Causal Network Analysis in the Human Brain:
Applications in Cognitive Control and
Parkinson’s Disease
A DISSERTATION
SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL
OF THE UNIVERSITY OF MINNESOTA
BY
Satya Venkata Sandeep Avvaru
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Prof. Keshab K. Parhi, Advisor
April, 2022
© Satya Venkata Sandeep Avvaru 2022
ALL RIGHTS RESERVED
Acknowledgements
I would like to express my sincere gratitude to my advisor Prof. Keshab Parhi for
his guidance throughout my Ph.D. journey and his continued support. I would
like to thank Prof. Alik Widge for his mentorship, encouragement, and invaluable
feedback. I would like to thank Prof. Emad Ebbini and Prof. Andrew Lamperski
for serving as members of my Ph.D. committee and for taking the time to review
my work.
I would like to thank all my current and former lab mates, especially Sand-
hya Koteshwara, Bhaskar Sen, Nanda Kumar Unnikrishnan, and Lulu Ge for their
friendship, encouragement and suggestions. I am also very thankful for my friends
in Minnesota, Krishna Sandeep Prata, Anirudh Reddy Ravula, Teja Dasari, Vas-
anth Ravikumar, Prabhavant Reddy Chilukuri, Nicole Shaffer and Ankit Moldgy,
for their constant moral support and ongoing friendship.
Lastly, I am incredibly grateful to my family, especially my parents, for their
unconditional love and belief in me. Without their support, this work would not
have been possible.
i
Dedication
I dedicate this dissertation to my mother, Prof. Annapurna Nowduri, and my
grandfather, Prof. Rajagopala Rao Nowduri, who are tremendous sources of
strength and inspiration in every sphere of my life.
ii
Abstract
The human brain is an efficient organization of 100 billion neurons anatomically
connected by about 100 trillion synapses over multiple scales of space and func-
tionally interactive over multiple scales of time. The recent mathematical and con-
ceptual development of network science combined with the technological advance-
ment of measuring neuronal dynamics motivated the field of network neuroscience.
Network science provides a particularly appropriate framework to study several
mechanisms in the brain by treating neural elements (a population of neurons,
a sub-region) as nodes in a graph and neural interactions (synaptic connections,
information flow) as its edges. The central goal of network neuroscience is to link
macro-scale human brain network topology to cognitive functions and pathology.
Although interactions between any two neural elements are inherently asymmetri-
cal, few techniques characterize directional/causal connectivity. This dissertation
proposes model-free techniques to estimate and analyze nonlinear causal interac-
tions in the human brain. The proposed methods were employed to build machine
learning models that decode the network organization using electrophysiological
signals.
Mental disorders constitute a significant source of disability, with few effec-
tive treatments. Dysfunctional cognitive control is a common element in various
psychiatric disorders. The first part of the dissertation addresses the challenge of
decoding human cognitive control. To this end, we analyze local field potentials
(LFP) from 10 human subjects to discover network biomarkers of cognitive con-
flict. We utilize cortical and subcortical LFP recordings from the subjects during
a cognitive task known as the Multi-Source Interference Task (MSIT). We pro-
pose a novel method called maximal variance node merging (MVNM) that merges
nodes within a brain region to construct informative inter-region brain networks.
Region-level effective (causal) networks computed using convergent cross-mapping
iii
and MVNM differentiate task engagement from background neural activity with
85% median classification accuracy. We also derive task engagement networks
(TENs) that constitute the most discriminative inter-region connections. Sub-
sequent graph analysis illustrates the crucial role of the dorsolateral prefrontal
cortex (dlPFC) in task engagement, consistent with a widely accepted model for
cognition. We also show that task engagement is linked to the theta (4-8 Hz)
oscillations in the prefrontal cortex. Thus, we decode the task engagement and
discover biomarkers that may facilitate closed-loop neuromodulation to enhance
cognitive control.
In the second part of the dissertation, the main goal is to use network fea-
tures derived from non-invasive electroencephalography (EEG) to develop neural
decoders that can differentiate Parkinson’s disease (PD) patients from healthy
controls (HC). We introduce a novel causality measure called frequency-domain
convergent cross-mapping (FDCCM) that utilizes frequency-domain dynamics
through nonlinear state-space reconstruction. Using synthesized chaotic time-
series, we investigate the general applicability of FDCCM at different causal
strengths and noise levels. We show that FDCCM is resilient to additive Gaus-
sian noise, making it suitable for real-world data. We used FDCCM networks
estimated from scalp-EEG signals to classify the PD and HC groups with ap-
proximately 97% accuracy. The classifiers achieve high accuracy, independent
of the patients’ medication status. More importantly, our spectral-based causal-
ity measure can significantly improve classification performance and reveal useful
network biomarkers of Parkinson’s disease. Overall, this dissertation provides
valuable techniques for causal network construction and analysis. Their usage
is demonstrated on two applications: decoding cognitive control and detecting
Parkinson’s disease. These methods can be extended to other neurological and
psychiatric conditions to elucidate their network mechanisms.
iv
Contents
Acknowledgements i
Dedication ii
Abstract iii
List of Tables x
List of Figures xii
1 Introduction 1
1.1 Challenges in Brain Network Analysis . . . . . . . . . . . . . . . . 1
1.2 Research Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Part I: Decoding Cognitive Control . . . . . . . . . . . . . 3
1.2.2 Part II: Parkinson’s Disease Detection . . . . . . . . . . . 3
1.3 Dissertation Structure and Outline . . . . . . . . . . . . . . . . . 5
1.4 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . 6
2 Background: Measures of Effective Connectivity 9
2.1 Brain Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Summary of Effective Connectivity Measures . . . . . . . . . . . . 10
2.2.1 Granger Causality . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Directed Transfer Function . . . . . . . . . . . . . . . . . . 12
2.2.3 Partial Directed Coherence . . . . . . . . . . . . . . . . . . 13
v
2.2.4 Transfer Entropy . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Model-Free Effective Connectivity Measures . . . . . . . . . . . . 15
2.3.1 Directed Information . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 Convergent Cross-Mapping . . . . . . . . . . . . . . . . . . 16
PART I: DECODING COGNITIVE CONTROL 18
3 Introduction to Cognitive Control 19
3.1 Human Cognitive Control Definition . . . . . . . . . . . . . . . . 19
3.2 Physiological Correlates of Cognitive Control . . . . . . . . . . . . 20
3.3 Cognitive Control Deficits and Psychiatric disorders . . . . . . . . 21
3.4 The Multi-Source Interference Task (MSIT) . . . . . . . . . . . . 21
3.5 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.5.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . 22
3.5.2 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.5.3 Signal Acquisition and Preprocessing . . . . . . . . . . . . 23
3.5.4 Defining Task and Non-Task Segments . . . . . . . . . . . 24
4 Decoding Cognitive Control Using Spectral features 27
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.1 Data Description . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.2 Features and Classification . . . . . . . . . . . . . . . . . . 28
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3.1 Classifier Performance . . . . . . . . . . . . . . . . . . . . 30
4.3.2 The Role of Theta and High Gamma Bands . . . . . . . . 31
4.3.3 Comparison of Regions . . . . . . . . . . . . . . . . . . . . 32
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5 Decoding Cognitive Control Using Channel Level Networks 35
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
vi
5.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . 37
5.2.1 Data Description . . . . . . . . . . . . . . . . . . . . . . . 37
5.2.2 Class Label Assignment . . . . . . . . . . . . . . . . . . . 37
5.2.3 Feature Extraction . . . . . . . . . . . . . . . . . . . . . . 37
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.3.1 PCA Features . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.3.2 Classification Results . . . . . . . . . . . . . . . . . . . . . 41
5.3.3 Classifier Runtimes . . . . . . . . . . . . . . . . . . . . . . 42
5.4 Comparison with Effective Networks . . . . . . . . . . . . . . . . 43
5.5 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . 45
6 Maximal Variance Node Merging and Decoding Cognitive Con-
trol Using Region-Level Networks 46
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . 49
6.2.1 Data Description . . . . . . . . . . . . . . . . . . . . . . . 49
6.2.2 Connectivity Measures . . . . . . . . . . . . . . . . . . . . 49
6.2.3 Maximal Variance Node Merging and Region-Level Networks 50
6.2.4 Edge Importance Score and Task Engagement Networks
(TENs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.2.5 Task vs. Non-Task Classification . . . . . . . . . . . . . . 56
6.2.6 Subband Networks . . . . . . . . . . . . . . . . . . . . . . 56
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.3.1 Identifying Task States . . . . . . . . . . . . . . . . . . . . 57
6.3.2 Classification Results Using Mean Region Networks . . . . 59
6.3.3 Task Engagement Networks . . . . . . . . . . . . . . . . . 59
6.3.4 Subject-Specific Task Engagement Networks . . . . . . . . 62
6.3.5 TENs in Left and Right Hemispheres . . . . . . . . . . . . 66
6.3.6 Increased Theta Band Activity During Task Performance . 66
vii
6.3.7 Theta Band Network Interactions Differentiate Task and
Non-task States . . . . . . . . . . . . . . . . . . . . . . . . 70
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
PART II: PARKINSON’S DISEASE DETECTION 76
7 Introduction to Parkinson’s Disease 77
7.1 Parkinson’s Disease . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.2 Network Biomarkers of Parkinson’s Disease . . . . . . . . . . . . . 78
7.3 Parkinson’s Data Used in the Dissertation . . . . . . . . . . . . . 79
7.3.1 Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7.3.2 EEG Recordings . . . . . . . . . . . . . . . . . . . . . . . 81
8 Distinguishing Parkinson’s Disease Patients Using Functional Brain
Networks 83
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
8.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . 84
8.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
8.2.2 Feature Extraction Using Network Analysis . . . . . . . . 85
8.2.3 Feature Selection and Classification . . . . . . . . . . . . . 87
8.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
8.3.1 Single-Channel Classification . . . . . . . . . . . . . . . . . 88
8.3.2 Multi-Channel Classification . . . . . . . . . . . . . . . . . 88
8.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
8.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
9 Frequency-Domain Convergent Cross-Mapping: A Novel Causal
Connectivity Measure 93
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
9.2 A Brief Introduction to Convergent Cross-Mapping (CCM) . . . . 94
viii
9.3 Frequency-Domain Convergent Cross-Mapping (FDCCM) . . . . . 96
9.3.1 The Basic Concept . . . . . . . . . . . . . . . . . . . . . . 96
9.3.2 Cross-Mapping in FDCCM . . . . . . . . . . . . . . . . . . 96
9.3.3 Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . 97
9.3.4 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
9.4 Toy Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 99
9.4.1 Data Generation . . . . . . . . . . . . . . . . . . . . . . . 99
9.4.2 Toy Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
9.4.3 Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . 100
9.4.4 Effect of Coupling Strength . . . . . . . . . . . . . . . . . 101
9.4.5 Effect of Volume Conduction . . . . . . . . . . . . . . . . . 102
9.4.6 Effect of Noise . . . . . . . . . . . . . . . . . . . . . . . . . 103
10 Distinguishing Parkinson’s Patients Using Causal Networks 106
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
10.2 Materials Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 107
10.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
10.2.2 Network Features . . . . . . . . . . . . . . . . . . . . . . . 108
10.2.3 Classification . . . . . . . . . . . . . . . . . . . . . . . . . 110
10.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
10.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
10.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
11 Conclusion and Future Directions 120
11.1 Implications for Causal Network Analysis . . . . . . . . . . . . . . 120
11.2 Implications for Neurological and Psychiatric Disorders . . . . . . 121
References 124
ix
List of Tables
2.1 Data-driven effective connectivity measures summarized from [1] 11
4.1 Summary of task vs. non-task classification results. Random label-
assignment would result in a baseline accuracy of 50% . . . . . . . 34
5.1 Accuracy of task vs. non-task classifiers for the ten subjects. Sen-
sitivity and specificity represent the task and non-task accuracies,
respectively. Random label-assignment would result in a baseline
accuracy of 50%. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.2 The time taken to predict whether the participant is engaged in the
MSIT or not. Each column shows the mean and standard deviation
of 100 runs of the algorithm on a 3.8 second multidimensional segment 43
5.3 Summary of task vs. non-task classification results. The classifiers
were trained separately for each subject. The table presents mean
and standard deviation values of classification accuracy, sensitivity
and specificity for each of the six network construction methods.
Random label-assignment would result in a baseline accuracy of 50% 43
6.1 Summary of task vs. non-task classification results. The classifiers
are subject specific. The table presents median and interquartile
range values of classification accuracy, sensitivity (task accuracy)
and specificity (non-task accuracy) for each of the three network
construction methods. Random label-assignment would result in
a baseline accuracy of 50%. The highest accuracy in each row is
presented in bold. . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
x
6.2 Summary of task vs. non-task classification results. The table
presents median and interquartile range values of classification ac-
curacy, sensitivity (task accuracy) and specificity (non-task accu-
racy) for each of the three network connectivity measures: R, DI
and CCM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
7.1 Parkinson’s dataset-1 subject demographics (mean ± SD) repro-
duced from [2]. Each control was matched to a person with PD
with respect to their age, sex and handedness. . . . . . . . . . . 79
7.2 Parkinson’s dataset-2 subject demographics (mean ± SD) repro-
duced from [3]. Each control was age and sex matched to a person
with PD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
8.1 Leave-one-subject-out cross validation results summary for HC vs.
PD classification. Sensitivity and specificity represent the healthy
control and PD accuracies, respectively. Random label-assignment
would result in a baseline accuracy of 50%. . . . . . . . . . . . . . 91
10.1 Summary of HC vs. PD classification results for PD Dataset-1.
The table presents classification accuracy, sensitivity (PD accu-
racy), specificity (HC accuracy) and AUC for each of the three
network construction methods. Random label-assignment would
result in a baseline accuracy of 50%. The highest values between
the three methods are shown in bold. . . . . . . . . . . . . . . . . 114
10.2 Summary of HC vs. PD classification results for PD Dataset-2.
The table presents classification accuracy, sensitivity (PD accu-
racy), specificity (HC accuracy) and AUC for each of the three
network construction methods. Random label-assignment would
result in a baseline accuracy of 50%. The highest values between
the three methods are shown in bold. . . . . . . . . . . . . . . . . 115
xi
List of Figures
1.1 Commonly used effective connectivity metrics. . . . . . . . . . . . 4
3.1 The Multi-Source Interference Task. . . . . . . . . . . . . . . . . . 23
3.2 Glass brain models showing the electrode locations. Colors repre-
sent different subjects. . . . . . . . . . . . . . . . . . . . . . . . . 25
4.1 Classification accuracy as a function of the number of features (k).
The reported values are mean 10-fold cross-validation accuracy.
Each plot represents a different subject. . . . . . . . . . . . . . . . 30
4.2 Proportion of optimal features from a specific frequency band. . . 32
4.3 Task vs. non-task classification accuracy using recordings from a
specific region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.1 Functional network of a randomly chosen task and non-task seg-
ments from one subject constructed using local field potential sig-
nals from 64 channels. . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 Two-dimensional scatter plot of two features before and after PCA
from task and non-task data of subject-1. . . . . . . . . . . . . . . 40
5.3 Accuracy, sensitivity and specificity of task vs. non-task classification. 41
5.4 Channel-level effective (causal) networks of subject-1. The net-
works were constructed using local field potential signals from 64
channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
xii
6.1 The MVNM algorithm and graph visualization of a sample causal
network before and after MVNM. The causal network has three
regions with two channels (each) in regions 1 and 2, and three
channels in region 3. . . . . . . . . . . . . . . . . . . . . . . . . . 51
6.2 Functional (correlative) and effective (causal) networks of subject-1
constructed from a randomly chosen task segment. . . . . . . . . . 52
6.3 Flowchart showing the key steps of ‘task’ vs. ‘non-task’ classifica-
tion process and determination of task engagement networks. . . 55
6.4 Task vs. non-task classification accuracy using networks constructed
using three connectivity measures: correlation (R), directed infor-
mation (DI), convergent cross-mapping (CCM). Each point within
the boxplots represents 10-fold cross-validation accuracy of a par-
ticipant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.5 Task engagement networks generated from the three network con-
struction methods. Each node represents one of the 14 regions of
interest (Acc: accumbens, Amyg: amygdala, caudate, Hipp: hip-
pocampus, dACC: dorsal anterior cingulate cortex, dlPFC: dor-
solateral prefrontal cortex, dlPFC: dorsomedial prefrontal cortex,
lOFC: lateral orbitofrontal cortex, mOFC: medial orbitofrontal cor-
tex, parahipp: parahippocampus, postCC: posterior cingulate cor-
tex, rACC: rostal anterior cingulate cortex, temporal lobe, vlPFC:
ventral lateral prefrontal cortex). The thickness of the edges rep-
resent edge strength, as described by (6.2). . . . . . . . . . . . . . 60
6.6 Node centrality of each region in the task engagement networks.
The bar plots represent node degree for undirected (R) networks
and outdegree for directed networks (DI and CCM). . . . . . . . 61
6.7 Task engagement networks derived using inter-region correlational
networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.8 Task engagement networks derived using inter-region DI networks. 64
6.9 Task engagement networks derived using inter-region CCM networks. 65
xiii
6.10 Task engagement networks in left and right hemispheres generated
using CCM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.11 Node centrality of each region in the left and right task engagement
networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.12 Task engagement network including inter-hemispheric connections. 69
6.13 Histogram of relative theta band power in left dorsolateral PFC of
subject-2 for task and non-task periods. . . . . . . . . . . . . . . . 70
6.14 Proportion of optimal features from each subband. . . . . . . . . 71
6.15 Outdegree of the regions in theta band TEN. . . . . . . . . . . . . 72
7.1 EEG channel locations plotted on a 2-D head diagram. Channels
plotted beyond the head limit extend below the head center’s hor-
izontal plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
8.1 Scalp topographical maps of average betweenness centrality. . . . 86
8.2 Single-channel classification performance comparison. . . . . . . . 89
8.3 Receiver operating characteristic (ROC) curves comparison between
3 node centrality measures. . . . . . . . . . . . . . . . . . . . . . . 90
9.1 Illustration of cross-mapping between X and Y when X influences
Y but Y has no (or minimal) effect on X. . . . . . . . . . . . . . . 98
9.2 Correlation coefficients of the two estimated timeseries, Xˆ|MY and
Yˆ |MX , with respect to library length (L). Coupling strengths: βxy =
0.05 and βyx = 0.5. Xˆ|MY represents the influence X → Y , and
Yˆ |MX represents the influence Y → X. . . . . . . . . . . . . . . 101
9.3 Difference between ρX→Y and ρY→X (denoted by ρdiff ) as a function
of coupling strength βyx. βxy = 0.5. . . . . . . . . . . . . . . . . 102
9.4 Difference between ρP→Q and ρQ→P (denoted by ρdiff ) as a function
of coupling strength βyx, with volume conducting. βxy = 0.5. . . 103
9.5 The effect of noise on CCM and FDCCM estimates. ρdiff as a func-
tion of increasing signal-to-noise ratio (SNR) for different coupling
strengths βyx. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
xiv
10.1 Example time-frequency representations (spectrogram) derived from
two arbitrarily chosen channels. The spectrograms correspond to
a Parkinson’s patient from PD dataset-1. Time resolution: 0.5-
second windows with 95% overlap. Frequency resolution: 5Hz, up
to 200 Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
10.2 HC vs. PD classification receiver operating characteristic (ROC)
curves - PD dataset-1. . . . . . . . . . . . . . . . . . . . . . . . . 112
10.3 HC vs. PD classification receiver operating characteristic (ROC)
curves - PD dataset-2. . . . . . . . . . . . . . . . . . . . . . . . . 113
10.4 Scalp topographical maps of average betweenness centralities of
healthy controls (HC) and PD patients (ON and OFF) from PD
dataset-1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
10.5 Scalp topographical maps of average betweenness centralities of
healthy controls (HC) and PD patients (ON and OFF) from PD
dataset-2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
xv
Chapter 1
Introduction
1.1 Challenges in Brain Network Analysis
Modern network science has posed exciting new opportunities for understanding
the brain as a complex system of interacting units. The increasing availability
of rich neuroimaging data combined with advances in mathematical modeling
contributed to this perspective of the brain as a large-scale network. This approach
has revealed fundamental aspects of the typical brain-network organization such
as small-worldness [4]. Small-world networks are comprised of highly connected
hub nodes and efficient long-distance connections. Therefore, these hub nodes
have relatively higher node centralities. Note that node centrality is a measure of
how well-connected a node is in a graph. This broad degree distribution implies
that different nodes of brain networks differ widely in terms of their centrality.
