampling rate of 256 Hz. The signals were
downsampled to 128Hz offline.
The data were obtained under a strict protocol from Derriford Hospital, Plymouth, UK, and had
been collected using normal hospital practices. The patients were referred to the hospital EEG
department from a specialist memory clinic where all patients undergo a battery of psychometric
tests before referral. The results from the psychometric tests were scored and interpreted by a
specialist psychologist. Each patient was given a diagnosis at the memory clinic on the basis of the
clinical and psychometric findings and discussions held by a multidisciplinary team. Each patient
was then referred to the hospital for EEG assessment. All age-matched controls were healthy
24
volunteers and had normal EEGs (confirmed by a Consultant Clinical Neurophysiologist).
For each subject, continuous epochs of 60 seconds were simultaneously extracted from the left
frontal (F3), right frontal (F4), left occipital (O1) and right occipital (O2) channels. The selection
of these electrodes is supported by the fact that AD is hypothesized to affect long-range
connectivity as a result of the loss of long cortico-cortical association fibers, which may play an
important role in functional interactions (Jeong, 2004). Moreover, selecting nearby channels would
probably result in all of them picking up identical sources, which may lead to spurious connectivity
levels reflecting simple volume conduction rather than true functional connectivity (Stam et al,
2009). The positions of the selected electrodes minimize possible effects of ocular activity.
The epochs of 60s were selected for having a small presence of artifacts. They were then band-pass
filtered in the range of 1 to 40 Hz with a band-pass Hamming window FIR filter with order 200.
The data were then demeaned and scaled by a factor of 1/100 for computational/numerical
convenience. Fig. 4.1 shows illustrative pre-processed time-series data over 3 sec and the respective
spectrogram for the O1 EEG signal of an AD patient. The spectral properties of this data segment
seem stationary.
25
Figure 4.1: Top panel: illustrative time-series data over 3 sec from the O1 EEG signal of AD patient #1.
Bottom panel: the spectrogram over 60 sec of the time-series data up to 40Hz for this patient.
4.3.2 Nonlinear Modeling Methodology
The proposed modeling approach utilizes the concept of Principal Dynamic Modes (PDM) that has
been pioneered by our group and applied successfully over the last 10 years to various physiological
systems (V.Z.Marmarelis, 2004). In this approach, we seek to determine from input-output data a
set of basis functions (the PDMs) that represent an efficient “coordinate system” for the
representation of the Volterra kernels of a given class of systems. Static nonlinear functions
associated with each PDM (termed ANF: Associated Nonlinear Functions) describe the (possible)
nonlinearities of the system. The PDM modeling approach relies on an efficient methodology for
the estimation of Volterra kernels using Laguerre expansions (V.Z.Marmarelis, 2004). To reduce
the complexity of the obtained PDM-based models and facilitate comparisons between different
cohorts, we seek to determine the "global" PDMs of a given system from the estimated kernels of
a cohort. This is accomplished through singular value decomposition (SVD) of a rectangular matrix
containing all estimated Volterra kernels in the cohort. We note that the computation of the global
PDMs must be based on all subjects because they represent a common frame of reference for all
subjects who are subsequently classified according to their respective ANFs. The global PDMs
correspond to the selected “significant” singular vectors by applying a selection criterion on the
respective singular values.
In this study, we analyze the causal relationship between two EEG signals, in which the frontal
signal is taken as the "output" and the occipital signal is taken as the "input". Using the Laguerre
expansion technique, we start with linear modeling (1st order Volterra kernel only) and proceed
with nonlinear modeling estimating the 2nd-order Volterra kernels as well. These kernel estimates
26
are used to compute the global PDMs of these cohorts via SVD of a rectangular matrix that contains
either all the 1st order kernels (Method 1) or the 1st and 2nd order kernels (Method 2) for all
subjects (patients and controls). The resulting PDMs are used to obtain nonlinear models of 5th
order. The key to the model estimation problem is the use of the Laguerre expansion technique
that keeps the number of free parameters manageable for all models. A detailed description of this
methodology is given in the monograph (V.Z.Marmarelis, 2004). We summarize below the
methodology of PDM-based modeling. The 1st order (linear) Volterra model is:
(4.1)
where
- x(n) is the input (occipital)signal
- y(n) is the output(frontal) signal
- {k 0, k 1} are the zeroth order kernel (constant) and the first order kernel respectively
- M is the system memory (M=70 here)
To limit the number of free parameters that must be estimated, the kernels are expanded onto a
basis of orthonormal discrete Laguerre functions {𝑏 𝑗 } (𝑗 = 1,2 … 𝐿 ). In this study, 7 discrete
Laguerre functions with Laguerre parameter 0.6 (L = 7 , α = 0.6) are found to be adequate to
represent the input-output dynamic relations. The optimal value of the Laguerre parameter α and L
is determined through a global search procedure that minimizes the normalized mean square error
(NMSE) of the model prediction for all subjects. The selected values of alpha and L determine the
system memory (M=70 in this case). After Laguerre expansion, the linear model is given by the
expression:
(4.2)
1
0
1 0
M
m
) m n ( x ) m ( k k ) n ( y
L
j
j
n V j c c ) n ( y
1
1 0
27
where
(4.3)
The expansion coefficients (c0, c1) are estimated by the ordinary least-squares method and the 1st
order kernel estimate is given by the expression:
(4.4)
This model has 8 free parameters, as compared to 71 free parameters for the original linear
Volterra model.The second-order Volterra model is given by:
(4.5)
where k 2 denotes the 2nd order kernel. Following the Laguerre expansion technique (L=7), we
have:
(4.6)
1
0
M
m
j j
m n x m b n V
m b ) j ( c m k
j
L
j 1
1
1
1 1 1
1
0 0
2 1 2 1 2
1
0
1 0
1
1
2
M
m
m
m
,
M
m
m n x m n x ) m m ( k
m n x m k k n y
n V n V j j c
n V j c c n y
j j ,
L
j
j
j
L
j
j
2 1
1
1
2
2 1
1 1
2
1
1 0
28
The number of free parameters in this model is 36, as compared to 2556 free parameter for the
original 2nd order Volterra model. The 2nd order Volterra kernel is expressed in terms of the
expansion coefficients as:
(4.7)
The PDM-based modeling approach seeks to find the “minimum set” of basis functions (the
"global" PDMs) that are able to represent the input-output dynamics adequately for each particular
system. This is achieved via SVD of a rectangular matrix composed of the estimated Volterra
kernels of the respective cohort using either of two methods:
Method 1: the kernel-based matrix is composed of the 1st order kernel estimates for all subjects;
Method 2: the kernel-based matrix is composed of the 1st and 2nd order kernel estimates for all
subjects.
In both methods, the global PDMs are determined as the significant singular vectors of the kernel-
based matrix that correspond to singular values satisfying a specified selection criterion (e.g. at
least 10% of the maximum singular value). In this study, 5 to 6 global PDMs were selected. The
physiological characteristics of these global PDMs will be discussed in the following section. The
global PDMs are used to describe the dynamics of this system (via expansions of the system kernels)
for all subjects. The possible nonlinearities of the system are described by the respective ANFs,
which are subject-specific and can be used for diagnostic purposes. The case of linear models is
included in this representation, when the ANFs are linear functions. The output equation for the
PDM-based model is:
2 1 2 1
1
2 2 1 2
2 1
1
1
2
m b m b j , j c m m k
j j
L
j
j
j
,
29
(4.8)
where
- 𝑝 𝑖 is the i th global PDM
- H is the number of global PDMs
- f i is the ANF of the i th PDM
In general, the ANFs are taken to be polynomials (typically of 3rd degree):
(4.9)
The polynomial ANF can be replaced by its best linear fit (in a least-squares sense) if reduction of
model complexity is desirable. In that case, the linear coefficient is an "effective gain constant"
for the respective PDM and can be used as an index for delineating AD patients from control
subjects. Fig.4.2 shows a schematic block-diagram of the PDM-based model.
Figure 4.2: Block-diagram of the PDM-based model of the O1-F3 system with 5 global PDMs. The output
𝑢 𝑗 of the jth PDM 𝑝 𝑗 is the convolution of the PDM with the input signal. In this study, the ANFs are taken
m n x m p f n y
M
m
i
H
i
i
∑ ∑
1
0 1
... u a u a u a f
3
j j , 3
2
j j ., 2 j j , 1 i
30
to be the 5th degree polynomials: 𝑧 𝑗 = 𝑎 1,𝑗 𝑢 𝑗 + 𝑎 2,𝑗 𝑢 𝑗 2
+ 𝑎 3,𝑗 𝑢 𝑗 3
+ 𝑎 𝑗 ,4
𝑢 𝑗 4
+ 𝑎 𝑗 ,5
𝑢 𝑗 5
based on a search
procedure that yields the best classification results for the smallest number of free parameters.
4.4 Results
The predictive capability of the obtained PDM-based model is assessed by the Normalized Mean Square
Error (NMSE) of the respective model prediction. The minimum NMSE among the four combinations of
occipital-to-frontal input-output systems was obtained for the nonlinear model of the O1-to-F3 system
(NMSE=89.7 %), only slightly better than its linear counterpart (NMSE= 91.2 %). It is evident that the
model prediction only accounts for a small portion of the output signal, but this should be expected in a
system of such low signal-to-noise ratio.
5 PDMs for the O1-to-F3 model were obtained using Method 2. For the sake of clarity, only 4 PDMs are
shown in Fig.4.3 for the time-domain and frequency-domain respectively. In the frequency domain, the
global PDMs exhibit spectral characteristics that correspond to the following neural rhythm bands:
- 1st PDM (red): beta band (~20 Hz)
- 2nd PDM (blue): alpha band (~12 Hz)
- 3rd PDM (green): low delta band (~1 Hz);
- 4th PDM (magenta): combination of theta (~8 Hz) with delta band (~3 Hz);
- 5th PDM (black): high delta (~4 Hz).
The 2nd and 4th PDMs were found to be the most differentiating between AD patients and control
subjects (see below).The average Associated Nonlinear Functions (ANFs) for the nonlinear models
of the O1-to-F3 system (defined as 5th degree polynomials in this application) are shown in Fig.4.4
with blue line for the 17 AD patients (bottom row) and the 24 control subjects (top row), along with
the best (in mean-square sense) linear fits shown in gray . It is evident in Fig.4.4 that the slope of
the 4th ANF changes sign for the patients (i.e. becomes positive for the AD patients from negative
31
for the controls), and the negative slopes of the 3rd and 5th ANFs decrease (in absolute value) for
the patients. This suggests that these three PDMs are more likely to provide the means for
differentiation between patients and controls. However, the difference between the average values
of ANF slopes may not portray correctly the separation between the two groups which relies on the
distribution of the individual values.
Figure 4.3: Time-domain representations (left) and frequency-domain representations (right) of the global
PDMs of the input-output model for O1-to-F3 system (four out of five PDMs are plotted for the sake of
clarity, see text).
32
Figure 4.4: Average ANFs (blue line) for the 5 PDMs of the 17 AD patients (bottom row) and 24 control
subjects (top row), along with the best linear fits (red line) for the O2-to-F3 system.
After examining the differentiating capability of all pair combinations of PDMs/ANFs, it was found
that the 2nd and 4th PDMs (and their respective linear trends) are the most differentiating between
patients and controls for O2-F3 system, as shown in the scatter-plot of Fig.4.6 (A). They result in
one false-positive (#40) and two false-negatives (#3 and #17). The sensitivity of 88.2 % and
specificity of 95.8 % are marked on the corresponding ROC curve shown in Fig.4.6 (B).
33
Figure 4.5: Time-domain representations (left) and frequency-domain representations (right) of the global
PDMs of the input-output model for O2-to-F3 system (four out of five PDMs are plotted for the sake of
clarity, see text).
(A) (B)
(C) (D)
Figure 4.6: (A): Scatter-plot of computed ANF linear trends (slopes) for 2nd and 4th PDMs of the O2-to-F3
system, corresponding to the alpha-delta and theta-delta bands. One false-positive and two false-negatives
are shown. (B): ROC curve for the scatter-plot (2nd versus 4th ANF/PDMs) of the O2-to-F3 system. (C):
Scatter-plot of computed ANF linear trends (slopes) for 1st and 4th PDMs of the O2-to-F3 system. One false-
positive and three false-negatives are shown. (D) Scatter-plot of computed ANF linear trends (slopes) for 3rd
and 4th PDMs of the O2-to-F3 system. One false-positive and three false-negatives are shown. The
classification line has been obtained by nonlinear regression algorithm.(with 150 000 iterations).
34
The combination of 1st and 4th PDMs and combination of 3rd and 4th PDMs also yield satisfactory
delineation between two groups. The differential capability of 4th PDM and its corresponding
dynamics are discussed in the later sections.
