DETECTING AND CHARACTERIZING LARGE-SCALE HUMAN BRAIN

NETWORKS

A DISSERTATION

SUBMITTED TO THE PROGRAM IN BIOMEDICAL INFORMATICS

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Kaustubh Satyendra Supekar

August 2010

© 2010 by Kaustubh Satyendra Supekar. All Rights Reserved. Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/pm061tq8052

ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Mark Musen, Primary Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Michael Greicius

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Vinod Menon

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Daniel Rubin

Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives.

iii Abstract

Understanding human brain function is one of the most important endeavors in mod- ern science. There is growing evidence that cognitive functions are executed by large- scale networks, comprising multiple interacting anatomically-connected brain areas. Al- though considerable progress has been made in understanding which specific brain areas are involved in particular cognitive functions, very little is known about the integrative functioning of large-scale brain networks. This is due in part to the lack of methods to pursue this line of research. This dissertation describes computational methods for de- tecting and characterizing large-scale human brain networks, combining data from task- free functional magnetic resonance imaging (fMRI) and structural diffusion tensor imag- ing (DTI), two complementary brain imaging modalities. Application of our methods to task-free fMRI and DTI data obtained from a wide range of subject populations pro- vided new insights into how large-scale human brain networks develop, mature, and get disrupted in psychiatric and neurological disorders. More generally, this work demon- strates the power of our multimodal network-analytic approach to obtain a system-level understanding of brain function across the human lifespan.

iv Acknowledgements

I thank my committee: Mark Musen, Vinod Menon, Daniel Rubin, and Michael Gri- sious. The mentorship, and more importantly, the incredible support and encourage- ment I have received from them, throughout the process, has been truly inspiring and awesome. I am grateful to my colleagues and collaborators: Bob Dougherty, Booil Jo,

Catie Chang, Elena Rykhlevskaia, Hitha Amin, Leeza Kondos, Lucina Uddin, Meghan

Meyer, Sridhar Devarajan, and Srikanth Ryali. I acknowledge Bruce Miller, Gary Glover,

Jose Anguiano, and Katherine Prater for their assistance with participant recruitment and data collection. I am also grateful to Carol Maxwell, Christine Hilliard, and MaryJeanne

Oliva for their compassion and care. I thank my friends and BMI students, including, but not limited to, Alex Morgan, Amit Kaushal, Chintan Patel, Holger Lewen, Madhura

Maideo, Marina Sirota, Maureen Hillenmeyer, Mayura Bhandarkar, Nigam Shah, Nikesh

Kotecha, Noah Zimmerman, Ray Lin, Rong Xu, and Seema Joshi. Last, but certainly not least, I would like to thank my mom, dad, and sister: without your unconditional love and support, this would have not been possible; I dedicate this dissertation to you.

v Contents

Abstract iv

Acknowledgements v

1 Introduction 1

2 Background and Methods 10

2.1 Detecting large-scale human brain networks ...... 11

2.1.1 Large-scale human brain networks ...... 11

2.1.2 Task-free fMRI ...... 14

2.1.3 Identifying nodes ...... 15

2.1.4 Identifying edges between the nodes ...... 35

2.2 Quantifying the topology of large-scale human brain networks ...... 43

2.2.1 Global topology ...... 48

2.2.2 Subnetwork topology ...... 54

2.2.3 Regional topology ...... 55

2.2.4 Statistical analysis ...... 58

vi 2.3 Assessing structure–function relationships in large-scale human brain net-

works ...... 59

2.3.1 Measuring structural connectivity underlying large-scale human

brain networks using DTI ...... 61

2.3.2 Correlating large-scale human brain networks with measures of

structural connectivity ...... 66

2.4 Comparing large-scale human brain networks across subject populations 66

2.4.1 Comparing network topology ...... 68

2.4.2 Comparing brain connectivity ...... 71

2.5 Summary ...... 74

3 Large-Scale Brain Networks in Alzheimer’s Disease 75

3.1 Abstract ...... 75

3.2 Introduction ...... 76

3.3 Materials and Methods ...... 78

3.4 Results ...... 86

3.4.1 Comparison of global topology of large-scale brain networks in

AD participants and age-matched healthy controls ...... 87

3.4.2 Specificity and sensitivity of global topological metrics in distin-

guishing AD participants from age-matched healthy controls . . . 93

3.4.3 Comparison of regional connectivity of large-scale brain networks

in AD participants and age-matched healthy controls ...... 93

3.4.4 Reproducibility of findings ...... 95

vii 3.5 Discussion ...... 95

4 Development of Large-Scale Brain Networks in Children 99

4.1 Abstract ...... 100

4.2 Introduction ...... 101

4.3 Materials and Methods ...... 104

4.4 Results ...... 115

4.4.1 Comparison of global topology of large-scale brain networks in

children and young-adults ...... 116

4.4.2 Comparison of global connectivity of large-scale brain networks

in children and young-adults ...... 118

4.4.3 Comparison of subnetwork topology of large-scale brain networks

in children and young-adults ...... 120

4.4.4 Comparison of subnetwork connectivity of large-scale brain net-

works in children and young-adults ...... 122

4.4.5 Comparison of regional topology of large-scale brain networks in

children and young-adults ...... 122

4.4.6 Comparison of regional connectivity of large-scale brain networks

in children and young-adults ...... 124

4.4.7 Developmental changes in regional connectivity with wiring dis-

tance ...... 124

4.4.8 Comparison of structure–function relationships within large-scale

brain networks in children and young-adults ...... 127

viii 4.4.9 Comparison of large-scale brain networks consisting of functionally-

defined nodes in children and young-adults ...... 130

4.5 Discussion ...... 131

5 Conclusions and Future Directions 142

5.1 Conclusions ...... 142

5.2 Future directions ...... 145

ix List of Tables

2.1 Comparative analysis of widely used anatomical atlases against desiderata

of a brain parcellation scheme ...... 22

2.2 Simulated datasets ...... 30

2.3 Percent error in partitioning voxels into correct clusters ...... 33

3.1 Demography and MMSE scores ...... 86

4.1 Demographic and cognitive profile...... 115

4.2 Brain regions identified as network hubs in children and young-adults. . . 125

x List of Figures

2.1 Flowchart depicting steps involved in detecting large-scale human brain

networks using task-free fMRI data...... 12

2.2 Schematic representation of brain network as a graph...... 13

2.3 Results of a typical fMRI study...... 14

2.4 Correlated spontaneous activity pattern observed during the task-free con-

dition ...... 16

2.5 Anatomy-based schemes to parcellate the human brain ...... 20

2.6 A simulated 64x64 image slice with 2 regions shown with two representa-

tive voxel timeseries...... 32

2.7 Illustrative example of application of wavelet transform ...... 38

2.8 Flowchart depicting steps involved in identifying an edge between a pair

of nodes ...... 40

2.9 Small-world network (0 < p < 1) as an intermediate state between regular

lattice-like network (p = 0) and random network (p = 1)...... 47 2.10 Illustration of key network properties...... 48

xi 2.11 Flowchart depicting steps involved in quantifying structural connectivity

between nodes of large-scale human brain networks...... 63

3.1 Global organization of large-scale brain networks in AD participants and

controls, at three frequency intervals of interest...... 88

3.2 Global organization of large-scale brain networks in AD participants and

controls, at the low frequency interval...... 89

3.3 Regional organization of large-scale brain networks in AD participants

and controls...... 91

3.4 Global efficiency of large-scale brain networks in AD participants and

controls...... 92

3.5 Specificity and sensitivity of quantitative metrics of global organization

of large-scale brain networks in distinguishing AD participants from con-

trols...... 94

4.1 Developmental changes in global organization of large-scale brain networks.117

4.2 Developmental changes in hierarchical organization of large-scale brain

networks...... 119

4.3 Developmental changes in subnetwork organization of large-scale brain

networks...... 121

4.4 Developmental changes in subnetwork connectivity of large-scale brain

networks...... 123

4.5 Regional connectivity in children and young-adults...... 126

xii 4.6 Developmental changes in regional connectivity with DTI-based wiring

distance...... 128

4.7 Structure–function relationships within large-scale brain networks in chil-

dren and young-adults...... 129

xiii Chapter 1

Introduction

Understanding human brain function is one of the most important endeavors in modern science. It is fascinating that 1.5 liters of tissue, can give rise to complex human behaviors.

The earliest notable systematic investigation of human brain function was performed by German physician Franz Gall. In the early 19t h century, Gall attempted to ascribe cognitive functions onto specific brain areas by relating personality traits with the size of bumps and fissures in the skull (Gall and Spurzheim, 1810). While these studies have long been discredited, Gall’s doctrine of “one-function-one-brain-region” still remains a dominant paradigm in modern brain science. Within such a phrenological framework, the vast majority of studies in recent decades have focused on identifying brain regions involved in functions such as vision, memory, learning, language, and attention.

Although these studies have contributed significantly to our knowledge about how in- dividual brain regions process information, very little is known about how these regions

1 CHAPTER 1. INTRODUCTION 2

interact and integrate information in order to engender cognition. Thus, our understand- ing of human brain function is somewhat akin to “looking out the window of an airplane at night. We can see patches of light from cities and towns scattered across the landscape, we know that roads, railways and telephone wires connect those cities, but we gain lit- tle sense of the social, political and economic interactions within and between cities that define a functioning society” (Nichols and Newsome, 1999). This analogy is meant to illustrate the fact that, achieving a more sophisticated understanding of cognition will require systematic investigation of interactions between multiple brain regions. In re- cent years, this newer interaction-based paradigm for the investigation of brain function has been increasingly advocated by several researchers (Bressler and Menon, 2010; Fuster,

2003; Greicius et al., 2003; McIntosh, 2000; Mesulam, 2000a; Sporns et al., 2004; Tononi and Sporns, 2003).

The interactions between brain regions during brain function are characterized by functional connectivity, which is defined as the “correlation between spatially remote neurophysiological events” (Friston et al., 1993). When spatially distinct brain regions exhibit synchronous patterns of neural activity, changes in the regions are said to be func- tionally connected, likely through neurotransmission via underlying axons (Bressler and

Kelso, 2001; Tononi et al., 1998). In order to comprehensively examine brain functional connectivity, it is desirable to have a neural recording technique with both high spatial and temporal resolution.

Neurophysiological techniques such as single-unit/multi-unit-recording measure elec- trophysiological activity from an individual neuron or from large populations of neurons CHAPTER 1. INTRODUCTION 3

(Baker et al., 1990). With very good spatial resolution and excellent temporal resolution

(in the order of milliseconds), these techniques are well suited for investigating functional connectivity. Activity data obtained from these techniques have been used to investi- gate neural connectivity during brain function, including processing of visual stimulus

(Nauhaus et al., 2009), working memory (Pesaran et al., 2002), and body movement

(Murthy and Fetz, 1996). Although neurophysiological studies are most desirable and would continue to be necessary for understanding the neural connectivity underlying brain function, these recording techniques are invasive and thus cannot be readily used in human subjects.

Electrophysiological techniques such as electroencephalography (EEG) and magneto encephalography (MEG) provide a non-invasive approach to record brain activity. EEG records the electrical activity on the scalp while MEG records the magnetic field in the brain. Both EEG and MEG signals reflect the ionic current flow in dendrites during neural activity. The temporal resolution of EEG and MEG (in the order of milli-seconds) is adequate for investigating brain connectivity. Data obtained from these techniques have been used to examine synchronization of brain areas during hand movements (Wheaton et al., 2005), auditory processing (Hsiao et al., 2010), and visuomotor behavior (Classen et al., 1998) , and to investigate epileptogenic networks in epilepsy (Wendling et al., 2009).