In the past few decades, functional neuroimaging techniques such as func-
tional magnetic resonance imaging and electroencephalography have become cost-
effective while the data analysis techniques have become more finely tuned. Con-
sequently, a plethora of studies have attempted to elucidate the complex network
properties of the human brain. However, the majority of the existing brain net-
work studies are limited to expressing patterns of activity in terms of correla-
tions or symmetric connections between brain regions [5–7]. While the underlying
1
2anatomical pathways between brain regions or populations of neurons are bidirec-
tional, we cannot assume that the connectivity is symmetrical. Although there
are several linear and nonlinear measures of undirected correlation, estimating the
directionality in brain networks is an important and largely unaddressed issue [8].
This dissertation proposes methods to estimate and analyze causal interactions
between brain regions and demonstrate their applicability on human brain data.
Although several techniques and studies exist for causal brain network analysis,
most of them are limited to data acquired through functional magnetic resonance
imaging (fMRI) [9,10]. fMRI is an indirect measure of neural activity and recorded
at a low temporal resolution, which is not ideal for capturing cognitive functions
that involve finer temporal dynamics. Electrical signals such as electroencephalo-
gram and local field potentials can sample neural activity at 100–1000x higher
time resolution than fMRI, making it more suitable to assess temporal dynamics.
Another significant challenge with decoding brain network organization from
distributed electrodes is an imbalance in the number of measurements between
nodes/edges. A given brain region (node) may have anywhere from 1 to 5 physi-
cal electrodes measuring it, depending on the region’s size and the specific clinical
placement of the electrode. Besides, electrode positions vary between subjects.
This imbalance makes it harder to interpret channel-level networks, where each
node corresponds to specific electrode contact. Despite identifying channels be-
longing to specific brain regions, the best way to combine these signals without
losing helpful information is still unclear. Current studies are based on a simplis-
tic assumption that an average of the measured recordings from channels in the
same region represent the neural activity of that region.
1.2 Research Overview
The main objective of this dissertation is to propose methods to infer and ana-
lyze causal interactions using electrophysiological signals. We apply the proposed
methods and demonstrate their validity in two specific domains: 1. Decoding
3human cognitive control, and 2. Parkinson’s disease detection.
1.2.1 Part I: Decoding Cognitive Control
This study uncovers the network mechanisms associated with cognitive control by
distinguishing cognitive task-based connectivity from resting-state connectivity.
The ability to consolidate large-scale heterogeneous channel-level networks into
smaller region-level interactions can help generalize the findings to broader groups
and make useful observations from a physiological standpoint. To this end, we
develop a novel node-merging mechanism by which one can translate a channel-
level network into a more interpretable region-level network.
The proposed method is called maximal variance node merging (MVNM). Ac-
cording to MVNM, new inter-region edges are estimated by computing the optimal
linear combination of connections between channels in two different regions such
that their variance is maximized. This process is equivalent to finding the first
principal component of the original edges between the two regions using principal
component analysis (PCA) – a dimensionality reduction method that attempts to
reduce the number of variables while preserving as much information as possible.
We construct these networks using electrical activity measures from cortical and
sub-cortical electrodes while subjects exert cognitive effort to perform a task. We
then use the network connections as features to classify the task states from non-
task states. The MVNM algorithm’s rationale is that a larger variance implies a
broader spread, which helps differentiate between two classes: task and non-task.
1.2.2 Part II: Parkinson’s Disease Detection
In this part of the dissertation, we propose a novel causal connectivity method and
apply it to accurately distinguish Parkinson’s patients from healthy controls us-
ing network features. Existing data-driven causal connectivity methods vary from
4Granger 
Causality (GC)
Dynamic Causal 
Modeling
Directed Transfer 
Function
Partial Directed 
Coherence
Frequency 
domain GC
Directed 
Information
Transfer Entropy
Convergent 
Cross- Mapping
--
Frequency-DomainTime-Domain
Model-Based
Model-Free
Figure 1.1: Commonly used effective connectivity metrics.
linear to nonlinear, model-based to model-free, and time-domain to frequency-
domain [1,11]. The most commonly applied causal connectivity measures in neu-
roscience are depicted in Fig. 1.1. The heterogeneity of neural interactions makes
it challenging to determine a unifying causal model. Therefore, any method that
relies on a mathematical model is inherently limited by the model assumptions.
Although a few model-free measures like convergent cross-mapping (CCM) and
directed information (DI exist, they are limited to time-domain interactions and
are sensitive to noise. We propose a model-free metric to estimate causal influ-
ence between interacting elements using nonlinear state-space reconstruction to
overcome these barriers.
The proposed solution exploits the frequency-domain dynamics to estimate
causal interactions from the power spectra of measured neural recordings. The
rationale behind FDCCM is based on the following intuition. Since the cause-
variable influences the effect-variable, we can reconstruct the causal timeseries
by finding its signature in the power spectrum of the effect timeseries. We first
apply the proposed method on toy data by simulating coupled logistic maps,
5an established mathematical system to simulate complex dynamics. We then
demonstrate our approach on two Parkinson’s datasets comprised of resting-state
scalp EEG.
1.3 Dissertation Structure and Outline
The dissertation is divided into Part I – Decoding Cognitive Control and Part II –
Parkinson’s Disease Detection. The subsequent chapters are organized as follows:
• Chapter 2 provides a brief background on brain networks and summarizes
commonly used effective (causal) connectivity measures.
PART I – Decoding Cognitive Control
• Chapter 3 provides the necessary background for chapters 4, 5, and 6. We
present an introduction to human cognitive control and the experimental
setup and data description for Part I of the dissertation.
• Chapter 4 presents an approach for differentiating task engagement in a
cognitive task from resting-state activity using spectral power features.
• Chapter 5 presents an approach for differentiating the two mental states,
task, and non-task, using correlational and causal brain networks.
• Chapter 6 presents a novel method called maximal variance node merging
to translate channel-level networks (presented in chapter 5) into region-
level networks. This chapter also classifies the task and non-task states and
compares the proposed method with existing methods.
PART II – Parkinson’s Disease Detection
• Chapter 7 provides the necessary background for chapters 8, 9, and 10. We
present an introduction to Parkinson’s disease and present details of the two
Parkinson’s datasets used in this study.
6• Chapter 8 presents an approach for differentiating Parkinson’s patients from
healthy controls using functional connectivity.
• Chapter 9 presents a novel effective connectivity method called frequency-
domain convergent cross-mapping (FDCCM). We also present the results of
the proposed method on a toy dataset.
• Chapter 10 applies FDCCM to the Parkinson’s dataset and develops classi-
fiers to distinguish Parkinson’s patients from healthy controls.
1.4 Summary of Contributions
The specific contributions of each section of the dissertation are outlined below:
Part I: Decoding Cognitive Control – Chapters 3 to 6.
• We analyze local field potentials (LFP) from 10 human subjects to discover
frequency-dependent biomarkers of cognitive conflict. We show that spectral
power features in predefined frequency bands can classify task and non-task
segments with a median accuracy of 88.1%. We also demonstrate that the
theta (4–8 Hz) band and high gamma (65–200 Hz) band oscillations are
modulated during the task performance.
• We construct and compare three different brain networks: one functional
and two effective networks). We derive causal networks based on a tech-
nique called convergent cross-mapping (CCM) [12] and show that the causal
networks help identify regions of interest associated with task engagement.
Thus, we utilize distributed brain connectivity analysis to detect task en-
gagement and identify potential biomarkers for cognitive control.
• We propose a novel technique called maximal variance node merging (MVNM)
to estimate region-level interactions. Unlike channel-level networks, region-
level networks are more interpretable and relevant for clinical translation.
7• We introduce and present task engagement networks (TENs) by combin-
ing the most explanatory network interactions from multiple subjects. The
TENS can be further analyzed to identify significant regions that function
as stimulation sites.
• We demonstrate that the causal inter-region networks can differentiate men-
tal states associated with task performance from resting-state activity with
85.2% median accuracy. A previous analysis using the same data attained
78% accuracy [13].
• We show that subband networks constructed from bandpass filtered signals
also encode task-specific activity. Especially, theta band (4–8 Hz) networks
play a significant role in detecting task engagement, consistent with prior
findings that theta-band oscillations are modulated during cognitive control.
Part II: Parkinson’s Disease Detection – Chapters 7 to 10.
• We graph theory network measures derived from non-invasive electroen-
cephalography (EEG) to develop neural decoders that can differentiate Parkin-
son’s disease (PD) patients from healthy controls (HC). Using functional
networks, we demonstrate that PD patients could be distinguished from
healthy controls with 89% accuracy – approximately 4% higher than the
state-of-the-art on the same dataset.
• We introduce a spectral measure of causality called frequency-domain con-
vergent cross-mapping or FDCCM. Unlike existing spectral measures of ef-
fective connectivity, FDCCM is model-free and can infer nonlinear interac-
tions.
• We describe the algorithm and validate our method on a toy dataset. We
illustrate the effect of coupling strength and noise on the quality of causal
inference; and demonstrate that FDCCM is more robust to external noise
than CCM.
8• We apply our method on resting-state scalp EEG recordings from two Parkin-
son’s datasets. We employ graph analysis to showcase the difference in be-
tweenness centrality between the patients and controls.
• We demonstrate that machine learning classifiers based on FDCCM causal
networks can differentiate between Parkinson’s patients and demographi-
cally matched healthy controls with 97% accuracy. The performance of FD-
CCM is shown to be better than correlational networks and CCM networks
on both datasets.
Chapter 2
Background: Measures of
Effective Connectivity
2.1 Brain Networks
Describing complex systems such as the brain as a network of interacting elements
can provide useful insights. A graph is defined as a collection of nodes and edges.
The interaction between two nodes is described by their edge(s) strength. A
graph with N nodes is characterized by an adjacency matrix of size N × N ,
whose elements indicate the edge strengths between the nodes. Network science
provides a particularly appropriate framework to study several mechanisms in the
brain by treating neural elements (a population of neurons, a sub-region) as nodes
in a graph and neural interactions (synaptic connections, information flow) as its
edges.
In order to answer questions and make observations about various cognitive,
pathological, or behavioral mechanisms, it is critical to define the network con-
nections appropriately. Brain connectivity is broadly categorized into structural
connectivity, functional connectivity, and effective connectivity. Structural con-
nectivity represents large-scale anatomical connections between cortical regions.
Functional and effective connectivity is generally estimated from time series of
9
10
brain dynamics [14,15]; The fundamental distinction between the two is that func-
tional networks represent patterns of cross-correlation, while effective networks
represent patterns of causal interactions. Several tools and network measures can
be adopted following the network construction, depending on the type of network
and application [14].
The applications of network analysis of the brain range from understanding
the dynamics behind cognition and behavior to diagnosing and monitoring dis-
eases, and is also beneficial in the treatment and rehabilitation of multiple clinical
conditions [16]. Several studies show that disorders such as Epilepsy, Alzheimer’s,
Schizophrenia, and Autism can be characterized as connectome abnormalities.
2.2 Summary of Effective Connectivity Measures
Causal connections can be inferred from dynamic causal modeling (DCM) [17]
which is based on biologically plausible neural mass models or can be estimated
from data. Other than DCM, There are numerous other effective connectivity
measures in the literature. However, a vast majority of them fall under one of the
three families: Granger Causality-based measures, coherence-based measures, and
information theory-based measures [1]. A summary of these measures is presented
in Table. 2.1. Some of the most commonly applied measures are described in this
section.
2.2.1 Granger Causality
Granger causality analysis is a well-established methodology and widely applied
in the neuroscience community [18]. Granger causality (from here on called GC)
or ‘Wiener-Granger causality’ was first introduced by Wiener in 1956 and later
formalized by Granger in 1969 [19]. Studies have shown that GC achieves similar
results to dynamic causal modeling [20, 21] and also has plausible estimates of
human seizure propagation pathways [22]. GC methodology helps answer two key
11
GC-Based Coherence-Based Information Theoretic
Linear GC Directed Coherence (DC) Transfer entropy
Conditional GC Directed transfer function Symbolic transfer
Partial GC (DTF) entropy
Copula-based GC Partial DC (PDC) Partial transfer entropy
Partial frequency- Direct DTF KL divergence
domain GC Extended DC and PDC Directed partial mutual
Multi-variate versions Phase locked value information
Table 2.1: Data-driven effective connectivity measures summarized from [1]
questions that provide supporting evidence for a causal interaction. First, can the
activity measured by electrode A be predicted now, if the activity measured by
electrode B in the past is known? Second, is this better than knowing only the
past of A [23]?
Mathematical Formulation of GC:
Suppose there are two time-series X and Y , and the aim is to investigate the
causal interaction from X to Y . We learn two auto-regressive models of order m
that describe the dynamics in Y: full model and reduced model. The full model
(FM) predicts Y (t) at time index t, using the past values of X and Y , and is
written as follows:
Y (t) =
m∑
j=1
ajX(t− j) + bjY (t− j) + ϵFM .
The reduced model (RM) predicts Y (t) by just using the past values of Y (or by
excluding X) and is given by,
Y (t) =
m∑
j=1
bjY (t− j) + ϵRM .
12
Here, ϵFM and ϵRM denote the prediction errors of FM and RM, respectively.
If the variance of ϵRM (σ
2
FM) is higher than the variance of ϵFM (σ
2
RM), i.e. if the
reduced model is less accurate than the full model, it implies a causal interaction
from X to Y . The magnitude of causality is given by log
(
σ2FM
σ2RM
)
.
Limitations of GC:
Despite its wide usage, there are several shortcomings to GC-based techniques [24].
Granger causality analysis neither establishes nor requires causality; it can, how-
ever, provide evidence in support of a hypothesis about causal interactions [23].
The GC approach is more suitable for stochastic, linear, and strongly coupled
systems. Interactions between neuronal subsystems are nonlinear and are char-
acterized by moderate to weak coupling. More importantly, GC estimates are
based on model assumptions. As described in [12], the critical requirement of GC
is separability, namely that information about a causative factor is independently
unique to one variable and that it can be removed by eliminating that variable
from the model. This separability is characteristic of purely stochastic and linear
systems and reflects the view that systems can be understood as one piece at a
time rather than as a whole. There is a need to develop more suitable techniques
to study the complex nonlinear, bidirectional, weakly coupled interactions in the
brain.
2.2.2 Directed Transfer Function
Consider a k-dimensional time-seriesX(t), represented by (X1(t), X2(t), . . . , Xk(t))
at time t. Directed transfer function (DTC) is based on multi-variate auto-
regressive (MVAR) modeling of the multivariate time-series. According to the
MVAR model, the signal can be expressed, at a given time t, as a weighted sum
of its p previous values and a k-dimensional random noise vector E(t):
13
X(t) =
p∑
τ=1
A(τ)X(t− τ) + E(t),
where A(i) are the model coefficients and p is called the model order. The above
expression can be transformed into frequency domain by computing its Fourier
transform. The resultant equation is given by
X(f) = A−1(f)E(f) = H(f)E(f),
where X(f), A(f) and E(f) are the transforms of X(t), A(i) and E(t), respec-
tively. H(f) is the transfer function of the system and its elements Hij(f) indicate
the causal influence from the j−th input to the i−th output at frequency f . The
DFT from Xj to Xi, denoted by βij is defined as [25,26]:
β2ij = |Hij(f)|2. (2.1)
Normalized DTF is defined as
γ2ij =
|Hij(f)|2∑k
m=1 |Him(f)|2
. (2.2)
2.2.3 Partial Directed Coherence
Partial directed coherence (PDC), introduced in 2001 [27], is based on the frequency-
domain MVAR model representation (like DTF). The PDC from Xj to Xi is
defined as:
πij(f) =
A¯ij(f)√
N∑
k=1
A¯kj(f)A¯∗kj(f)
,
where A¯ij(f) represents the elements of the matrix A¯(f) = I − A(f). That is,
A¯ij(f) =
1−
∑p
k=1 aij(k)e
−2jπfk, if i = j
−∑pk=1 aij(k)e−2jπfk, otherwise
14
An essential difference between DTF and PDC is that DTF is normalized with
respect to the structure that receives the signal, whereas PDC is normalized with
respect to the structure that sends the signal.
2.2.4 Transfer Entropy
Transfer entropy or TE is the most well-known non-parametric effective connec-
tivity measure used in neuroscience research. TE is an information-theoretic ap-
proach that models timeseries as random processes and measures causal effects
as a function of their probability distributions. Assume that two random time
series X(t) and Y (t) can be estimated by generalized Markov processes as follows,
which m and n indicate the orders of random time series X and Y , respectively.
Xmt = (X(t), . . . , X(t−m+ 1))
Y nt = (Y (t), . . . , Y (t− n+ 1))
Note that when there is no causal interaction from X to Y , we can assume the
following equation is true
p(Y (t+ 1)|Y nt , Xmt ) = p(Y (t+ 1)|Y nt ).
Transfer entropy is defined as the Kullback-Leibler divergence (KLD) between
the two conditional distributions in the previous equation: p(Y (t + 1)|Y nt , Xmt )
and p(Y (t+ 1)|Y nt ). That is,
TE(X → Y ) =∑
Y (t+1),Y nt ,X
n
t
p(Y (t+ 1), Y nt , X
m
t ).log
(
p(Y (t+ 1)|Y nt , Xnt )
p(Y (t+ 1)|Y nt )
)
15
2.3 Model-Free Effective Connectivity Measures
This section presents two measures to infer causality between observational data
that do not rely on mathematical models: directed information (DI) and conver-
gent cross-mapping (CCM). Consequently, these measures can estimate nonlinear
causal interactions. Note that all our analyses in this dissertation utilize one or
both of these measures.
2.3.1 Directed Information
Directed information is an information-theoretic measure that estimates causal
interactions between two jointly distributed sequences (two timeseries). It quan-
tifies the amount of causal information in one timeseries explained by the other
timeseries. DI was initially defined for discrete-time, discrete-valued random pro-
cesses and was later extended to discrete-time continuous-valued processes [28,29].
Let XN and Y N be N samples of continuous-valued sequences X and Y . Directed
Information form XN to Y N , denoted I(XN → Y N), can be written as
I(XN → Y N) = h(Y N)− h(Y N∥XN),
where h(Y N) and h(Y N ||XN) represent the differential entropy of the random
vector Y N and the differential entropy of Y N causally conditioned on XN . The
parameter h(Y N ||XN) is defined as
h(Y N∥XN) =
N∑
n=1
h(Yn|Y n−1, Xn).