Table 4.1: Statistic Results of PDM 4 Gain Values of O2-to-F3 System
We note that satisfactory delineation between the two groups is also achieved in the O1-F3 system
(see scatter-plot in Fig.4.7 (A)) using the pair of 2nd and 4th PDMs/ANFs that correspond to the
alpha-delta and theta-delta bands respectively, as shown in Fig.4.3. Two false-negatives (#13, #17)
result in this case (sensitivity of 88.2 %) and two false-positives (#29,#40. 91.7% specificity). This
suggests that the use of more than two PDMs/ANFs ought to be explored for differentiation of
patients from controls.
Statistic Results of PDM 4 Gain Values
Mean Standard Deviation p-value:
Alzheimer’s Group 0.015 0.016 8.890e-07
Control Group -0.015 0.016
35
(A) (B)
(C) (D)
Figure 4.7: (A): Scatter-plot of computed ANF linear trends (slopes) for 2nd and 4th PDMs of the O1-to-F3
system, corresponding to the alpha-delta and theta-delta bands. Two false-negatives and two false-positives
are shown. (B) ROC curve for the scatter-plot (2nd versus 4th ANF/PDMs) of the O1-to-F3 system. (C):
Scatter-plot of computed ANF linear trends (slopes) for 1st and 4th PDMs of the O1-to-F3 system. One false-
positive and four false-negatives are shown. (D): Scatter-plot of computed ANF linear trends (slopes) for 3rd
and 4th PDMs of the O1-to-F3 system. One false-positive and three false-negatives are shown. The
classification line has been obtained by nonlinear regression algorithm (with 150 000 iterations).
Similarly, the combination of 1st and 4th PDMs and combination of 3rd and 4th PDMs also yield
satisfactory delineation between two groups. The differential capability of 4th PDM is also
demonstrated in Table 4.2 and its corresponding dynamics will be discussed in the later sections.
Table 4.2: Statistic Results of PDM 4 Gain Values of O1-to-F3 System
36
4.5 Discussions and Conclusions
We have presented a methodology for input-output modeling of the dynamic relationships between
EEG recordings in AD patients and control subjects that can be used for diagnostic delineation of
the two groups. The methodology is based on the concept of Principal Dynamic Modes (PDMs)
and their associated nonlinear functions (ANFs) that has been recently developed and applied
successfully to various physiological systems.
Preliminary results of the application of this methodology to data collected from 17 AD patients
and 24 control subjects offer considerable promise. Specifically, when the effective gain
coefficients of the 2nd and 4th PDMs (i.e. the slopes of the linear trends in their respective ANFs)
are used as classifiers for the O2-F3 system, we have one false-positve and two false-negatives (see
Fig.3.6 (A).) – i.e. 88.2% sensitivity and 95.8% specificity. Likewise, when the effective gain
coefficients of the 2nd and 4th PDMs are used as classifiers for the O1-F3 system, we have two
false-negatives and two false-positves (see Fig.4.7(A), i.e. 82.3% sensitivity and 91.7%
specificity). This suggests that the use of more than two PDMs/ANFs ought to be explored for
differentiation of patients from controls. The classification line is obtained through nonlinear
regression. The ROC curve also demonstrates promising performance of these classifiers (see
Fig.4.6(B), Fig.4.7(B)). The best classifiers for both O1-F3 and O2-F3 systems corresponded to
the PDMs with theta-delta spectral characteristics, consistent with previously reported observations
of increased theta and delta activity in the left hemispheric frontal region in AD patients
compared to control subjects, as well as decreased alpha activity in AD patients (Sankari et al,
Statistic Results of PDM 4 Gain Values
Mean Standard Deviation p-value:
Alzheimer’s Group 0.016 0.018 1.163e-05
Control Group -0.013 0.015
37
2011; Ponomareva et al, 2008; Adler et al, 2003). If these results become confirmed in larger
numbers of subjects, then the proposed approach will offer a valuable non-invasive diagnostic tool
for AD. These initial results are consistent with the current view that elevated theta activity in the
awake adult may indicate abnormal neurological conditions, and reduced alpha activity may reflect
(in part) a state of heightened anxiety in AD patients. We note, however, that our PDM-based
analysis yields classification features that concern the causal relation between two EEG signals
(e.g. O1 as a putative “input” and F3 as a putative “output”), while activity within a neural-rhythm
band concerns simply the spectral characteristics of the signals themselves.
Even though the coherence c(f) only captures linear interactions between signals, previous research
has suggested that it is strongly correlated with other commonly used synchronization measures
(Dauwels et al, 2010). However, there have been differences in the findings of previous studies
about how AD affects brain connectivity. This might be due to differences in the analyzed
populations, the heterogeneity of the disease and small differences in the connectivity metrics
Escudero et al, 2013. The use of PDM-based connectivity models addresses some of these issues
by extending the analysis of the data into the nonlinear domain and, more importantly, by focusing
on the dynamic relation between two EEG signals (measured at the frontal and occipital lobes in
this case) and not the temporal or spectral structure of the signals themselves. This distinction may
prove useful because it removes part of the potential ambiguity in differentiating patients from
controls by virtue of the fact that the employed "classification feature" (i.e. the slope of the ANFs
in this case) is independent of the particular neural activity that defines the spectro-temporal signal
structure at the time of data collection. In other words, the PDM-based approach focuses on the
system between the two signals and not on the signals themselves.
38
The findings of the PDM analysis imply that AD patients may have slower neural connectivity than
controls between the occipital and the frontal cortical regions, as suggested by the higher gains in
theta band and lower gains in alpha band. This is consistent with current views of the progressive
impairment of cortical connectivity in neurodegenerative diseases.
Although our sample size is insufficient to prove the clinical utility of the reported EEG analyses
for AD diagnosis, it is beneficial to relate our research to the current framework for AD diagnosis
in clinical practice and research (McKhann et al, 2011; Sperling et al, 2011). Current criteria
distinguish between the pathological process of AD and the observable symptoms caused by that
process (McKhann et al, 2011; Sperling et al, 2011). Whereas the clinical diagnosis of AD must be
performed using only the patient’s cognitive and behavioral symptoms (McKhann et al, 2011) , a
few biomarkers (magnetic resonance imaging, biochemical levels in the cerebrospinal fluid,
specific genetic factors and positron emission tomography) can increase or decrease the certainty
that clinical symptoms are due to an underlying AD pathology (McKhann et al, 2011; Sperling et
al, 2011). Although EEG is not currently included in such list of biomarkers, it provides a direct
measure of the brain activity. Furthermore, it is noninvasive and affordable. Therefore, it holds
promise to become, after suitable signal processing, a widely available method to support clinicians
in the diagnosis of the disease.
Our preliminary results are promising but they are inevitably affected by various sources of errors,
including the variability in physiological mechanisms and measurement instrumentation.
Therefore, these potential errors must be further examined in future studies. We must emphasize
that the sensitivity of parameter selection for model estimation is a critical issue for the
reproducibility of results in a clinical context and, therefore, it should be examined in future studies
with larger sample size and different clinical settings.
39
Another limitation of this study is that the average ages of the two subject groups were different.
However, the AD patients were recruited following standard clinical procedures and the dataset
have been used in a number of research studies (Henderson et al, 2006). Moreover, the probable
AD subjects had not previously been diagnosed (prior to the assessment at the memory clinic that
led to their referral to the EEG department). Thus, they were in the early stages of exhibiting clinical
symptoms. Finally, the subjects did not perform any task. Hence, the classification performance
might improve by analyzing signals acquired during specific experimental settings (Dauwels et al,
2010).
40
Chapter 5: Principal Dynamic Mode (PDM) Analysis of Hemodynamic
Signal for Assisting the Diagnosis of Alzheimer’s Disease
5.1 Introduction and Overview:
The possible impairment of autonomic activity in Alzheimer’s disease has been consistently
observed and studied by researchers and clinicians. Other common types of dementia including
vascular dementia, Lewy body dementia and Parkinson’s disease are also widely explored and
investigated. Many results have agreed on the altered autonomic nervous system (ANS) failure as
an important complication in neurological diseases.
The Autonomic Nervous System (ANS), composed of sympathetic and parasympathetic (vagal)
division, controls internal organs unconsciously and regulates body functions including heart rate,
respiratory rate and digestion. Through the interplay of sympathetic and parasympatheic (vagal)
outflows, the ANS is mainly responsible for the neural regulation of circulatory function within the
brain. Therefore, the ANS, characterized by sympathetic and vagal modulation, is considered to be
one of the potent factors that affect the vascular function from outside of vessels and its dysfunction
has been seen as a risk factor for atherosclerosis (Amiya et al, 2014). Algotsson A performed a
number of tests measuring the parasympathetic and sympathetic functions in Alzheimer’s patients
and control subjects, and suggests autonomic dysfunction affecting parasympathetic, as well as
vasomotor sympathetic functions in AD patients (Algotsson et al, 1995). In the study of Benedetto
Vitiello, the analysis of hemodynamic signals including blood pressure, pulse and plasma
epinephrine indicates that sympathetic response is functionally impaired in Alzheimer’s patients,
and becomes especially evident when AD is accompanied by depression (Vitiello et al, 1993). The
possible correlation between autonomic cardiac activity and the level of
acetylcholinesterase(AChE) is examined by F Giubilei(Giubilei et al, 1998), who hypothesizes that
41
the autonomic dysfunction in AD patients might be due to cholinegic deficit in the peripheral
autonomic nervous system.
In the present study, we focus on the modeling and analysis of the possible causal relationship
between cerebral hemodynamic recordings in order to generate model-based indices to assess the
cerebral metabolism of Alzheimer’s patients. The causality relationship between signals is
modelled via Volterra modeling approach using Laguerre expansions of the kernels and the featured
dynamics is then represented by the Principal Dynamic Modes (PDM) (V.Z.Marmarelis, 2004).
By using linear model in this study, we were able to limit the number of parameters significantly
and result with reliable estimation under the low SNR condition. This linear modeling approach
yields with diagnostic indices which are much simpler in computation as compared to their
counterparts in nonlinear modeling, and shows differential potential to diagnose AD patients from
control subjects. The results to date further corroborates the potential and feasibility of PDM-based
modeling approach, which is proven to be compatible for clinical applications on both nonlinear
and linear modeling systems, as to make it practicable to fit different types of physiological
systems.
5.2 Methodology
5.2.1 Data Collection and Pre-processing
This study involves 13 control subjects and 17 Alzheimer’s patients who voluntarily participated
and signed the Informed Consent Form according to institutional guidelines. Finger arterial blood
pressure (ABP) is measured with Finapres, cerebral blood flow velocity in the middle cerebral
artery (MCA) is measured with Transcranial Doppler and end-tidal CO2 (ETCO2) is collected by
capnography. For each subject, continuous signals of 5 minutes were simultaneously recorded. The
42
data was then clipped using +-3RMS for outlier removal. Data interpolation is performed with
sampling frequency at 2Hz. The signals were then demeaned and high-passed using Hanning
window (+-60sec) to get rid of low frequency noise component. After subtracting the low-
frequency noise the data is clipped by +-3RMS. Fig.5.1 shows representative examples of pre-
processed signals of one Alzheimer’s patient and one control subject.
Figure 5.1: Illustrative time-series data over 5 min of representative AD patient #6(left) and representative
control subject #11(right).
5.2.2 Linear Modeling Methodology
We analyze the causal relationship between hemodynamic signals through linear Volterra modeling
approach. In the previous Alzheimer’s study, Global PDMs have proven to be an effective basis
set for representing system characteristic dynamics. Therefore, we employ the same modeling PDM
modeling concept in the case of Type 2 diabetes study. We start with single-input-single-output
linear modeling (1st order Volterra kernel only), where the blood pressure is taken as input and
cerebral blood flow velocity as the output. The global PDMs of these cohorts are computed via
SVD of a rectangular matrix that contains all the 1st order kernels from control subjects only.
It should be noted that we perform SVD on the kernel matrix that includes kernels of control
subjects only. By including the controls’ kernels only we expect the resulting PDMs to represent
dynamics occurred under physiological state without specific pathology, so as to make it a
standardized and stable reference to compare patients group versus control subjects. With the linear
43
Volterra modeling approach based on Laguerre expansion technique, we are able to reduce model
complexity and limit the number of free parameters. The estimated linear coefficients are used as
diagnostic indices directly relate to corresponding PDM dynamics. A detailed description of this
methodology is given in the monograph (V.Z.Marmarelis, 2004). We summarize below the
methodology of PDM-based modeling. The 1st order (linear) single-input-single-output Volterra
model is:
(5.1)
where
- x(n) is the input (blood pressure)signal
- y(n) is the output(cerebral blood flow velocity) signal
- {k 0, k 1} are the zeroth order kernel (constant) and the first order kernel respectively
- M is the system memory (M=60 here)
To limit the number of free parameters that must be estimated, the kernels are expanded onto a
basis of orthonormal discrete Laguerre functions {𝑏 𝑗 } (𝑗 = 1,2 … 𝐿 ). In this case, 3 discrete
Laguerre functions with Laguerre parameter 0.4 (L = 3 , α = 0.4) are found to be adequate to
represent the input-output dynamic relations. The optimal value of the Laguerre parameter α is
determined through a global search procedure that minimizes the averaged normalized mean square
error (NMSE) of the model prediction for all subjects (Fig.5.2).