However, EEG and MEG have major limitations; most importantly, surface recordings cannot be mapped into individual brain regions. Furthermore, functional connectivity in EEG data is also highly contaminated due to artifacts and volume conduction effects.

Functional magnetic resonance imaging (fMRI) provides an alternate approach for CHAPTER 1. INTRODUCTION 4

non-invasive examination of functional connectivity in the human brain. It has a spatial resolution of 2-3 mm across the entire brain and a temporal resolution that is adequate for studying cognitive information processing. fMRI records changes in blood-oxygenation- level-dependent (BOLD) signal arising from changes in metabolic demand due to fluctu- ations in local neural activity. During the past decade, fMRI has emerged as powerful non-invasive tool that has good spatial and temporal resolution for investigating brain connectivity. fMRI data has been used to investigate interregional brain connectivity during a wide variety of cognitive functions including autobiographical memory (Addis et al., 2004), motion processing (Caplan et al., 2006), visual spatial information processing

(Sugiura et al., 2004) and speech processing (Mashal et al., 2005).

Although most prior fMRI studies have investigated interregional functional con- nectivity during cognitive tasks, there has been growing interest in examining intrin- sic functional connectivity in task-free states. Recent work has shown that most of the brain’s energy is consumed when the brain is not performing any task (“task-free” or

“rest” condition) (Raichle and Mintun, 2006) . This energy is thought to support neu- ral activity that is not directly related to external stimuli. Additionally, low-frequency spontaneous fluctuations in the fMRI BOLD signal have been observed in several brain regions during the resting state. Biswal and colleagues were the first to demonstrate that these BOLD signal fluctuations were correlated between motor regions both within and across hemispheres at rest (Biswal et al., 1995). Remarkably, this correlation pattern re-

flected the same functional network that is engaged during motor task, a finding that has been replicated several times (Cordes et al., 2001; Lowe et al., 1998; Xiong et al., 1999). CHAPTER 1. INTRODUCTION 5

Subsequently, several independent groups have observed task-free correlation in other networks including those involved in motor (Biswal et al., 1995), sensory (De Luca et al.,

2005), attention (Fox et al., 2006), executive control (Seeley et al., 2007), and memory processes (Greicius et al., 2003; Vincent et al., 2006). The presence of these networks has been demonstrated in the human as well as macaque brain (Vincent et al., 2007).

Evidence from these studies suggests that brain networks engaged during performance of a cognitive task are manifested by the correlation pattern of spontaneous BOLD sig- nal fluctuations observed during the task-free condition. A more recent study by Smith and Colleagues provides further evidence in this regard. They examined 7342 functional task-activation images; each image consisting of brain areas that were active during an experimental task. They reported that brain areas that routinely coactivate during task conditions show correlation between their task-free fMRI signals (Smith et al., 2009) .

Additionally, other studies have reported relationships between functionally specialized task-free networks and behavior (Fox and Raichle, 2007). For example, differences in spa- tial extent of these networks have been shown to correlate with performance on working memory tasks (Hampson et al., 2006). Collectively, these findings indicate that, un- like fMRI signals recorded during task performance, fMRI signals recorded during the resting-state may reflect the global functional organization of the brain spanning multi- ple functionally specialized networks, and thereby has a great potential as a technique to address whole-brain architecture.

Understanding the functional architecture of the human brain is fundamentally im- portant for gaining insights into cognitive function and dysfunction. However, very CHAPTER 1. INTRODUCTION 6

little is known about functional architecture of the the human brain, particularly at the whole-brain level. More specifically, there is limited knowledge about how functional connectivity in the brain is organized, how functionally specialized networks/systems interact with one another and integrate information, how brain organization and con- nectivity changes across cognitive conditions, and how functional architecture relates to the underlying brain anatomy. Progress in this area has been limited due in part to the lack of methods to pursue this line of research. Without adequate methods, a compre- hensive system-level understanding of brain function cannot be achieved.

In this dissertation, we developed new methods for analyzing brain imaging data in order to quantitatively examine key aspects of brain architecture and function. Our ap- proach is as follows: We developed a method to detect large-scale brain networks com- prising distinct interacting brain areas spanning the entire brain using task-free fMRI data. Notably, our method captures functional interactions subtended at specific tempo- ral scales of interest between brain areas circumscribed at multiple spatial resolutions at the whole-brain level. To characterize the organization of the detected large-scale brain networks, we use a network-analytical approach. The emerging field of network science, based on the more traditional discipline of graph theory, provides a powerful and elegant approach for examining the statistical mechanics of complex networked systems such as the brain, and how it gives rise to network behavior. We implemented network-analytical methods to characterize various aspects of global brain organization. To further charac- terize the brain organization, we used a novel approach of network partitioning com- bined with network analysis. More specifically, this approach allows the examination of CHAPTER 1. INTRODUCTION 7

network topology and connectivity within and between anatomically defined functional systems of the brain (Mesulam, 2000a). Next, we implemented statistical methods for comparing the network topology, and used a novel machine learning based approach to quantify differences in the underlying patterns of network functional connectivity, so that we could examine how the multilevel functional organization of the human brain changes, across subject populations. Lastly, we developed methods for combining task- free fMRI data with diffusion tensor imaging (DTI) data in order to examine the relation- ship between functional connectivity and anatomy within large-scale brain networks.

The algorithmic and implementation details for each of the methods described above, along with the relevant background information is presented in Chapter 2.

In Chapter 3, we examine the global functional organization of the brain in Alzheimer’s disease (AD) by applying our methods for (1) detecting large-scale brain networks from task-free fMRI data, (2) characterizing the organization of these networks using metrics of global topology, and (3) comparing these metrics between AD and age-matched con- trol subjects. Results from these analyses revealed that functional brain organization at the global level was significantly disrupted in AD. Notably, metrics measuring the global functional organization could accurately distinguish AD participants from the controls.

This is the first use of network-analytical approach to quantify functional organization of the brain in clinical populations using task-free fMRI data, and it suggests that these quantitative metrics may be useful as an imaging-based biomarker of disease conditions

(Supekar et al., 2008).

In Chapter 4, we investigate the ontogeny of functional organization of the human CHAPTER 1. INTRODUCTION 8

brain – from childhood to young adulthood. To this end, in addition to examining func- tional organization at the global level as described above, we characterize and compare the organization at the subnetwork level—within functional systems of the brain—along with the underlying functional connectivity patterns by applying our network partition- ing and machine learning based methods. The results from this analysis showed that although brains of children and young-adults have similar organization at the global level; they differ significantly in subnetwork organization and functional connectivity.

This work is the first to use network-analytical approach to quantitatively examine and compare functional organization of the human brain at multiple levels of granularity.

Additionally, this is the first use of machine learning to characterize differential brain functional connectivity patterns (Supekar et al., 2009). Next, we investigate how the re- lationship between functional connectivity and anatomy within the brain develops, by applying our methods for computing quantitative measures of white-matter within brain networks using DTI data, relating these indices of strength of brain structure with mea- sures of functional connectivity, and comparing these associations between children and young-adults. This combined analysis revealed that functional maturity of large-scale brain networks depends on structural maturity of the underlying white-matter. This work is the first to simultaneously quantify and relate functional connectivity and struc- ture within large-scale whole-brain networks, and compare the structure-function rela- tionships, by using a multimodal imaging approach combining task-free fMRI and DTI data (Supekar et al., 2010). CHAPTER 1. INTRODUCTION 9

In summary, we have developed novel methods for detecting large-scale brain net- works using brain imaging data, and for characterizing the topology and connectivity of these networks at multiple levels of granularity. Additionally, our methods allow us to quantify structure–function relationships within these networks, and to compare these characteristics across subject populations. Application of these methods to task-free fMRI and DTI data collected from subject populations including children, young adults, and the elderly provided new quantitative insights into how brain networks develop, mature, and get disrupted in psychiatric and neurological disorders. Importantly, our findings demonstrate the usefulness of our methods for multimodal characterization of large-scale human brain networks across a wide range of subject populations. More generally, this research provides a quantitative multimodal framework for the in vivo investigation of how human brain systems operate in health and illness, and will ultimately help us to achieve a more complete understanding of brain architecture and cognitive function. Chapter 2

Background and Methods

In this chapter, we describe our methods for analyzing task-free fMRI and DTI data in or- der to quantitatively examine key aspects of brain architecture and function. We describe each method we developed in detail, along with the necessary background material. Our methodological approach is as follows:

We first present our methods for detecting large-scale human brain networks by ana- lyzing task-free fMRI data (Section 2.1). We then describe a network-analytical approach, combined with network partitioning, that we use to quantify topology of the large-scale human brain networks at the global, subnetwork, and regional level (Section 2.2). The analysis of network topology allows us to quantitatively examine the functional organiza- tion of the human brain at multiple levels of granularity. Next, we present a multimodal imaging approach (Section 2.3); we use it to combine task-free fMRI and DTI data, and then assess structure–function relationships in large-scale human brain networks so that we can examine how the functional organization of the human brain emerges from the

10 CHAPTER 2. BACKGROUND AND METHODS 11

underlying brain anatomy. Finally, we describe our methods for comparing the topology and connectivity of large-scale human brain networks between subject populations in or- der to examine how the functional organization of the human brain changes across the human lifespan (Section 2.4).

2.1 Detecting large-scale human brain networks

In this section, we describe our methods for detecting large-scale human brain networks by analyzing task-free fMRI data. We first present background information about large- scale human brain networks, highlighting their significance in investigating functional brain organization, and provide a graph-theoretic formalism to model a brain network as a collection of nodes and edges that connect the nodes. We then introduce in detail task-free fMRI—a powerful new technique that provides a promising way to detect large- scale brain networks. Finally, we describe in detail our methods for identifying anatomy- based and function-based nodes, and the edges of large-scale human brain networks, by analyzing task-free fMRI data (Figure 2.1).

2.1.1 Large-scale human brain networks

There is increasing evidence that human brain function is executed through dynamic interactions between distinct brain regions. To understand the cognitive information- processing architecture of the human brain, it is thus imperative to investigate how these interactions are organized and coordinated. The first significant step towards achieving this goal is to map large-scale human brain connectivity networks consisting of functional CHAPTER 2. BACKGROUND AND METHODS 12

Figure 2.1: Flowchart depicting steps involved in detecting large-scale human brain net- works using task-free fMRI data. We detect large-scale brain human brain networks by first identifying anatomy-based or function-based nodes, and then identifying edges be- tween the identified nodes, by analyzing task-free fMRI data. CHAPTER 2. BACKGROUND AND METHODS 13

links between all constituent brain regions at the whole-brain level1 (Sporns et al., 2005).

To model large-scale brain networks, we use a graph-theoretic approach that provides an elegant and powerful analytical framework for subsequent investigations of functional organization and connectivity. A graph is a mathematical structure to model pair-wise relations between a set of objects. More specifically, a graph G is an ordered pair consisting of a set V of nodes and a set E of edges that specify connection between pairs of nodes in V. In a graphical representation of a brain network, a node corresponds to a brain region whereas an edge corresponds to the functional interdependence (alterna- tively referred to as functional connectivity) between two brain regions (Figure 2.2).