DI is not restricted to a particular class of statistical models and is non-
parametric [30]. Two widely used causality metrics, Granger causality and transfer
entropy are closely related to DI [19, 31]. If the signals are assumed to originate
from an autoregressive model with Gaussian noise, DI is equivalent to Granger
causality [30]. DI can be extended to more general systems than transfer entropy;
it is not limited to stationary Markov processes and can quantify the instantaneous
causality [32].
16
2.3.2 Convergent Cross-Mapping
Dynamical system theory suggests that each causally linked variable in a dynam-
ical system can be used to estimate the state of another variable since they share
a common manifold (M). Also, when one variable X drives another variable Y ,
information about the states of X can be recovered from Y . In other words, the
ability to predict X from Y is a necessary condition to establish a causal link from
X to Y . This rationale forms the basis for convergent cross-mapping.
Convergent cross-mapping, introduced by Sugihara in 2012 [12], tests for cau-
sation between two time-series X and Y by looking at the (temporal) correspon-
dence between their shadow manifolds. The shadow manifolds, MX and MY , are
constructed from time-lagged coordinates of the time series values of X and Y ,
respectively. Specifically, CCM measures the extent to which the nearby points
in MY estimate the states of X. This process of estimating states of X from MY
(or vice-versa) is called cross-mapping.
Consider two time-series of length L, XL and Y L. As a result of time-delayed
embedding, the shadow manifold MX is formed by the time-lagged coordinate
vectors xt = (xt, xt−τ , xt−2τ . . . xt−(E−1)τ ) for t ∈ [1+(E−1)τ, L]. The embedding
thus depends on two parameters: the time delay τ and the embedding dimension
E. The cross-map of xt, denoted xˆt∥MY is computed by first identifying yt
and its E + 1 nearest neighbors in MY , denoted {y1(t),y2(t), . . . ,yk(t)}. As
a consequence of Taken’s theorem, MX is dieffomorphic to MY , i.e., each point in
MX can be mapped to a unique point in MY [12]. Therefore the neighborhood of
yt is mapped to a set of points in MX , represented as {x1(t),x2(t), . . . ,xk(t)}.
The weighted mean of {x1(t),x2(t), . . . ,xk(t)} provides an estimate of x(t) as
shown in the equation, ˆx(t)∥MY =
∑E+1
i=1 wixi(t) The weighting wi is based on the
distance between y(t) and its ith nearest neighbor yi(t) as given by the equations
wi = ui/
D+1∑
j=1
uj and ui = exp
[
− d(y(t),yi(t)
d(y(t),y1(t)
]
where d(., .) represents the Euclidean distance.
17
A benefit of using CCM for causal inference is that, unlike Granger-related
causality measures, CCM does assume ‘separability’ between variables, which is
usually valid in linear and strongly coupled non-linear systems. The separability
assumption implies that ifX causes Y , then the prediction accuracy of the variable
Y from the historical record of a set of variables U diminishes when X is excluded
from U . Granger’s approach could lead to ambiguity in biological and ecological
networks due to non-separable dynamics. Additionally, complex subsystems such
as the brain are characterized by moderate to weak coupling and are affected by
unobserved/external variables.
18
PART I:
DECODING COGNITIVE CONTROL
Chapter 3
Introduction to Cognitive Control
This chapter provides a brief introduction to cognitive control networks in humans
and describes the task and data used in this study to decode human cognitive
control. Hence, this chapter provides the necessary background for chapters 4, 5,
and 6.
3.1 Human Cognitive Control Definition
In contemporary cognitive neuroscience, cognitive control refers to the adaptation
of information processing, and hence behaviors, depending on current goals. This
ability to coordinate thoughts and actions concerning internal goals is often re-
quired in our everyday lives and forms the basis of higher cognition processes such
as planning and reasoning. Cognitive controls involves a broad range of mental
processes that can be consolidated into three key elements: 1. updating (monitor-
ing and changing working memory contents), shifting (flexible changes between
task-sets or goals), and inhibition (overriding habitual or prepotent/default re-
sponses) [33, 34]. For example, an application of successful cognitive control in
everyday life is switching from using social media to studying for an upcoming test
while inhibiting the desire to return. A closely-related counterpart of cognition,
attention, relates to the mechanisms used for selecting environmental information
19
20
relevant for generating adaptive response (i.e., responses that are appropriate for
the subject’s context or task). In the past 25 years, a substantial theoretical and
experimental progress has been made to decipher the neural mechanisms that
enable cognitive control [35–40]. However, there is no clear consensus regarding
the neural signature of cognitive control, and a great deal still remains to be
understood [41,42].
3.2 Physiological Correlates of Cognitive Con-
trol
Mechanisms of control have been studied using two different perspectives [43,44].
The first approach is based on understanding the specialized processing within
individual brain regions, especially in the prefrontal cortex [45–47]. The second
approach is focused on the distributed processing across different brain regions
organized as large-scale complex networks. The latter approach has become more
popular recently due to the advancement in brain imaging and network analysis
techniques. The methods in this dissertation are also based on the second ap-
proach. It is essential to be familiar with the neuroscience of cognition to validate
and interpret the findings of the empirical observations in our study.
A number of studies indicate that the prefrontal cortex (PFC) subserves cogni-
tive control [45,46]. Specifically, lateral PFC/dorsolateral PFC has been observed
to exhibit a higher activation while implementing cognitive control in several func-
tional magnetic resonance imaging studies in humans [48–52]. This role of PFC is
supported by some transcranial brain stimulation studies that indicate that cog-
nitive enhancement can be achieved by stimulating the dorsolateral PFC [53,54].
Moreover, neurophysiological studies of cognitive control that analyze oscillatory
activity of signals recorded from the PFC suggest that theta activity is increased
with the need for control [55–60].
21
3.3 Cognitive Control Deficits and Psychiatric
disorders
Since cognitive control is crucial in making goal-directed behavioral decisions, it
impacts social stability, success, and other measures of quality of life [61]. There-
fore, cognitive dysfunction is a common feature of psychiatric disorders such as
including schizophrenia, bipolar or unipolar depression, anxiety disorders, and
substance use disorders [62]. Dysregulation of the brain’s cognitive control sys-
tems is evident across multiple disorders (i.e., transdiagnostically) [62–64]. Brain
networks provide a unifying for characterizing how information is encoded in the
brain and understanding the neurobiological basis of psychiatric disorders. In par-
ticular, aberrations in large-scale brain networks that implement cognitive control
have been the underpinning of virtually all psychiatric disorders [65].
3.4 The Multi-Source Interference Task (MSIT)
The Multisource Interference Task (MSIT) was developed to test cognitive control
in normal and pathological conditions, such as schizophrenia, attention deficit
hyperactive disorder (ADHD), and obsessive-compulsive disorder (OCD). In 2003,
Bush et al. developed the Multi-Source Interference Task (MSIT) that reliably and
robustly activates the cingulo-frontal-parietal (CFP) network in individual healthy
subjects [66]. The CFP network plays a crucial role in cognitive processing.
Functional imaging studies showed that the MSIT could be used to i) identify
the cognitive/attention network in normal volunteers and (ii) test its integrity
in people with neuropsychiatric disorders [67]. EEG studies also show that the
MSIT reliably modulates brain electrical activity related to cognitive control and
attention [68]. Thus, electrical activity (from EEG or LFP) obtained during the
22
performance of this task may be useful for exploring the functioning of cogni-
tive/attentional networks in healthy and clinical populations. Subsequent exper-
iments also showed that the MSIT performance is affected by electrical stimula-
tion [69,70].
3.5 Data Description
3.5.1 Experimental Setup
The experimental setup, as depicted in Fig. 3.1(a), consisted of 1–5 blocks of
trials. Each trial-block had 32 or 64 trials. The task stimuli in each trial com-
prised of an array of three numbers (1, 2, or 3) presented at the center of a
computer screen. The subjects were asked to report, via button press, the value
of the unique number that differs from the other two distractors (see 3.1(b)). If
the distractors were a ‘0’ and the target’s position matched its value, the trials
were called congruent trials. Otherwise, they were referred to as incongruent tri-
als. Each experimental run comprised a roughly equal number of congruent and
incongruent trials. The incongruent trials were also characterized by a slightly
lower success rate of 97.1± 5.52% compared to 100%± 2.47% associated with the
congruent trials [13].
3.5.2 Subjects
Fourteen subjects participated in the experiment when they were hospitalized
for invasive epilepsy monitoring and subsequent seizure localization. Use of in-
tracranial recordings of patients undergoing epilepsy monitoring to study cognitive
phenomena is gaining popularity [45,71–73]. Each subject had a history of drug-
resistant complex-partial seizures. We discarded the data from 4 out of the 14
subjects due to lack of statistically sufficient task/non-task recordings. The re-
maining ten subjects were included this study. All surgical decisions, including the
location, type, and the number of electrodes, were made by clinicians independent
23
(a) Block structure of the MSIT trials
+
1  2  3
1  2  3
Fixation
cross
1 0 0
✔
✘
+
1  2  3
1  2  32 1 1
✔
✘
Fixation
cross
Congruent
trial
Incongruent
trial
(b) Examples of congruent and incongruent trials
Figure 3.1: The Multi-Source Interference Task.
of this study. The participants were informed that participation in the experiment
would not affect their treatment. They were allowed to withdraw at any point
during the task. According to the study sponsor guidelines, each participant gave
fully informed consent. The original study was approved by the Institutional Re-
view Board of Massachusetts General Hospital and the US Army Human Research
Protection Office. The present study re-analyzed a publicly available, de-identified
copy of the published dataset, and thus did not require further review [13].
3.5.3 Signal Acquisition and Preprocessing
Local field potential (LFP) signals were recorded through depth electrodes surgi-
cally implanted for seizure monitoring in each participant. Between five and nine
electrodes with diameters 0.8-1.0 mm were placed in each hemisphere. Each elec-
trode consisted of 8-16 platinum/iridium contacts. The distribution of electrodes
24
is illustrated in Fig. 3.2. The Multi-Modality Visualization Tool was used to cre-
ate the visualization [74]. The signals were acquired at a 2 kHz sampling rate via
neural signal processor recording systems from Blackrock Microsystems Inc., Salt
Lake City, UT. All signals were referenced to a scalp EEG electrode. Electrodes
with excessive line noise (60 Hz), close to seizure focus (based on clinical reports),
and other artifacts found on visual inspection were removed. Each channel was
down-sampled to 1000 Hz. The line noise and its harmonics were removed. Adja-
cent channels were then bipolar re-referenced to each other to alleviate the effect
of volume conduction [7]. This data was previously reported in [13], and was
analyzed using a different approach.
Electrode Localization
Spatial coordinates of the electrodes were determined manually through post-
operative computerized tomography (CT). Pre-operative T1 weighted MRI were
aligned with the anatomical CT images through a volumetric image co-registration
method utilizing the FreeSurfer software package [75, 76]. An electrode labeling
algorithm was employed to estimate the probability that a particular brain region
contributes to the signal’s source at each electrode [77]. The regions of interest
were parcellated based on the Desikan-Killiany-Tourville brain atlas [78]. The
number of bipolar re-referenced channels ranged between 64 and 195 based on the
subjects’ electrode montage, and these channels were mapped to 17-23 regions.
3.5.4 Defining Task and Non-Task Segments
The neural activity recorded during MSIT blocks is referred to as task data, and
the data recorded during rest periods (before or after task blocks) is referred
to as non-task data. To differentiate between the task and non-task states, the
signals were divided into multiple task segments and non-task segments. On
average, each MSIT trial was approximately 4 s long; each trial’s actual duration
varies depending on the subject’s reaction time. The time when the fixation cross
25
(a) Anterior (b) Posterior
(c) Inferior (d) Superior
(e) Lateral left (f) Lateral right
(g) Medial left (h) Medial right
Figure 3.2: Glass brain models showing the electrode locations. Colors represent
different subjects.
26
was presented during a trial was marked as the trial’s start. The time duration
between two consecutive fixation crosses determined the length of each trial. The
minimum trial length for most subjects was approximately 3.8 s. Therefore, the
3.8-second time segments from every trial’s start were labeled as ‘task’ data. The
signals recorded during rest periods were windowed into ‘non-task’ segments with
a window length equal to the minimum task duration.
Overlapping windows were used when the number of non-task segments was
less than the number of task segments. If the amount of task data was less than
the amount of non-task data, only a subset of the non-task data was used for
classification. Thus, the two classes were balanced to make sure the classifiers
were not biased. The multidimensional time-series corresponding to task and
non-task segments were then used to construct task and non-task networks.
Chapter 4
Decoding Cognitive Control
Using Spectral features
4.1 Introduction
Neuropsychiatric disorders are the leading cause of disability in the United States;
about one in every five American adults experiences mental illness. Existing treat-
ments for mental illness are less than 50% effective, which calls for a better under-
standing of the mechanisms underlying these disorders that can lead to alleviation
of impaired cognitive control. Electrical deep brain stimulation (DBS) has been
shown to be promising, but it suffers from ambiguous clinical outcomes, which
limit its usage [79–81]. The action mechanisms of DBS are still unclear, and sev-
eral questions are yet to be answered: What should be the target stimulation site?
What are the best stimulation parameters (e.g., current, frequency, and duty cy-
cle)? Dysfunctional decision-making and cognitive control are common features
in a wide range of mental disorders such as depression, addiction, anxiety disor-
ders, autism spectrum disorders, schizophrenia, and obsessive-compulsive disorder
(OCD) [62, 82]. Cognitive control involves restricting and controlling default re-
sponses in favor of a more desired adaptive response.
Developing an adaptive system that can calibrate stimulation in response to
27
28
predefined biomarkers (for cognitive effort) may improve DBS efficacy, but this
requires further knowledge about its neural signatures [83, 84]. A closed-loop
direct brain stimulation strategy was developed in a recent study to enhance cog-
nitive control [69]. However, it is still unclear when to automatically activate
the intervention. Therefore, further research is necessary to discover the best
biomarkers for cognitive control in humans. This chapter attempts to uncover
frequency-dependent biomarkers by classifying task engagement from background
(non-task) activity. To this end, we utilize local field potential signals as ten
subjects perform the Multi-Source Interference Task (MSIT), a well-established
experimental paradigm to study cognitive control [66]. The MSIT has been shown
to evoke connectivity changes related to cognitive impairment in major depressive
disorder (MDD), OCD, and schizophrenia [85, 86]. A similar decoding of task
activity based on fixed canonical correlation analysis was demonstrated in [13].
However, the canonical correlation operators are not readily implementable on
an implanted device. The main advantage of this approach is that the proposed
features make it feasible to develop, implement and evaluate an adaptive neuro-
modulation mechanism using existing hardware devices.
4.2 Materials and Methods
4.2.1 Data Description
The experimental setup, data collection, and prepossessing are described in 3.
4.2.2 Features and Classification
Extracting task and non-task segments
The onset of the fixation cross marked the beginning of each trial. The trials
lasted at least 3.8 s. Therefore, 3.8 s segments of neural recordings from the
onset of each trial constitute task data. The recordings during the rest phase, i.e.,
29
before and after the task activity are considered non-task data (see Fig. 3.1(a)).
Unbiased classification of the two mental states requires class-balancing. For
subjects with insufficient non-task data, overlapping windows were used to create
more segments.
Feature extraction and selection
Spectral powers in predefined frequency bands were used as features to differenti-
ate between the two classes. Prior studies demonstrate that spectral power based
features can distinguish psychiatric and neurological disorders [87–90]. Five fre-
quency bands between 4 Hz and 200 Hz were considered. These bands are defined
as follows: theta (4–8 Hz), alpha (8–13 Hz), beta (13–30 Hz), low gamma (30–55
Hz), and high gamma (65–200 Hz). Additionally, the total power (1–200 Hz) is
also considered a feature. The spectral powers were computed as averaged peri-
odogram estimates in the frequency bands using the Matlab function bandpower.
Consequently, a subject with N channels has 6×N total features. The number of
bipolar re-referenced channels ranged between 64 and 195 based on the subjects’
electrode montage.
The features were then ranked using the Bayes factor. The Bayesian approach,
unlike p-values, yields an intuitive interpretation of the evidence supported by
data [91]. Although significant p-values can provide evidence against the null
hypothesis, the inverse may not be true [92]. This ambiguity and lack of a formal
calculus of inference make p-values elusive to interpret [93]. In contrast, the Bayes
factor (sometimes referred to as likelihood ratio) measures the strength of relative
evidence that the data provide for one hypothesis versus the other.
Consider two possible hypotheses H0 and H1 for a data. The evidence for the
hypothesis can be compared by looking at the posterior odds Ω, which can be
computed as,
Ω =
Pr(H0|data)
Pr(H1|data) =
Pr(data|H0)
Pr(data|H1)
Pr(H0)
Pr(H1)
In practice, it is reasonable to set the prior odds Pr(H0)
Pr(H1)
= 1, to be unbiased
30
0 50 100 150 200 250 300
Num. of features (k)
60
65
70
75
80
85
90
95
Ac
cu
ra
cy
 (%
)
Figure 4.1: Classification accuracy as a function of the number of features (k). The
reported values are mean 10-fold cross-validation accuracy. Each plot represents
a different subject.
towards either hypotheses. The data in the two classes were balanced making
this a reasonable assumption. This assumption reduces Ω to the ratio of marginal
likelihoods Pr(data|H0) and Pr(data|H1). This ratio, known as the Bayes factor
BF , is given by the equation,
BF =
Pr(data|H0)
Pr(data|H1) .
The likelihoods were computed assuming the data in both classes are Gaussian.
4.3 Results
4.3.1 Classifier Performance
For each subject, the data were split into ten subsets via sequential sub-sampling
to ensure that test samples are not in the training samples’ temporal vicinity. One
31
of the ten folds acts as the test set in each iteration, while the other nine act as
the training data. This procedure ensures that all the data are tested and makes
the classifiers less prone to overfitting.
Classification accuracy of each of the ten test sets was computed using the top
k features (ranked using Bayes factor) as inputs to linear support vector machine
(SVM) classifiers. This process was repeated by changing the value of k up to
a maximum of 600 features. The top k∗ features with maximum accuracy are
considered the optimal features for each subject. The median value of k∗ was
observed to be 184. Fig. 4.1 illustrates how the accuracy changes as a function
of k till k = 300. It can be observed that the accuracy increases with the value
of k. All subjects attain a near-maximum accuracy with 50 features, after which
the improvement is marginal.
The best accuracy for the 10 subjects varied between 82.5% to 95%. The
median classification accuracy is 88.1%, with a standard deviation of 3.7%. These
results show that frequency-domain features can reliably distinguish task states
from non-task states. The low standard deviation shows the robustness of the
approach across multiple subjects. The task and non-task classification rates
(sensitivity and specificity) are 90 ± 4.7% and 87 ± 4.3%, respectively. These
rates are significantly higher than a prior approach based on the fixed canonical
correlation analysis (FCCA) for the same data [13].