1
0
1 0
M
m
) m n ( x ) m ( k k ) n ( y
44
Figure 5.2: Averaged Normalized Mean Square Error( NMSE) for 30 subjects. The global minimum NMSE
is searched for α ranging from 0.2 to 0.8. Parameter α yields low NMSE are highlighted with red circle (α =
0.4)
The selected values of alpha and L determine the system memory (M=60 samples in this case).
After Laguerre expansion, the linear model is given by the expression:
(5.2)
where
(5.3)
The 4 expansion coefficients (c0, c1) are estimated by the ordinary least-squares method and the
1st order kernel estimate is given by the expression:
(5.4)
L
j
j
n V j c c ) n ( y
1
1 0
1
0
M
m
j j
m n x m b n V
m b ) j ( c m k
j
L
j 1
1
1
1 1 1
45
This model has only 4 free parameters, as compared to 61 free parameters for the original linear
Volterra model.The PDM-based modeling approach seeks to find the “minimum set” of basis
functions (the "global" PDMs) that are able to represent the input-output dynamics adequately for
each particular system. As discussed previously, this is achieved via SVD of a rectangular matrix
composed of the estimated Volterra kernels of the controls subjects only.
The global PDMs are determined as the significant singular vectors of the kernel-based matrix that
correspond to singular values satisfying a specified selection criterion (e.g. at least 5% of the
maximum singular value). The physiological characteristics of these global PDMs will be discussed
in the following section. The global PDMs are used to describe the dynamics of this system (via
expansions of the system kernels) for control subjects, which are expected to be stable and reliable.
The respective linear coefficients are then computed through least-square estimation, which are
subject-specific and can be used for diagnostic purposes. Fig.5.3 shows a schematic block-diagram
of the PDM-based model.
Figure 5.3: Block-diagram of the PDM-based model of the ABP-MCAL system with 3 global PDMs. 𝑐 𝑗 is
the least square estimation of linear coefficient of the jth PDM j.
As shown by the block-diagram, the output equation for the PDM-based model is represented as:
46
𝑦 (𝑛 ) = ∑ 𝑐 𝑖 𝐻 𝑖 =1
{∑ 𝑝 𝑖 (𝑚 )𝑥 (𝑛 − 𝑚 )
𝑀 −1
𝑚 =0
} (5.5)
where
- 𝑝 𝑖 is the i th global PDM
- H is the number of global PDMs (H<=L)
- c i is the linear coefficient of the i th PDM
The linear coefficient is an "effective gain constant" for the respective PDM and can be used as an
index for delineating Alzheimer’s disease patients from control subjects.
5.3 Results
The predictive capability of the obtained PDM-based model is assessed by the Normalized Mean
Square Error (NMSE) of the respective model prediction. The averaged NMSE for the linear model
of the ABP-to-MCAL system is 61.3%. It is evident that the model prediction only accounts for a
small portion of the output signal, but this should be expected in a system of such low signal-to-
noise ratio.
Three Global PDMs for the ABP-to-MCAL model were obtained, and their time-domain and
frequency-domain representation were showed respectively in Fig.5.4. In the frequency domain
(Fig.5.4: right), the global PDMs exhibit spectral characteristics that correspond to the following
resonance peaks, and their physiological implications will be further discussed in the “Discussion
and Conclusion” section.
- 1st PDM (blue): resonance peak at 0.18Hz
- 2nd PDM (red): resonance peak at 0.1 Hz
47
- 3rd PDM (green): resonance peak at low-frequency (<0.05Hz)
Figure 5.4: Time-domain representations (left) and frequency-domain representations (right) of the global
PDMs of the input-output model for the ABP-to-MCAL system.
It was found that the 1st and 2nd PDMs (Fig.5.4: red and blue plots) and their linear coefficients
reveal differentiating capability between patients and controls for ABP-MCAL system, as shown
in the scatter-plot of Fig.5.5. Three false negative and two false positives where misclassified with
sensitivity of 82.3 % and specificity of 84.6 %. The 1st and 2nd PDMs/linear coefficients
correspond to the resonance peaks at 0.18Hz and 0.1Hz respectively. For each Global PDM, the
statistics of the linear coefficient values (diagnostic indices) are computed and the corresponding
significance level is assessed by p-value. (Table 5.1)
48
Figure 5.5: Left: Scatter-plot of computed linear coefficients (diagnostic indices) for 1st and 2nd PDMs of
the ABP-to-MCAL system, corresponding to the 0.1Hz and 0.18 Hz. Three false-negatives and two false-
positives are shown. Right: frequency-domain representations of the 1st and 2nd Global PDMs of the input-
output model for the ABP-to-MCAL system.
Table 5.1: Statistic Results of PDM Gain Values of ABP-to-MCAL System
5.4 Discussion and Conclusion
The use of PDM-based models addresses the connectivity issues by focusing on the dynamic
relation between hemodynamic signals (arterial blood pressure and cerebral blood flow velocity in
this case) and not the temporal or spectral structure of the signals themselves. This distinction may
prove useful because it removes part of the potential ambiguity in differentiating patients from
controls by virtue of the fact that the employed "classification feature" (i.e. the linear coefficient
this case) is independent of the local vascular activity that defines at the time of data collection. In
other words, the PDM-based approach focuses on the system between the two signals and not on
the signals themselves.
Previous studies have explored the ANS functioning in the frequency domain through power
spectral analysis approach and wavelets analysis, including rhythm oscillations of hemodynamic
Statistic Results of PDM 1 Gain Values
Mean Standard Deviation p-value:
Alzheimer’s Group 0.44 0.18 0.037
Control Group 0.59 0.19
Statistic Results of PDM 2 Gain Values
Mean Standard Deviation p-value:
Alzheimer’s Group -0.03 0.08 0.17
Control Group 0.007 0.07
Statistic Results of PDM 3 Gain Values
Mean Standard Deviation p-value:
Alzheimer’s Group -0.005 0.04 0.7
Control Group 0.001 0.05
49
signals such as arterial blood pressure, RR interval variability and heart rate variability. A LF
component with center frequency of approximately 0.1 ±0.02 Hz (i.e. the Mayer waves in humans)
is widely hypothesized to be caused by sympathetic activity(Amiya et al, 2014; Furlan et al ,2000;
Julien, 2006; Algotsson et al, 1995;), whereas a HF component with center frequency of
approximately 0.27±0.02 Hz is commonly interpreted as an index of the parasympathetic tone.(
Amiya et al, 2014; Algotsson et al, 1995; Perini et al, 2006).
In the preliminary results of this methodology to data collected from 17 AD patients and 13 control
subjects , the effective gain coefficients of the 1st and 2nd PDMs (i.e. the linear coefficients) are
used as classifiers and yield 82.3% sensitivity and 84.6% specificity(see Fig.5.5). The classifiers
for ABP-MCAL systems correspond to the PDMs with resonance peaks at 0.1Hz and 0.18Hz
respetively, which are consistent with the resonance rhythms agreed by the current view for
sympathetic and vagal modulation rhythms. Therefore, in the specific case of this study, the
0.1Hz(PDM2 ) is hypothezied as the marker of sympathetic modulations and 0.18Hz (PDM1) as
the marker of vagal modulations. If these associations become confirmed in larger numbers of
subjects, then the model-based PDMs and corresponding diagnostic indices will offer a valuable
non-invasive diagnostic tool for AD patients.
We note that in the classification plot (Fig.5.5), the Alzheimer’s patients possess lower values in
both PDM 2 (0.1Hz) and PDM 1(0.18Hz) gains. This indicates possible impairment of
autonomic nervous system, characterized by the attenuation in both sympathetic and vagal
modulations, might associate with the Alzheimer’s disease pathology. This hypothesis agrees with
the observations reported in previous studies of Alzheimer’s disease (Vitiello et al, 1993). One
possible mechanism is demonstrated by F Giubilei, who studies the possible correlation between
autonomic cardiac activity and the level of acetylcholinesterase (AChE) , and hypothesizes that the
50
autonomic dysfunction in AD patients might be due to cholinergic deficit in the peripheral
autonomic nervous system.
It should be noted that our PDM-based analysis yields classification features that concern the causal
relation between two hemodynamic signals (e.g. blood pressure as a putative “input” and cerebral
blood flow velocity as a putative “output”), while previous studies concern the spectral
characteristics of the signals themselves (e.g Power spectral analysis of Heart Rate Variability,
Respiratory Rate Interval, and Systolic Arterial Pressure (SAP) Variability Signal).
51
Chapter 6: Model-based Indices of Cerebral Hemodynamics as
Diagnostic Markers in Type 2 Diabetes Mellitus
6.1 Introduction and Overview:
The prevalence of Type 2 diabetes has been increased markedly in worldwide range with growing
clinical significance. Because Type 2 diabetes is characterized by the body’s inability to regulate
blood glucose properly, conventional research efforts have been focused on the body’s insulin
deficiency and insulin resistance which are directly involved in the regulation mechanism of blood
sugar. However, due to the damage to blood vessel, long-term health complications including
cardiovascular disease and small vessel diseases, such as hypertension, stroke and neuropathy, have
been widely and consistently observed in the cases of Type 2 diabetes, and eventually become the
leading lethal factors for the diabetic population (e.g. 75% of deaths in diabetes are due to the
coronary artery disease (O’Gara et al, 2013). These clinical observations therefore offer an
alternative perspective for researchers and clinicians to explore the pathophysiology of Type 2
diabetes. A growing number of studies have investigated the disease through analysis of
hemodynamic signals including heart rate variability, respiratory rate variability, systolic blood
pressure, and end-tidal carbon dioxide (CO2, based on the notion that Type 2 diabetes syndrome
may correlate with impaired physiology activities upon the blood vessel and the corresponding
control systems (Iellamo et al, 2006; Lindmark et al, 2003; V.Z.Marmarelis, 2004; Thayer et al,
2010). Specifically, the autonomic nervous system, which controls respiration, cardiac regulation,
vasomotor activity and other reflex actions, has been previously hypothesized to associate with
diabetes pathological conditions. Other studies also examine the local mechanisms of blood flow
control, and state the possible impairment in endothelial functions in Type 2 diabetes patients,
which alters the regulation in basal vascular tone and vascular reactivity.
52
Diverse measurements and approaches are applied to study hemodynamic features in Type 2
diabetes, including flow-mediated endothelium-dependent and –independent vasodilation of artery
(Iellamo et al, 2006) and plasma levels of cellular adhesion molecules (CAMs) (Meigs et al, 2004).
In the frequency domain, spectral features of heart rate (HR) and systolic blood pressure (SBP)
variability are examined as possible biomarker for Type 2 diabetes (Iellamo et al, 2006). Through
the calculation of spectral powers and associated spectral power ratio (low frequency(LF)/high
frequency(HF) spectral power ratio), Thayer has demonstrated that altered balance of the
autonomic nervous activity might contribute to the development of insulin resistance and Type 2
diabetes( Thayer et al, 2010). These observations corroborate the possible associations between
Type 2 diabetes and vascular controlling and functioning.
The incidence of Type 2 diabetes mellitus (T2DM) has increased markedly worldwide in recent
years and has caused intense concern because of its wide-ranging clinical implications. T2DM is
characterized by the inability to regulate blood glucose properly, with detrimental chronic effects
on small-vessel dysfunction and cardiovascular disease. Most research efforts to date have focused
on the issues of insulin deficiency and insulin resistance, which are directly involved in the
regulation of blood glucose [Smyth, & Heron 2006; Weyer et al. 2001]. Due to the damage caused
by T2DM to small blood vessels, long-term health complications of T2DM include hypertension,
stroke, retinopathy, nephropathy and neuropathy. T2DM is associated with serious cardiovascular
morbidity (e.g. 75% of deaths in diabetes are due to coronary artery disease [O’Gara et al. 2013]).
These clinical facts have motivated the intense study of the cardiovascular effects of T2DM.