Figure 2.2: Schematic representation of brain network as a graph. Brain regions are rep- resented as nodes (circles). The functional interdependence between two regions is repre- sented as an edge (lines) between the nodes representing those two regions.

1In this dissertation, we alternatively refer to large-scale functional connectivity networks at the whole brain level as “large-scale brain networks at the whole-brain level,” or “large-scale, whole-brain networks,” or “large-scale brain networks.” We refer to networks as being plural because it has been suggested that the human brain has multiple functional connectivity networks at the whole-brain level, contingent on how the nodes and edges are selected. In our work, too, we develop methods to detect two configurations of whole-brain networks—one network with nodes as anatomically defined areas and another network with nodes as functionally defined areas (see following sections for details). CHAPTER 2. BACKGROUND AND METHODS 14

2.1.2 Task-free fMRI fMRI is a powerful technique to noninvasively examine macroscopic neural activity dur- ing brain function. Specifically, fMRI records changes in local blood flow during brain function. The blood flow—blood-oxygenation-level-dependent (BOLD)—signal is thought to reflect changes in metabolic demand caused by changes in local neural activity. In a typical fMRI study, the 3D volume of a participant’s brain is scanned every one or two seconds for a period of 8–12 minutes. During the scan, the participant is instructed to perform an experimental task of interest. The experimental task is interspersed with a control task, typically a “rest” (or “task-free”) condition where the participant is in- structed to close his eyes and not to move. The 3D volume fMRI signal collected while the participant is performing the experimental task is then contrasted with the fMRI sig- nal collected during rest. The comparison identifies brain areas putatively associated with the experimental task (Figure 2.3).

Figure 2.3: Results of a typical fMRI study. 3D surface rendering of the brain depicting regions that showed significant activity (in red) when the participant was performing an experimental (arithmetic) task contrasted against task-free (rest) condition. CHAPTER 2. BACKGROUND AND METHODS 15

In contrast to the above described conventional task-based fMRI studies, there has recently been increased interest in examining the fMRI signal during the task-free condi- tion. This increased interest is driven by the observation that most of the brain’s energy is consumed when the brain is not performing any task (Raichle and Mintun, 2006) .

This energy is thought to support ongoing neural activity that is purportedly not related to specific tasks. More importantly, during the task-free condition, spontaneous fluctua- tions in the fMRI signal are observed in several brain regions. Remarkably, the sponta- neous fluctuations during the task-free condition are correlated among brain regions that are coactive while the participant is performing a task (Smith et al., 2009). These patterns of correlated spontaneous activity between a set of brain regions are described as task- free brain networks. Several such task-free brain networks have been reported, including those involved in motor (Biswal et al., 1995) , sensory (De Luca et al., 2005), attention

(Fox et al., 2006), and memory (Greicius et al., 2003; Vincent et al., 2006) processes (Fig- ure 2.4). These findings suggest that the correlated spontaneous activity pattern observed during the task-free condition may reflect the large-scale functional organization of the human brain, spanning multiple functionally specialized networks. In sum, task-free fMRI provides a promising way to investigate large-scale human brain networks.

2.1.3 Identifying nodes

Unlike most complex networks, including biological networks and social networks where there is a precise definition of what constitutes a node, in brain networks there is no gold-standard node definition. This is mainly because, at the macroscopic level, there are CHAPTER 2. BACKGROUND AND METHODS 16

Figure 2.4: Correlated spontaneous activity pattern observed during the task-free con- dition in network of regions involved in (A) memory, (B) salience detection, and (C) executive function. CHAPTER 2. BACKGROUND AND METHODS 17

no distinct anatomical boundaries that can be used to demarcate one brain region from another. As a consequence, a large number of anatomy-based approaches to partition

(hereafter referred to as parcellate) the human brain have been developed—each differing in the extent of coverage, node size, parcellation criteria, and number of nodes. The lack of one commonly agreed upon parcellation scheme poses a significant challenge for map- ping large-scale brain networks. Critically, brain regions that constitute network nodes must be selected appropriately because the choice of nodes greatly influences network structure and connectivity.

In Section 2.1.3.1, we enumerate desiderata for a brain parcellation scheme. We then present widely used anatomical parcellation schemes and systematically evaluate each one of them against the desiderata, choosing a parcellation scheme that provides the best match. We use this chosen anatomical parcellation scheme to define a set of anatomically defined nodes in the large-scale brain network.

In addition to delineating brain regions on the basis of anatomical criteria defined by the chosen parcellation scheme, a brain region can be delineated from its neighbors if it has a distinguishing functional activity pattern. Brain networks consisting of function- ally defined areas provide insights into network operation that are complementary to those obtained from networks consisting of anatomically defined areas (Mesulam, 2000a)

Whereas the parcellation schemes allow identification of anatomically defined areas, to our knowledge there is a lack of methods to identify functionally defined areas. We de- velop a novel data-driven method to parcellate the human brain into functionally ho- mogeneous areas. We describe this method in Section 2.1.3.3. We use this method to CHAPTER 2. BACKGROUND AND METHODS 18

define a set of functionally defined nodes of the large-scale brain network. The use of an anatomy-based parcellation scheme and a function-based parcellation produces two com- plementary network configurations: one with nodes as anatomically defined areas and another with nodes as functionally defined areas.

2.1.3.1 Desiderata of a brain parcellation scheme

We list desirable characteristics of a brain parcellation scheme on the basis of emerging trends from brain network research and our requirement to detect large-scale whole-brain networks.

1. A parcellation scheme should provide complete coverage of the brain, including

cortical and subcortical regions. A parcellation scheme with limited coverage is

likely to miss critical contributions of the excluded regions.

2. Parcellated regions should not overlap.

3. Neighboring parcellated regions should be distinguishable anatomically and/or functionally.

4. A parcellation scheme should provide adequate spatial resolution. Brain networks

consisting of nodes with poor spatial resolution may be less meaningful. CHAPTER 2. BACKGROUND AND METHODS 19

2.1.3.2 Anatomy-based parcellation

One brain region can be demarcated from another using a number of anatomical features including but not limited to cytoarchitecture, gyral folding patterns, and neurotransmit- ter profiles. Several researchers have published anatomical atlases that parcellate the hu- man brain into distinct regions using a particular anatomical feature. We present some of the widely used anatomical atlases below.

The most notable among the anatomical atlases is the Brodmann atlas (Figure 2.5A) , which subdivides the brain into 43 regions based on differences in the cellular architecture across various parts of the cortex (Brodmann, 1994). A more recent Julich-Dusseldorf probabilistic atlas (Figure 2.5B) provides a more refined subdivision of a few cortical re- gions into 61 regions using observer-independent mapping of the cytoarchitecture (Zilles and Amunts, 2010). The Gyral atlas (Figure 2.5C) subdivides the brain into 66 regions by using gyral patterns (Desikan et al., 2006). The automated anatomical labeling (AAL) atlas (Figure 2.5E), primarily used for localization of functional brain imaging data, sub- divides the brain into 116 cortical and subcortical regions using landmarks identified on structural magnetic resonance imaging data (Tzourio-Mazoyer et al., 2002). Some researchers have recently applied an arbitrary regional parcellation approach instead of defining brain regions by using anatomical features. Hagmann and colleagues applied a random-sampling method (Figure 2.5D) and subdivided the brain into 998 regions of equal size (Hagmann et al., 2008).

We evaluated the aforementioned anatomical atlases against the desiderata enumer- ated in the previous section. The results of the comparative analysis are summarized in CHAPTER 2. BACKGROUND AND METHODS 20

Figure 2.5: Anatomy-based schemes to parcellate the human brain; each scheme using a particular anatomical feature. (A) Brodmann atlas based on cytoarchitecture, (B) Julich- Dusseldorf atlas based on probabilistic cytoarchitecture, (C) Gyral atlas based on gyral patterns, (D) Hagmann atlas based on voxel geometry, and (E) AAL atlas based on imag- ing features (B,C,D: adapted from (Bressler and Menon, 2010)) CHAPTER 2. BACKGROUND AND METHODS 21

Table 2.1. Parcellation provided by each atlas has nonoverlapping regions. The number of parcellated regions in the atlases is approximately similar, except in the Hagmann atlas, which (at the expense of interpretability) has the best spatial resolution. Although the

Brodmann, Julich-Dusseldorf, Gyral, and Hagmann atlases provide coverage for cortical regions, the AAL atlas is the only atlas that provides whole-brain coverage, including both cortical and subcortical regions. Except for the Hagmann atlas regions, the parcel- lated brain regions are homogeneous with respect to the associated anatomical feature.

Based on the findings of the comparative analysis, we choose to use the AAL atlas to anatomically parcellate the brain. This parcellation provided 116 regions, of which we discard 26 cerebellar regions because of poor task-free fMRI signals in the cerebellar regions. The remaining 90 regions constitute the anatomically defined nodes of the large- scale brain network.

2.1.3.3 Function-based parcellation

In complement to the anatomy-based parcellation, the human brain can be subdivided into functionally separable areas. A functionally separable area is suggested to have a local neural activity pattern that is distinct from its neighbors. The earliest proponents of function-based parcellation of the human brain were researchers Wernicke and Broca.

They located and delineated boundaries of brain areas linked to speech perception and production, based on findings from lesion studies (Broca, 1861; Lichtheim, 1885). In subsequent years, the approach of attributing function to a brain region by studying the effect of lesion in that region on brain function led to the identification of numerous pu- tative functional areas. Thereafter, the advent of sophisticated brain imaging techniques CHAPTER 2. BACKGROUND AND METHODS 22

Table 2.1: Comparative analysis of widely used anatomical atlases against desiderata of a brain parcellation scheme Brodmann Julich- Gyral AAL Hagmann Dusseldorf Parcellation Cytoarchitecture Cytoarchitecture Gyral pat- Structural Arbitrary criteria terns MRI fea- tures Extent of Cortical Few cortical re- Cortical Whole Cortical coverage gions brain Non- Yes Yes Yes Yes Yes overlapping parcellated regions Spatial 43 61 66 116 998 resolution (number of parcellated regions) has significantly contributed to the refinement and expansion of this set of functionally separable regions. Although there has been progress in identifying functional nodes, the large-scale, function-based parcellation of the brain is far from complete (Mesulam,

2000b).

The recently introduced task-free fMRI is a promising approach to localize activity patterns across a large portion of the brain. Taking advantage of this utility of task-free fMRI, Cohen and colleagues used an image segmentation approach to demarcate bound- aries of functional areas (Cohen et al., 2008). More specifically, they implemented the

Canny edge detection algorithm (Canny, 1986) for identifying sharp transitions in task- free fMRI patterns on the brain surface. They reported reliable detection of boundaries CHAPTER 2. BACKGROUND AND METHODS 23

of two brain regions—the angular gyrus and the supramarginal gyrus—in individual sub- jects and at the group level. Although the findings from the study reinforce the utility of task-free fMRI as a tool for large-scale function-based parcellation of the human brain, there were several methodological limitations. Since the segmentation was performed on the brain surface, the parcellation was limited to cortical areas: it could not analyze critical deep-brain structures. Critically, the method involves progressive scanning of the entire cortical surface using a small 2D grid of voxels, which renders the task of entire cortical surface parcellation (consisting of approximately 104–106 voxels) very expensive computationally.