4.3.2 The Role of Theta and High Gamma Bands
Prior studies show that specific frequency bands could be associated with cognitive
control [58, 58, 60, 70]. To determine the contribution of each of the five bands,
we categorize the optimal features into five groups based on their corresponding
frequency bands. Let F be set of all available features for a given subject. The
number of features in F , i.e., |F| depends on the number of channels of signals
recorded from the subject. The set of optimal features selected by the features
selection method is denoted by F∗, where F∗ ⊂ F . The proportion of optimal
32
1 2 3 4 5 6 7 8 9 10
Subject Number
0
5
10
15
20
25
30
35
40
45
50
55
Pr
op
or
tio
n 
of
 F
ea
tu
re
s
Theta
Alpha
Beta
Low Gamma
High Gamma
Figure 4.2: Proportion of optimal features from a specific frequency band.
features (p) in a subband B is given by p = |F∗B|/|F∗|, where F∗B ⊂ F∗ is the set
of optimal features corresponding to the frequency band B.
We observe that at least 40% of the optimal features originate from theta band
(4–8 Hz) activity in six subjects. In the remaining four subjects, high gamma (65–
200 Hz) is more involved. Fig. 4.2 presents the proportion of optimal features (p)
in each of the five bands: theta, alpha, beta, low gamma, and high gamma. It
shows that the theta (median p = 32.8%) and the high gamma (median p = 24.3%)
bands play a dominant role in the MSIT task engagement.
4.3.3 Comparison of Regions
Next, we isolated the recordings from specific regions of interest. We observed
each region’s ability to decode task states. The ten regions of interest span across
at least nine subjects: amygdala, caudate, dorsal anterior cingulate cortex, dor-
solateral prefrontal cortex, dorsomedial prefrontal cortex, hippocampus, lateral
orbitofrontal cortex, medial orbitofrontal cortex, temporal lobe, and ventrolateral
prefrontal cortex. Fig. 4.3 shows a comparison of classifier performance of the ten
33
Figure 4.3: Task vs. non-task classification accuracy using recordings from a
specific region.
regions of interest. The results illustrate that a subset of optimal features from
one brain region can maintain the decoding ability. The dorsolateral PFC is the
most contributory region in all ten subjects with a median classification accuracy
of 86.6 ± 5.2%. The number of features required to achieve the best accuracy
was 115 (median of the ten subjects). We can attain an accuracy of 88.1% using
all available regions (see Fig. 4.1), which is only marginally higher. The second
and the third best decoding performances are from the temporal lobe and the
dorsomedial PFC with median accuracies of 83.6% and 81.6%, respectively. The
summary of prediction accuracies is presented in Table 4.1.
4.4 Conclusion
Effective treatment of psychiatric diseases requires detecting cognitive control
states, identifying lapses in control, and neurostimulation as patients go about
34
Table 4.1: Summary of task vs. non-task classification results. Random label-
assignment would result in a baseline accuracy of 50%
Features FCCA [13] Proposed–all reg. Proposed–dlPFC
Accuracy 78.1 88.07 86.57
Sensitivity 71.0 90.05 86.97
Specificity 79.2 87 85.07
their daily lives. The ability to differentiate task and non-task mental states with
high accuracy, as demonstrated in this chapter, is crucial to identify objective
biomarkers of cognitive control. The cross-validation ensures that the results gen-
eralize across time, and the low standard deviation of 3.7% indicates the validity
of the approach for multiple subjects. The discriminatory capacity of theta band
(see Fig. 4.2) corroborates recent findings [58, 60]. Disorders such as schizophre-
nia and OCD have been linked to dysfunctional modulation in dlPFC [94,95]. As
shown in [53, 96], using dlPFC as a stimulation site may enhance cognitive con-
trol. The results in Fig. 4.3 validate the hypothesis that cognitive effort involves
modulation of dlPFC. Additionally, the decoders presented here utilize spectral
powers in pre-defined frequency bands, which can be computed using existing
neuromodulation devices without a significant computational overhead.
Chapter 5
Decoding Cognitive Control
Using Channel Level Networks
5.1 Introduction
Neuropsychiatric disorders are the leading cause of disability in the United States;
about one in every five American adults experiences mental illness. Existing
treatments for mental illness are less than 50% effective, which leaves many pa-
tients with behavioral disorders with degraded well-being [5]. The ineffectiveness
of existing treatments is partly due to a lack of mechanistic understanding of
the disorders and the consequent inability to address the cognitive symptoms.
Dysfunctional cognitive control characterizes a wide range of mental disorders
such as depression, addiction, anxiety disorders, autism spectrum disorders, and
schizophrenia [62, 82, 97–99]. Therefore, there is a pressing need to study the
neurological mechanisms underlying these disorders and develop new ways to rec-
tify impaired cognitive control. Effective cognitive control involves restricting and
controlling default responses in favor of a more desired adaptive response.
Electrical deep brain stimulation (DBS) has shown some promise in modu-
lating the brain circuits underlying abnormal behaviors. It has been proposed
as a more effective approach for treating mental illnesses such as Parkinson’s
35
36
disorder, major depressive disorder (MDD), and obsessive-compulsive disorder
(OCD) [79–81]. However, it suffers from ambiguous clinical outcomes, which
limits its usage [80]. Therefore, further research is required to understand its
mechanisms of action fully. Additionally, the optimal parameters of stimulation
are still unknown. Increasing evidence suggests that adapting DBS parameters to
a desired psychological effect, commonly known as closed-loop DBS, can be help-
ful [69,83,84]. Since stimulation during healthy activity can interfere with normal
function, it is critical to identify mental states of cognitive effort (e.g., decision
making during a task) to target for intervention. However, there is no established
signature for engagement in mentally demanding tasks.
This chapter decodes local field potential (LFP) signals recorded from ten
participants performing the multi-source interference task. The goal is to differ-
entiate task engagement from background mental activity. Brain connectivity can
be used to discover biomarkers that distinguish psychiatric disorders [100–102].
To this end, LFP based functional networks were utilized. Reliable detection of
task-engagement can provide objective biomarkers to trigger stimulation. Thus, it
could facilitate the development of closed-loop neuromodulation to prospectively
bias a decision-making process before it begins. A prior study showed that task
and rest states could be separated [13]. However, we found that the analysis
in [13] suffers from a few drawbacks. The algorithm suffers from data-leakage,
which results in an unreliable evaluation of the classifiers. More specifically, (1)
the feature extraction utilizes test data that should be independent of the train-
ing data, and (2) the training and test data were not temporally separated. The
proposed network approach outperforms the previous methods by identifying task
engagement with 89.7% median classification accuracy.
The rest of the chapter is organized as follows. Section II describes the task,
data and methods. Section III presents the results. Section IV concludes the
chapter.
37
5.2 Materials and Methods
5.2.1 Data Description
The experimental setup, data collection, and prepossessing are described in 3.
5.2.2 Class Label Assignment
The neural activity recorded during MSIT trials is referred to as task data, and
the data recorded during rest periods (before or after trial blocks) is referred to as
non-task data. To differentiate between the task and non-task states, the signals
were divided into multiple task segments and non-task segments. The time when
the fixation cross was presented during a trial was marked as the trial’s start. The
time duration between two consecutive fixation crosses determined the length of
each trial. The duration of trials varies depending on the subjects’ reaction times.
3.8-second (minimum trial duration for most subjects) time segments from every
trial’s start were labeled ‘task’ data. The signals recorded during rest periods were
windowed into ‘non-task’ segments with a window length equal to the minimum
task duration. Overlapping windows were used when the number of non-task
segments was less than the number of task segments. If the amount of task data
was less than the amount of non-task data, only a subset of the non-task data
was used for classification. Thus, the two classes were balanced to make sure the
classifiers are not biased.
5.2.3 Feature Extraction
Functional networks were then constructed for each task/non-task segment by
computing its correlation matrix. Fig. 5.1 depicts examples of the task and non-
task functional networks in the form of adjacency matrices. Each entry in an
adjacency matrix represents the strength of the connection (also known as the
edge strength) between the two channels given by its row and column numbers.
38
10 20 30 40 50 60
To Channel
10
20
30
40
50
60
Fr
om
 C
ha
nn
el
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(a) Task
10 20 30 40 50 60
To Channel
10
20
30
40
50
60
Fr
om
 C
ha
nn
el
0
0.1
0.2
0.3
0.4
0.5
0.6
(b) Non-Task
Figure 5.1: Functional network of a randomly chosen task and non-task segments
from one subject constructed using local field potential signals from 64 channels.
39
The adjacency matrices are symmetric matrices indicating that they are undi-
rected correlational networks. The diagonals were set to zeros for better visual-
ization. To extract useful patterns in these networks and eliminate redundancy,
we employ principal component analysis (PCA). PCA is a dimensionality reduc-
tion method that attempts to reduce the number of variables while preserving
as much information as possible. The resultant principal components are unique
linear combinations of the edge strengths such that their variance is maximized.
Maximizing the variance aids in differentiating between the two states: task and
non-task. The PCA coefficients were computed only using the training data to
ensure no information leakage into the test data.
5.3 Results
5.3.1 PCA Features
Functional networks shown in Fig. 5.1 contain task-specific patterns of brain
activity. A timeseries with N channels represents a network with N nodes, and(
N
2
)
connections. For example, a 64-channel recording would create 2016 features.
The high dimensionality of the data makes it challenging to identify the patterns.
PCA transforms the feature space such that the variance of the projections (in
the new space) is maximized. The resultant features are usually more separable,
aiding the classification process. Fig. 5.2(a) illustrates that when edge strengths
are used as features, the two classes are not easily separable. In Fig. 5.2(b), we
present a two-dimensional scatter plot of the first two principal components of
subject-1. It can be observed that the task and non-task data are separable in the
resultant feature space. Thus, PCA helps in finding patterns that differentiate
task and non-task functional networks.
40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Feature 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Fe
at
ur
e 
2
Task
Non-task
(a) Edge Strengths
-1.5 -1 -0.5 0 0.5 1 1.5
Principal Component 1
-1
-0.5
0
0.5
1
1.5
Pr
in
ci
pa
l C
om
po
ne
nt
 2
Task
Non-task
(b) First two principal components
Figure 5.2: Two-dimensional scatter plot of two features before and after PCA
from task and non-task data of subject-1.
41
Figure 5.3: Accuracy, sensitivity and specificity of task vs. non-task classification.
5.3.2 Classification Results
For each subject, the data were split into ten subsets via sequential sub-sampling
to ensure that test samples are not in the training samples’ temporal vicinity.
One of the ten folds acts as the test set in each iteration, while the other nine act
as the training data. This procedure, known as ten-fold cross-validation, ensures
that all the data are tested and makes the classifiers less prone to overfitting.
The PCA features were used as inputs to linear support vector machine (SVM)
classifiers. The mean classification accuracy of the ten test sets was recorded.
This process was repeated by changing the number of features/inputs from 1 to
150. The features with the highest cross-validation accuracy are considered the
optimal features. Results of the classification for all subjects are presented in
Table 4.1. The median task vs. non-task prediction accuracy is 89.7± 6.5%. This
is a significant improvement over the 78.1± 7.39% reported in [13]. The task and
non-task accuracies are 93.7±6.05% and 90.2±9.69%, respectively. The summary
of prediction accuracies is presented in Fig. 5.3.
42
Table 5.1: Accuracy of task vs. non-task classifiers for the ten subjects. Sensitivity
and specificity represent the task and non-task accuracies, respectively. Random
label-assignment would result in a baseline accuracy of 50%.
Sub. Num. ch. Acc. Sens. Spec. Num. of PCs
1 64 87.17 95.22 79.13 36
2 150 92.27 94.55 90.00 92
3 141 86.49 92.78 80.53 113
4 162 98.75 100.00 97.50 14
5 189 85.20 79.17 90.77 13
6 183 94.29 95.71 92.86 53
7 130 77.08 86.94 67.22 115
8 194 93.93 91.43 96.43 73
9 195 93.54 96.67 90.42 108
10 126 82.63 87.32 77.69 149
5.3.3 Classifier Runtimes
Table 5.1 shows that the number of channels and, consequently, the number of
optimal features, i.e., principal components (PCs), varies among the subjects. The
computational complexity of the decoders is relatively low due to the simplicity
of the approach. We computed the time taken to process a randomly chosen LFP
segment, extract the features and determine its classifier outcome for each subject.
These classifiers can be used to detect the task engagement in 2 seconds or less, as
illustrated in Table 5.2. The runtimes were calculated using MATLAB programs
implemented on a general-purpose machine with an Intel Core i7-8565U processor
and 16 GB memory.
43
Table 5.2: The time taken to predict whether the participant is engaged in the
MSIT or not. Each column shows the mean and standard deviation of 100 runs
of the algorithm on a 3.8 second multidimensional segment
Subject 1 2 3 4 5 6 7 8 9 10
µ(sec.) 2.09 1.99 2.04 1.57 1.65 1.88 1.89 1.42 1.55 1.50
σ(sec.) 0.09 0.15 0.07 0.09 0.13 0.18 0.09 0.03 0.11 0.04
Table 5.3: Summary of task vs. non-task classification results. The classifiers
were trained separately for each subject. The table presents mean and standard
deviation values of classification accuracy, sensitivity and specificity for each of
the six network construction methods. Random label-assignment would result in
a baseline accuracy of 50%
Connectivity type Functional – R Effective – DI Effective – CCM
Accuracy 89.13 ± 6.5 84.7 ± 5.8 86.6 ± 5.06
Sensitivity 91.98 ± 6.05 87.7 ± 6.3 89.18 ± 5.3
Specificity 86.25 ± 9.69 81.9 ± 7.33 84.01 ± 7.4
5.4 Comparison with Effective Networks
Inter-channel DI and CCM connections calculated from 64-dimensional time se-
ries from subject-1 are depicted in Fig. 5.4. The task vs non-task classification
accuracy using effective networks is presented in Table .5.3. The results from
correctional networks are also shown for comparison. The correlational networks
outperform causal networks in this context. This is possibly due to redundancy
added by the additional features from causal network. Note that causal networks
have twice as many edges compared to correctional networks due to their direc-
tionality. This leads to redundant information unless there is a way to combine
these edges in a fashion that retains useful information. Next chapter presents a
way to consolidate these networks into more meaningful region-level networks.
44
0
0.2
0.4
0.6
0.8
1
(a) DI
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
(b) CCM
Figure 5.4: Channel-level effective (causal) networks of subject-1. The networks
were constructed using local field potential signals from 64 channels.
45
5.5 Discussion and Conclusion
Cognitive control refers to the effortful deployment of cognitive resources for
adaptive response to the environment. Intact cognition consists of interrelated
executive functions, including updating (i.e., monitoring working memory), in-
hibition (resisting prepotent responses), and shifting (switching between mental
states) [43]. There is no well-defined neural signature for the mental effort asso-
ciated with these coordinated cognitive processes that facilitate decision-making.
Several studies show that cognitive control deficits are central symptoms in many
psychopathological conditions, including schizophrenia, depression, and addiction.
Interventions such as DBS that target the cognitive control networks could be
influential for mitigating symptomatic distress, functional impairments, and di-
minished quality of life prevalent across psychiatric disorders. Developing effec-
tive therapeutics through adaptive neuromodulation requires rapid detection of
focused mental activity.
This chapter demonstrates that such mental states are encoded in the func-
tional connectivity of the brain. Fig. 5.2 illustrates that neural correlates of
task-related mental effort can be separated from background activity. The results
in Fig. 5.3 and Table 4.1 show that task engagement can be detected with high
accuracy. The proposed approach attains a median accuracy of 89.7%, a substan-
tial increase from the 78.1% reported in [13]. There is some variation between
the subjects, partly due to variation in the electrode implant setups; the number
of channels varied between 64 and 195. Moreover, the non-task data involved
recordings during free-behavior without any restrictions or standardization be-
tween the participants. This heterogeneity in the non-task activity might explain
why the classifiers have slightly higher sensitivity than specificity. A limitation
of the current work is that it is limited to a single task. The future work will be
focused on applying the algorithm to multiple cognitive tasks.
Chapter 6
Maximal Variance Node Merging
and Decoding Cognitive Control
Using Region-Level Networks
6.1 Introduction
Neuropsychiatric disorders impose an enormous global disease burden that leads
to premature mortality and degraded quality of life. Existing treatments for these
disorders are less than 50% effective [103]. Many patients with mental illness do
not get relief from gold-standard clinical therapies, resulting in a pressing need
for new treatments. Recent studies indicate that these treatments might emerge
from measuring and remediating cognitive deficits underpinning mental illness,
e.g., through electric stimulation [84,104,105]. Dysfunctional decision-making and
cognitive control are common features in a wide range of mental disorders such as
depression, addiction, anxiety disorders, autism, and schizophrenia [62, 82, 106].
Cognitive control is a set of interrelated executive functions, including updating
(i.e., monitoring working memory), inhibition (resisting prepotent responses), and
shifting (switching between mental sets) [43]. It is, therefore, crucial to accom-
modating daily life requirements, ultimately affecting the quality of life [5]. The
46
47
ability to remediate cognitive control might thus be a new approach to treating
mental disorders.
Cognitive control can be measured in real time through standard laboratory
tasks and direct brain stimulation can improve the performance during these
tasks [69, 70, 96]. It is, however, unclear when this type of intervention should
be automatically triggered to achieve a desired psychological effect. Increasing
evidence indicates, however, that cognitive dysfunction in mental disorders can
be described as aberrant patterns of interactions between neural elements in a
large-scale brain network [101, 102, 104, 107]. It should therefore be possible to
decode this dysfunction by examining changes in functional network communica-
tion.
The majority of the existing brain network studies related to cognitive control
are limited to functional connectivity [5, 6]. Although some effective connectiv-
ity studies exist, they are based on signals acquired through functional magnetic
resonance imaging (fMRI) [9, 10]. fMRI is an indirect measure of neural activity
and recorded at a low temporal resolution, which is not ideal for capturing cog-
nitive functions that involve finer temporal dynamics. A better approach would
be direct decoding of cognitive control and control lapses from electrical brain
recordings [69].
A recent attempt to decode cognitive control task engagement reported suc-
cessful classification [13, 108], but only analyzed functional connectivity. Such
correlational analyses cannot identify the direction of information flow in brain
networks, a critical variable for deciding how to stimulate. The analysis in [13]
also suffered from data leakage, which may have lead to unreliable evaluation of
the classifiers. More specifically, (1) the feature extraction utilized test data that
should be independent of the training data, and (2) the training and test data
were not temporally separated. Another challenge is that the underlying datasets
come from human participants with highly variable placement of their brain elec-
trodes in each brain region. Data interpretation requires methods for measuring
and controlling for that variability across participants.
48
Deriving meaningful causal networks from task-related activity has remained
a challenge. Granger causality has been used in numerous neuroscience appli-
cations [19]. However, Granger’s approach could lead to ambiguity in biological
and ecological networks due to non-separable dynamics [24]. This chapter uses
directed information and convergent cross-mapping, causal inference techniques
that are not based on Granger’s theory. The problem of electrode variability can
be addressed by merging several channels (electrodes) associated with a region
to form region-level networks. In most prior research, region-level signals were
computed by averaging signals from multiple channels in a region [109]. These
averaged signals do not necessarily correlate to the tasks, as classifiers based on
these networks fail to achieve high accuracy (as described in Section IV). We over-
come this challenge by using the proposed novel maximal variance node merging
(MVNM) approach. Causal cognitive control networks based on electrophysiolog-
ical signals have not been constructed before. These networks not only confirm
known network properties of cognitive control but also lead to new findings that
can be explored further.
The contributions of this chapter are five-fold.
1. We construct and compare three different brain networks: one functional
and two effective networks). We derive causal networks based on a tech-
nique called convergent cross-mapping (CCM) [12] and show that the causal
networks help identify regions of interest associated with task engagement.
