Abstract
Abstract
In this dissertation, we focus on developing novel statistical
methodology for high-
dimensional neuroimaging data (HND) to yield insights about the
complex neural
processing characteristics associated with mental diseases and
furthermore to provide
clinically relevant predictive information to aid with treatment
selection and progno-
sis. Our proposed methods would extract new information content
from neuroimaging
data, while coping with the many analytical challenges posed by
these massive data
sets. Specifically, we propose three new statistical frameworks:
(i) to predict disease
progression and therapeutic treatment response based on temporal
trends in longi-
tudinal neuroimaging data, e.g. repeatedly collected over weeks or
months; (ii) to
determine population-level brain networks revealed by functional
(or structural) con-
nectivity properties within regions of interest (ROI) and between
ROIs, while charac-
terizing whole-brain properties of these identified networks, such
as the 'small world'
property; (iii) to analyze resting-state functional magnetic
resonance imaging (fMRI)
data by constructing methodology to determine localized estimates
of resting-state
brain activity and simultaneously yield functional connectivity
information based on
spatial correlations in the data.
Table of Contents
Contents
1 Introduction 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 1
1.2 Basic Knowledge of Human Brain . . . . . . . . . . . . . .
. . . . . . 2
1.3 Neuroimaging Techniques . . . . . . . . . . . . . . . . .
. . . . . . . 4
1.3.1 MRI and fMRI . . . . . . . . . . . . . . . . . . . . . .
. . . . 5
1.3.2 PET . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 9
1.4 Preprocessing and Data Analysis Methods for Neuroimaging
Data . . 10
1.4.1 Preprocessing Procedures . . . . . . . . . . . . . . . .
. . . . 11
1.4.2 Statistical Modeling for Activation Studies . . . . . .
. . . . . 12
1.4.3 Connectivity Analysis . . . . . . . . . . . . . . . . .
. . . . . 14
1.4.4 Classication and Prediction . . . . . . . . . . . . . .
. . . . . 20
1.5 Motivation Examples . . . . . . . . . . . . . . . . . . .
. . . . . . . . 22
1.5.1 An fMRI Resting-state Study of Depression . . . . . . .
. . . 22
1.5.2 A PET Study of Alzheimer's Disease . . . . . . . . . . .
. . . 23
1.6 Proposed Research . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 23
2 Topic 1: A Novel Support Vector Classier for Longitudinal
High-
dimensional Data and Its Application to Neuroimaging Data
25
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 25
2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 28
2.2.1 Classical Support Vector Classier . . . . . . . . . . .
. . . . 28
2.2.2 Longitudinal Support Vector Classier - LSVC . . . . . .
. . 30
2.2.3 Nonlinear Kernel Functions . . . . . . . . . . . . . . .
. . . . 33
2.2.4 Feature Selection and Parameter Tuning . . . . . . . . .
. . . 34
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 35
2.3.1 Simulation study . . . . . . . . . . . . . . . . . . . .
. . . . . 35
2.3.2 Data Example . . . . . . . . . . . . . . . . . . . . . .
. . . . . 38
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 40
2.5 Appendix: Proof of Convexity of Objective function w.r.t.
and . 41
3 Topic 2: Bayesian Hierarchical Model for Comprehensive Brain
Con-
nectivity Analysis 44
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 44
3.2 Motivating Example . . . . . . . . . . . . . . . . . . . .
. . . . . . . 47
3.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 49
3.3.1 Bayesian Hierarchical Model . . . . . . . . . . . . . .
. . . . . 49
3.3.2 Estimation and posterior inference . . . . . . . . . . .
. . . . 54
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 56
3.4.1 MDD Study Using Resting-state fMRI Data . . . . . . . .
. . 56
3.4.2 Simulation Study . . . . . . . . . . . . . . . . . . . .
. . . . . 62
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 65
4 Topic 3: An Unied Bayesian Framework for Resting-state
fMRI
Data Analysis: Jointly Modeling Frequency Activity and
Connec-
tivity 67
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 67
4.2 Motivating Example . . . . . . . . . . . . . . . . . . . .
. . . . . . . 69
4.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 70
4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 76
4.4.1 Voxel-level results . . . . . . . . . . . . . . . . . .
. . . . . . . 76
4.4.2 Regional results . . . . . . . . . . . . . . . . . . . .
. . . . . . 77
4.4.3 Regional connectivity networks . . . . . . . . . . . . .
. . . . 80
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 84
5 Summary and Future Work 85
About this Dissertation
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