To address these limitations, we pose the task of large-scale function-based parcella- tion as a clustering problem rather than an image segmentation one. More formally,

1 2 3 n i given a set of task-free timeseries of n voxels X = x( ), x( ), x( ),... x( ) where x( ) is the { } timeseries of the i t h voxel, the task of parcellation is equivalent to grouping the voxels into a few cohesive clusters. A cluster identified using this approach would contain voxels that show similar neural activity patterns. This formalism not only addresses the afore- mentioned limitations, which can be mainly attributed to the use of an image segmen- tation approach, but also allows us to capitalize on the powerful analytical framework and algorithms developed by the machine learning community. To explore the utility of unsupervised machine-learning for our purposes, we implemented four types of clus- tering methods. These include: (1) the simple and elegant k-means, (2) the hierarchical clustering method, (3) the powerful spectral clustering method, and (4) a more recently CHAPTER 2. BACKGROUND AND METHODS 24

developed independent component analysis (ICA) method. We test and compare the per- formance of these implementations on computer simulated datasets. We hypothesize that

ICA will be the most accurate in identifying functionally homogeneous clusters of the brain, outperforming k-means, hierarchical clustering, and spectral clustering methods.

This hypothesis is based on the premise that ICA is better suited for analyzing data with a poor signal-to-noise ratio, which is likely to be the case for task-free fMRI signal. In the following text, we describe the four methods, provide details about the simulations, and present the evaluation results.

2.1.3.3.1 k-means clustering k-means, a partitioning method, subdivides the dataset

X consisting of n objects (or in this case, voxels) into k clusters wherein each object belongs to the cluster with the nearest mean (Lloyd, 1982). The k-means algorithm is as follows:

1. Initialize k cluster means: µ1,µ2,..µk

2. For each object x(i), assign x(i) to the cluster with the nearest mean.

3. For each cluster p (1 < p < k), recalculate the cluster mean µp

4. Repeat steps 2 and 3 until convergence

In the algorithm above, the initial value of cluster means is to be prespecified. Since the clustering solution is dependent on this initialization, we choose to run the algorithm for N 0 (=100) iterations. In each iteration, we randomly pick k samples of X , and assign CHAPTER 2. BACKGROUND AND METHODS 25

the value of those samples to the k cluster means. Additionally, k the number of clus- ters we want to find has to be pre-specified. In our k-means implementation, we use the widely-used gap statistic method (Tibshirani et al., 2001) for estimating k. The idea be- hind the gap statistic is to vary k, then for each k compare the within-cluster dispersion with that expected from a null data distribution, and select the number of clusters as the smallest k which shows the largest difference. We estimate the optimal k using the gap statistic as follows:

1. For each k where k = 1 : K

(a) For each cluster Cp in C1,C2, ..Ck calculate the sum of pairwise distances dp { } between all objects in the cluster as:

X dp = d(i,j) i,j Cp ∈

(b) Calculate the pooled within-cluster sum of pairwise distances Wk as:

Xk Wk = dp p=1

2. Generate T reference datasets from the data. For each generated dataset compute

Wk∗ as in step 1.

3. For each k where k = 1 : K, calculate Gapk as CHAPTER 2. BACKGROUND AND METHODS 26

! 1 XT Gapk = log(W∗) log(Wk) T k t=1 −

4. Select the optimal number of clusters as smallest k such that Gap Gap – k = k+1

stdev where stdev is the standard deviation of T replicates of log W∗ cal- k+1 k+1 ( k+1) culated as:

v u T T u 1 X 1 X stdevk 1 = t (log(W∗ ) ( log(W∗ )) + T k+1 T k+1 t=1 − t=1

We choose T = 500, which specifies the number of randomly generated datasets for estimating the null distribution. To partition the dataset X , we apply the k-means algorithm to X with k equal to the identified optimal number of clusters.

2.1.3.3.2 Hierarchical clustering Hierarchical clustering, an agglomerative method, divides the dataset X consisting of n objects (or in this case, voxels) into a hierarchy of clusters (Johnson, 1967). Each object is assigned to its own cluster at the first step, and pairs of clusters that are most similar are successively merged until all the objects are clustered into a single cluster of size n. The clustering solution is chosen by specifying the hierarchy level l. In our hierarchical clustering implementation, we use the gap statistic method to estimate the value of l. CHAPTER 2. BACKGROUND AND METHODS 27

2.1.3.3.3 Spectral clustering Spectral clustering, a graph-based method, subdivides the dataset X consisting of n objects (or in this case, voxels) into k clusters where each ob- ject belongs to the cluster with the nearest mean in the reduced dimension Laplacian space

(von Luxburg, 2007). Spectral clustering does not make any assumptions about cluster shapes; therefore, it works well with forms of clusters including nonconvex clusters— which cannot be partitioned using conventional k-means.

In spectral clustering, one first constructs a similarity matrix S between objects. The similarity matrix is then represented as an undirected weighted graph G. Each node in this graph represents an object x(i). Two nodes x(i) and x(j) are connected if the value of

Si j is above a certain threshold and the weight of the connected edge is Si j . Conceptually, the task of clustering is equivalent to partitioning the graph in such a way that the sum of edge weights within the subgraphs is much larger compared to sum of edge weights between the subgraphs. Partitioning of the data represented as Graph G into k clusters is achieved by using the following algorithm:

1. Compute the graph Laplacian matrix L of the graph G as:

L = D W −

where

D is diagonal degree matrix of G; •

Dii is the number of edges incident on node i in graph G. • CHAPTER 2. BACKGROUND AND METHODS 28

W is the weighted adjacency matrix of graph S. •

Wi j = Si j if Si j > threshold; otherwise Wi j = 0. •

2. Compute the first k eigenvectors v1, v2,..vk of L.

i 3. For i = 1 t o n, compute y( ) as:

(i) y = [v1 (i), v2 (i), ..vk (i)]

where

y(i) is the projection of x(i) in the k-dimension Laplacian space, and • t h vr (i) is the i element of the eigen vector vr (1 < r < k). •

4. Partition y using k-means into clusters C1,C2, ..Ck.

Similar to k-means and hierarchical clustering, the spectral method also requires pre- specification of k (the number of clusters we want to find). In our implementation, we use the gap statistic method to estimate the value of k. For computing the similarity ma- trix, we use the Gaussian similarity function. We choose the Gaussian function because it is the preferred option in the graph-based clustering literature. The similarity Si j between objects x(i) and x(j) was computed as:

2 x(i) x(j) − − || σ2 || Si j = e where CHAPTER 2. BACKGROUND AND METHODS 29

2 x(i) x(j) is the functional distance between x(i) and x(j), and • −

σ controls the kernel width. •

2.1.3.3.4 Independent Component Analysis Independent component analysis (ICA) is a statistical method for uncovering hidden signal sources from observed multivariate data such that the sources are maximally independent (Bell and Sejnowski, 1995). An example of this is the cocktail party problem: Assume a room that contains n speak- ers, all of whom are speaking simultaneously, and n microphones; each microphone is recording an overlapping combination of voices from the n speakers. The microphones are arranged such that each one records a distinct combination of the speakers’ voices.

Given the recordings from n microphones, can we uncover the hidden sources (that is, identify the original voices) of the n speakers? If the voices of the n speakers are suffi- ciently independent, application of ICA to the recordings separates the mixed signal into

n signal sources that reflect the original voices of n speakers. The example illustrates the use of ICA for unmixing temporal signals. In addition to timeseries data, ICA has been similarly used to decompose spatial data as well as spatiotemporal data. More formally, application of ICA to a n x p data matrix whose cell (i, j) corresponds to a signal from the i t h point in space at time j decomposes the data matrix into a set of timeseries and associated spatial maps.

Intuitively, the ICA conceptualization maps well with the problem of grouping spa- tial data—such as voxels—on the basis of their spatial and temporal characteristics. More specifically, the problem of function-based clustering is equivalent to decomposing the

t h n x p data matrix whose cell (i, j) corresponds to a signal from the i voxel at time CHAPTER 2. BACKGROUND AND METHODS 30

Table 2.2: Simulated datasets Dataset Number of re- SNR gions sim_data1 2 0.1 sim_data2 2 0.05 sim_data3 2 Sampled from task-free fMRI data sim_data4 3 0.1 sim_data5 3 0.05 sim_data6 3 Sampled from task-free fMRI data

j. Application of ICA to this data matrix will produce a set of timeseries and associ- ated spatial maps. Spatially contiguous groups of voxels in each spatial map correspond to clusters that are of interest to us. To clarify further, using this approach to create a function-based parcellation of the brain consisting of n voxels, with each voxel having an associated task-free fMRI timeseries of length p, involves: (1) application of ICA to de- compose the n x p data matrix, and (2) identifying spatially contiguous voxel clusters in the resulting ICA spatial maps. There are multiple implementations of ICA, each vary- ing in terms of the algorithm used to decompose the data (Hyvarinen and Oja, 1997; Lee et al., 1999). We use the FastICA based implementation which is suggested as being likely to perform better compared to other implementations (Hyvarinen and Oja, 1997).

Simulated data

We assess the performance of the four methods described above using a number of computer- simulated datasets, as a function of the number of regions to be clustered and the signal-to- noise ratio (SNR). We generated six datasets (see Table 2.2) while assessing the methods. CHAPTER 2. BACKGROUND AND METHODS 31

The number of regions and SNR values for the simulations were chosen to approximately match the corresponding values in real fMRI data. The datasets sim_data1, -2, -4, and -5 included simulated Gaussian white noise. In order to simulate the real noise spectrum, sim_data3 and -6 included profiles from real fMRI data.

Each dataset consisted of a set of thirty 2D slice images of size 64 X 64. Each of the 4,096 voxels in the 2D slice had an associated signal timeseries of length 600 sampled every two seconds. These parameters were chosen so that they roughly match the real fMRI data acquisition parameters.

The simulated timeseries were constructed by implementing a general linear model, which is often used to simulate fMRI data, as follows:

X = bφM + " where

X is the simulated timeseries, •

φis a 2 x L matrix whose rows include the hemodynamic response function (HRF) • and its derivative,

b is a 1 x 2 coefficient vector representing the weights associated with the HRF • bases functions,

M is the design matrix, •

" is a white noise process with zero mean and variance σ 2. • CHAPTER 2. BACKGROUND AND METHODS 32

SNR was varied by changing ". Contrast between regions was obtained by varying

b. Figure 2.6 shows an illustrative example.

To simulate the profile of real fMRI data, we extracted the timeseries (t s 1, t s 2, t s 3) of three brain areas, which are known to be uncorrelated, from task-free fMRI data acquired from an individual subject. The pairwise correlation between these timeseries were ver- ified to be approximately 0. The timeseries X of a voxel belonging to the region i was generated by adding the corresponding extracted timeseries t s i to the HRF convolved signal (bφM), instead of ". To assess how well each of the four methods clustered the voxels, we examined the percentage error in the cluster assignment.