Thus, we utilize distributed brain connectivity analysis to not only detect
task engagement, but also identify potential biomarkers for cognitive control.
2. We propose a novel technique referred to as maximal variance node merging
(MVNM) to estimate region-level interactions. Unlike channel-level net-
works, region-level networks are more interpretable and more relevant for
clinical translation.
3. We introduce and present task engagement networks (TENs) by combin-
ing the most explanatory network interactions from multiple subjects. The
49
TENS can be further analyzed to identify significant regions that may be
useful as stimulation sites.
4. We demonstrate that the causal inter-region networks can differentiate men-
tal states associated with task performance from resting-state activity with
85.2% median accuracy. A previous analysis using the same data attained
78% accuracy [13].
5. We show that subband networks constructed from bandpass filtered signals
also encode task specific activity. Especially, theta band (4–8 Hz) networks
play a major role in detecting task engagement, consistent with prior findings
that theta band oscillations are modulated during cognitive control.
6.2 Materials and Methods
6.2.1 Data Description
The experimental setup, data collection, and prepossessing are described in 3.
6.2.2 Connectivity Measures
Network science provides a particularly appropriate framework to study brain
mechanisms by treating neural elements (a population of neurons, a subregion)
as nodes in a graph and neural interactions (synaptic connections, information
flow) as its edges [110]. Structural connectivity represents large-scale anatomical
connections between cortical regions. Functional and effective connectivities are
generally estimated from the time-series of brain signals. A fundamental distinc-
tion between the two is that the edge weights in functional networks correspond
to cross-correlation coefficients, while those in effective networks correspond to
patterns of causal interactions. Quantifying (correlative or causative) interactions
between time-series is of particular interest in studying complex network systems
such as the brain [14]. This study estimates and analyzes functional connectivity
50
and effective connectivity between the electrodes and the regions. The effective
networks were constructed using two methods: directed information (DI) and
convergent cross-mapping (CCM). These methods were described in Chapter 2.
Instead of assuming parametric models such as the auto-regressive model used
by Granger causality, DI is based on information theory [29]. It can therefore
measure nonlinear interactions and is not dependent on accurate estimation of
model parameters. A benefit of using CCM for causal inference is that, unlike
Granger-related causality measures, CCM does not assume ‘separability’ between
variables [12]. The separability assumption is usually valid in linear and strongly
coupled non-linear systems. Complex subsystems such as the brain are charac-
terized by moderate to weak coupling and are affected by unobserved/external
variables.
The cross-mapping in CCM was implemented in MATLAB based on the algo-
rithm presented in [111]. A library of L points is estimated, and the correlation
coefficient ρxxˆ is used as an indicator of the influence of X on Y . The causal
connection from Y to X can also be determined analogously. Library length (L)
of 3000 is used in this study since all signals are at least 3000 samples long. The
parameters τ and E are chosen to be 5 and 10, respectively, after extensive trial
and error.
6.2.3 Maximal Variance Node Merging and Region-Level
Networks
A significant challenge in this specific application space, read-out of cognition
from distributed electrodes, is an imbalance in the number of measurements be-
tween nodes/edges. A given brain region (node) may have anywhere from 1 to
5 physical electrodes measuring it, depending on the size of the region and the
specific clinical placement of the electrode. This imbalance makes it harder to in-
terpret channel-level networks, where each node corresponds to a specific electrode
contact. Similarly, since electrode positions vary between subjects, it is unclear
51
(a) Original network (b) Inter-region network after MVNM
(c) Illustration of the MVNM algorithm. N is the number of task/non-task
segments
Figure 6.1: The MVNM algorithm and graph visualization of a sample causal
network before and after MVNM. The causal network has three regions with two
channels (each) in regions 1 and 2, and three channels in region 3.
52
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53
which channels can be safely averaged/combined. That combination is achievable
if we can identify channels as belonging to specific brain regions, such that we
can work in terms of the dominant signal within each region and the inter-region
interactions.
We introduce maximal variance node merging (MVNM) as an approach to
combine nodes in a channel-level network that were mapped to the same brain
region to generate a region-level network. Each node in a region-level network is
associated with a brain region. This enables us to interpret the network connec-
tions better and, consequently, detect specific task engagement regions.
First, the channels were organized into their corresponding regions based on
electrode localization results. Then, region-level networks were constructed from
channel-level networks using MVNM. For each pair of regions, all the network
connections between the regions (inter-region connections) were replaced by one
representative connection in the case of undirected networks. Note that intra-
region connections were discarded. There would be two resultant connections in
directed networks: one representing all the edges from region-A to region-B and
the other for the edges from region-B to region-A. Fig. 6.1(a) and Fig. 6.1(b)
depict an example network before and after the node merging process, respectively.
These new inter-region edges were estimated by computing the optimal lin-
ear combination of the original edges to maximize the variance over time. This
process is equivalent to finding the first principal component of the original edges
between the two regions using principal component analysis (PCA) – a dimen-
sionality reduction method that attempts to reduce the number of variables while
preserving as much information as possible. This approach is beneficial since the
goal is to use these edges as features for classification. The MVNM algorithm’s
rationale is that a larger variance implies a broader spread in the feature space,
which helps find the decision boundary.
Fig. 6.1(c) illustrates this process for two regions A and B with m and n
channels, respectively. There can be mn edges between the two regions in an
undirected network (functional) and 2mn edges in a directed network (effective).
54
Intra-region connections can be ignored here. If there are N such networks in the
dataset, it can be represented by a matrix of dimensions N ×mn, denoted by X.
Note that N is the number of time-series segments (task and non-task) extracted
for a given subject. There would be two such matrices, Xin and Xout, for effective
networks. The optimal linear combination of the columns of X that maximizes
its variance is given by Xw, where the mn× 1 weight vector w is computed as:
w = arg max
∥w∥=1
{
wTXTXw
}
. (6.1)
The optimal linear combination of these connections, Xw, provides the inter-
region edge strengths for the N networks. Note that Xw is the first principal
component of X. In effective networks, the incoming and outgoing connections
were processed separately to determine the two inter-region connections. It can
be noticed that the adjacency matrices in effective networks (Fig. 6.2(b) and Fig.
6.2(c)) are not symmetric, indicating the directionality of the networks.
6.2.4 Edge Importance Score and Task Engagement Net-
works (TENs)
Once all the networks were computed, PCA of the edges was used for feature
extraction. Task engagement networks were constructed from the most significant
connections that were effective in identifying MSIT states. Note that principal
components of the network edges were used as the features for classification. The
PCA assigns a weight to each network connection to compute optimal principal
components. These PCA coefficients were used as an indicator of the significance
of the connections. For a given connection between two regions, the sum of its
coefficients linked to the top p features (principal components) is defined as its
importance score. The edges were then ranked based on their importance scores
and the q highest-ranked edges were deemed significant edges – represented by the
set Ssub for a given subject sub. Parameters p = 10 and q = 60 were used in our
analysis. Note that p and q were chosen such that the choice of these parameters
55


	



		


	




	


 
	







   
	
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Figure 6.3: Flowchart showing the key steps of ‘task’ vs. ‘non-task’ classification
process and determination of task engagement networks.
leads to high classification accuracy (see subsection below). This algorithm is
depicted in Fig. 6.3.
A 10-fold cross-validation split was performed on the data before the PCA as
show in fig. 6.3. Since the cross validation results in ten models for each subject,
Ssub is the intersection of significant edges from the ten models. This is given by
the expression,
Ssub =
⋂
fold
Ssub,fold.
This ensures that the edges are not specific to a subset of the data and generalize
across the dataset. The mean network of all Ssub constitutes the task engagement
56
network STEN . That is, the edge strength eAB from regions A to B is defined as
eAB =
∑
sub eAB,sub
|sub| , (6.2)
where eAB,sub ∈ Ssub and |sub| is the number of subjects. Therefore, the edges in
the TEN signify their prevalence among multiple subjects.
6.2.5 Task vs. Non-Task Classification
The PCA features were used as inputs to linear support vector machine (SVM)
classifiers to distinguish task data from non-task data. For a given subject, train-
ing and testing sets for each of the ten folds were selected via sequential sub-
sampling to ensure that test samples are not in the temporal vicinity of the train-
ing samples. Essentially, data from each class are sequentially partitioned into ten
subsets (folds). In each iteration, one of the ten folds is used for testing, while the
other nine are used for training. This setup ensures that all the data are tested,
and the classifiers are less prone to overfitting. Fig. 6.3 depicts the classification
process. Classifiers with a varying number of inputs were trained with a maximum
limit of 100 features and the testing accuracy with the optimal number of features
is reported.
6.2.6 Subband Networks
Neurophysiological studies indicate that theta activity increases with the need
for cognitive control [55, 58–60]. We constructed subband networks to analyze
the network interactions of frequency-specific neural activity. First, the neural
recordings were bandpass filtered into five pre-defined subbands to quantify the
role of individual frequency bands on task engagement. These bandpass filtered
signals were then used to construct band-specific networks, named subband net-
works. The frequency bands considered in the study are theta (4-8 Hz), alpha
(8-13 Hz), beta (13-30 Hz), gamma-1 (30-55 Hz), and gamma-2 (65-100 Hz). The
bandpass filtering was implemented using 6th order Butterworth IIR filters. All
57
R DI CCM
60
70
80
90
100
A
cc
ur
ac
y(
%
)
Figure 6.4: Task vs. non-task classification accuracy using networks constructed
using three connectivity measures: correlation (R), directed information (DI),
convergent cross-mapping (CCM). Each point within the boxplots represents 10-
fold cross-validation accuracy of a participant.
signals were filtered bidirectionally to avoid undesired phase shifts introduced by
the filtering, which can affect causal inference.
6.3 Results
6.3.1 Identifying Task States
The SVM models were evaluated based on how accurately they could distinguish
between task and non-task states for all subjects. Their classification accuracy,
sensitivity (true-positive rate), and specificity (true-negative rate) were calcu-
lated; the task data was considered as the positive class. Fig. 6.4 presents the
58
Table 6.1: Summary of task vs. non-task classification results. The classifiers are
subject specific. The table presents median and interquartile range values of clas-
sification accuracy, sensitivity (task accuracy) and specificity (non-task accuracy)
for each of the three network construction methods. Random label-assignment
would result in a baseline accuracy of 50%. The highest accuracy in each row is
presented in bold.
Network Functional Effective
Method FCHA [13] R+MVNM DI+MVNM CCM+MVNM
Acc. 78.1 ± 7.39 82.74 ± 7.45 80.85 ± 4.9 85.17 ± 5.0
Sens. 71.0 ± 10.3 84.86 ± 8.57 82.58 ± 8.57 87.49 ± 8.77
Spec. 79.2 ± 7.7 83.7 ± 9.31 79.74 ± 6.38 82.12 ± 13.2
SVM classification accuracy for all the subjects evaluated based on the three net-
work construction approaches. The reported values represent the mean accuracy
over 10-fold cross-validation. The plot illustrates that all network types attain
accuracies substantially higher than the baseline of 50%, suggesting that there
are patterns of interaction in the neural activity that can be used to identify task
engagement. CCM networks perform the best with 85.2 ± 5.0% accuracy. The
high accuracy indicates that inter-region interactions contain useful task-related
information. The median accuracy and interquartile range values across the ten
subjects are summarized in Table 6.1. The median accuracy, sensitivity, and speci-
ficity of all MVNM-based networks exceed 80%. The interquartile range values
are also low, indicating the algorithm’s reliability and robustness across multiple
human subjects. The slightly lower specificity compared to sensitivity may be
attributed to heterogeneity in the non-task data. It is to be noted that the non-
task represents free-behaviour of the subjects between trials. All three methods
outperform fixed canonical coherence analysis (FCHA) presented in [13].
59
6.3.2 Classification Results Using Mean Region Networks
This section presents a summary of task vs. non-task classification results using
networks computed from averaged time-series in each region. The local field po-
tential signals from all channels with a region of interest are averaged, and the
resulting time-series is used to generate the networks. It can be observed that this
approach attains about 10% lower classification accuracy compared to MVNM.
Results from MVNM and FCHA are also included in Table S1 for comparison.
Table 6.2: Summary of task vs. non-task classification results. The table presents
median and interquartile range values of classification accuracy, sensitivity (task
accuracy) and specificity (non-task accuracy) for each of the three network con-
nectivity measures: R, DI and CCM.
Method Averaged time-series MVNM
Conn. FCHA [13] R DI CCM R DI CCM
Acc. 78.1 ± 7.39 75.79 ± 7.59 70.04 ± 10.7 66.9 ± 8.87 82.74 ± 7.45 80.85 ± 4.9 85.17 ± 5.0
Sens. 71.0 ± 10.3 78.45 ± 11.39 69.8 ± 23 56.53± 26.36 84.86 ± 8.57 82.58 ± 8.57 87.49 ± 8.77
Spec. 79.2 ± 7.7 76.7 ± 14.1 67.97 ± 9.6 82.89± 16.84 83.7 ± 9.31 79.74 ± 6.38 82.12 ± 13.2
6.3.3 Task Engagement Networks
Fig. 6.5 depicts the TENs from functional (R) and effective networks (DI and
CCM). Each edge in the graphs represents the number of times a specific con-
nection appears in STEN . Out of the fourteen regions of interest that emerged
from the analysis, connections between some regions are more prominent than
the others. More interestingly, the graph visualizations in Fig. 6.5(c) showcase a
close resemblance to the results in Fig. 6.5(b), which are based on an independent
causal approach.
To quantify the importance of each of the regions in task engagement, we mea-
sured the node centralities of the regions in each TEN (see Fig. 6.6). Node degree
and outdegree were computed for functional and (two) effective networks, respec-
tively. The dorsolateral PFC (dlPFC) and temporal lobe show more centrality in
60
(a
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61
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(D
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).
62
all three cases, although the distinction is more prominent in effective networks.
In correlation networks, the difference between regions is less noticeable, making
it harder to discriminate key hubs using just correlation analysis. However, dlPFC
has a considerably higher outdegree in effective networks estimated from causal
interactions, followed by temporal lobe and ventrolateral PFC (vlPFC).
6.3.4 Subject-Specific Task Engagement Networks
Task engagement networks (TENs) for each subject are presented in this section.
Fig. 6.7 , Fig. 6.8 and Fig. 6.9, respectively, show subject-specific TENs de-
rived using correlation coefficient (R), DI and CCM. By visual inspection, we can
observe that dlPFC and the temporal lobe are major hubs in the graphs. This
observation is more pronounced in causal networks (DI and CCM). The regions
of interest are labelled as follows: Acc– accumbens, Amyg– amygdala, caudate,
Hipp– hippocampus, dACC– dorsal anterior cingulate cortex, dlPFC– dorsolat-
eral prefrontal cortex, dlPFC– dorsomedial prefrontal cortex, lOFC– lateral or-
bitofrontal cortex, mOFC– medial orbitofrontal cortex, parahipp– parahippocam-
pus, postCC– posterior cingulate cortex, rACC– rostal anterior cingulate cortex,
temporal lobe, vlPFC– ventral lateral prefrontal cortex.
63
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6.3.5 TENs in Left and Right Hemispheres
Task engagement networks for both the hemispheres are shown in Fig. 6.10. These
directed networks were constructed using CCM. The corresponding node central-
ities are also presented in Fig. 6.11. The networks depicted in Fig. 6.12(a) include
intrahemispheric (within-hemisphere) and interhemispheric (cross-hemisphere) links.
The node centrality values indicate no significant differences in the main hub re-
gions in both hemispheres: dlPFC, temporal and vlPFC. Some interhemispheric
links can be observed between the high centrality nodes. However, these connec-
tions should not be confused with true information flow or structural connectiv-
ity. They may indicate functional correlations or zero-lag interactions between
the nodes.
6.3.6 Increased Theta Band Activity During Task Perfor-
mance
Greater theta band activity is known to be associated with cognitive control [55,
56, 58–60, 72]. Using bandpass filtering, the neural activity in the task and non-
task periods was divided into five subbands: theta (4-8 Hz), alpha (8-13 Hz),
beta (13-30 Hz), gamma-1 (30-55 Hz), and gamma-2 (65-100 Hz). Relative power
in the theta band was computed as a ratio of the spectral power in the 4-8 Hz
frequency range to the total power spectral density in 4-100 Hz. Fig. 6.13 shows a
distribution of relative power in theta band in the left dlPFC of subject-2 in task
vs. non-task segments. Theta power during the task and non-task states has a
log-normal distribution, with means 0.28 and 0.21, respectively, demonstrating an
increased theta band power during this cognitive control task. We also observed
an enhanced dlPFC theta activity in seven out of the ten subjects. The increased
mean relative power in the seven subjects is also associated with p-values < 0.05
and Bayes factor > 9 (in 6 of the 7 cases) according to the two-sample t-test. This
is consistent with a wide range of prior reports implicating modulated theta-band
activity during cognitive control [55, 56,58–60,112].
67
(a) Left hemisphere.
(b) Right hemisphere.
Figure 6.10: Task engagement networks in left and right hemispheres generated
using CCM.
68
LA
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(b) Right hemisphere.
Figure 6.11: Node centrality of each region in the left and right task engagement
networks.
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(a) Task engagement network.
LA
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(b) Node centrality.
Figure 6.12: Task engagement network including inter-hemispheric connections.
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Figure 6.13: Histogram of relative theta band power in left dorsolateral PFC of
subject-2 for task and non-task periods.
6.3.7 Theta Band Network Interactions Differentiate Task
and Non-task States
To evaluate the role of inter-region subband activity of the five subbands in the
MSIT, we decode the task states using the subband networks. The aim is to
discern and compare the discriminative ability of network dynamics associated
with each of the five subbands. Since CCM networks have the best performance,
CCM based subband networks are used. We observe that the median classification
accuracy of the subband networks is 79.5% – marginally less than the networks
without frequency filtering. This implies that subband dynamics also encode task-
related information. By measuring the number of significant edges corresponding
to each subband, we observe that 4-8 Hz activity distinguishes task states better
than other frequencies. This is illustrated in Fig. 6.14.
TENs built using only significant theta subband edges also highlight the in-
fluence of dlPFC and temporal lobes in the MSIT, as shown in Fig. 6.15. The
71
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
0 20 40 60 80 100
% of top features
Pa
tie
nt
 Id
.
 Gamma_2
 Gamma_1
 Beta
 Alpha
 Theta
Figure 6.14: Proportion of optimal features from each subband.
dorsomedial PFC (dmPFC) attains the third highest centrality. This shows that
theta oscillations (especially in dlPFC) and their network-level interactions can
act as biomarkers for task engagement.
6.4 Discussion
Despite its pressing need, devising an effective neurological mechanism-based
treatment to enhance cognitive control is still a major challenge. This might
be achieved through adaptive brain stimulation that intervenes when cognitive
control lapses [69, 70,113]. Developing such a treatment requires a deeper under-
standing of cognitive control that may be provided by network analysis.
Authors in [13] describe a unique approach to construct inter-region networks
using canonical correlation analysis, called fixed canonical coherence analysis
(FCHA). Even though both FCHA and MVNM involve estimating a linear com-
bination of multiple variables, there are fundamental distinctions between them.
For a given pair of regions X and Y , the FCHA maximizes the coherence between
72
Am
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Figure 6.15: Outdegree of the regions in theta band TEN.
multivariate time-series in X and Y . This optimization is accomplished by esti-
mating the optimal linear combination of multiple channels within each region.