Several studies have investigated the cardiovascular effects of T2DM through analysis of
hemodynamic signals including blood pressure and flow, heart rate, respiratory rate, and end-tidal
CO2, based on the notion that the T2DM syndrome may correlate with impaired physiology in the
blood vessels and the associated regulatory mechanisms, primarily related with the autonomic
53
nervous system and neurovascular coupling [Thayer et al. 2010; Iellamo et al. 2006; Lindmark et
al. 2003]. Some studies have also examined the possible impairment of endothelial function in
T2DM patients, which alters the regulation of blood flow via flow-mediated endothelium-
dependent and endothelium-independent vasodilation [Iellamo et al. 2006] and plasma levels of
cellular adhesion molecules [Meigs et al. 2004]. Spectral features of heart rate and systolic blood
pressure variability were also examined as possible markers for T2DM [Iellamo et al. 2006].
Finally, the spectral power ratio that reflects the balance of the sympathetic/parasympathetic
autonomic activity has been associated with the development of insulin resistance and T2DM
[Thayer et al. 2010].
In the present study, we focus on the analysis of dynamic relationships between beat-to-beat
spontaneous variations of measured arterial blood pressure (ABP) and/or end-tidal CO2 (ETCO2),
viewed as two concurrent inputs, and cerebral blood flow velocity (CBFV) viewed as the
corresponding output signal, under resting conditions. The latter is measured via Transcranial
Doppler (TCD), a non-invasive and comfortable measurement. These dynamic relationships are
quantified by predictive input-output models using the method of Principal Dynamic Modes
(PDMs) pioneered by our lab [Marmarelis 2004]. Key parameters of the estimated models and
model-based indices of cerebral hemodynamic function (e.g. dynamic cerebral autoregulation and
CO2 dynamic vasomotor reactivity) are explored as markers that may differentiate T2DM patients
from age-matched control subjects in order to assist clinical diagnosis of T2DM and monitoring of
disease progression. The presented results indicate that the marker of dynamic CO2 vasomotor
reactivity has potential diagnostic utility because it quantifies a key aspect of cerebro-vascular
function and was found to be reduced in T2DM patients.
54
6.2 Data Collection and Pre-processing
Three channels of hemodynamic signals are measured: finger arterial blood pressure (ABP) is
measured with Finapres, cerebral blood flow velocity in the middle cerebral artery (left branch :
MCAL; right branch: MCAR) is measured with Transcranial Doppler and end-tidal CO2 (ETCO2)
is collected by capnography. Data were obtained from subjects at sitting position with frequency
of 1kHz. For each subject, continuous signals of 5 to 6 minutes were simultaneously recorded.
Fig.6.1 shows representative examples of the raw data from representative diabetes patient and
control subject.
Figure 6.1: Illustrative time-series data over 5 min of representative diabetes patients #790527 (left) and
representative control subject #790064(right).
To remove oscillation components due to noise, the signal is smoothed through moving-average
approach (±10 samples). For ABP and MCAL, the mean value is computed over each cardia cycle
(~1sec) as the beat-to-beat data, and for ETCO2 the maximum value is selected over each
respiratory interval as the breath-to-breath data. Fig.6.2 illustrates the pre-processed data samples
of this step:
55
Figure 6.2: Representative example of data pre-processing. Left: Arterial Blood Pressure. Middle: Cerebral
Blood Flow Velocity. Right: End-tidal CO2. Signals between red circles represent each cardiac cycle for
ABP and MCAL (left and middle), and each breath interval for ETCO2 respectively (right). Blue circles
represent the mean values over each cardiac cycle (i.e. beat-to-beat data) for ABP and MCAL, and the plateau
values over each breath interval (i.e. breath-to-breath data) for ETCO2.
In this specific dataset, artifacts due to measurement/calibration issue are carried by the data
recordings along with the real physiological oscillations (Fig.6.3). The length of artifact varies from
2s to 7s depending on individuals, therefore specific interpolation approach should be examined to
address the issue, as to maintain signal integrity and avoid spurious results.
56
Figure 6.3: Top panel: illustrative example of blood pressure signal artifacts in the raw data. Bottom panel:
zoom in on artifacts in pre-processed time-series signal.
Interpolation Simulation on Signal with artifacts:
Cubic spline interpolation is commonly used as an effective technique for signal analysis. However,
for this specific dataset where the signal carries periods of measurement artifacts (over several
seconds), the intrinsic polynomial form( called the ‘spline’) of cubic spline may lead to augemented
artifacts when interpolating through data samples. Taken this into consideration, we propose an
approach based on the original cubic spline interpolation, and perform linear interpolation on the
segments where the artifacts/signal loss occurred.
The feasiblity and effectiveness of this interpolation method is assessed through linear input-output
modeling based on Laguerre expansion, using Gaussian white noise (GWN) as the input signal. For
each input signal with simulated signal loss (over a few seconds), we compare the NMSE of model
57
estimation with proposed method and with conventional cubic spline interpolation .The linear
model used for simulation is given by the following expression:
(6.1)
where
(6.2)
Five discrete Laguerre functions with Laguerre parameter 0.5 (L = 5 , α = 0.5) are set to represent
the input-output dynamic relations, with linear coefficient (c1-j) set to c = [3,2,1,-1,0.5]. A
representative input GWN signal and the model-based output signal are shown as following:
Figure 6.4: Illustrative Example of GWN Input Signal and Simulated Output Signal
L
j
j
n V j c c ) n ( y
1
1 0
1
0
M
m
j j
m n x m b n V
58
Now that the input and output signals with their linear Volterra model are known to us, a certain
lengths of segment (3s/5s/8s) is cut off from the input signal to simulate the artifacts in real datasets.
We then apply both interpolation methods to recover the original input signal:
1) Cubic spline interpolation on entire signal, with sampling frequency = 2Hz
2) Linear interpolation on cut-off segment and cubic spline interpolation elsewhere, with
sampling frequency = 2Hz
The following plots show examples on the interpolated signals based on two approaches
respectively. It is observed that the original cubic interpolation approach is likely to augment the
artifact in this specific dataset due to its dependency on the gradients at both ends of the cut-off
segment. (Fig. 6.5: top panel, curve shape in green)
59
Figure 6.5: Input signal interpolation simulation with 8-seconds segment cut off. Top panel: Gaussian white
noise signal with cubic spline interpolation. Bottom panel: Gaussian white noise signal with cubic spline
interpolation and linear interpolation for cut-off segment. Red box highlights the cut-off signal segment
(signal value set to 0 in the simulated cut-off signal).
The resulting interpolated signal (input signal) is then applied into the linear model for output signal
estimation. Fig.6.6 offers visual comparison of impulse response function (IRF) with the model
estimation IRF. The squared estimation error of Laguerre function linear coefficients c1-j, as well
as NMSE are given in Table 6.1:
60
Table 6.1: Average Square Deviation and Normalized Mean Square Error (NMSE) for Simulation Model
Cubic Spline
Interpolation
Linear Interpolation with Cubic Spline
Interpolation
Average NMSE 1.3e-05 7.92e-06
Average Square
Deviation of c1-j
0.024
0.017
Figure 6.6: Impulse response function estimation simulation with 8 sec signal cut off. Left: Gaussian white
noise signal with cubic spline interpolation. Right: Gaussian white noise signal with cubic spline interpolation
and linear interpolation for cut-off segment.
Comparing to conventional cubic spline method, the interpolation approach that combines cubic
spline and linear interpolation preserves the signal integrity and system dynamics (as shown by
estimated IRF and Laguerre function linear coefficients) , enabling reliable modeling estimation of
input-output system(i.e. NMSE). The ABP, MCAL and ETCO2 are interpolated with sampling
frequency at 4 Hz and demeaned. Fig.6.7 shows representative examples of the pre-processed
dataset.
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Figure 6.7: Illustrative time-series data over 150 sec of hemodynamic signals of representative diabetes
patients (left) and control subject (right).
6.3 Modeling Methodology and Results:
A. Data Collection and Pre-processing
Time-series data were collected over 5 minutes under resting conditions at sitting position with
sampling frequency of 1 kHz from 12 patients with T2DM but without cognitive impairment (75%
male; average age: 62.55±10.07 years), and 5 control subjects without T2DM, hypertension or
cognitive impairment (60% male; average age: 63.89±9.82 years) in the laboratory of Dr. Vera
Novak at Harvard University, Beth-Israel DMC. For each subject, three signals were recorded:
arterial blood pressure (ABP) with Finapres at the finger (in mmHg), cerebral blood flow velocity
(CBFV) with Transcranial Doppler (TCD) at the middle cerebral artery (in cm/sec), and end-tidal
CO2 (ETCO2) via a nasal cannula of capnography (in mmHg).
The recorded data of ABP and CBFV were reduced to beat-to-beat data by computing the average
value over each R-R interval. The data were subsequently resampled every 0.25 sec using cubic
spline interpolation. The ETCO2 value for each breath was found and the time-series data were
resampled at 0.25 sec using cubic spline interpolation. Outliers from occasional artifacts in each
dataset were clipped at +/- 25% of the respective average value. The signals were de-meaned and
high-pass filtered with cut-off frequency of 0.008 Hz using a Hanning window. Fig.6.8 shows
illustrative pre-processed data.
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Figure 6.8: Illustrative pre-processed time-series data over 5 min for a representative control subject. Top:
Arterial Blood Pressure (ABP) in mmHg, middle: end-tidal CO2 (ETCO2) in mmHg, and bottom: cerebral
blood flow velocity (CBFV) in cm/sec. The pre-processed signals are de-meaned and high-pass filtered above
0.008 Hz.
B. Modeling Methodology:
In this study, we use the novel method of Principal Dynamic Modes (PDMs) that has been
pioneered by our lab [Marmarelis 2004] in order to extract predictive dynamic models with two
inputs (ABP and ETCO2) and one output (CBFV) from the beat-to-beat data over 5 min. This
methodology has been applied to several physiological domains over the last 20 years and
particularly to cerebral hemodynamics [Marmarelis et al. 2013, 2014, 2015, 2016, 2017; Hajjar et
al. 2014]. In this approach, we seek to determine a set of basis functions (the PDMs) for the efficient
representation of the system kernels that define the predictive dynamic input-output model (linear
or nonlinear). The specifics of this methodology are summarized in the Appendix for the linear
case of the application at hand. A block diagram of the subject-specific PDM-based model is shown
in Fig.6.9, where the PDMs represent a characteristic set of filters for each input that are estimated
from the data and are common for all subjects in the study cohort. In addition to the PDMs, the
linear PDM-based model contains subject-specific gain coefficients, or simply “Gains”, that
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quantify the relative contribution of each PDM to the model CBFV output prediction for each
subject. These Gains constitute a vector of values characteristic for each subject.
Figure 6.9: Block-diagram of the linear PDM-based model of the ABP/ETCO2-CBFV system with 4 global
PDMs for each input. The output 𝑢 𝑖 ,𝑗 of the ith PDM 𝑝 𝑖 is the convolution of the PDM with the jth input
signal. The linear coefficients 𝑐 𝑖 ,𝑗 of the ith PDM 𝑝 𝑖 (Gains) are computed through linear regression (see
Appendix).
6.4 Results
The PDM-based model prediction had an average Normalized Mean-Square Error (NMSE) of 54%
over the cohort. Illustrative traces of the model prediction and its two components generated by the
ABP and the ETCO2 inputs are shown in Fig.6.10, along with the actual output CBFV signal. We
observe that rapid variations of the CBFV output are due to variations of the ABP input, while the
ETCO2 input contributes slower variations to the CBFV output. Upon estimation of the Volterra
kernels of the model for each subject, the “global” PDMs for each input are extracted through
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Singular Value Decomposition of the rectangular matrix that contains all the estimated 1st-order
kernels of the control subjects as column vectors (see Appendix). The global PDMs are selected
by applying a threshold criterion on the computed singular values and constitute an orthogonal
basis for the kernels of all subjects.
Figure 6.10: Illustrative traces of the model prediction (blue) and its two components generated by the ABP
input (red) and the ETCO2 input (green) versus the actual output CBFV signal (black) for a control subject.
The obtained global PDMs for this cohort of control subjects are shown in Fig.6.11 for the ABP-
to-CBFV dynamic relationship and in Fig.6.12 for the ETCO2-to-CBFV dynamic relationship in
the dual-input model. The left panels show the global PDMs in the time domain (akin to Impulse
Response Functions of a filter-bank) and the right panels show their frequency-domain counterparts
(magnitude of FFT). The frequency-domain representations of the three global PDMs for the ABP-
to-CBFV dynamic relationship exhibit distinct spectral characteristics with the following resonant
peaks:
- 1st PDM (blue): high-pass characteristic (traditional Windkessel cerebrovascular model)
- 2nd PDM (red): resonance peak around 0.2Hz
- 3rd PDM (green): resonance peak around 0.1 Hz
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- 4th PDM (black): low-pass characteristic
Figure 6.11: Time-domain (left) and frequency-domain (right) representations of the four global PDMs for
the ABP-to-CBFV dynamic relationship in the dual-input model.