Figure 2.6: A simulated 64x64 image slice with 2 regions shown with two representative voxel timeseries.The timeseries associated with each voxel was generated by convolving the design matrix with the HRF bases functions. Contrast between the two regions was generated by varying beta (b). CHAPTER 2. BACKGROUND AND METHODS 33

Table 2.3: Percent error in partitioning voxels into correct clusters Number of Signal to noise Percent error regions ratio (SNR) k- Hierarchical Spectral Spatial means Clustering Clustering ICA 2 0.1 3.95 5.73 2.49 7.6 2 0.05 5.37 10.08 5.17 10.32 2 sampled from 37.45 39.57 30.41 20.8 task-free fMRI data 3 0.1 12.64 21.58 11.96 12.98 3 0.05 22.26 31.94 20.14 19.82 3 sampled from 46.1 53.9 30.41 22.99 task-free fMRI data

Results

We compared the performance of k-means, hierarchical clustering, spectral clustering, and ICA on simulated datasets by evaluating the error statistic provided by each of these methods. The results are summarized in Table 2.3. Overall, the performance of the methods was sensitive to the SNR value and the number of regions/clusters: the percent error ranged from 4 to 54%.

In this analysis, we were particularly interested in evaluating the methods’ perfor- mance as a function of SNR. When the SNR value was high, k-means, hierarchical clus- tering, spectral clustering, and ICA performed equally well. In contrast, when the SNR value was low, ICA outperformed k-means, hierarchical clustering, and spectral cluster- ing. The difference in the performance was significant, particularly when the simulated dataset included unmodeled noise from task-free fMRI data. This result may be due to two reasons: First, when applied to low SNR fMRI data, ICA is likely to isolate noise as CHAPTER 2. BACKGROUND AND METHODS 34

one or more distinct, independent components. This suggests that the performance of

ICA in identifying spatial clusters of interest is relatively less influenced by the presence of noise in the data. In contrast, the performance of k-means, hierarchical clustering, and spectral clustering methods, which rely on distance measures and do not explicitly model noise, is likely to be more influenced by the presence of noise in the data. Second,

ICA does not make any assumptions about the spatial partitions in the data. There- fore, for an example set of voxels V consisting of two clusters, V1 and V2, such that

V 1 V 2 is a subset of V, ICA is likely to correctly partition V into V1 and V2. This ∪ partial clustering solution is in contrast to k-means, hierarchical clustering, and spectral clustering methods, which assume complete partitioning: V 1 V 2 = V . As a result, ∪ partitioning V using any of these three methods is likely to incorrectly assign the voxels

(V (V 1 V 2)) to V1, V2, or one or more erroneous clusters. The partial clustering − ∪ solution support provided by ICA is highly advantageous for partitioning the brain data, which has nonparticipating gray-matter voxels.

Critically, while ICA has been applied to fMRI data for identifying spatiotemporal activity patterns (Calhoun and Adali, 2006), to our knowledge this work is the first to systematically evaluate and subsequently apply ICA for the purposes of identifying func- tionally homogenous nodes of brain networks. Taken together, the above described find- ings suggest that ICA is well-suited for accurately identifying functional subunits of the brain using task-free fMRI.

From the ICA output, we delineate functional areas by (1) identifying noise-related spatial maps by using a high-pass filter (> 0.1Hz) on the associated timeseries, and (2) CHAPTER 2. BACKGROUND AND METHODS 35

splitting the nonnoise spatial maps into a collection of functionally homogeneous clusters of voxels by using a simple thresholding procedure. These clusters of voxels constitute the set of functionally-defined nodes of the large-scale brain network.

2.1.4 Identifying edges between the nodes

In the previous section we presented our methods for identifying nodes of large-scale brain networks. The output of these methods is a set of anatomically-parcellated brain regions, where each region has a distinct anatomical profile, and a set of functionally- parcellated brain regions, where each region has a distinct functional profile. The next step in constructing large-scale brain networks is to identify edges between pairs of re- gions belonging to the same set.

An edge between a pair of brain regions in large-scale brain networks reflects func- tional interdependence of the two regions. During cognitive function, interacting brain regions exhibit functional interdependence through synchrony in neural activity, at mul- tiple time scales. It is suggested that this synchronous activity carries different informa- tion at each temporal scale (Bressler and Menon, 2010). For example, the synchronous activity at the fast temporal scale is thought to reflect transient dynamic information exchange between regions with rapidly changing environmental demands, while that at the slower temporal scale is thought to support the integrity of the information-carrying links. To understand brain function, therefore, it is critical to study large-scale functional interdependence at multiple time scales. The limitations of current experimental tech- niques preclude us from studying rapid functional interaction changes; however, we can CHAPTER 2. BACKGROUND AND METHODS 36

examine the slow and more stable interactions by using the recently introduced task-free fMRI.

The simplest approach of measuring functional interdependence, and thereby the edge, between a pair of brain regions, is to compute the coherence between task-free signals extracted from the two regions. Many coherence measures, including Pearson’s correlation and cross-correlation, have been used for these purposes. However, the physi- ologically meaningful component of this task-free fMRI signal is predominantly observed at lower frequencies (< 0.1 Hz). It logically follows that results obtained by direct ap- plication of the above-mentioned coherence measures may not reflect true connections, since they are likely to be contaminated with nonphysiological fluctuations, including those associated with head movement and/or cardiac and respiratory activity. To overcome this problem, recent task-free fMRI studies have included an additional

filtering step before computing the coherence. A bandpass filter (0.01 < f < 0.1 Hz) is used to remove the unwanted signal. However, low-frequency bandpass filters are known to not perform well, particularly at the boundaries. Another important problem related to the use of traditional coherence measures such as Pearson’s correlation is that they as- sume the underlying signal is stationary. A stationary signal is a stochastic process whose statistical properties, including mean and variance, are constant over time; an example of this would be a sinusoidal timeseries. A nonstationary signal is a stochastic process whose statistical properties vary with time; an example of this is economic timeseries data, which are likely to contain transient spikes as stock prices fluctuate with time. Re- cent studies have suggested that the task-free fMRI signal is nonstationary (Chang and CHAPTER 2. BACKGROUND AND METHODS 37

Glover, 2010; Cordes et al., 2001). Application of traditional coherence measures to task- free fMRI data is thus likely to ignore the important time-varying information present in the underlying signal.

We attempt to address these issues through a wavelet-based approach. Wavelets are so- phisticated new analytical tools that transform the input continuous-time signal, whether stationary or nonstationary, into different frequency components that are commonly re- ferred to as Scales. More generally, wavelets provide an orthonormal set of basis functions that can be used to decompose the total variance of a timeseries into a set of contributing variances at different frequency components (Figure 2.7 shows an illustrative example). In the decomposed signal, the coefficients of an orthonormal basis function defined for a fre- quency is a measure of the contribution of the observational signal at that frequency. The ability of wavelets to analyze time-varying signals at multiple resolutions makes them an attractive tool for the analysis of fMRI signals, which exhibit fractal properties. While wavelets have been extensively adopted in a wide range of applications including image compression, seismology, and computer graphics, their application to fMRI signal analy- sis has been relatively limited (Bullmore et al., 2003).

Using the wavelet framework, we identify edges between nodes of the large-scale brain networks by (1) extracting the task-free fMRI timeseries of each node of interest (Step

1, Figure 2.8), (2) applying wavelet decomposition to measure the contributing signal of each extracted timeseries in frequency components (scales) of interest (Step 2, Figure

2.8), (3) calculating wavelet correlation between wavelet transformed signals, at each scale

(Step 3, Figure 2.8), and (4) assigning a binary edge between a pair of nodes if the wavelet CHAPTER 2. BACKGROUND AND METHODS 38

Figure 2.7: Illustrative example of application of wavelet transform decomposing the total variance of an example raw fMRI timeseries into a set of contributing variances in three frequency components (scales).Scale 1 (in green), scale 2(in red), and scale 3 (in blue). The example highlights the utility of wavelet analysis in extracting contributing signal at multiple frequency intervals of interest. CHAPTER 2. BACKGROUND AND METHODS 39

correlation between the wavelet transformed signals of those nodes at specific scale of interest is above a certain threshold (Step 4, Figure 2.8).

A detailed version of this algorithm is given below:

Let,

¦ 1 2 r © Na = Na ,Na ,... Na be the set of r anatomically-parcellated brain regions, n o 1 , 2,... s be the set of functionally-parcellated brain regions. Nf = Nf Nf Nf s  N if constructing brain network with nodes as anatomically  a    parcellated brain regions   N =     Nf if constructing brainnetwork with nodes as functionally   parcellated brain regions be the set of either r or s nodes of interest

1. Extract task-free fMRI timeseries for each node of interest

For each node Ni N, calculate ∈

t s i = Average all voxels within Ni at each time point in the task-free fMRI time series.

where t s i is the average task-free fMRI timeseries of node Ni . 2. Apply wavelet decomposition to measure the contributing signal of each extracted timeseries in three frequency components.

The three frequency components of our interest are scale 1 (0.125 to 0.25 Hz), scale 2

(0.062 to 0.125 Hz), and scale 3 (0.01 to 0.06 Hz).

For each node timeseries t s i t s, calculate the wavelet decomposition of t s i such ∈ that, CHAPTER 2. BACKGROUND AND METHODS 40

Figure 2.8: Flowchart depicting steps involved in identifying an edge between a pair of nodes using a wavelet approach. We identify edge between a pair of nodes by (1) ex- tracting the regional timeseries of the two nodes, (2) applying wavelet transform to the regional timeseries, (3) computing wavelet correlation, wrj(1,2), as the correlation be- tween wavelet transformed regional timeseries of node 1 and node 2, at scale j, and (4) assigning an edge between node 1 and node 2, if wrj(1,2) > correlation threshold (R) CHAPTER 2. BACKGROUND AND METHODS 41

X XX tsi = νJ ,k φj,k+ ξj,kψj,k k j J k ≤ where

1. ξj,k is the contribution of the timeseries tsi at scale j at time-point k where k =

1,2,..T/2j. T is the length of the timeseries. It follows that ξj represents the con-

tributing signal of the timeseries tsi at scale j. J = 3 is the number of scales.

2. νJ ,k is the residual signal at time point k and scale J.

3. ψj,k and φj,k are mother wavelet and father wavelet respectively, such that

! 1 t 2jk ψ t ψ − j,k ( ) = p j 2j 2

Z ψ(t) d t = 0

! 1 t 2jk φ t φ − j,k ( ) = p j 2j 2

Z φ(t) d t = 1 CHAPTER 2. BACKGROUND AND METHODS 42

At each scale, the signal is factorized into a major coefficient, ξj,k, which is the index of the mother wavelet; and a minor residual, νj,k , which is the index of the father wavelet.

Taken together, the tsi equation represents decomposition of the timeseries into three contributing signals: ξ1 at Scale1; ξ2 at Scale2; ξ3 at Scale3; and a residual signal, ν3 , at Scale 3. We choose three as the number of scales for two reasons: (1) the highest frequency encoded in our data is 0.25 Hz, and (2) the frequency of interest (<0.1Hz) is to be captured in one scale. Intuitively, the wavelet decomposition process transforms an input timeseries signal into contributing signals at multiple frequency components of interest.

3. At each scale, calculate wavelet correlation between wavelet transformed signals.

From the wavelet transformed signals, frequency dependent correlations between pairs of node timeseries can be calculated by computing the wavelet correlation between the corresponding scale-specific wavelet coefficients, as follows.