MVNM is a novel method that optimizes the variance of the network interactions
over time. Unlike FCHA, MVNM converts (possibly informative) channel-level
networks into more interpretable region-level networks. This method can be ap-
plied to correlational or causal networks.
Averaging time-series recordings is a common approach to combine neural
signals from the same anatomical region [109, 114]. Such techniques may dis-
card valuable network dynamics. Classification results presented in the Table 6.2
demonstrate that the averaged connectivity is not well-suited to uncover the opti-
mal causal interactions between the regions. Table S1 shows that MVNM attains
a 10% increase in accuracy compared to the time-series averaging. The proposed
methods help detect task engagement with approximately 85% median accuracy,
a notable improvement over [13]. In addition, the classifiers are characterized by
low variation across cross-validation folds and across subjects indicating the ro-
bustness of the approach. However, it should be noted that these classifiers are
73
subject-specific. A generalized decoder for all subjects may lead to lower accuracy.
A high classification accuracy may not always lead to advances in understand-
ing underlying brain mechanisms. Hence, we use graph analysis of the networks to
determine TENs presented in Fig. 6.5. TENs highlight changes in network inter-
actions across the subjects due to task-related effort. The causal TENs highlight
dorsolateral PFC, temporal lobe, and ventrolateral PFC as the most influential
regions of interest with high outdegree. The observations from CCM and DI net-
works – independent causality measures – corroborate each other, supporting the
validity of our approach. The involvement of dlPFC in cognitive control, espe-
cially in tasks involving conflict or inhibition of irrelevant information, is reported
in prior research [45, 50, 70]. Schizophrenia and OCD have been linked to dys-
functional modulation in dlPFC and vlPFC [94, 95]. Our TENs emphasize the
activation of dlPFC better than [13]. dlPFC was also used as a stimulation site to
enhance cognitive control successfully [53]. Several studies suggest that increased
frontal theta activity is associated with cognitive control [57–60, 70]. Fig. 6.14
shows that the majority of the discriminative features used in the classifiers orig-
inate from theta band activity in all the subjects. Fig. 6.15 implies that theta
interactions in dlPFC, dmPFC and the temporal lobe play an important role in
cognition. The alignment of our data-driven findings with prior studies validates
the ability of our approach to discover true mechanistic network structure.
The role of the temporal lobe, which is outside the canonical frontoparietal
cognitive control networks, is not entirely understood [115, 116]. This is partly
because most cognitive control studies are focused on the frontal regions instead of
observing a global brain network. It is shown in [117] that the temporal lobe had
the largest response to a cognitive task among non-frontal regions. Alternately,
the temporal lobe weighting could be related to the participants’ epilepsy. Pa-
tients with temporal lobe epilepsy have been reported to suffer from dysfunctional
control characterized by interactions between the epileptogenic temporal lobe and
the PFC [118,119].
74
Even though the MSIT has been shown to activate cognition/attention net-
works [66, 85, 120], clinical translation towards a viable treatment for psychiatric
disorders presents significant challenges. First, any task performance can include
several other behavioral and physiological mechanisms that may not be related
to cognitive effort. For example, task engagement can provoke anxiety, leading to
engagement of emotional arousal networks. Therefore, further research involving
multiple tasks and a larger cohort of subjects is needed to form robust conclusions
about the neural encoding of cognitive control. Another challenge is that the effi-
cacy of adaptive DBS on psychiatric disorders is not sufficiently understood. We
believe that objective network biomarkers at an electrophysiological level can help
detect and rectify cognitive dysfunction [69,104]. Future studies may also explore
non-invasive recording/stimulating modalities
6.5 Conclusion
Network representations can decode cognitive control and other mental functions
by identifying relevant cross-region interactions. We show that network connec-
tions between dorsolateral PFC, temporal lobe and ventrolateral PFC were dis-
criminative through graph analysis of causal task engagement networks. More-
over, independent causal inference techniques (DI and CCM) indicate a higher
outdegree in those regions, supporting the potential for dlPFC as a stimulation
site [53, 96, 104, 121]. Subband network analysis reveals that enhanced cognitive
control is associated with modulated theta band activity.
There is substantial evidence supporting stimulation-induced modulation of
pathological network activity as a therapeutic mechanism of treatments such as
deep brain stimulation [122–124]. The methods developed in this chapter enable
the discovery of objective biomarkers, localized regions of interest, and band os-
cillatory activity associated with task engagement. This knowledge can facilitate
a transition from symptom-based treatments to more effective mechanism-based
treatments for mental illness.
75
The network analysis methods described in this chapter may be used to de-
scribe other neurological phenomena beyond the specific task considered here. For
example, the algorithm used to determine task engagement networks can also be
used to identify network interactions that are dysfunctional in specific disorders.
Such an inference can be made by comparing patients to healthy controls (instead
of task vs. non-task).
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PART II:
PARKINSON’S DISEASE DETECTION
Chapter 7
Introduction to Parkinson’s
Disease
7.1 Parkinson’s Disease
Parkinson’s disease (PD) is the second most common neurodegenerative disease,
affecting 1 in every 100 adults over the age of 65. PD is characterized by a gradual
loss of dopaminergic nigrostriatal neurons in a part of the brain called substan-
tia niagra. Its common clinical symptoms include progressive tremor, rigidity,
bradykinesia (slowness of movement), unstable posture, balance and gait abnor-
malities, and dysphonia (voice disorders). Eventually, the neural loss can spread
to non-motor regions leading to cognitive defects ranging from mild cognitive im-
pairment (MCI) to dementia. Parkinson’s disease can be challenging to diagnose
in its early stages. We currently have no definitive diagnostic test for PD; the
diagnosis is clinical, and an autopsy is considered necessary for disease confirma-
tion. This lack of reliable diagnosis is partly because patients’ symptoms vary
vastly. PD has traditionally been considered idiopathic (no known cause), and
there is no cure. Reliable biomarkers of symptomatic and presymptomatic dis-
ease can help with an automatic and accurate diagnosis. In addition, biomarkers
provide objective targets for developing and evaluating the clinical efficacy of new
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78
treatments.
7.2 Network Biomarkers of Parkinson’s Disease
A biological marker or biomarker is defined as a characteristic that is objectively
measured and evaluated as an indicator of normal biological processes, pathogenic
processes, or pharmacological responses to a therapeutic intervention [125, 126].
One of the main goals for biomarker identification is facilitating or improving dis-
ease diagnosis. This objective is critical in the case of PD because the accuracy
of gold-standard clinical diagnosis is only about 80% and has not improved in the
last 30 years [127]. This accuracy is much lower in patients with no severe symp-
toms. Since PD is a degenerative disease, longitudinal treatment after diagnosis
determines the patients’ well-being. Another application of biomarkers in PD is
monitoring disease progression and demonstrating treatment efficacy. Therefore,
a necessary characteristic of biomarkers is to accurately differentiate patients and
susceptible individuals from healthy controls.
Several studies have shown that whole-brain network connectivity estimated
from resting-state or task-related functional MRI are altered in patients with
PD [128–132]. Some functional imaging studies found disrupted connectivity in
crucial networks such as sensorimotor network [133, 134] and default mode net-
work (DMN) [135] in PD patients [136]. Recent findings also suggest that network
measures such as node centrality of specific regions (modeled as nodes in a graph)
can differentiate PD patients from healthy controls [129,136–138]. The majority of
these studies are focused on functional imaging data and functional (undirected)
networks. This dissertation is focused on novel methods to extract those net-
work biomarkers by estimating and analyzing effective (causal) brain networks in
Parkinson’s patients.
79
Table 7.1: Parkinson’s dataset-1 subject demographics (mean ± SD) reproduced
from [2]. Each control was matched to a person with PD with respect to their
age, sex and handedness.
Condition PD Control
Age (years) 62.62±8.32 63.50±9.66
Sex 8M 8F 7M 9F
Handedness All R All R
MMSE 28.94±1 29.19±1.10
NAART 46±6.27 49.12±7.14
BDI Off medication 9.44±5.07 3.27±3.20
BDI On medication 7.76±5.05 -
UPDRS III Off medication 41.5±12.95 -
UPDRS III On medication 33.68±10.86 -
Abbreviations: MMSE = Mini Mental State Exam; UPDRS = United Parkinson’s Disease
Rating Scale (motor); Dx = Parkinson’s diagnosis;BDI=Beck Depression Inventory;
NAART=North American Adult Reading Test
7.3 Parkinson’s Data Used in the Dissertation
7.3.1 Subjects
We used two Parkinson’s datasets in this study. The first dataset includes EEG
data from 15 PD patients (mean age 63.2± 8.2 years) and 16 healthy, age-matched
control participants (mean age 63.5 ± 9.6 years). The PD and control groups
include eight and nine females, respectively. All PD patients were diagnosed
by a movement disorder specialist at Scripps Clinic in La Jolla, California. All
participants provided written consent as per the Institutional Review Board of the
University of California, San Diego, and the Declaration of Helsinki. Additional
information about this data can be found in [2,139]. The demographic and rating
scale measures of the subjects are presented in Table 7.1.
The second dataset includes scalp EEG recordings from 27 patients with PD
80
Table 7.2: Parkinson’s dataset-2 subject demographics (mean ± SD) reproduced
from [3]. Each control was age and sex matched to a person with PD.
Condition PD Control
Sex 17M 10F 17M 10F
Age 69.5±8.7 69.5±9.3
MMSE 28.7±1 28.8±1
UPDRS 22.2±10.3 -
Year since Dx 5.7±4.2 -
EEG recording (min) 3.59±1 3.63±1.8
BDI 7.6±5.3 4.8±4.8
Year of Ed 17.3±3.3 16.6±3.1
Year of Ed (Parents) 12.5±3.8 12.5±3.1
LED (mg) 707.4±448.6 -
NAART 45.2±10.3 47.1±7.5
Abbreviations: MMSE = Mini Mental State Exam; UPDRS = United Parkinson’s Disease
Rating Scale (motor); Dx = Parkinson’s diagnosis;BDI=Beck Depression Inventory;
NAART=North American Adult Reading Test; LED=L-Dopa equivalence dose in mg.
who were recruited from the Albuquerque, New Mexico community and an equal
number of demographically matched (sex and age) controls. The PD and control
groups did not differ on education or premorbid intelligence measurements. All
participants were evaluated using Mini-Mental State Exam (MMSE) and achieved
a score above 26. All procedures were approved by the University of New Mexico
Office of the Institutional Review Board, and the participants were paid $20/hour.
The data were also reported in previous studies [3, 140, 141], and can be down-
loaded from [142]. Subject demographics and and assessment scores are presented
in Table 7.2.
Both datasets include data collected from PD patients in ‘on medication’ (PD-
ON) and ‘off medication’ (PD-OFF) states. Data from on and off medication
were collected on different days. The patients discontinued their dopaminergic
81
medicines at least 12 hours before the experiment for the PD-OFF phase.
7.3.2 EEG Recordings
In PD dataset-1, EEG data were acquired using a 32-channel BioSemi ActiveTwo
system, sampled at 512 Hz. Resting data were recorded for at least 3 min while
the participants were told to fixate on a cross presented on a screen. PD dataset-
2 consists of EEG signals recorded via Ag/AgCl electrodes with a sampling rate
of 500 Hz on a 64-channel Brain Vision system. The signals were referenced
the ‘CPz’ channel, resulting in 63 timeseries. This analysis considers resting-state
EEG signals of one-minute duration recorded while the participants had their eyes
closed (unlike PD dataset-1). The EEG channel locations in the two datasets are
depicted in Fig.7.1.
We high-pass filtered the signals at 0.5 Hz cut-off to remove low frequency
drift. We also filtered all signals using a 6th order IIR filter, to remove the power-
line noise and its harmonics. We used two-way (bidirectional) filtering to avoid
any phase shifting that can affect causal inference between the signals.
82
(a) PD Dataset-1 (32 channels)
(b) PD Dataset-2 (63 channels)
Figure 7.1: EEG channel locations plotted on a 2-D head diagram. Channels
plotted beyond the head limit extend below the head center’s horizontal plane.
Chapter 8
Distinguishing Parkinson’s
Disease Patients Using Functional
Brain Networks
8.1 Introduction
Parkinson’s disease (PD) is a neurodegenerative disorder that predominately af-
fects dopamine-producing (“dopaminergic”) neurons in a specific area of the brain
called substantia nigra, which impacts communication pathways of the brain. PD
affects the lives of more than 10 million people worldwide and is expected to be-
come more prevalent in the future [143]. The main symptoms of PD are tremor,
muscle stiffness, bradykinesia (slowness of movement), unstable posture, balance
and gait abnormalities, and dysphonia (voice disorders). Non-motor symptoms
can range from mild cognitive impairment (MCI) to dementia.
Diagnosis of PD remains complicated, especially in patients without severe
symptoms. Accuracy of gold-standard clinical diagnosis is only about 80% and
has not improved in the last 30 years [127]. Considering that most PD patients
develop dementia in 15-20 years, there is an urgent need to identify biomarkers for
early diagnosis, monitor disease progression, and establish efficacious therapies. It
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84
is established that cognitive dysfunction in neurological disorders can be described
as aberrant patterns of interactions between neural elements in a large-scale brain
network [101, 102, 144]. We hypothesize that network analysis may hold the key
to understanding the electrophysiological basis of PD.
Although functional network analysis of Parkinson’s was addressed in past
literature, majority of these studies are limited to functional magnetic resonance
imaging (fMRI) [134,145–147]. Scalp EEG is optimal for clinical, commercial, and
research purposes because of its non-invasive nature and wide availability. More
importantly, EEG can sample neural activity at 100–1000x higher time resolu-
tion than fMRI, making it more suitable to assess temporal dynamics. Previous
EEG research on Parkinson’s was focused on spectral features, or event-related
potentials [3, 148–151]. However, these approaches do not consider simultaneous
interactions between multiple brain areas, i.e., EEG network functional connec-
tivity.
This chapter presents a functional network analysis to decode scalp EEG sig-
nals and detect node centrality modulations indicative of PD. Recent studies
demonstrated statistical differences in network measures such as node central-
ity between PD patients and healthy controls [129, 136–138]. Here, we present
perhaps the first EEG-based machine learning analysis that utilizes node central-
ity features to differentiate between Parkinson’s patients and healthy controls to
the best of our knowledge.
8.2 Materials and Methods
8.2.1 Data
The dataset used in this chapter is Parksinon’s dataset-2, described in Chapter
7. The data included scalp EEG recordings from 27 patients with PD who were
recruited from the Albuquerque, New Mexico community and an equal number of
demographically matched (sex and age) controls. All participants were evaluated
85
using Mini-Mental State Exam (MMSE) and achieved a score above 26. The
PD and control groups did not differ on any education or premorbid intelligence
measurements. All procedures were approved by the University of New Mexico
Office of the Institutional Review Board, and the participants were paid $20/hour.
Each PD patient visited the lab twice: on medication (PD-ON) and off medication
(PD-OFF). In the PD-OFF phase, the patients took their most recent dose of
dopaminergic medicines at least 12 hours before the experiment.
EEG was recorded from Ag/AgCl electrodes with a sampling rate of 500 Hz
on a 64-channel Brain Vision system. The signals were referenced to the ‘CPz’
channel, resulting in 63 timeseries. The original dataset consisted of two one-
minute segments per subject: eyes-open and closed conditions. This analysis uses
resting-state EEG signals of one-minute duration recorded under the eyes-open
condition. The data were also reported in previous studies [3,140,141], and can be
downloaded from https://narayanan.lab.uiowa.edu/article/datasets. Power line
noise and its harmonics were removed using 6th order IIR filters.
8.2.2 Feature Extraction Using Network Analysis
Functional Networks were constructed by computing absolute Pearson’s correla-
tion coefficient between all pairs of channels. In this case, each EEG channel
is a node. Therefore, an edge with high connectivity displays a strong correla-
tion between the interacting channels. Since a value between 0 and 1 represents
each connection, these are weighted-undirected networks. For each subject, the
one-minute recording was divided into 11 30-second segments with 90% overlap.
Functional networks for each of the 11 segments were computed. The final repre-
sentative network was the mean of these 11 networks. The mean networks were
considered to minimize the effects of non-stationarity.
The node centrality of a given node measures its importance within the net-
work. We compute three node centrality metrics: betweenness centrality, node
degree, and eigenvector centrality. Betweenness centrality measures the extent to
86
(a) Healthy controls (HC) (b) Parkinson’s– on medication (PD-ON)
(c) Parkinson’s– off medication (PD-OFF)
Figure 8.1: Scalp topographical maps of average betweenness centrality.
87
which a given node falls in the shortest path between any two other nodes [152].
Node degree quantifies the number of connections to a node. Eigenvector central-
ity is a measure of the influence a node has on a network and was found to be
linked to firing rates of neurons [153]. The node centrality values were used as
features for classification.
Fig. 8.1 shows the two-dimensional scalp topographic maps depicting the
average betweenness centrality of nodes in the three groups: healthy controls
(HC), PD-ON, and PD-OFF. All three scalp maps were plotted on the same scale
for comparison. We observe that the betweenness centrality in HC is higher in
the mid-frontal region compared to PD-ON and PD-OFF.
8.2.3 Feature Selection and Classification
Naive Bayes classifiers with Gaussian kernel were trained to differentiate PD pa-
tients from healthy controls. The classifiers were modeled separately for PD-ON
and PD-OFF patients. For single-channel classification, the betweenness central-
ity of a single node was used as the input feature. For multi-channel classifi-
cation, sequential forward feature selection was employed to select the optimal
features/channels. That is, we first start with an empty candidate set. In each
iteration, a new feature is sequentially added to the set to minimize classification
error. The process is stopped when the accuracy cannot be improved further.
The classifiers were evaluated using leave-one-subject-out cross-validation. The
cross-validation prevents overestimating the accuracy due to over-fitting of train-
ing data and ensures the models were evaluated on all subjects.
88
8.3 Results
8.3.1 Single-Channel Classification
Fig. 8.2(a) and Fig. 8.2(b) depict single-channel classification performance for
HC vs. PD-ON and HC vs. PD-OFF, respectively. Each value is the mean cross-
validation accuracy. The best HC vs. PD-ON accuracy was 75.93% for channel
C2. For HC vs. PD-OFF, the highest accuracy of 79.63% was attained by channel
PO7.
8.3.2 Multi-Channel Classification
The results presented here are based on Naive Bayes classifiers with Gaussian ker-
nels. We observed that these models performed the best with minimal overfitting
compared with other machine learning models such as support vector machines,
linear discriminant analysis, and decision trees. The receiver operating character-
istic (ROC) curves comparing the three node-centrality measures are depicted in
Fig. 8.3. ROC curve can be used to evaluate the performance of binary classi-
fiers. The higher the area under the ROC curve (AUC), the better the models
distinguish between the two classes. The plots illustrate that betweenness cen-
trality differentiates the healthy subjects from PD patients, with the highest AUC
in PD-ON and PD-OFF conditions. The betweenness centrality-based classifiers
achieved an AUC of 91.63% and 88.6% for HC vs. PD-ON and PD-OFF, respec-
tively.