The computed Gains for the contributions of the various ABP-PDMs to the model-predicted CBFV
output are shown in Table 6.2 and indicate statistically significant difference between T2DM
patients and controls for the Gains of ABP-PDM4 (p=0.006) and the Gains of ABP-PDM3
(p=0.029).
Table 6.2: Mean (SD) values of ABP-PDM Gains for T2DM patients and controls, and corresponding p-
values.
ABP-PDM1 ABP-PDM2 ABP-PDM3 ABP-PDM4
T2DM 0.368(0.124) -0.023(0.073) 0.038(0.036) -0.034(0.034)
Controls 0.326(0.179) 0.037(0.118) -0.003(0.028) 0.001(0.008)
p-value 0.655 0.333 0.029 0.006
The global PDMs for the ETCO2-to-CBFV dynamic relationship (shown in Fig.6.12) also exhibit
distinct spectral characteristics, the physiological interpretation of which requires future study (see
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Discussion). We note that the Gains of the original 1st and 3rd PDMs obtained from SVD of the
kernel matrix had p-values just over 0.05 in differentiating between patients and controls,
motivating an orthogonality-preserving rotation in order to explore better differentiation between
patients and controls. Indeed this was achieved for the 1st PDM (p=0.009) and the PDMs shown
in Fig.6.12 include the rotated 1st and 3rd PDMs. The 1st ETCO2-PDM (blue) exhibits a
frequency-response characteristic with a resonant peak around 0.04 Hz. The 2nd PDM (red)
exhibits a resonant peak around 0.03Hz. The 3rd PDM (green) exhibits a low-pass frequency-
response characteristic. The 4th PDM (black) has a resonant peak around 0.035 Hz. These resonant
peaks at 0.03-0.04 Hz may be associated with the chemoreflex loop. The computed Gains for the
contributions of the various ETCO2-PDMs to the model-predicted CBFV output are shown in
Table 6.3 and indicate statistically significant difference between T2DM patients and controls for
the Gains of ETCO2-PDM1(p= 0.009), suggesting possible impairment of the chemoreflex loop
gain in T2DM (see Discussion).
Figure 6.12: Time-domain (left) and frequency-domain (right) representations of the four global PDMs for
the ETCO2-to-CBFV dynamic relationship in the dual-input model.
Table 6.3: Mean (SD) values of ETCO2-PDM Gains for T2DM patients and controls, and corresponding p-
values.
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ETCO2-PDM1 ETCO2-PDM2 ETCO2-PDM3 ETCO2-PDM4
T2DM -0.075(0.137) 0.032(0.123 0.050(0.151) -0.029(0.121)
Controls 0.059(0.045) 0.019(0.053) 0.124(0.095) -0.003(0.007)
p-value 0.009 0.753 0.250 0.466
Scatter-plots of the obtained Gains for ETCO2-PDM1 (the most differentiating of ETCO2-PDMs)
versus the Gains for ABP-PDM4 (the most differentiating of the ABP-PDMs) and the Gains for
ABP-PDM3 (the second most differentiating of the ABP-PDMs) are shown in Fig.6.13, for the 12
T2DM patients (red circles) and 5 controls (blue stars). Visual inspection of these scatter-plots
reveals excellent differentiating capability between T2DM patients and control subjects based on
these pair-Gain combinations, illustrated in Fig.6.13 by the drawn boundary line that corresponds
to two potential “composite markers” with smaller p-values.
Figure 6.13: Scatter-plots of obtained Gains for the contributions to the model-predicted CBFV output of the
1st ETCO2-PDM versus the 3rd ABP-PDM (left) and versus the 4th ABP-PDM (right). The linear
combinations of these Gain pairs corresponding to the drawn line represent potential “composite indices”
that yield smaller p-values.
The classification line in Fig.6.13 (left) is obtained through nonlinear regression algorithm and is
expressed as:
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y = 1.134 ∗ x + 0.019 (6.1)
where x represents gain values of ABP PDM3 (horizontal axis) and y represents gain values of
CO2 PDM1(vertical axis) . The “Composite Gains” (CG) for each individual is therefore computed
as the linear combination of the two gain values according to Eq.(1), as:
𝐶𝐺 =
(y−1.134∗x)
0.019
− 1 (6.2)
The resulting Composite Gains, combining the two gain values from each input, offer promising
classification capability between T2DM and control groups (Table 6.4). Similarly, the Composite
Gains using ETCO2-PDM1 and ABP-PDM4 (Figure 6, right) reveal significant differences
between groups (Table 6.5)
Table 6.4: Mean (SD) values of estimated Composite Gains(ABP-PDM3, ETCO2-PDM1) for T2DM patients
and controls, and corresponding p-values.
Composite Gains
T2DM -7.091(7.223)
Controls 2.236(2.562)
p-value 0.001
Table 6.5: Mean (SD) values of estimated Composite Gains (ABP-PDM4, ETCO2-PDM1) for T2DM
patients and controls, and corresponding p-values.
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Composite Gains
T2DM -4.144(4.905)
Controls 1.008(1.471)
p-value 0.005
The average model-predicted CBFV responses to an ABP input impulse (i.e. the kernels of the
ABP-to-CBFV dynamic relationship) are shown in the top panels of Fig.6.14 for the 12 T2DM
patients (left) and 5 controls (right), along with the model-predicted CBFV responses to a 5-sec
unit-pulse ABP input shown at the bottom panels. There is no clearly discernible difference in the
ABP-to-CBFV kernels or pulse responses between patients and controls, even though there is a
statistically significant difference in the Gains of the 3rd and 4th ABP-PDMs (see Table 6.7).
Figure 6.14: The average kernel estimates and SD bounds (top panels) of the ABP-to-CBFV dynamic
relationship for the 12 T2DM patients (left) and the 5 control subjects (right), as well as the model-predicted
average response to an ABP input pulse over 5 sec (bottom panels).
For the ETCO2 input, the average model-predicted CBFV responses to an impulse (top) and 5-sec
unit pulse (bottom) of the ETCO2 input are shown in Fig.6.15 for patients (left) and controls (right).
We observe a clear difference in the responses of the patients relative to controls, whereby the early
portion of the patient average response is smaller (or negative). This is consistent with the negative
average Gain of ETCO2-PDM1 for the patients (see Table 6.3).
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Figure 6.15: The average kernel estimates and SD bounds (top panels) of the ETCO2-to-CBFV dynamic
relationship for the 12 T2DM patients (left) and the 5 control subjects (right), as well as the model-predicted
average response to an ABP input pulse over 5 sec (bottom panels).
The model-predicted CBFV responses to the 5-sec unit-pulse ETCO2 or ABP input (shown in the
bottom panels of Fig.6.14 and Fig.6.15) can be used to compute indices of Dynamic Vasomotor
Reactivity (DVR) and Dynamic Cerebral Autoregulation (DCA), respectively. The DVR index is
defined as the time-average of the model-predicted CBFV response over 5 sec of ETCO2 unit-
pulse. The resulting mean (SD) values of DVR for the 12 T2DM patients and 5 controls are shown
in Table 6.6, indicating a statistically significant difference in DVR between patients and controls
(p=0.003). This is the main finding of our study, which indicates significantly reduced Dynamic
Vasomotor Reactivity in T2DM patients relative to controls. This may be due to impaired
cerebrovascular regulation in T2DM (see Discussion).
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Table 6.6: Mean (SD) values of DVR indices for T2DM patients and controls, and corresponding p-value.
DVR index
T2DM -0.158(0.264)
Controls 0.143(0.09)
p-value 0.003
The DCA index is defined as the difference between the peak value of the model-predicted CBFV
response over 5 sec of ABP unit-pulse minus the CBFV value at 5 sec, normalized by the peak
value. This is a measure of the proportional autoregulatory reduction of the peak CBFV response
to a unit-pulse increase of ABP. The resulting mean (SD) values of DCA for the 12 T2DM patients
and 5 controls are shown in Table 6.7, indicating no statistically significant difference in DCA
between patients and controls (p=0.352).
Table 6.7: Mean (SD) values of DCA indices for T2DM patients and controls, and corresponding p-value.
DCA index
T2DM 0.895(0.229)
Controls 0.770(0.238)
p-value 0.352
6.5 Conclusions and Discussions
We propose an input-output modeling approach for the analysis of cerebral hemodynamic data in
T2DM in order to elucidate the effects of diabetes upon cerebral hemodynamics and provide a
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quantitative basis for constructing diagnostic indices and formulating mechanistic hypotheses. The
study involves data collected from 12 T2DM patients and 5 age-matched non-diabetic controls (The
concept of Principal Dynamic Modes (PDM) is employed in modeling the dynamic relationships
between beat-to-beat measurements of spontaneous variations of arterial blood pressure (ABP) and
end-tidal CO2 (ETCO2), as the two putative “inputs”, and cerebral blood flow velocity (CBFV)
measured via transcranial Doppler at the middle cerebral arteries, as the putative “output”. The
extracted models describe the dynamic characteristics of the cerebral vasculature with all its (auto)
regulatory mechanisms and can be used to quantify the Dynamic Cerebral Autoregulation (DCA)
and Dynamic Vasomotor Reactivity (DVR) under spontaneous resting conditions. We have shown
how the proposed modeling approach can extract quantitative measures of DCA and DVR in the
form of model-based indices. We posit that the latter may attain diagnostic utility in T2DM because
of its significant cerebrovascular component. Furthermore, we posit that the obtained PDM-based
dynamic models may eventually advance our understanding of the underlying physiological
mechanisms that are impaired in T2DM. This, of course, will require extensive work in the future.
The initial results presented in this study indicate that model-based quantitative and potentially
interpretable markers can be reliably obtained that have the diagnostic potential to delineate T2DM
patients from control subjects. These markers take the form of either “Gains” of specific PDM
contributions to the model prediction of the CBFV output or the form of the DVR index.
Specifically, we found that the Gain values of 1st PDM of the ETCO2 input, as well as the 3rd and
4th PDMs of the ABP input, have statistically significant differences between T2DM patients and
controls (p-values of 0.009, 0.029 and 0.006, respectively). We posit that the spectral characteristics
of these three PDMs offer the prospect of discovering the physiological hemodynamic mechanisms
that are affected by T2DM. For example, the 3rd PDM of ABP exhibits a resonant peak around
0.1 Hz, where the patients have higher Gain values relative to controls (see Table 6.2). Since this
resonant peak has been associated with sympathetic activity (Mayer waves), the result indicates
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increased sympathetic activity in the T2DM patients – which would be consistent with the
hyperactivity of sympathetic modulation observed in previous studies of T2DM, where concurrent
depressed vagal activity was also observed [Thayer 2010; Flaa et al. 2008; Lindmark et al. 2003;
Huggett et al. 2003].
These results suggest autonomic imbalance in T2DM patients that has been observed in previous
studies as the consequence of persistently elevated glucose damaging peripheral nerve fibers
[Carnethon et al. 2003; Lindmark et al. 2003; Huggett et al. 2003]. Kaaja et al. (2006) studied a
female cohort with persistent insulin resistance and observed the close interrelationship between
insulin resistance and sympathetic over-reactivity[Kaaja et al. (2006)]. Still, the specific
mechanisms and sites of possible insulin-induced sympathetic excitation remain unclear. It is also
plausible that this autonomic imbalance may reflect the reduction of baroreceptor sensitivity in
patients with insulin resistance [Okada et al. 2010; Kaaja et al. 2006; Lindgren et al 2006; Egan
2003]. In Lindgren’s study, the fluctuations in blood pressure and heart rate were examined and
the conclusion was drawn that autonomic imbalance, measured as reduced baroreflex sensitivity,
is present in subjects with insulin resistance. Such reduced baroreflex sensitivity may be indicated
by the integrative characteristic of the 4
th
ABP-PDM.
Another differentiating marker relates to the Gain of the 1st PDM of the ETCO2 input, where
T2DM patients exhibit smaller Gain values relative to controls, resulting in reduced CO2 dynamic
vasomotor reactivity in T2DM that has been explored previously as a major physiological regulator
of cerebral blood flow [Bor-Seng-Shu et al. 2012; Lu et al. 2004; Markwalder 1984]. Dynamic
vasomotor reactivity refers to the well-established fact in healthy subjects that a blood CO2 increase
causes vasodilation or, conversely, a blood CO2 decrease causes vasoconstriction. Our result of
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reduced DVR in T2DM may be associated with the observed significant change in the Gain of the
1st PDM of ETCO2 that peaks around 0.04 Hz (see Fig.6.12, right) where oscillations related to
the chemoreflex have been reported [Nava-Guerra et al 2016; Mitsis et al 2009; Van den Aardweg
et al 2002; .]. This advances the hypothesis that T2DM may be related to impairment of the
chemoreflex[Bottini P,2003] .