For each pair of node timeseries (t s i , t s p ), for each scale j, calculate wavelet correla- tion as:

w r i, p i , p j ( ) = < ξj,k ξj,k > where i and p are wavelet coefficients of timeseries t s , t s at scale j. ξj,k ξj,k i p The output of this step is an n x n correlation matrix at each scale j, where n is the number of nodes of interest. A cell (u, v) in the matrix corresponding to scale j is a measure of functional interdependence between node u and node v, in the frequency component associated with scale j. CHAPTER 2. BACKGROUND AND METHODS 43

4. Identify edges

The wavelet correlation computed in the previous step is a measure of functional interde- pendence between a pair of nodes, at a specific scale of interest. We assign an unweighted edge between the node pair if the value of wavelet correlation is above a certain threshold.

There is currently no formal consensus regarding threshold selection, so we choose to use threshold values from 0.01 to 0.99 in increments of 0.01.

2.2 Quantifying the topology of large-scale human brain

networks

In the previous section, we described our methods for detecting large-scale human brain networks using task-free fMRI data. Understanding the topology of these networks, and therefore the functional organization of the brain, is fundamentally important for gain- ing system-level insights into brain function. More specifically, the configuration of brain network connectivity determines the characteristics of functional interactions, the com- plexity of emergent brain dynamics, the principles governing information processing, network robustness and vulnerability to insult, and the network growth model. For example, knowing that a brain network at the global level has a regular lattice-like struc- ture, where brain regions only interact with other brain regions nearby, signifies locally specialized information processing with no interactions between widely distributed func- tionally specialized set of brain regions. The complexity of brain dynamics emerging from a brain network with a regular lattice-like structure is low because majority of the CHAPTER 2. BACKGROUND AND METHODS 44

constituent brain regions do not interact and are thus statistically independent. Further- more, the lattice-like structure also suggests a network growth model that is optimized to minimize wiring costs at the expense of efficiency. Knowing that a brain network has a modular organization indicates that the pattern of network connectivity can be parti- tioned into a set of modules with each module having dense within-module connectivity and sparse between-module connectivity. Such a modular architecture supports a partic- ular type of network growth model that allows each individual module to evolve without affecting the functioning of other modules. Knowing the hierarchical organization of a brain network informs us about how specific brain regions exert influences while coordi- nating information-flow among other participating brain regions during brain function- ing. Knowing the connectivity pattern of a brain region indicates the importance of that region in information processing. Regions with high connectivity are likely to play a key role in facilitating integration among distributed brain regions. Furthermore, a brain net- work consisting of a few brain regions with many connections, and many brain regions with a few connections, is likely to be more vulnerable to the disruptions of highly con- nected regions compared to disruptions of less-connected brain regions. These examples are meant to illustrate the fact that knowing the topology of brain networks at the global and regional level provides key insights into how constituent interacting brain regions process information during brain function.

In addition to knowing the global and regional topology of brain networks, it is also equally important to know the topology of the subnetworks. The human brain can be subdivided into five subnetworks – primary sensory, association, paralimbic, subcortical, CHAPTER 2. BACKGROUND AND METHODS 45

and limbic (Mesulam, 2000a). Each subnetwork has a distinct cytoarchitectonic profile and subserves a unique set of functions. These subnetworks collectively are thought to map the external sensory information to cognition. The primary sensory subnetwork is thought to encode the sensory information from the external world. More specifically, through serialized processing, the subnetwork is responsible for first encoding the visual and auditory information, then accurately extracting informative features such as color and motion from the first level encoding, and finally using the extracted information for perceptual encoding of the objects. The association subnetwork is thought to integrate this perceptual information derived from primary sensory modalities, and then subse- quently to link the integrated information to higher order processes such as emotion, memory, and action, which are collectively supported by the other three subnetworks.

The regions of the association subnetwork, along with those belonging to the limbic and paralimbic subnetworks, are important for transforming perceptual information into identification, meaning, and encoded memory. Taken together, the five anatomically dis- tinct subnetworks purportedly support a multistage information processing architecture that includes recognition using perceptual information, attention to the recognized event, linking the event to emotion and past experiences, and planning and execution of action in response to the event. Each of the five subnetworks contributes distinct function to this processing architecture. It is thus of great importance to know the functional topol- ogy of these subnetworks. In sum, knowing the topological properties of brain networks at the global, subnetwork, and regional levels is critical for understanding the cognitive information processing architecture of the human brain. CHAPTER 2. BACKGROUND AND METHODS 46

To this end, we use a graph-theoretic approach to quantify the topological proper- ties of large-scale brain networks at multiple levels of granularity. The field of graph theory provides a new and elegant approach for measuring the statistical mechanics of complex networks such as the brain, and how it gives rise to network behavior. The earliest notable application of graph theory to the study of complex networks was per- formed by Watts and Strogatz (Watts and Strogatz, 1998). They reported that the net- work representing the electric power grid of the western United States exhibited a non- random architecture characterized by the presence of densely connected nodes mostly connected by a short path. They referred to this architecture as “small-world” and pro- posed a mathematical model to generate such a network topology. In this model, an n node network having a small-world topology is generated by beginning with a ring lattice with n nodes and k edges per node and then rewiring each edge at random with proba- bility p [0 < p < 1]. The small-world network topology is thus an intermediate state between regular lattice-like network topology (p = 0) and random network topology

(p = 1) (Figure 2.9). Complex systems modeled as small-world networks were shown to exhibit increased computational power and optimal synchronizability, compared to those modeled as regular or random networks.

Since the Watts and Strogatz work was published, a wide range of complex systems including biological networks and social networks have been reported to exhibit such nonrandom optimally connected architecture, providing key mechanistic insights into the network functioning. This type of characterization is well-suited for analyzing large- scale brain networks because these networks are complex and optimally connected to CHAPTER 2. BACKGROUND AND METHODS 47

minimize information processing costs. More importantly, in addition to providing in- sights into brain network functioning at the global level, the recent growth in statistical physics of complex networks promises new approaches to examine other local topologi- cal aspects of brain networks.

Figure 2.9: Small-world network (0 < p < 1) as an intermediate state between regular lattice-like network (p = 0) and random network (p = 1). p is the probability of rewiring an edge in the regular network (Watts and Strogatz, 1998).

A graph-theoretical approach is well suited for quantifying the topological properties of large-scale brain networks at multiple levels of granularity. We now describe our graph- based methods for quantifying the topology of brain networks at three levels of granu- larity: global, subnetwork, and regional level. At each level of granularity we present relevant neuroscientific questions highlighting the significance of the questions, and then describe our graph-based methods for analyzing brain networks in an attempt to answer these critical questions. CHAPTER 2. BACKGROUND AND METHODS 48

2.2.1 Global topology

We first describe our graph-based methods for quantifying the topology of brain net- works at the global level.

2.2.1.1 Localized processing

In a modular view of brain function, complex cognitive functions are localized to densely interconnected brain regions, commonly referred to as modules or clusters.

Figure 2.10: Illustration of key network properties. A densely interconnected cluster is shown in green; path connecting two nodes is shown in black; the degree of a node (number of edges incident on the node) is shown in gray. Nodes are shown in blue, edges connecting the nodes are shown in red.

Each cluster performs a distinct function and is autonomous. Investigating whether the information processing in the human brain is predominantly localized is equivalent to determining the number of autonomous, densely connected local clusters in brain net- works. Networks having a large number of statistically independent clusters are indica- tive of highly specialized localized processing during brain function, thereby supporting CHAPTER 2. BACKGROUND AND METHODS 49

a modular view of brain function.

The clustering coefficient—a graph metric—is a useful measure for identifying local clusters (Figure 2.10). It is based on the operating principle that, if the neighbors of a node are interconnected, they collectively form a cluster. Formally, the clustering coefficient

Ci of a node ni in the network is defined as:

1 X Ci = e(nj,nk) k k 1 /2 ( ) nj,nk neigh(ni) − ∈ where

neigh(ni) is the set of k neighboring nodes of node ni, and •

e(nj,nk) = 1 if there is a direct connection between node nj and node nk in the •

network; e(nj,nk) = 0 otherwise

A network consisting of nodes with a high clustering coefficient is characterized by densely connected local clusters.

To quantify the extent of localized processing in the brain, we compute the clustering coefficient (C) of the brain network as the mean of the clustering coefficients of all the nodes in the network. The clustering coefficient of every node is calculated as the ratio of the number of connections between its neighbors, divided by the maximum possible connections between its neighbors. CHAPTER 2. BACKGROUND AND METHODS 50

2.2.1.2 Distributed processing

In contrast to the modular view of brain function, brain function alternatively can be viewed as holistic. In this view, complex cognitive functions are executed through widely distributed brain areas, and they cannot be partitioned into functionally specialized clus- ters. The brain anatomy provides synaptic pathways that support communication be- tween widespread brain regions. Investigating whether the information processing in the human brain is predominantly distributed is thus equivalent to determining how effi- ciently widely distributed brain regions can communicate with each other. The efficiency of communication can be measured by evaluating the average number of synapses—the path length—between any pair of nodes in the network. The path length determines the potential for distributed processing in the network. Networks having a connectivity configuration where nodes are separated from each other by a few synapses would be in- dicative of efficient distributed processing during brain function, which in turn supports the holistic view of brain function.

The characteristic path length—a graph metric—is a useful measure for evaluating the minimum number of connections that must be traversed for a node pair in the network to interact (Figure 2.10). More generally, it is a measure of how well a network is connected.

Formally, the path length Li of a node ni in the network is defined as:

1 X Li = d(ni,nj) N 1 ni ,nj V, i =j − ∈ 6 where CHAPTER 2. BACKGROUND AND METHODS 51

d(ni,nj) is the length of the shortest path between from node ni to node nj, •

V is the set of nodes in the network, and •

N is the number of nodes in the network. •

A network consisting of nodes with a low characteristic path length is characterized by short distances between any two nodes.

To quantify the extent of distributed processing in the brain, we compute the charac- teristic path length (L) of the brain network as the average of the mean minimum path lengths of all the nodes in the network. The mean minimum path length of a node is calculated as the average of minimum distances from that node to all the remaining nodes in the network, using Dijkstra’s algorithm.

The graph-based metrics such as the path length are not meaningful when the graph contains disconnected nodes. To address this issue, we compute a related measure— efficiency—which is defined as the inverse of the harmonic mean of the minimum path length between each pair of nodes (Latora and Marchiori, 2001); efficiency as a graph metric is not susceptible to disconnected nodes. Formally, the efficiency Ei of node ni in the network is defined as:

1 X 1 Ei = N 1 d n ,n ( ) ni ,nj V, i =j ( i j) − ∈ 6 where

d(ni,nj) is the length of the shortest path between from node ni to node nj, • CHAPTER 2. BACKGROUND AND METHODS 52

V is the set of nodes in the network, and •

N is the number of nodes in the network. •

2.2.1.3 Interplay between localized processing and distributed processing

Large-scale brain networks with high clustering coefficients provide supporting evidence for a localized modular view of brain function, whereas those with low path lengths provide supporting evidence for a distributed holistic view of brain function. There is a longstanding controversy in brain science about which one of these two views accurately describes brain function. Neither of these views exclusively accounts for the complex large repertoire of brain connectivity patterns. Accumulating evidence suggests that the human brain may have a hybrid processing architecture during brain functioning, where information processed in local functionally specialized clusters that are distributed across the brain is integrated through efficient intercluster connections (Bressler and Tognoli,

2006). The small-world model introduced previously is very well-suited to quantify this complex interplay between localized processing and distributed processing. It follows that large-scale brain networks exhibiting small-world topology may provide supporting evidence to the hybrid information processing architecture.