The individual classification results are presented in Table 8.1. It can be
observed that betweenness centrality (BC) outperforms node degree (ND) and
eigenvector centrality (EC) in both cases. For HC vs. PD-ON, the accuracy,
sensitivity, and specificity were 88.9% each. Betweenness centrality of nodes rep-
resented by EEG electrodes FT9, PO5 and PO7 were the most discriminatory
between the two classes. In the case of HC vs. PD-OFF, the accuracy, sensitiv-
ity, and specificity were 88.89%, 92.59%, and 88.6%, respectively. Betweenness
89
(a) Healthy controls vs. PD-ON
(b) Healthy controls vs. PD-OFF
Figure 8.2: Single-channel classification performance comparison.
90
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
False positive rate
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Tr
ue
 p
os
iti
ve
 ra
te
Betweenness
Node Degree
Eigen Vector
(a) Healthy controls vs. PD-ON
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
False positive rate
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Tr
ue
 p
os
iti
ve
 ra
te
Betweenness
Node Degree
Eigen Vector
(b) Healthy controls vs. PD-OFF
Figure 8.3: Receiver operating characteristic (ROC) curves comparison between
3 node centrality measures.
91
Table 8.1: Leave-one-subject-out cross validation results summary for HC vs.
PD classification. Sensitivity and specificity represent the healthy control and
PD accuracies, respectively. Random label-assignment would result in a baseline
accuracy of 50%.
Classifier HC vs. PD-ON HC vs. PD-OFF HC vs. PD
(ON+OFF)
Features BC ND EC BC ND EC LEAPD [3]
Accuracy(%) 88.9 74.1 83.3 88.9 83.3 63 85.2
Sensitivity(%) 88.9 63 85.2 92.6 77.8 63 88.9
Specificity(%) 88.9 85.2 81.5 88.2 88.9 63 81.5
AUC(%) 91.6 63.92 77.2 88.6 82.7 61.2 93.8
Abbreviations: HC=Healthy controls, PD=Parkinson’s disease, BC = Betweenness centrality,
ND=Node degree, EC=Eigenvector centrality, LEAPD=Linear-predictive-coding EEG
Algorithm for PD [3]
centralities of P5, PO7 and PO3 were chosen as the optimal features for HC vs.
PD-OFF.
8.4 Discussion
There is a growing consensus in modern neuroscience that human brain function
is encoded as complex small-world networks. In other words, functional brain
networks contain a combination of dense local connectivity and sparse yet efficient
long-distance (global) connectivity. Some nodes are more important (hub nodes)
than other as a result of this small-worldness. This node importance can be
measured using node centrality metrics such as betweenness centrality. Our work
showed that betweenness centrality differentiates PD patients from age-matched
controls. We also show that this effect is independent of the patients’ medication
status. Besides PD, modulated betweenness centrality has been also implicated
in other neurological disorders such as Alzheimer’s, Schizophrenia and Epilepsy
92
[144,154–156].
Our method achieved higher leave-one-out cross-validation accuracy (88.9%)
than the state-of-the-art (85.2%) on this dataset [3]. The decoders in [3] are
based on spectral properties of individual channels but do not take into account
the interactions between the channels. One limitation of the proposed approach is
that the neural activity is recorded from the scalp. Scalp EEG is typically affected
by confounding factors such as volume conduction. Also, compared to fMRI, EEG
has a lower spatial resolution, making it difficult to localize the source of the
activity. However, the proposed approach is amenable to real-time applications
since it only requires 1-minute resting-state EEG recordings. All existing methods
use longer recordings or employ computationally complex algorithms like deep
learning [3, 150,157].
8.5 Conclusion
This work demonstrates that metrics like betweenness centrality can measure how
functional networks encode PD [158]. We employed graph analysis to develop
neural classifiers that accurately separate PD patients from healthy age-matched
controls regardless of their medication status. Such decoders can assist clinicians
as a cost-effective diagnostic tool, crucial for prognostic and therapeutic purposes.
These decoders can also be used to find biomarkers of PD for developing inter-
ventional therapies such as adaptive deep-brain stimulation or transcranial direct-
current stimulation [159]. Future research can be directed towards validating this
approach on multiple datasets. Automatic monitoring of disease progression in
Parkinson’s can also be explored using similar network-based methods.
Chapter 9
Frequency-Domain Convergent
Cross-Mapping: A Novel Causal
Connectivity Measure
9.1 Introduction
Data-driven effective connectivity measures can vary from linear to nonlinear,
model-based to model-free, and time-domain to frequency-domain [1, 160]. Ma-
jority of the existing measures are based on Granger’s approach [1, 18, 19]. How-
ever, these Granger-based measures such as Granger causality, directed transfer
function (DTF), and partial directed coherence (PDC) are only applicable to
strongly-coupled, linear, and stochastic systems [23,24]. Granger causality is also
model-based and does not always reveal causal interactions [12,23].
A newly developed method of assessing causation between timeseries, conver-
gent cross-mapping (CCM) [12], has been shown to identify causal relationships
that Granger causality may miss due to nonlinearity or deterministic nature. CCM
has been applied in a limited number of studies to characterize neurological dis-
orders [161–164]. CCM is based on time-domain dynamics and does not include
spectral information. Frequency-based methods such as PDC [27], DTF [26] and
93
94
dynamic causal modeling [17] have been shown to be useful in detecting brain dis-
orders [165–169]. However, these methods are derived using Granger’s approach
and are model-based [170]. This chapter introduces the first frequency-based
causality measure that can infer nonlinear causal interactions between neuronal
populations without requiring any model estimation.
The proposed method called frequency-domain convergent cross-mapping (FD-
CCM) is a nonlinear state-space reconstruction technique similar to CCM [171].
For two causally coupled neuronal dynamics, the rationale behind causal infer-
ence using FDCCM is based on the following intuition. Since the cause-variable
influences the effect-variable, we can reconstruct the causal timeseries by finding
its signature in the power spectrum of the effect timeseries. In other words, we
utilize the mapping between the power spectra of the two timeseries to estimate
the causal influence of one on the other. This chapter illustrates the principle of
our approach on simple toy data, coupled logistic maps; and show that FDCCM
reliably estimates interactions.
In this chapter, we introduce a spectral measure of causality called frequency-
domain convergent cross-mapping or FDCCM. Unlike existing spectral measures
of effective connectivity, FDCCM is model-free and can infer nonlinear interac-
tions. We describe the algorithm and validate our method on a toy dataset. We
illustrate the effect of coupling strength and noise on the quality of causal infer-
ence; and demonstrate that FDCCM is more robust to external noise than CCM.
9.2 A Brief Introduction to Convergent Cross-
Mapping (CCM)
In dynamical systems, causally interacting variables (e.g., two electrode record-
ings) share a trajectory in the underlying state-space called ‘attractor’ space. In
other words, each time-point corresponds to a location in this space. Mathe-
matical theorems guarantee that the temporal sequence of a single variable has
95
sufficient information about the entire system’s dynamics. Accordingly, the dy-
namics of one variable constrain the dynamics of other variables, and can be used
to reconstruct the original global attractor topology.
Consider two timeseries, X and Y , part of a deterministic dynamical sys-
tem denoted by M . We can then express the temporal dynamics of X in a
delay-coordinate state-space that consist of the set of D-dimensional state vec-
tors: x(t) = {x(t), x(t− 1), . . . , x(t− (D − 1))}. The time delays are assumed to
be 1 for simplicity. This transformed state-space of X is called its attractor mani-
fold MX . This process of transforming a sequence into its delay-coordinate space
is called time-delay embedding. As proven by Takens theorem [172], a general
principle in dynamical systems is that the states of the global attractor M have
a one-to-one mapping to the the local attractors MX and MY . Consequently the
local attractors (also known as shadow manifolds) MX and MY have a one-to-one
correspondence with each other.
Based on this property, a protocol for inferring causation in complex systems
was proposed by Sugihara et. al., using K-nearest-neighbor state-space recon-
struction [12]. To understand the intuition behind this method, called convergent
cross-mapping (CCM), consider two variables X and Y with asymmetric interac-
tion. That is, X influences Y but not vice-versa. The aim is to infer the causal
interactions from observational timeseries X and Y . Since there is a causal con-
nection from X to Y , the history of Y has information about X. In other words, a
local neighborhood in MY corresponds to a local neighborhood in MX . Therefore
the ‘cause-variable’ X can be accurately reconstructed using the nearest neighbors
in the shadow manifold MY , if and only if there is causal connection from X to
Y . As the causal influence of X on the dynamics of Y increases, more informa-
tion about X is encoded in the manifold MY constructed from a fixed number of
observations of Y. This rationale acts as the basis for causal inference using CCM.
96
9.3 Frequency-Domain Convergent Cross-Mapping
(FDCCM)
9.3.1 The Basic Concept
In the proposed frequency-domain convergent cross-mapping (FDCCM), we ex-
tend the idea of causal inference using nonlinear state-space reconstruction to
frequency-domain. Intuitively, any linear transformation of a manifold should
preserve its topology: a corollary of random projection theory [173]. For a
given frequency, Fourier transform is a linear transformation. Hence, we can
preserve the geometry by transforming the delay-coordinate space to frequency
space, by computing the power spectrum of x(t). This transformation is equiv-
alent to computing short-time Fourier transform (STFT) with pre-defined fre-
quency bands. The time-delayed embedding in CCM is now replaced by spectro-
grams, such that each point in the resultant attractor manifold (MX) is x(t) =
{xf1(t), xf2(t), . . . , xfD(t))}, where the subscripts represent D different frequency
bands. Before outlining the algorithm of FDCCM, we describe two key ingredients
of the method: cross-mapping and convergence.
9.3.2 Cross-Mapping in FDCCM
If X has a causal influence on Y , then X will influence the frequency dynamics
of Y . This ‘imprint’ of X on Y means that topology of MY obtained from Y
can be used to estimate values of X. This estimate at a given time instant t is
called the cross-map of x(t) given MY , and is denoted xˆ(t)|MY . If X and Y are
causally coupled, then each point x(t) in MX is can be mapped to a unique point
in MY [12].
To compute the cross-mapped estimates xˆ(t)|MY , we use simplex-projection al-
gorithm as described by (9.1) and (9.2). We first obtain a small region around y(t),
represented by its k nearest neighbors: {y1(t),y2(t), . . . ,yk(t)}. This neighbor-
hood is then mapped to a set of points inMX , represented as {x1(t),x2(t), . . . ,xk(t)}.
97
To form a bounding simplex in D-dimensional space, we need k ≥ D + 1. The
weighted mean of {x1(t),x2(t), . . . ,xk(t)} provides the estimate of x(t) as shown
in the equation,
xˆ(t)|MY =
D+1∑
i=1
wix1(t). (9.1)
The weighting wi is based on the distance between y(t) and its i
th nearest
neighbor yi(t) as given by the equations,
wi = ui/
D+1∑
j=1
uj and ui = exp
[
− d(y(t),yi(t)
d(y(t),y1(t)
]
(9.2)
where d(., .) represents the Euclidean distance.
The cross-mapping was implemented for L points in the timeseries X algo-
rithm. The correlation coefficient between the original timeseries and the esti-
mated timeseries, i.e., ρxxˆ is used as an indicator of the influence of X on Y .
The cross-mapping yˆ(t)|MX can be estimated analogously. Fig. 9.1 illustrates
the cross-mapping at time instant t for a bi-variate example where X influences
Y , but there is no causal link from Y to X. The state-space reconstruction of X
using MY (i.e., xˆ(t)|MY ) would be accurate due to the effect X has on Y, but not
vice-versa.
9.3.3 Convergence
For practical application, the cross-mapping estimates of timeseries are evaluated
using correlation coefficient, mean absolute error, or similar metrics. We use
correlation coefficient (ρ) as the accuracy metric in this study. The total number
of time points, i.e., the ‘library’ of points in the attractors used for cross-mapping
is called library length (L). As L increases, attractors get more dense in the
state-space, resulting in closer nearest neighbors, and more accurate estimation.
This increasing cross-mapping accuracy with increase in L is a key property for
98
(a) Estimating x(t) from MY with high accuracy
(b) Estimating y(t) from MX with low accuracy
Figure 9.1: Illustration of cross-mapping between X and Y when X influences Y
but Y has no (or minimal) effect on X.
99
causal interactions [12]. We use the cross-mapping accuracy at maximum L to
infer network interactions.
9.3.4 Algorithm
Here, we outline the main steps in computing FDCCM between two timeseries.
For a given library length L, the basic algorithm for cross-mapping X using the
shadow attractor MY is given by:
• Compute the time-frequency spectrograms MX and MY . Note that L is the
number of time windows and D is the number of frequency bands.
• For each time index t = 1 to L, find D+1 nearest neighbors of y(t) in MY .
• Generate weights wi according to (9.2).
• Estimate xˆ(t)|MY using (9.1).
• Calculate correlation coefficient ρXˆ|MY between X = {x(t) : 1 ≤ t ≤ L} and
Xˆ = {xˆ(t)|MY : 1 ≤ t ≤ L}.
9.4 Toy Data Analysis
9.4.1 Data Generation
Three datasets are used in this analysis. The first is a toy dataset that simulates
nonlinear causal interactions between two variables. The second and third datasets
contain experimental resting-state scalp EEG recordings from Parkinson’s patients
and healthy controls.
100
9.4.2 Toy Data
The logistic map is a well-established nonlinear dynamic equation that generates
periodic and chaotic behavior [174]. Despite its mathematical simplicity, a lo-
gistic map exhibits a high degree of complexity. Two logistic maps with chaotic
dynamics can be coupled to create a complex system akin to biological systems.
Two timeseries in a coupled logistic map can be correlated, uncorrelated, or anti-
correlated at different times [12]. The coupled logistic maps timeseries X and Y
were synthesized using the following equations:
x(t+ 1) = x(t)[rx(1− x(t))− βxyy(t)]
y(t+ 1) = y(t)[ry(1− y(t))− βyxx(t)].
(9.3)
The variables X and Y have a nonlinear dependence on their own past values
parameterized by the growth rates rx and ry. The coupling constants βyx and βxy
characterize the coupling strengths from X to Y and from Y to X, respectively.
The variables have chaotic dynamics at values of rx and ry above 3.57. We chose
the rx = 3.65 and ry = 3.77, so we are in the chaotic regime of the logistic
map [111].
9.4.3 Convergence
We synthesized coupled logistic maps, X and Y , using (9.3) with parameters:
rx = 3.65, ry = 3.77, βxy = 0.05, andβyx = 0.5. 25,000 samples were generated and
the first 10,000 were discarded to avoid the effects of transient behaviour of the
model. The remaining 15,000 points were used for the analysis, assuming a 500
Hz sampling rate— a total duration of thirty seconds. To estimate spectrograms
and FDCCM, we used a 5Hz frequency resolution, up to 200 Hz, analogous to the
Parkinson’s data. Fig. 9.2 illustrates how the cross-mapping accuracy between X
and Y grows with increasing library length L. The increasing trend of ρXˆ|MY and
ρYˆ |MX validate the causal influence from X to Y and Y to X, respectively. It can
be observed that the difference ρXˆ|MY − ρYˆ |MX is always positive, supporting the
101
500 1000 1500 2000 2500
Library length L
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Figure 9.2: Correlation coefficients of the two estimated timeseries, Xˆ|MY and
Yˆ |MX , with respect to library length (L). Coupling strengths: βxy = 0.05 and
βyx = 0.5. Xˆ|MY represents the influence X → Y , and Yˆ |MX represents the
influence Y → X.
fact that βyx > βxy.
9.4.4 Effect of Coupling Strength
We denote the difference ρXˆ|MY − ρYˆ |MX by ρdiff , which is a measure of relative
causal influence from X to Y . To test how the relative causality varies with
coupling strength, we fix βxy at 0.5, and estimate ρdiff at different values of βyx.
Fig. 9.3 demonstrates that ρdiff increases with increasing βyx. More importantly,
when βyx < 0.5 = βxy, ρdiff is negative. Each value in the plot is the average result
of 100 simulations. Although the direction of causality is correct, the magnitude
of causal strength is not reliable when there is weak coupling. Note that there is
a monotonous increase in ρdiff only for coupling strengths higher than 0.35.
102
0 0.2 0.4 0.6 0.8 1
yx
-0.05
0
0.05
0.1
0.15
0.2
0.25
di
ff
Figure 9.3: Difference between ρX→Y and ρY→X (denoted by ρdiff ) as a function
of coupling strength βyx. βxy = 0.5.
9.4.5 Effect of Volume Conduction
Scalp EEG signals tend to be highly correlated with each other due to volume
conduction. The volume conduction effect is a result of a mixture of concurrently
active brain and non-brain electrical sources. One way to simulate the effect of
volume conduction is to use a mixture matrix M that transforms source activity
into measured activity as described in [175]. We assume that x(t) and y(t) syn-
thesized using (9.3) are two cortical sources. The mixing matrix M containing
the weights that mix the source activities (x(t) and y(t)) to two scalp activities
(p(t) and q(t)). This transformation can be expressed as(
p(t)
q(t)
)
=M
(
x(t)
y(t)
)
(9.4)
103
0 0.2 0.4 0.6 0.8 1
yx
-0.05
0
0.05
0.1
0.15
0.2
0.25
di
ff
Figure 9.4: Difference between ρP→Q and ρQ→P (denoted by ρdiff ) as a function
of coupling strength βyx, with volume conducting. βxy = 0.5.
where M is a 2x2 matrix. We assume M =
(
15 1.5
2 20
)
. When βxy = 0.5 and
βyx = 0.6, the Pearson’s correlation coefficient between between x and y is 0.7. As
a result of volume conduction the correlation between p and q increases to 0.79,
a 9% increase. We repeat the analysis shown in Fig. 9.3 with volume conduction
by fixing βxy at 0.5, and estimating ρdiff at different values of βyx. These results
are presented in Fig. 9.4. Comparing the results with Fig. 9.3, it can be noticed
that volume conduction does not have a notable effect on FDCCM estimates.
9.4.6 Effect of Noise
Since real-world signals such as electrophysiological data are affected by environ-
mental and measurement noise, it is important to study the effect of noise. It is
known that cross-mapped estimates of CCM deteriorate as more noise is present
in the data [12, 111]. To characterize the effect of noise on FDCCM, we simulate
104
noisy timeseries given by the equations,
x(t+ 1) = x(t)[rx(1− x(t))− βxyy(t)] + ϵx(t)
y(t+ 1) = y(t)[ry(1− y(t))− βyxx(t)] + ϵy(t).
(9.5)
Here, ϵx and ϵy are the noise terms, that were modeled as additive Gaussian
noise with zero mean and standard deviation σ. We repeated the simulations at
different signal-to-noise ratios (SNR), and a different coupling strengths βyx =
{0.6, 0.7, 0.8, 0.9}. Note that βxy was kept constant 0.5. We evaluated (time-
domain) CCM and FDCCM by quantifying the effect of noise level on ρdiff . This
effect of noise on CCM and FDCCM is presented in Fig. 9.5.
For βyx > 0.5, we expect ρdiff > 0, a demonstrated in Fig. 9.1. Additionally,
we expect ρdiff to be higher for higher values of βyx as the influence of X on
Y becomes stronger. When the noise is high, i.e., SNR is zero (dB) the two
timeseries become uncorrelated resulting in ρdiff = 0. As the SNR increases, and
the signal tends to dominate the noise, we notice that ρdiff converges to more
accurate values that are greater than zero. We can observe that both methods
showcase the expected trend at high SNR: ρdiff ∝ βyx. However, empirical data
often contains a moderate level of noise. It is, therefore, important to determine
the threshold at which the methods become unreliable. As shown in Fig. 9.5(a),
when the SNR is less than 16 dB, CCM does not perform as expected at different
coupling strengths. Fig. 9.5(b) shows that as long as the SNR is not too low,
i.e., for SNR ≥ 3 dB FDCCM results in reliable estimates of ρdiff . These plots
illustrate that FDCCM is more robust to noise.