It has been reported that the chemoreflex elicits both hyperventilation and sympathetic activation,
while the peripheral chemoreflex activation has an inhibitory effect on arterial baroreflex responses
[Schultz et al. 2007; Cooper V L, 2005; Yamada et al. 2004; Kara et al. 2003]. Therefore, it is
intriguing to relate in our study the bidirectional interaction between baro-reflex and chemo-reflex,
and their concomitant afferent influence on the sympathetic nerve activity. Our preliminary results
are intriguing but tentative due to the small cohort size. However, they offer some stimulating
suggestions for the effects of T2DM upon the cerebrovascular dynamics that ought to be explored
further in the future.
6.6 Type 2 diabetes: gender differences and medication assessment
Gender Difference Analysis
It is widely observed that women with type 2 diabetes have higher risks for the development of
cardiac diseases and nephropathy comparing to men with T2DM, leading to the higher mortality of
T2DM female patients as well. This may due to biological differences including body fat
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distribution, insulin resistance, sex hormones etc [Kautzky-Willer et al, 2016; Meisinger et al, 2002
] . The disparity between genders also arises the question of whether medical treatment and risk
factors should be sex-specific for T2DM patients ([Arnetz et al, 2014]).
Following our preliminary result of Type 2 diabetes hemodynamic analysis, we proceed with the
study on gender differences using model-based analysis, and examine whether the model-based
biomarkers reveal useful prognostic information between male and female patients. The recruited
subjects include 5 controls (3 female, 2 male) and 12 T2DM patients (4 female, 8 male).
Fig.6.16 depicts scatter-plots of PDM-based gain values of all subjects, with blue stars represent
healthy male, black stars represent healthy female, and red circles for diabetic female as well as
pink circles for diabetic male. Although the diabetic patients and controls were clearly separated
in the plots, no clear discernable differences were observed between male and female cohorts.
Figure 6.16: Gender differences in scatter-plots of obtained Gains for the contributions to the model-predicted
CBFV output of the 1st ETCO2-PDM versus the 3rd ABP-PDM (left) and versus the 4th ABP-PDM (right).
The DVR index (See section 6.3) were then calculated for diabetic male and female group along
with model-predicted CBFV responses to ETCO2 pulse input. In Figure 6.17, increases in CO2
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induce the elevation of cerebral blood flow perfusion ( Figure 6.17, right panel) for both male and
femal subjects, whereas in patients with T2DM syndrome, cerebral blood flow drops in response
to CO2 input pulse. It is worth noting that CBFV in female T2DM patients (left top panel) drops
significantly comparing to male counterparts, indicating a higher level severity of impairment on
CO2 vasomotor reacitivty. It is intriguing to relate the gender differences of vasomotor reacitvity
deteriotion in our study to the higher mortality and higher risk of vascular diseases found in female
T2DM patients. [Kautzky-Willer et al, 2016; Arnetz et al, 2014; Meisinger et al, 2002 ]
Figure 6.17: Gender difference in model-predicted average response to an ETCO2 input pulse over 5 sec for
the 12 T2DM patients (Left: top panel: female; bottom panel: male) and the 5 control subjects (Right: top
panel: female; bottom panel: male)
Table 6.8: Mean (SD) values of DVR indices for T2DM female and male patients, and corresponding p-value.
DVR index
T2DM (Female) -0.298(0.498)
T2DM (male) -0.090(0.186)
p-value 0.471
T2DM Medication (Metformin) Model-based Analysis
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Metformin is generally the first medication prescribed for type 2 diabetes. It lowers glucose
production in the liver and improves the sensitivity of body tissues to insulin at the same time so
that insulin is used more effectively.
We therefore relate our hemodynamic analysis with the pharmaceutical information of recruited
diabetic patients and examine the “biomarkers” of two specific groups: 7 T2DM patients are under
medication (metformin) treatment and 5 T2DM patients without medication (metformin). Fig.6.18
depicts the three cohorts (including controls) with respect to the linear gain values (biomarkers).
However, no clear separation was observed between patients with and without metformin
treatment.
Figure 6.18: Metformin treatment in scatter-plots of obtained Gains for the contributions to the model-
predicted CBFV output of control subjects (blue), T2DM patients with metformin treatment (pink) and
T2DM patients without metformin treatment(red).
We proceed to the DVR analysis for the above two cohorts and control subject. Figure 6.19
depicts the model-based CBFV response to 5sec ETCO2 input pulse.
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Figure 6.19: Model-predicted average response to an ETCO2 input pulse over 5 sec for the 5 controls (top
panel), 5 T2DM patients without metformin treatment (middle panel) as well as 7 T2DM patients under
metformin treatment (bottom panel).
Table 6.9: Mean (SD) values of DVR indices for T2DM patients with and without metformin, and
corresponding p-value.
DVR index
T2DM ( w/o met) -0.242(0.468)
T2DM (w/ met) -0.101 (0.166)
p-value 0.549
In control subjects, increase in CBFV was observed to restore the sudden elevation of blood CO2
concentration (Fig.6.19, top panel), whereas in patients without metformin treatment CO2 increase
induces the drop of CBFV (Fig.6.19, middle panel) , which will lead to even higher CO2
concentration. These opposite mechanisms observed in T2DM patients were “improved” in
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patients with metformin. In Fig.6.19 (bottom panel), CBFV reveals a small magnitude negative
value in the metformin group, implying the improvement on CO2 vasomotor reactivity after
metformin treatment. Although the significance of group differences is not as pronounced (Table
6.9 ) , the averaged CBFV responses between two groups may prove the efficiency of metformin
in T2DM patients, in particular its effect on cerebral vasomotor regulations.
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Chapter 7: Model-based Indices of Cerebral Hemodynamics as
Diagnostic Markers for MCI Patients with Executive Dysfunction
7.1 Introduction
The effects of essential hypertension on blood flow regulation have been extensively studied for its
association with cardiovascular disease as well as mild cognitive impairment (MCI). The effects in
MCI and age-related dementia have attracted much attention because of the potential impact on
public health and rising evidence that hypertension may contribute to the progress of dementia
[Oveisgharan, S. et al, 2010; Vicario, A. et al, 2005]. However, a direct link between mechanisms
of blood flow dysregulation and cognitive impairment has not yet been established.
Multiple regulation mechanisms are involved in maintaining homeostasis of cerebral blood
perfusion. Increased vascular resistance and reduced regional cerebral blood flow (rCBF) have
been generally observed in patients with essential hypertension (HT), while performing cognitive
tasks [Dai, W. et al, 2008; Iadecola, C. 2008; Jennings, J. R. et al, 2005; Oparil, S. et al, 2003;
Greene, A. S. et al, 1989; Kety, S. S. et al 1948]. In this study, we sought to advance our quantitative
understanding of two of the most critical regulatory processes for cerebral homeostasis: cerebral
autoregulation and cerebral vasomotor activity [Hajjar, I. et al, 2010; Paulson, O. B. et al 1989;
Immink, R. V. et al 2004; Novak, V. et al, 2004; Aaslid, R. et al, 1989]. Specifically, “cerebral
autoregulation” refers to the physiological process that maintains stable cerebral blood perfusion
when systemic blood pressure changes abruptly, while “cerebral vasomotor reactivity” refers to the
physiological process that increases cerebral blood flow via vasodilation in response to rising CO2
tension in the blood. Both of these processes are critical for proper brain metabolism and cognitive
function.
In Rogier’s study [Immink, R. V. et al, 2004], dynamic cerebral autoregulation (CA) was expressed
as the phase lead of cerebral blood flow velocity relative to arterial blood pressure. Impairment of
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CA was observed in patients with malignant hypertension [Immink, R. V. et al, 2004]. Novak’s
study [Novak, V. et al, 2004] reports similar discovery in stroke and hypertension patients using
the multimodal pressure-flow analysis. Hypertension patients were also studied for having impaired
cerebral vasomotor reactivity [Kurtel, H.et al 2013; Hajjar, I.et al, 2010; Lavi, S. et al, 2006;
Marmarelis, V. Z. 2004]. In Hajjar’s study, HT patients exhibited lower global vasoreactivity with
regional decreases in the frontal, temporal, and parietal lobes [Hajjar, I.et al, 2010].
In the present study, the cerebral autoregulation and CO2 vasomotor reactivity were analyzed using
hemodynamic signals (arterial blood pressure, end-tidal CO2 and cerebral blood flow velocity)
collected noninvasively from Mild Cognitive Impairment (MCI) patients with executive
dysfunction (ED) due to chronic hypertension, and from normotensive controls. Dynamic analysis
was employed to examine the concurrent variations of these physiological signals based on the
concept of Principal Dynamic Modes (PDMs) to obtain predictive dynamic models of the
relationships between these variables. This methodology has been pioneered by our group and has
been successfully applied to the study on multiple physiological systems and diseases over the last
20 years [Geng, K. et al, 2015; Kang, Y. et al, 2015; Marmarelis, V. Z. et al, 2014; Marmarelis,
V. Z. 2004]. The modeled dynamics are used to generate subject-specific markers that we posit to
be able to delineate MCI-ED patients from normotensive controls. Since the model was extracted
from spontaneous beat-to-beat data under resting conditions, the computed markers quantify the
dynamic cerebral autoregulation (DCA) and dynamic cerebral vasomotor reactivity (DVR).
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7.2 Methods
A. Data Collection and Pre-processing
Cerebral hemodynamic signals at resting/sitting position were collected over 5 minutes from 43
MCI-ED subjects in Prof. Ihab Hajjar’s lab and from 5 aged-matched controls from Prof. Vera
Novak’s lab at Harvard University. Both groups voluntarily joined the program and signed the
inform consent form. Specifically, for each subject: arterial blood pressure (ABP) was measured
through Finapres at the finger (in mmHg), end-tidal CO2 ( ETCO2 ) was measured with
capnography in mmHg and cerebral blood flow velocity (CBFV) with Transcranial Doppler (TCD)
at the middle cerebral artery in cm/sec.
Continuous time-series signals were reduced to beat-to-beat data by calculating the average value
over each R-R interval. Data was then resampled with 4Hz using cubic spline interpolation and
clipped at +/- 25% of the respective mean value to avoid outlier values. We concern that functional
connections between signals to be higher than 0.01Hz therefore the signals were demeaned and
high-pass filtered with Hanning window with cut-off frequency at 0.008Hz. Fig.7.1 shows
illustrative pre-processed data for a representative control subject.
Figure 7. 1: Illustrative pre-processed time-series data over 4 min for representative control subject. Top:
Arterial Blood Pressure (ABP) in mmHg, middle: end-tidal CO2 (ETCO2) in mmHg, and bottom: cerebral
blood flow velocity (CBFV) in cm/sec. The pre-processed signals are demeaned and high-pass filtered above
0.008 Hz.
83
B. Modeling Methodology:
To quantitatively analyze cerebral blood regulation in the manner by which changes in ABP and
ETCO2 affect cerebral blood perfusion, we construct the dual-inputs-single-output model, in which
ABP and ETCO2 were taken as inputs and CBFV as the output. We employed the Volterra
modeling based on Laguerre expansion technique to construct predictive input-output model. The
employed kernel expansion technique yields with significantly reduced number of parameters as
well as improved estimation accuracy comparing to traditional Volterra modeling. We then seek to
build a set of basis functions that represents the featured dynamics of input-output relationships,
i.e. the global PDMs. PDMs were generated from the fuse of first-order kernels (i.e. impulse
response functions) of a cohort of controls through singular value decomposition (SVD). Featured
PDMs were then selected by specific thresholding criteria based on their respective singular values.
For each subject, Global PDMs were then used as a referenced “filter bank” and the corresponding
PDM-based model concerns the dynamic relationship between each input and output signal. The
linear coefficients of each PDM were computed by linear regression and these subject-specific gain
values were proposed to serve as diagnostic indices for the two cohorts. A block diagram of PDM-
based model is shown in Fig.7.2. Readers are referred the Appendix for detailed modeling
methodology.
84
Figure 7.2: Block-diagram of the PDM-based model of the ABP/ETCO2-CBFV system with 4 global PDMs
for ABP and 4 global PDMs for ETCO2. The output u
i,j
of the ith PDM p
i
is the convolution of the PDM
with the jth input signal. In this study, z
j,1
= c
j,1
u
j,1
for ABP input whereas z
j,2
= c
j,2
u
j,2
for ETCO2. The
linear coefficients c
i,j
of the ith PDM p
i
are computed through linear regression (see Appendix).