A network is said to exhibit small-world topology if the ratio of clustering coefficient to the characteristic path length is greater than one. Formally, the small-world measure— a graph metric—of a network is defined as:

C σ = L CHAPTER 2. BACKGROUND AND METHODS 53

where

C is the clustering coefficient of the network, and •

L is characteristic path length of the network. •

From the definition, small-world networks are characterized by high clustering coef-

ficients and low characteristic path lengths.

To quantify the interplay between localized and distributed processing, we compute the small-world metric of the brain network by calculating the ratio of the clustering coefficient to the characteristic path length of the brain network.

2.2.1.4 Hierarchy

The small-world metric informs us whether the network consists of local clusters that are mostly connected with one another by short paths. These clusters may be organized in a systematic configuration. One such organization is the hierarchical configuration, where small, densely connected clusters combine to form large, less-interconnected clus- ters, which combine again to form larger, even less-interconnected clusters. Such hier- archical organization supports top-down relationships between node clusters, which is postulated to be the case in the human brain. For example, fronto-parietal regions have been thought to control and coordinate the interactions, between lower-level sensory and motor areas, during perceptuomotor processing (Bressler et al., 2008; Corbetta and Shul- man, 2002). However, the hierarchical nature, if any, of large-scale human brain networks has not been quantitatively evaluated. CHAPTER 2. BACKGROUND AND METHODS 54

The β parameter—a graph metric—is a useful measure for evaluating the hierarchical nature of a network (Ravasz and Barabasi, 2003). β measures the extent of the power-law relationship between the clustering coefficient and the average number of edges (degree) in the network. Formally, the β of a network is defined as:

β C = k− where

k is the degree of the network, and •

C is the clustering coefficient of the network. •

A network with a high β value is said to exhibit hierarchical organization character- ized by highly connected nodes whose neighbors are not necessarily connected to one another.

To quantify the hierarchical nature of the large-scale brain network organization, we compute β by fitting a linear regression line to the plot of log(C ) versus log(k).

2.2.2 Subnetwork topology

The human brain can be subdivided into the five subnetworks mentioned previously (pri- mary sensory, association, paralimbic, subcortical, and limbic). To quantify the topology of these subnetworks, we detect the subnetworks from large-scale human brain networks and then apply the graph based methods described above to the detected subnetworks. CHAPTER 2. BACKGROUND AND METHODS 55

In order to detect subnetworks, we first partition the set of nodes belonging to the large-scale human brain network, identified using the methods described in Section 2.1.3, into five subsets. Each subset consists of nodes belonging to a particular subnetwork.

For example, the primary-sensory subset consists of network nodes that are thought to be involved in primary sensory processing. The exact assignment of a node to a subset is done using the partition scheme proposed by Mesulam (Mesulam, 2000a). The partition scheme provides a one-to-one mapping between a distinct brain region and a subnetwork.

For example, the thalamus and the basal ganglia regions belong to the subcortical subnet- work; the insula and the anterior cingulate cortex belong to the paralimbic subnetwork.

After partitioning using these assignments, the five subsets correspond to the nodes of the five subnetworks. We identify edges between the nodes of the subnetwork by using the wavelet-based implementation described in Section 2.1.4.

To examine the topology of the five subnetworks, we use our graph-based methods described in Section 2.2.1 to quantify the extent of localized processing, the extent of dis- tributed processing, the interplay between the two modes of processing, and the hierar- chical organization in each subnetwork. More specifically, graph metrics of a subnetwork were computed by aggregating the metrics of the nodes belonging to that subnetwork.

2.2.3 Regional topology

Participating brain regions are thought to play different roles in a large-scale brain net- work. Some regions are likely to interact with many other regions, integrating informa- tion processed in those regions; some are likely to exert influences or coordinate activity CHAPTER 2. BACKGROUND AND METHODS 56

in other regions; some are likely to process low-level sensory information. Elucidating the exact role, and thus the importance of each participating brain region, is critical for gaining insights into the network operation.

We assess the importance of a brain region (node) in network operation by comput- ing the relevant graph metrics for that node: degree, betweenness centrality, closeness centrality, eigenvector centrality. These metrics assess the importance of a node on the following criteria: Is the node well connected (degree)? Is the node part of many short paths within the network (betweenness centrality)? Is the node close in terms of path length to all other nodes in the network (closeness centrality)? Is the node connected to other important nodes in the network (eigenvector centrality)? We now describe below how we compute these metrics.

The degree of a node in the network is a measure of connectivity of that node. We compute degree ki of a node ni in the network by counting the number of edges incident upon the node ni. The betweenness centrality of a node in the network is a measure of how many times a node participates in the shortest paths between other nodes. Formally, betweenness centrality BC i of a node ni in the network is defined as:

ϑ n X nj nk ( i ) BC i = ϑ ni ,nj ,nk V,j = i =k nj nk ∈ 6 6 where

ϑn n is the number of shortest paths from node nj to node nk, • j k CHAPTER 2. BACKGROUND AND METHODS 57

ϑn n (ni ) is the number of shortest paths from node nj to node nkthat pass through • j k

node ni, and

V is the set of nodes in the network. •

We compute the betweenness centrality of a node by first finding the shortest paths between each pair of nodes in the network, using Dijkstra’s algorithm, and then counting the number of times the node participates in these shortest paths.

The closeness centrality of a node in the network is a measure of how close is that node to other nodes in the network. Formally, closeness centrality CC i of a node ni in the network is defined as:

1 X CC i = d(ni,nj) N 1 ni ,nj V,i = j − ∈ 6 where

d(ni,nj) is the length of the shortest path between from node ni to node nj, •

V is the set of nodes in the network, and •

N is the number of nodes in the network. •

We compute the closeness centrality of a node by calculating the length of shortest path between that node and all other nodes in the network, using Dijkstra’s algorithm.

The closeness centrality CC i of a node is equivalent to its characteristic path length Li . CHAPTER 2. BACKGROUND AND METHODS 58

The eigenvector centrality of a node in the network is a measure of connectivity of that node to other important nodes in the network. We compute the eigenvector central-

t h ity EC i of a node ni in the network by calculating the i component for the principle eigenvector of the network’s adjacency matrix.

We identify the important “hub” nodes of the networks as those whose value, for one of the four graph metrics, is at least two standard deviations greater than the mean over all nodes in the network.

2.2.4 Statistical analysis

The values of graph metrics used to quantify aspects of global, subnetwork, and regional topology are greatly influenced by the characteristics of the network under investigation.

For example, the path length of a network consisting of a large number of edges is bound to be very low, compared to a sparsely connected network. To address this issue, we normalize every computed network metric of interest to its null distribution. The null distribution of a network metric describes the expected value of that metric in a random network.

The empirical null distribution is computed by generating 1,000 surrogate datasets.

We generate an instance of the surrogate dataset by constructing a random network with the same number of nodes and connectivity distribution. We subsequently compute the network metric of interest, by using methods described in Sections 2.2.1 and 2.2.2, for each surrogate dataset, thereby computing the null distribution. We identify the network metric value as being significant if the value is significantly different (q < 0.01) from the CHAPTER 2. BACKGROUND AND METHODS 59

mean of the null distribution. We further explain this statistical inference procedure with the help of the following example: Assume β0 is the computed hierarchy value of a brain network consisting of N nodes and k average edges per node. To evaluate the significance of β0, we estimate the null distribution by computing β1,β2,..β1000 of the 1000 random networks, each with N nodes and k average edges per node. The brain network is said to have hierarchical organization if β0 is significantly different (q < 0.01) from β∗, where

β∗ is the mean of β1,β2,..β1000.

2.3 Assessing structure–function relationships in large-

scale human brain networks

In the previous section, we described our methods to quantify the topology of large-scale human brain networks. A related and important question in modern brain science is how brain networks emerge from the underlying brain anatomy. The human brain consists of complex, yet elegantly organized, anatomical elements that are densely interlinked through structural connections. These structural connections are thought to shape the functional interactions between constituent elements.

At the cellular level, it is known that neurons functionally interact with other neu- rons by sending electrical signals over the axons interconnecting the neurons, clearly indicating a one-to-one correspondence between structural and functional connectivity.

At the microscopic level, there is evidence that suggests populations of neurons are CHAPTER 2. BACKGROUND AND METHODS 60

preferentially connected to other neuronal populations that have similar function (An- gelucci et al., 2002; Peters and Sethares, 1996; Malach et al., 1993). It also has been re- ported that the structural connectivity patterns among neuronal populations shape the functional connectivity among them (Buzsaki et al., 2004; Ostojic et al., 2009), the tempo- ral organization of this functional connectivity (Roopun et al., 2008), and the emergent functional dynamics (Binzegger et al., 2009). Taken together, findings from these studies indicate that, at the microscopic level, there is a strong correspondence between struc- tural and functional connectivity among populations of neurons.

At the macroscopic level, however, there is limited evidence about the exact relation- ships between structural and functional connectivity between brain regions. Each region consists of 105 to 107 neurons. In particular, less is known about the structure–function relations in large-scale networks at the whole-brain level, including both cortical and sub- cortical regions (Damoiseaux and Greicius, 2009). This is due in part to the difficulty in assessing large-scale structural connectivity in the human brain. Until recently, the ax- onal pathways, and therefore the structural connectivity, could only be measured using autoradiographic tracing, histological dissection and staining, or electron microscopy.

Although these techniques have played a key role in mapping the anatomical wiring dia- gram of nonhuman primates including macaques (Kobayashi and Amaral, 2003; Lavenex et al., 2002; Morris et al., 1999; Parvizi et al., 2006; Suzuki and Amaral, 1994) and cats

(Scannell et al., 1999), their direct application to humans is prohibitive for several rea- sons: These techniques allow examination of only a few brain regions at a time, and are therefore not scalable; are labor intensive and time consuming; and more importantly CHAPTER 2. BACKGROUND AND METHODS 61

are invasive, which limits their application to postmortem brain tissue. Recent advances in diffusion tensor imaging (DTI) have provided researchers with the unique opportu- nity noninvasively to assess white matter fibers—axonal bundles connecting macroscopic brain regions—in individual humans.

In the following text, we first provide an overview of DTI, highlighting its utility in assessing large-scale structural connectivity in the human brain, and then describe our methods for analyzing DTI data to measure structural connectivity between the nodes of large-scale human brain networks. Finally, we present our methods to quantify the relationship between the measured structural connectivity and the embedded functional connectivity at the large-scale level.

2.3.1 Measuring structural connectivity underlying large-scale hu-

man brain networks using DTI

In this section, we provide an overview of DTI, highlighting its utility in assessing large- scale structural connectivity in the human brain, and then describe our methods for an- alyzing DTI data to measure structural connectivity between the nodes of large-scale human brain networks.

2.3.1.1 DTI

Difffusion tensor imaging (DTI) is a relatively new technique based on magnetic reso- nance (MR). It measures diffusion characteristics of water molecules at each imaged loca- tion; for a detailed review, see (Johansen-Berg and Rushworth, 2009). Water molecules CHAPTER 2. BACKGROUND AND METHODS 62

in a medium undergo random motion due to thermal noise, causing the molecules to dif- fuse. In an unrestricted environment, the water molecules diffuse freely in all directions.