105
0 5 10 15 20 25 30
SNR (dB)
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
di
ff
16 dB
yx=0.6
yx=0.7
yx=0.8
yx=0.9
yx=1
(a) CCM
0 5 10 15 20 25 30
SNR (dB)
-0.05
0
0.05
0.1
0.15
0.2
0.25
di
ff
3 dB
yx=0.6
yx=0.7
yx=0.8
yx=0.9
yx=1
(b) FDCCM
Figure 9.5: The effect of noise on CCM and FDCCM estimates. ρdiff as a function
of increasing signal-to-noise ratio (SNR) for different coupling strengths βyx.
Chapter 10
Distinguishing Parkinson’s
Patients Using Causal Networks
10.1 Introduction
The human brain is an efficient organization of 100 billion (1011) neurons anatom-
ically connected by about 100 trillion (1014) synapses over multiple scales of space
and functionally interactive over multiple scales of time [176]. The recent mathe-
matical and conceptual development of network science combined with the tech-
nological advancement of measuring neuronal dynamics motivated the field of
network neuroscience. Network science provides a particularly appropriate frame-
work to study several mechanisms in the brain by treating neural elements (a
population of neurons, a sub-region) as nodes in a graph and neural interactions
(synaptic connections, information flow) as its edges. The central goal of network
neuroscience is to link macro-scale human brain network topology to cognitive
functions and clinical disorders. It is established that neurological disorders and
cognitive phenomena can be described as aberrant patterns of interactions be-
tween neural elements in a large-scale brain network [101,102,144].
Apart from the anatomical/structural connectivity, measured neural dynam-
ics can be used to estimate functional and effective networks. While functional
106
107
connectivity is defined as a statistical dependence between the neurophysiological
signals, effective connectivity characterizes patterns of causal interactions [152].
While the underlying anatomical pathways between brain regions or populations
of neurons are bidirectional, we cannot assume that the connectivity is symmet-
rical. Although there are several linear and nonlinear measures of undirected
correlation, estimating the directionality in brain networks is an important and
largely unaddressed issue [8]. This chapter applies FDCCM to real-world datasets
and evaluate its performance in detecting biomarkers for Parkinson’s disease using
resting-state EEG.
The specific contributions of this chapter are outlined below:
• We estimate effective networks by applying FDCCM on resting-state scalp
EEG recordings from two Parkinson’s datasets. We employ graph analysis
to showcase the difference in betweenness centrality between the patients
and controls.
• We demonstrate that machine learning classifiers based on FDCCM causal
networks can differentiate between Parkinson’s patients and demographi-
cally matched healthy controls with 97% accuracy. The performance of FD-
CCM is shown to be better than correlational networks and CCM networks
on both datasets. novel machine-learning approach to diagnose Parkinson’s
disease with EEG.
10.2 Materials Methods
10.2.1 Data
The dataset used in this chapter is described in Chapter 7.
108
10.2.2 Network Features
The analysis for Parkinson’s data consists of three steps: construct networks,
compute node centrality of every node in the network, and learn HC vs. PD
classifiers using the node centralities as features. Each of these steps is described
below.
First, we construct networks using thirty-second epochs of the EEG signals.
We split the recordings into multiple thirty-second epochs with 90% overlap. Since
each subject PD dataset-1 has signals of duration three minutes, there are 51
such epochs per subject leading to 51 networks. In the case of PD dataset-2, the
one-minute recordings produce 11 networks. The average of these networks de-
fines the resting-state connectivity for each subject. Each network was estimated
using three network measures: correlation coefficient, CCM (time-domain) and
FDCCM.
To construct networks using FDCCM, we determine the spectrograms (time-
frequency matrices) for each EEG recording. Fig. 10.1 presents spectrograms
associated with two different electrodes from a PD patient in PD dataset-1. To
generate the spectrograms, we compute power spectrum with 0.5-second sliding
windows with 95% overlap. The frequency resolution used was 5 Hz, up to 200 Hz.
These spectrograms are then used to estimate the causal connectivity between all
pairs of channels.
Thus, each healthy control subject has a representative functional or effective
connectivity graph. Each PD patient has two graphs (on and off medication). We
then compute betweenness centrality of the nodes in these graphs. For a subject
with N channels, effective networks can have up to N(N − 1) connections. That
is, 992 connections if N = 32, and 3906 connections if N = 63. Node centrality is
a way to extract interpretable information from the networks, while reducing the
number of features. Betweenness centrality measures the extent to which a given
node falls in the shortest path between any two other nodes [152]. Therefore, it
is a measure of importance of the node acting as a bridge between other nodes in
the graph.
109
5 10 15 20 25
Time (s)
50
100
150
200
Fr
eq
ue
nc
y 
(H
z)
-30
-20
-10
0
10
Po
w
er
 (d
B)
(a) Channel-X
5 10 15 20 25
Time (s)
50
100
150
200
Fr
eq
ue
nc
y 
(H
z)
-30
-20
-10
0
10
Po
w
er
 (d
B)
(b) Channel-Y
Figure 10.1: Example time-frequency representations (spectrogram) derived from
two arbitrarily chosen channels. The spectrograms correspond to a Parkinson’s
patient from PD dataset-1. Time resolution: 0.5-second windows with 95% over-
lap. Frequency resolution: 5Hz, up to 200 Hz.
110
10.2.3 Classification
We train separate classifiers to differentiate PD-ON and PD-OFF from controls.
Betweenness centrality of the nodes in each subject’s network are used as fea-
tures. Since each subject has 32 or 63 features, sequential forward selection was
employed to select the optimal features/channels. We employ Naive Bayes clas-
sifiers with Gaussian kernels which learns a nonlinear decision boundary between
the two classes. We observed that these models perform better than other linear
models such as support-vector machines (SVM) and linear discriminant analysis;
and nonlinear models such as polynomial SVM and decision trees. The classifiers
were evaluated using leave-one-subject-out cross-validation. The cross-validation
prevents overestimating the accuracy due to over-fitting of training data and en-
sures the models were evaluated on all subjects.
10.3 Results
We employ three network connectivity measures: functional (correlational) net-
works based on Pearson’s correlation coefficient, and effective (causal) networks
based on CCM and FDCCM. We compare the three methods by evaluating their
performance in differentiating PD (ON and OFF) patients from healthy controls.
Receiver operation characteristic (ROC) curves for the classification models based
on the three network types are compared in Fig. 10.2 and Fig. 10.3 for PD
dataset-1 and PD dataset-2, respectively. The ROC curves plot true-positive rate
vs. false-positive rates for a given binary classifier at different model thresholds.
As classifiers attain higher true-positive rates and lower false-positive rates, the
curve moves closer to the top-left corner of the plot. Fig. 10.2 and Fig. 10.3 show
that FDCCM outperforms the CCM and correlation as the preferred connectivity
measure.
We report the leave-one-patient-out classification accuracy, sensitivity and
specificity of the models in Tables 10.1 and 10.2. FDCCM outperforms the
111
other two methods in both datasets. In PD dataset-1, FDCCM-based decoders
can distinguish PD patients (both on and off medication) with 96.8% accuracy
(AUC=0.98): a substantial improvement over the other two methods. The opti-
mal features selected by the feature selection correspond to EEG electrodes F7
and PO4, for HC vs. PD-ON; and CP5, O1, and Oz, for HC vs. PD-OFF. The op-
timal features and the decoding performance varies depending on the connectivity
measure used. In PD dataset-2, FDCCM achieves 96.23% accuracy (AUC=0.96)
and 88.68% accuracy (AUC=0.92) for HC vs. PD-ON and HC vs. PD-OFF,
respectively. These accuracies are significantly higher than the best accuracy of
85.2% (AUC=0.94) previously reported on this dataset [3].
10.4 Discussion
Most PD patients develop dementia in 15-20 years. Accuracy of gold-standard
clinical diagnosis of PD is only about 80% and has not improved in the last 30 years
[127]. Existing studies on Parkinson’s were either limited to functional magnetic
resonance imaging (fMRI) data [134, 145–147], or focused on spectral features
[3,148–151]. However, these approaches do not consider simultaneous interactions
between multiple brain areas. We believe that network analysis may hold the
key to identify biomarkers for early diagnosis, monitor disease progression, and
establish efficacious therapies.
Modern neuroscience has shown that human brain networks exhibit high lev-
els of clustering, a pattern indicative of a small-world architecture [4, 177]. In
other words, some nodes (hub nodes) play a more important role in information
transfer between different regions. This node importance can be measured using
node centrality metrics such as betweenness centrality. Modulated betweenness
centrality has been implicated in a wide variety of neurological disorders such as
Alzheimer’s, Schizophrenia and Epilepsy [144,154–156]. Some prior studies on PD
also showed an altered hub organization between PD and HC subjects. In par-
ticular, they showed that important nodes, i.e., nodes with higher betweenness
112
0 0.2 0.4 0.6 0.8 1
False positive rate
0
0.2
0.4
0.6
0.8
1
Tr
ue
 p
os
iti
ve
 ra
te
Correlation Coeff.
CCM
FDCCM
(a) HC vs. PD-ON
0 0.2 0.4 0.6 0.8 1
False positive rate
0
0.2
0.4
0.6
0.8
1
Tr
ue
 p
os
iti
ve
 ra
te
Correlation Coeff.
CCM
FDCCM
(b) HC vs. PD-OFF
Figure 10.2: HC vs. PD classification receiver operating characteristic (ROC)
curves - PD dataset-1.
113
0 0.2 0.4 0.6 0.8 1
False positive rate
0
0.2
0.4
0.6
0.8
1
Tr
ue
 p
os
iti
ve
 ra
te
Correlation Coeff.
CCM
FDCCM
(a) HC vs. PD-ON
0 0.2 0.4 0.6 0.8 1
False positive rate
0
0.2
0.4
0.6
0.8
1
Tr
ue
 p
os
iti
ve
 ra
te
Correlation Coeff.
CCM
FDCCM
(b) HC vs. PD-OFF
Figure 10.3: HC vs. PD classification receiver operating characteristic (ROC)
curves - PD dataset-2.
114
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116
centrality, lost significance and the nodes with a less central role have become
more important [129,178,179].
Fig. 10.4 and Fig.10.5 illustrate this distinction between patients and healthy
age-matched controls on two independent resting-state datasets. The scalp topo-
graphical maps of average betweenness centrality in each group— HC, PD-ON
and PD-OFF— show that the spatial distribution of betweenness centrality varies
between the HC and PD groups. The HC controls have higher node centrality in
the mid-frontal regions while, the PD groups show higher values in mid-parietal
regions. Note that these scalp maps are derived from FDCCM networks.
We quantify these changes by building classifiers that accurately differentiate
the two groups, independent of the patients’ medication status. Our method
achieved more than 96% leave-one-out cross-validation accuracy on both datasets.
In PD dataset-2, FDCCM attains an accuracy of 96.2% and AUC of 0.96, which is
significantly higher than the best accuracy (85.2%) on this dataset using existing
methods [3]. The decoders in [3] are based on spectral properties of individual
channels but do not take into account the interactions between the channels.
The neural activity analyzed here was recorded from the scalp, which is affected
by confounding factors such as volume conduction [7]. Also, compared to fMRI,
EEG has a lower spatial resolution, making it difficult to localize the source of the
activity. Table 4.1 shows that the optimal EEG channels selected by our algorithm
can change depending on the classification problem and the connectivity metric
used. Future research can be focused on network analysis of source-localized EEG
signals or invasive recordings such as local field potentials to gain more insight into
the underlying neural mechanisms of PD. A benefit of using EEG is that it can
sample neural activity at 100–1000x higher time resolution than fMRI, making it
more suitable to assess temporal dynamics. While more research is necessary to
develop clinically applicable decoders for PD diagnosis, our work indicates that
FDCCM characterizes separability between PD patients and controls.
117
(a) HC (b) PD-ON
(c) PD-OFF
Figure 10.4: Scalp topographical maps of average betweenness centralities of
healthy controls (HC) and PD patients (ON and OFF) from PD dataset-1.
118
(a) HC (b) PD-ON
(c) PD-OFF
Figure 10.5: Scalp topographical maps of average betweenness centralities of
healthy controls (HC) and PD patients (ON and OFF) from PD dataset-2.
119
10.5 Conclusion
In conclusion, this study provides a novel strategy for constructing causal net-
works by utilizing the spectral dynamics of electrophysiological signals [171]. We
showed that our method could be applied to recognize altered network patterns
in patients with PD. We conducted graph analysis and classification analysis, and
demonstrated that FDCCM helps quantify these changes between patients and
healthy controls. Given its excellent classification performance in distinguishing
between healthy individuals and PD patients on and off dopaminergic medication,
FDCCM could detect abnormalities and track disease progression using EEG sig-
nals. These decoders, in combination with graph theory, can also be used to
develop interventional therapies such as adaptive deep-brain stimulation or tran-
scranial direct-current stimulation [159]. Due to its non-invasiveness and wide
availability, scalp EEG is also optimal for clinical, commercial, and research pur-
poses. Further research on causal connectivity of cortical activity and comparison
with source-level connectivity can help understand the underlying pathophysiol-
ogy of neurodegenerative and neuropsychiatric disorders.
Chapter 11
Conclusion and Future Directions
11.1 Implications for Causal Network Analysis
Causality is an epistemological concept whose mathematical definition is not well-
established. True causality is often difficult to estimate from a model or a set of
equations because one’s intuitive understanding of causality becomes inherently
constrained when one tries to build a model. The heterogeneity of neural interac-
tions makes it challenging to determine a unifying causal model. Electrophysiolog-
ical signals such as electroencephalogram (EEG) measure direct brain electrical
activity (unlike fMRI, which measures blood flow) at relatively high temporal
resolution, making it more suitable for causal inference. Hence, this dissertation
studies effective (causal) connectivity using model-free methods using electrophys-
iological signals. There are two distinct ways (at the least) to define causality [17].
First, in terms of time-precedence, i.e., causes precede their effects: the intuition
behind Granger’s prediction [19]. Second, in terms of physical influence/control,
i.e., changing one (the cause) changes the other (the effect). We adopt the latter
definition and develop a state-space reconstruction technique that infers causality
using the spectral dynamics of electrophysiological recordings.
120
121
The proposed method in chapter 9, called frequency-domain convergent cross-
mapping (FDCCM) [12], is based on the rationale used in convergent cross-
mapping (CCM) to infer dynamic causality. While CCM relies on time-delay
embedding a timeseries into a higher-dimensional space, the proposed method,
FDCCM, incorporates spectral information through time-frequency embedding of
timeseries. By using power spectra instead of raw time-domain data, FDCCM
blurs the effect of noise as illustrated in Fig. 9.5. Thus, FDCCM overcomes a
significant weakness of CCM [111].
There is no universal model or metric to infer causality in complex networks
such as the brain. The choice depends on the merits and demerits of various
approaches. As observed from Fig. 9.3, FDCCM may not be reliable at low
coupling strengths; this lack of reliability at some coupling strengths is also a
limitation of CCM as demonstrated in [111]. In the current form, FDCCM is a
bi-variate measure of relative causality. Further research is required to extend it
to a multivariate measure that can infer the causal effect between more than one
timeseries, e.g., multiple channels in a brain region [164,180].
11.2 Implications for Neurological and Psychi-
atric Disorders
It is established that a wide variety of neurological disorders can be described as
aberrant patterns of interactions between neural elements in a large-scale brain
network [102,136,144,181–184]. The clinical application of brain network analysis
confirms that pathological patterns accumulate in network hubs, and the network
topology constrains their spread/neurodegeneration. Identifying dysfunctional
brain circuits can aid in detecting, tracking, and predicting patterns of disease in
brain disorders.
A variety of psychiatric disorders are linked to cognitive dysfunction. These in-
clude, but not limited to, major depressive disorder [99,185], obsessive-compulsive
122
disorder (OCD) [186], schizophrenia [187], autism spectrum disorders [188] and
addiction [97]. One of the critical bottlenecks in diagnosing such disorders is the
lack of well-established neural mechanisms that explain the pathology. We believe
that effective network analysis, a less explored approach than functional network
analysis, may hold the key to this problem. From a physiological standpoint
and an empirical or statistical standpoint, directed networks provide twice the
information provided by functional networks.
The methods proposed in this dissertation, combined with prior neuroscience
knowledge, may help understand the network patterns reflective of the neurolog-
ical basis of these disorders. For example, the involvement of dlPFC in cognitive
control, especially in tasks involving conflict or inhibition of irrelevant informa-
tion, is reported in prior research [45, 50, 70]. Schizophrenia and OCD have been
linked to dysfunctional modulation in dlPFC and vlPFC [94, 95]. Our research
also implies that theta interactions in dlPFC, dmPFC, and the temporal lobe play
an important role in cognition.
Many patients with mental illnesses characterized by impaired cognitive con-
trol have no relief from gold-standard clinical treatments resulting in a pressing
need for new alternatives. Enhancing cognitive control can dramatically impact
the health and well-being of millions of patients suffering from refractory mental
disorders. Modulating the neural activity, e.g., through deep brain stimulation,
during mental states associated with executive function can achieve this goal.
Detecting such complex states of engagement in mentally demanding tasks is a
challenge. Since these tasks adopt multiple brain regions, fundamental mecha-
nisms underlying cognitive control cannot be observed solely from localized neu-
ral recordings. The findings presented in this research demonstrates that network
science can help discover these patterns.
Although initial studies of deep brain stimulation (DBS) have shown promise,
clinical trials have yielded inconsistent results [79–81, 189, 190]. Recent studies
suggest that adaptive deep-brain stimulation (aDBS) can be used to improve
cognitive control in psychiatric patients prospectively [122–124]. Developing such
123
closed-loop neuromodulation treatments requires automatic and reliable detection
of cognitive effort in humans. However, therapeutic efficacy is critically related to
the connectivity of its target site or target brain region [191].
Task engagement networks (see chapter 6) emphasize the activation of dlPFC
due to its relatively higher node centrality. Similarly, in chapter 10, we observed
that certain brain regions have higher betweenness centrality, implying they are
more connected to other brain regions. Although further research is required to
generalize these findings [129, 156, 178], our work indicates that causal network
analysis could help answer the following questions that are crucial for stimulation
therapies [70, 80, 81, 192]. What is a good biomarker that acts as the trigger for
intervention? What is the optimal target site for a specific clinical outcome? Fu-
ture work can apply the proposed methods to other disorders to discover network
biomarkers. These biomarkers can be used to develop and evaluate adaptive brain
stimulation therapies.
Besides cognitive disorders, this dissertation also demonstrates the applica-
bility of the proposed methods on neurodegenerative disorders. We show that
network features of the estimated causal networks, namely betweenness centrality
of different brain regions, are modulated in patients suffering from Parkinson’s
disease. The classification models built from these network features can assist
clinicians as a cost-effective diagnostic tool, crucial for prognostic and therapeu-
tic purposes. Note that these classifiers utilize scalp-EEG signals for identifying
biomarkers of Parkinson’s disease. Due to its non-invasiveness and wide avail-
ability, scalp EEG is also optimal for clinical, commercial, and research purposes.
These methods can also be used to study disease progression, and develop/evaluate
stimulation therapies [159].
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