7.3 Results:
The obtained global PDMs are shown in Fig.7. 3 for the ABP-to-CBFV dynamic relationship and
in Fig.7.4 for the ETCO2-to-CBFV dynamic relationship. Global PDMs are shown in both time
domain (left panel, akin to the impulse response functions) and frequency-domain (right panel,
magnitude of FFT). Four global PDMs were obtained of ABP-to-CBFV relationship and they
exhibit distinct spectral characteristics. The 1st ABP-PDM (blue) shows a high-pass characteristic
and resembles the traditional Windkessel cerebrovascular model in the time-domain. The 2nd and
3rd PDM peak at frequency around 0.2 Hz and 0.1Hz respectively, the physiological interpretation
of which requires detailed discussion (see Conclusion). The 4th PDM shows a sustained
accumulation effect over several seconds as well as low-pass characteristic in frequency domain.
85
Figure 7.3: Time-domain (left) and frequency-domain (right) representations of the global PDMs for the
ABP input when the output is CBFV measured via TCD.
The contributions of each Global PDM to the output prediction (CBFV) are estimated as linear gain
coefficients through least square estimation technique. In Table 7.1, the computed gain values (the
diagnostic indices) are shown for the two cohorts, indicating statistically significant difference
between MCI-ED patients and controls (p<0.05) for the Gains of ABP-PDM4 (p=0.001).
Table 7.1 : Mean (SD) values of ABP-PDM Gains for MCI-ED patients and controls, and corresponding p-
values.
ABP-PDM1 ABP-PDM2 ABP-PDM3 ABP-PDM4
MCI-ED 0.263(0.146) -0.052(0.075) -0.016(0.027) -0.021(0.028)
Controls 0.326(0.179) 0.037(0.118) -0.003(0.028) 0.001(0.008)
p-value 0.482 0.165 0.378 0.001
Four Global PDMs generated for ETCO2-to-CBFV dynamic relationship are shown in Fig.7.4. The
Gains of the original 1st and 3rd PDMs obtained from SVD of the kernel matrix had p-values just
over 0.05 in differentiating between two cohorts, motivating an orthogonality-preserving rotation
in order to explore better differentiation between patients and controls. The rotated 1st PDM attain
great delineating capability (p=0.034) and the PDMs shown in Fig.7.4 include the rotated 1st and
86
3rd PDMs. The 1st ETCO2-PDM (blue) shows a frequency-response characteristic with a resonant
peak around 0.04 Hz. The 2nd PDM (red) exhibits a resonant peak around 0.03Hz. The 3rd PDM
(green) exhibits a low-pass frequency-response characteristic and 4th PDM (black) peaks around
0.035 Hz. We speculated that low-frequency oscillations at around 0.04Hz observed in ETCO2-
PDMs may be associated with the chemo-reflex loop and discussed this in the Conclusion section.
Figure 7.4 : Time-domain (left) and frequency-domain (right) representations of the global PDMs for the
ETCO2 input (bottom) when the output is CBFV measured via TCD.
The computed Gains for the contributions of the various ETCO2-PDMs to the model-predicted
CBFV output are shown in Table 7.2 and indicate statistically significant differences between MCI-
ED patients and controls for the Gains of ETCO2-PDM1(p= 0.034) and ETCO2-PDM4(p=0.0004).
It is worth noting that both PDMs reveal low-frequency oscillations at around 0.04Hz, suggesting
possible impairment of the chemo-reflex loop gain in MCI-ED patients (see Conclusion and
Discussion).
Table 7.2: Mean (SD) values of ETCO2-PDM Gains for MCI-ED patients and controls, and corresponding
p-values.
87
ETCO2-PDM1 ETCO2-PDM2 ETCO2-PDM3 ETCO2-PDM4
MCI-ED -0.004(0.111) 0.007(0.131) 0.053(0.075) -0.057(0.091)
Controls 0.059(0.045) 0.019(0.053) 0.124(0.095) -0.003(0.007)
p-value 0.034 0.710 0.173 0.0004
The scatter-plots of two cohorts using gain values of the most “differentiating” PDMs (smallest p-
values) from both ABP and ETCO2 inputs are then generated for visual inspection. Specifically,
ETCO2-PDM4 Gains (the most differentiating of the ETCO2-PDMs) and the ETCO2-PDM1
Gains( the second most differentiating of the ETCO2-PDMs) versus the ABP-PDM4 Gains (the
most differentiating of the ABP-PDMs) are shown in Fig.7.5, in which MCI-ED patients are
represented as red circles and controls as blue stars.
Figure 7.5 : Scatter-plots of computed Gains (coefficients) for the contributions to the CBFV output the 1
st
ETCO2-PDM (second most differentiating for ETCO2) and 4
th
ETCO2-PDM (most differentiating for
ETCO2) versus the 4
th
ABP-PDM (most differentiating for ABP).
Fig.7.6 depict the average estimated 1st-order kernels and the CBFV response induced through 5-
sec unit-pulse of the ABP input for patients (left) and controls (right), while the ETCO2 input is
kept at baseline. We observe a slight smaller average response for the patients, which is consistent
with the smaller average Gains for ABP-PDM4 (see Table 7.1). From the model-based CBFV
response simulation, we can define a “Dynamic Cerebral Autoregulation” (DCA) index as the
difference between the peak response and the steady-state response after 5 sec with normalization
-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
BP PDM4 Gain
CO2 PDM1 Gain
MCI-ED Patients
Healthy Controls
-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
BP PDM4 Gain
CO2 PDM4 Gain
MCI-ED Patients
Healthy Controls
88
by the peak response value. However no statistically significant difference was found in the DCA
index between MCI-ED patients and controls (Table 7.3, p= 0.523).
Figure 7.6 : The average kernel estimates and +/- one standard deviation bounds (top panels) of the ABP-
to-CBFV dynamic relationship for the 43 MCI-ED patients (left) and the 5 control subjects (right), as well
as the model-predicted average response to an unit ABP input pulse over 5 sec (bottom panels).
Table 7.3: Mean (SD) values of DCA indices for MCI-ED patients and controls, and corresponding p-value
DCA Index
MCI-ED 0.790(0.233)
Controls 0.725(0.172)
p-value 0.47
For the ETCO2 input, the average responses to an impulse (top) and 5-sec unit pulse (bottom) of
ETCO2 input are shown in Fig.7.7 for patients (left) and controls (right). It is observed that patients
have significantly smaller CBFV response comparing to controls, which is consistent with the
smaller average Gains for all ETCO2 PDMs, especially for ETCO2-PDM1 and ETCO2-PDM4 (see
Table 7.2). This pronounced difference is further demonstrated by the DVR index in the later
section. These observations suggest that an index based on the peak CBFV response to one RMS-
pulse ETCO2 input may be differentiating between patients and controls. However, Table 7.4
0 1 2 3 4 5 6 7 8 9 10
-0.2
0
0.2
0.4
0.6
Average PDM based Kernel(MCI-ED Patients)
Average 1st Order Kernel
Standard Deviation
0 1 2 3 4 5 6 7 8 9 10
-1
0
1
Cerebral Blood Flow Velocity Reponse(HT Patients)
Time(sec)
Model-predicted CBFV response
ABP Pulse
0 1 2 3 4 5 6 7 8 9 10
-0.2
0
0.2
0.4
0.6
Avereage PDM based Kernel(Controls)
Average 1st Order Kernel
Standard Deviation
0 1 2 3 4 5 6 7 8 9 10
-1
0
1
Cerebral Blood Flow Velocity Reponse(Controls)
Time(sec)
Model-predicted CBFV response
ABP Pulse
89
shows that the smaller response for the patients is not statistically significant due to high variance
through subjects (p=0.217).
Figure 7.7 : Average model-predicted CBFV response to a positive ETCO2 5-sec unit pulse change for the
43 MCI-ED patients (left) and the 5 controls (right).
Table 7.4: Mean (SD) values of peak CBFV response to unit-step ETCO2 change for MCI-ED patients and
controls, and corresponding p-value
Peak CBFV Response
to RMS-pulse ETCO2
MCI-ED 0.191(0.284)
Controls 0.343(0.225)
p-value 0.217
We can also quantify the differences between patients and controls by computing the time-average
of the CBFV response to a 5-sec pulse with unit-step ETCO2 input, while the ABP input is kept at
baseline. This time-average value will be termed the “Dynamic Vasomotor Reactivity” (DVR) and
shown in Table 7.5. We observed significant difference in the DVR index between patients and
controls (p=0.018).
0 5 10 15 20 25 30
-0.2
-0.1
0
0.1
0.2
Avereage PDM based Kernel((MCI-ED Patients))
Average 1st Order Kernel
Standard Deviation
0 5 10 15 20 25 30
-2
-1
0
1
2
Cerebral Blood Flow Velocity Reponse
Time(sec)
Model-predicted CBFV response
ETCO2 Pulse
0 5 10 15 20 25 30
-0.1
-0.05
0
0.05
0.1
Avereage PDM based Kernel(Controls)
Average 1st Order Kernel
Standard Deviation
0 5 10 15 20 25 30
-2
-1
0
1
2
Cerebral Blood Flow Velocity Reponse
Time(sec)
Model-predicted CBFV response
ETCO2 Pulse
90
Table 7.5: Mean (SD) values of DVR indices for MCI-ED patients and controls, and corresponding p-
value.
DVR index
MCI-ED 0.006(0.267)
Controls 0.205(0.125)
p-value 0.018
7.4 Conclusion and Discussions
We proposed a novel and feasible modeling approach for physiological system analysis and applied
to the cerebral vascular functioning analysis for MCI-ED patients. Time-series signals of ABP,
ETCO2 and CBFV were collected from 43 MCI-ED patients due to chronic hypertension disease
and 5 age-matched healthy controls. PDM-based modeling analysis was then employed to study
the casual relationship between these signals. The diagnostic utility of model-based markers was
explored with focus on two cerebral blood regulatory mechanisms: Cerebral Autoregulation and
Cerebral Vasomotor Reactivity. Model-based PDMs exhibit distinctive spectral characteristics and
the associated subject-specific “biomarkers” allow the separation between patients and controls.
Specifically, pronounced group differences were observed for gain values of ABP-PDM4, ETCO2-
PDM1 and ETCO2-PDM4 (Table 7.3, Table 7.4), whose spectral characteristics and physiological
implications are discussed in details in the later section. We also proposed the model-based DCA
and DVR index to quantify cerebral autoregulation and vasomotor reactivity at resting state, by
which changes of ABP or ETCO2 affect the cerebral blood perfusion. Our preliminary results
91
showed that MCI-ED patients exhibit lower DVR values in comparison with controls, whereby the
DCA values are comparable between cohorts.
In the frequency plot (Fig.7.3, right), ABP-PDM3 exhibit a distinct spectral peak at 0.1Hz, the
resonance agreed by the current view for sympathetic modulation rhythms (i.e. the Mayer waves)
[Amiya, E. et al, 2014; Julien, C. 2006; Julien, C. 2006;Furlan, R. et al, 2000; Algotsson, A. et al,
1995] , whereas ABP-PDM2 exhibit a high frequency resonance at around 0.2Hz, commonly
interpreted as an index of the parasympathetic tone [Amiya, E. et al, 2014; Perini, R. et al, 2003;
Algotsson, A. et al, 1995]. Although the two PDMs do not delineate the two cohorts (Table 7.1),
MCI-ED patients exhibit generally lower gain values in both ABP-PDM3 and ABP-PDM2
comparing to controls, indicating possible attenuation in both sympathetic and vagal modulations.
In 2011, Collion’s study reported depressed autonomic function, especially parasympathetic
dysfunction in MCI patients [Collins, O. et al, 2012]. Earlier study observed similar autonomic
deficiency using heart rate variability [Zulli, R. et al 2005]. This is important since the ANS
deficiency a well-known feature of Alzheimer’s disease (AD). In 1995, Algotsson A performed a
number of tests measuring the parasympathetic and sympathetic functions in Alzheimer’s patients
and control subjects, and suggests autonomic dysfunction affecting parasympathetic, as well as
vasomotor sympathetic functions in AD [Algotsson, A. et al, 1995]. In Collette’s study, AD patients
exhibit lower performance in all executive tasks comparing to normal controls [Collette, F. et al,
1999]. Since MCI represents the early translational stage of Alzheimer’s disease, we suspect that
the ANS attenuation observed in the recruiting MCI-ED subjects, although not pronounced, may
perform as a potential indicator for the progression of abnormal aging and the progresses of
dementia. This prognostic information is line with Grober’s study, who reported that declined
performance on executive function test was observed 2-3 years before the diagnosis of Alzheimer’s
disease [Grober, E. et al, 2008]. The underlying mechanism of such ANS denervation may due to
the deficiency of acetylcholine, a major neurotransmitter of ANS system [Collins, O. et al, 2012].
92
Interestingly, in Pfeifer’s study, age-related changes such as a decline of baroreceptor sensitivity
may lead to compensatory autonomic nervous system response, which could mask underlying
functional defects in ANS system [Fujishiro, H. et al, 2012]. This compensatory mechanism may
explain the comparable DCA index values observed in the two groups.
The 4th PDM of ABP-CBFV dynamic relationship peaks at low-frequency ranges and exhibits
significant delineating capability between groups. Oscillations in such low-frequency range (0.03–
0.07 Hz) were suggested by previous studies to represent the autoregulatory process, a homeostatic
mechanism that usually takes several seconds to engage [Serrador, J. M. et al, 2005; Narayanan, K.
et al. 2001; Zhang, R. et al, 1998 ]. In Table 7.1, MCI-ED patients showed negative gain values
for ABP-PDM4, indicating a slow decrease of cerebral blood flow in response to sudden blood
pressure increase (Fig.7.3). The negative gain values therefore suggest a sustained vessel
constriction over a relatively long period of time for MCI-ED patients, whereas controls exhibit
small positive gain values with respect to PDM4 (Table7.1). These small magnitude gain values
observed in control subjects is in line with Serrador’s study, who proposed that slow fluctuations
in pressure should be attenuated in cerebral blood flow if autoregulation is intact [Serrador, J. M.
et al, 2005].
For ETCO2-CBFV dynamic relationship, the most differentiating PDMs are ETCO2-PDM1 and
ETCO2-PDM4, in which the MCI-ED patients exhibited lower gain values with respect to both
PDMs, resulting in the reduced CO2 dynamic vasomotor reactivity (Table 7.2). This impaired
vasomotor activity was further demonstrated by the cerebral blood flow simulation in response to
increasing blood CO2 (see Fig.7.7). In Fig.7.7, increase in blood CO2 induces cerebral vasodilation
for control subjects but vasoconstriction for MCI-ED patients. The proposed DVR index quantified
these opposite blood regulation mechanisms and showed statistically significant differences
between cohorts. This can be explained by the increased vascular resistance or local endothelium
93
dysfunction previously found in HT patients [Baszczuk, A. et a, 2013; Iadecola, C. et al, 2008 ;
Nitenberg, A. 2006; Oparil, S. et al, 2003; Greene, A. S. et al, 1989; Kety, S. S. et al, 1948]. Since
both differentiating PDMs peak at around 0.04Hz in the frequency domain, we postulate that
oscillations at such low-frequency could be the enabling component for the diagnostic delineation
between groups. In fact, the distinct rhythms observed in our study agrees with previous studies
who reported that a low frequency component at 0.04Hz to be associated with chemo-reflex
modulation [Nava-Guerra, L. et al, 2016; Mitsis, G. D. et al, 2009; Van den Aardweg, J. G., et al,
2002]. If this premise holds true, the lower values in MCI-ED patients may reveal impaired
functioning of chemoreceptors.
The preliminary result of our study, although promising, is limited by the number of recruited
subjects and remains to be evaluated with larger cohorts. However the altered regulatory
mechanisms suggested by model-based biomarker offer potential diagnostic information for MCI
and prognostic information for cognitive deterioration such as executive dysfunction and
Alzheimer’s disease. Besides, our current result also agrees with Oveisgharan’s study, and proves
that hypertension predicts the progression of dementia in elderly group with executive dysfunction
[Oveisgharan, S. et al, 2010]. Although the underlying mechanism of the onset for MCI or
Alzheimer’s disease is still debated, it is beneficial to relate our study with current physiology and
clinical studies to facilitate the interpretation of the pathology of MCI as well as its predictive
capability for neurodegenerative diseases including Alzheimer’s disease.
7.5 T2DM, Mild Cognitive Disease and Neurodegenerative Diseases:
Altered vascular mechanisms have been widely observed in Type 2 diabetes mellitus and diabetes
is therefore also a disease of the vasculature. Diabetic patients face a considerably higher risk of
developing cardiovascular and cerebrovascular diseases, where both large and small blood vessels
94
are susceptible to alterations from diabetes. The relationship between diabetes and cognitive
impairment and neurodegenerative disease including Alzheimer’s disease was studied by previous
studies yet the underlying pathological mechanisms as well as causal relationships remain unclear.
To address this issue from a diagnosis standpoint, model-based analysis was applied to T2DM
patients, MCI patients as well as healthy controls. The group differences was then observed with
respect to model-based “biomarkers”. This PDM-based analysis on different patients offer
important implications for disease pathology and may prove to be beneficial for clinical and
diagnosis applications.
Note that previous studies on MCI and T2DM disease share the same group of control subjects,
therefore Global PDMs remain the same for both cohorts and can be used as a common reference
for the comparison between patients with different pathologies in this study.The linear gain
coefficients of each PDM were compared between three clusters. It was found that T2DM patients
and MCI patients showed pronounced differences with respect to the 3rd PDM of ABP input.
Fig.7.8 depicts ABP-PDM3 (pink) in both time-domain and frequency domain. As discussed in
previous sections (Chapter5, Chapter 6), ABP-PDM3 exhibit resonance peak at rhythms of
sympathetic modulations (around 0.1Hz).
It was found that T2DM and MCI patients share common features when comparing to healthy
control subjects. Specifically, linear gain values with respect to both ABP-PDM4 as well as
ETCO2-PDM1 were significantly lower in both patient groups comparing to controls. Figure 7.8
depicts the two “differentiating” global PDMs with both time and frequency representations. The
mean values with standard deviation were then presented in Table 7.6 and Table 7.7.
95
Figure 7.8 : Time-domain (left) and frequency-domain (right) representations of the global PDMs for the
ABP input (top) and for the ETCO2 input (bottom) when the output is CBFV measured via TCD.
Table 7.6: Mean (SD) values of ABP-PDM4 Gains for T2DM patients, MCI-ED patients and controls, and
corresponding p-values.
ABP-PDM4 p-value( patients and controls)
T2DM -0.034(0.034) 0.006
MCI -0.021(0.028) 0.001
Controls 0.001(0.008)
96
Table 7.7: Mean (SD) values of ETCO2-PDM1 Gains for T2DM patients, MCI-ED patients and controls,
and corresponding p-values.
ETCO2-PDM1 p-value( patients and controls)
T2DM -0.075(0.137) 0.009
MCI -0.004(0.111) 0.034
Controls 0.059(0.045)
As discussed in previous sections (Chapter 5.5, Chapter 6.4), the 4th PDM of ABP with low-
frequency characteristics was related to baroreceptor modulations of blood pressure changes. If this
premise holds true, the lower values observed in both T2DM and MCI patients were then in line
with the observations found in previous studies, which described the impaired baroreceptor
sensitivity associated with type 2 diabetes [Okada et al. 2010; Kaaja et al. 2006; Lindgren et al
2006; Egan 2003] as well as cognitive diseases.[Meel-van den Abeelen, 2013; Szili-Török, 2001];
DVR indices in patients with T2DM or MCI pathology are generally smaller comparing to its
counterparts in normal subjects (Table 7.8). Specifically, elevations in blood CO2 concentration
induce CBFV decrease (vessel constriction) in model-based prediction for T2DM patients, and a
slight CBFV increase in MCI patients. The altered or attenuated CO2 vasomotor reactivity may be
associated with the observed significant change in ETCO2-PDM1 gain values in both groups. As
mentioned previously, ETCO2-PDM1 peaks at 0.04Hz where oscillations related to the chemo-
reflex have been reported [Nava-Guerra et al 2016; Mitsis et al 2009; Van den Aardweg et al 2002
] We therefore relate the reduced DVR indices with possible chemo-reflex denervation as well as
local endothelial dysfunction.
97
Table 7.8: Mean (SD) values of DVR index for T2DM patients, MCI-ED patients and controls, and
corresponding p-values.
DVR index p-value( patients and controls)
MCI-ED 0.006(0.267) 0.018
T2DM -0.158(0.264) 0.003
Controls 0.143(0.09)
Figure 7.9: Time-domain (left) and frequency-domain (right) representations of the global PDMs for the
ABP input when the output is CBFV measured via TCD.
While both patient groups share common features when comparing to controls, T2DM patients
exhibit higher gain values with respect to PDM 3, whereas the MCI patients possess a lightly lower
gain values compared to control group. In Figure 6.9, scatter-plots of both T2DM and MCI subjects
illustrates the discernible differences between two groups using “biomarkers” of ABP-PDM3.
Table 7.9 shows the mean (standard deviation) of PDM3 gain values with p-value.
98
Figure 7.10: T2DM and MCI-ED difference in scatter-plots of computed Gains (coefficients) for the
contributions to the CBFV output the 1st ETCO2-PDM and the 4th ETCO2-PDM versus the 3rd ABP-
PDM (most differentiating PDM for T2DM and MCI patients).
Table 7.9: Mean (SD) values of ABP-PDM3 Gains for T2DM patients and MCI-ED patients, and
corresponding p-values.
ABP-PDM3 Gain Values
MCI-ED Patients -0.016(0.027)
T2DM Patients 0.038(0.036)
p-value 0.0002
In previous study on type 2 diabetes, we postulated that over-reactivity of sympathetic modulations
( higher gain values with respect to ABP-PDM3) may due to impaired baroreceptor sensitivity
associated with the T2DM pathology (lower gain values with respect to ABP-PDM4), since the
later performs inhibitory effect on sympathetic activities. However, in patients with mild cognitive
disease, baro-reflex dysregulation and sympathetic denervation were concurrently observed. We
hypothesized that sympathetic nervous system activity decreased with age in MCI patients, and
therefore leads to a compensatory effect for the sympathetic over-reactivity due to baro-reflex
impairment. In Pfeifer’s study [Pfeifer, M. A et al 1983], the relationship between aging and
autonomic nervous system functioning was examined with 103 normal male. Our current
hypothesis parallels Pfeifer’s conclusion that ANS function declines with aging, but decline of
99
baroreceptor sensitivity may lead to compensatory response which could mask such functional
defects. Since MCI is often defined as the “onset” stage of abnormal neurodegeneration, it is
beneficial to perform our model-based analysis to progressed cognitive diseases including
Alzheimer’s disease and Parkinson’s disease, where the decline in ANS modulation are expected
to be more pronounced.
It has been reported that the chemoreflex elicits both hyperventilation and sympathetic activation,
while the peripheral chemoreflex activation has an inhibitory effect on arterial baroreflex responses
[Schultz et al. 2007; Cooper V L ,2005; Yamada et al. 2004; Kara et al. 2003]. Therefore, it is
intriguing to relate in our study the bidirectional interaction between baroreflex and chemoreflex,
and their concomitant afferent influence on the sympathetic nerve activity.
Our preliminary results are intriguing but tentative due to the small cohort size. However, they offer
some stimulating suggestions for the effects of vascular diseases and promising prognostic
information for neurodegenerative diseases including Alzheimer’s disease that ought to be explored
further in the future.
100
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Abstract (if available)
Abstract
Led by Dr. Marmarelis, my work focuses on the use of advanced methods of physiological system modeling to improve clinical diagnosis and minimally-invasive treatment in various clinical domains. The proposed modeling approach examines the causal relationship between cerebral hemodynamic signals. This input-output modeling approach utilizes the concept of Principal Dynamic Modes (PDM) which has been pioneered by our group and applied successfully over the last 10 years to various physiological systems. The concept of PDM and PDM-based modeling approach were investigated for the study of cerebral hemodynamic signals, where the modeled dynamics are used to generate subject-specific markers that we posit to be able to delineate patients from healthy controls. The PDM-based analysis and group differences offer important implications for disease pathology and may prove to be beneficial for clinical and diagnosis applications.
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Asset Metadata
Creator
Kang, Yue
(author)
Core Title
Principal dynamic mode analysis of cerebral hemodynamics for assisting diagnosis of cerebrovascular and neurodegenerative diseases
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Biomedical Engineering
Publication Date
06/20/2017
Defense Date
05/08/2017
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
cerebral hemodynamics,diagnostic biomarkers,OAI-PMH Harvest,PDMS,predictive dynamic modeling,principal dynamic modes
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Marmarelis, Vasilis Z. (
committee chair
), Khoo, Michael C.K. (
committee member
), Mather, Mara (
committee member
)
Creator Email
ee07b661@gmail.com,yuekang@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c40-388154
Unique identifier
UC11259103
Identifier
etd-KangYue-5437.pdf (filename),usctheses-c40-388154 (legacy record id)
Legacy Identifier
etd-KangYue-5437.pdf
Dmrecord
388154
Document Type
Dissertation
Rights
Kang, Yue
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
Tags
cerebral hemodynamics
diagnostic biomarkers
PDMS
predictive dynamic modeling
principal dynamic modes