This phenomenon can be observed for example after an ink drop on a porous paper, which produces a blot that is largely circular in shape indicating isotropic diffusion. In the brain, however, the motion of water molecules is restricted due to the barriers cre- ated by cellular membranes and axonal myelin sheaths. These barriers cause the water molecules to diffuse more rapidly along the axons and less freely as they travel along the direction perpendicular to the preferred direction (Basser et al., 1994; Douek et al., 1991).

DTI measures the direction of water diffusion at the imaged location, which in turn pro- vides a measurement for the orientation of axons at that location. Therefore, assessing axonal pathways from one brain region to another is equivalent to beginning at the lo- cation of the start region and then following the axonal orientations until the location of the end region is reached; this process is commonly referred to as tractography (Con- turo et al., 1999; Mori et al., 1999). The DTI-based tractography process thus allows the in vivo quantitative assessment of axonal pathways, which in turn reveals the structural connectivity between large-scale brain regions.

2.3.1.2 Quantifying structural connectivity between nodes of large-scale human

brain networks using DTI

Figure 2.11 depicts the steps involved in quantifying structural connectivity between nodes of large-scale human brain networks using DTI; each step is explained in detail below.

The DTI analyses are performed in individual subject space, whereas the network CHAPTER 2. BACKGROUND AND METHODS 63

Figure 2.11: Flowchart depicting steps involved in quantifying structural connectivity between nodes of large-scale human brain networks using DTI. We quantified struc- tural connectivity between nodes of large-scale human brain networks by (1) warping the nodes from normalized space to individual subject space in which the DTI analysis is performed, (2) computing fiber tracks between every brain voxel using DTI-based trac- tography, (3) intersecting the computed tracks with a pair of subject space nodes to deter- mine the structural white-matter pathways connecting the node pair, and (4) measuring the number of detected fiber pathways and fractional anisotropy along the pathway to quantify structural connectivity between the node pair. CHAPTER 2. BACKGROUND AND METHODS 64

node identification and characterization analyses are performed in normalized standard space. We therefore first warp the nodes of large-scale brain networks, which are in the normalized standard space, to each individual brain so that they could be used for subsequent DTI tractography analyses (Step 1, Figure 2.11). This is done by applying the inverse of the spatial normalization transformation.

We then use DTI fiber tractography to estimate the likely connections between the regions of interest (ROIs), one pair at a time. Using a matlab-based implementation, we initiate the tractography procedure by whole-brain fiber tracking, which produces many

fiber paths (Step 2, Figure 2.11). We discard tracts that do not end in both ROIs (Step

3, Figure 2.11). We use a deterministic tracking algorithm (Basser et al., 2000; Conturo et al., 1999; Mori et al., 1999) with a fourth order Runge-Kutta path integration method and 1 mm fixed step size, to estimate each fiber tract. We use trilinear interpolation of the tensor elements to estimate the continuous tensor field. Starting from the initial seed point, we trace fiber paths in both directions along the principal diffusion axis. Path tracing proceeds until the fractional anisotropy falls below 0.15 or until the minimum angle between the current and previous path segments is larger than 30◦.

The methods described above detect fiber pathways, and thus the structural connec- tivity, between each pair of brain regions belonging to the large-scale brain network. To quantify the structural connectivity, we compute length, density, and fractional anisotropy of the detected fiber pathways (Step 4, Figure 2.11), as follows.

The fiber length is a measure of anatomical distance between the regions of interest interconnected by those fibers. We compute the fiber length by averaging the length of CHAPTER 2. BACKGROUND AND METHODS 65

all detected fibers connecting those regions.

The fiber density is a measure of the strength of the fiber pathways interconnecting the regions of interest. We compute the density of fibers (the number of fibers per unit area) connecting two regions n1and n2 as:

2 X 1 f iberdensity (n1, n2) = S n S n l f ( 1) + ( 2) f F (n1,n2) ( ) ∈ where

F (n1, n2) is a set of all the fibers connecting n1 and n2, •

l(f ) length of the individual fiber, and •

S (n1) and S (n2) are the sizes of the ROIs. •

The fractional anisotropy (FA) is another measure of the strength of the fiber path- ways interconnecting the regions of interest. We compute the fractional anisotropy (FA) of a fiber pathway by averaging the FA values along the detected fibers.

Fiber density and FA are two complementary measures of the strength of structural connectivity between two brain regions. Fiber density measures the strength of struc- tural connectivity by evaluating the number of underlying fiber pathways whereas FA measures the strength of structural connectivity by evaluating the integrity of the under- lying fiber pathway (Beaulieu, 2002). CHAPTER 2. BACKGROUND AND METHODS 66

2.3.2 Correlating large-scale human brain networks with measures

of structural connectivity

We first quantify the relationship between functional connectivity within large-scale hu- man brain networks and the underlying structural connectivity. To this end, we corre- lated the following across all pairs of regions belonging to the large-scale brain network:

(1) the strength of interregional functional connectivity as measured by wavelet correla- tion, and (2) the strength of interregional structural connectivity, as measured by fiber density or fractional anisotropy.

Next, we quantify the relationship between functional connectivity within large-scale human brain networks and the anatomical distance. We accomplish this by using the cor- relation analysis described above, although with length of fibers instead of fiber density or FA. Analyzing this relationship is important for investigating whether functional con- nectivity is influenced by spatial variations.

2.4 Comparing large-scale human brain networks across

subject populations

In the previous sections, we described our methods for quantifying the topology and structure–function relationships in large-scale human brain networks. The added value of these methods is that they allow quantitative comparison of brain networks across subject populations. The subject populations can be age-based (children, adults, and elderly); they can also include those who are in healthy or diseased populations. CHAPTER 2. BACKGROUND AND METHODS 67

The human brain undergoes massive changes from childhood to adulthood, character- ized by axonal pruning and myelination (Huttenlocher et al., 1982). These cellular-level changes cause changes to both the brain’s gray matter and white matter (Gogtay et al.,

2004; Thompson et al., 2005), which possibly reconfigures the networks that emerge from this structural substrate. Similarly, changes in the human brain have been observed during aging (Andrews-Hanna et al., 2007; Damoiseaux et al., 2009; Fotenos et al., 2008).

The period from adulthood to old age is marked with neuronal loss and the degeneration of white matter, which possibly decreases the efficiency of network interactions.

In addition to changes that occur from childhood to old age, the healthy human brain is significantly altered when it is diseased (Greicius, 2008, 2003; Kennedy and Courch- esne, 2008; Tian et al., 2006). In particular, a widely accepted theory in modern brain sci- ence postulates that brain diseases can be described as disconnectivity syndromes (Catani and ffytche, 2005). According to this theory, cognitive dysfunction in brain diseases is a manifestation both of poor network coordination and integration of information from distributed brain regions.

In sum, the extant evidence suggests that large-scale networks of the human brain undergo changes during its lifespan. Knowledge about the exact nature of these network- level changes, however, is very limited.

Building on the methods discussed previously, this section describes the methods we developed to compare brain networks. These methods can help investigate network- level changes across subject populations in a quantitative way, which in turn allows us to examine changes in the functional organization of the human brain across subject CHAPTER 2. BACKGROUND AND METHODS 68

populations. Specifically, the methods allow quantitative examination of differences in key aspects of brain networks, including its topology and the underlying connectivity, between two subject populations at a time. Hereafter, we refer to the subject populations as groups.

2.4.1 Comparing network topology

In this Section, we describe our methods to compare the topology of large-scale human brain networks at the global, subnetwork, and regional level.

2.4.1.1 Global topology

We compute and compare the graph metric values—the clustering coefficient γ (= C /Cran), path length λ (= L/Lran), global efficiency Eg l obal (= E/Eran), small-worldness (σ), and hierarchy (β/βran)—that quantify global topology of large-scale brain networks in the two groups in Scale 3 (0.01 to 0.05 Hz). Cran, Lran, βran are graph metric values we obtained from equivalent random networks (see Section 2.2.4 for details).

Each group consists of a set of subjects who are participating in the study; each subject satisfies the group participation criteria for that study. For example, one group could be children and the other group could be adults; the group of children consists of n1 subjects within a certain age range; the group of adults consists of, say, n2 subjects within a certain age range.

We focus on the frequency interval 0.01 to 0.05 Hz—Scale 3— because the included frequencies subtend the meaningful task-free fMRI signal. In group comparisons, we CHAPTER 2. BACKGROUND AND METHODS 69

control for the average wavelet correlation value (r ), because it varies considerably across subjects. Thus, for a given correlation threshold (R), the number of edges in the graph is likely to be different, resulting in different graph metric values. To ensure that graphs in both groups have the same number of edges, we set the threshold for the wavelet correlations such that the resultant graph has on average K 0 edges per node. K 0 is the average number of edges per node in the graph. We obtain it by setting a threshold for individual correlation matrices with R = ri (ri is the average correlation value for subject i, i = 1 to (n1 + n2), averaged across subjects). This procedure not only ensures that both groups have the same number of edges, but also selects a conservative K 0 such that the networks generated are not disconnected. Connected networks are particularly important for network characterization because graph metrics are not interpretable when the network is disconnected.

In sum, we determine brain network global topological differences between the two groups by (1) computing K 0, (2) setting a correlation threshold for each subject’s Scale 3 wavelet correlations such that the detected brain network has K 0 edges, (3) computing the graph metrics of interest for the detected network, (4) normalizing the values with the corresponding values obtained from equivalent random networks, and (5) comparing the normalized metric values between the two groups by using a statistical test. We further explain this comparative analysis procedure with the help of the following example: As-

1 2 sume ri and rj are average correlation within the brain network of subject i in group 1 and subject j in group 2, where 1 < i < n1;; 1 < j < n2. n1 is the number of subjects in group 1 and n2 is the number of subjects in group 2. To compute global topological CHAPTER 2. BACKGROUND AND METHODS 70

differences between group 1 and group 2, we first compute K 0 by using the procedure described above; second, threshold the wavelet correlation matrix of each subject such that the detected brain network has K’; third, compute the graph metrics of interest of the detected network , by using methods described in Section 2.2.1; four, normalize the values with the corresponding values obtained from equivalent random networks, by us- ing methods described in Section 2.2.4; five, comparing the normalized values using a two-sample t-test.

2.4.1.2 Subnetwork topology

The human brain can be subdivided into the five subnetworks mentioned previously

(primary sensory, association, paralimbic, subcortical, and limbic) (Mesulam, 2000a). We compare the topology of these subnetworks for the two groups in Scale 3 (0.01 to 0.05

Hz), as follows.

We first compute the graph metric values—the clustering coefficient (Ci /Cran), path length (Li /Lran), efficiency (Ei /Eran), and degree (Ki /Kran)—for each node i of each sub- network. We compute the metric value for a subnetwork by averaging the corresponding metric values across all the nodes belonging to that subnetwork. For each subject, this aggregation step yields four metric values, for each of the five subnetworks, at each thresh- old (0 < R < 1, in increments of 0.01). We use growth curve modeling, with an intercept, linear, and quadratic terms, in order to determine subnetwork topology differences be- tween the two groups.

Growth curve models describe change (growth) with respect to a control variable. CHAPTER 2. BACKGROUND AND METHODS 71

They are well-suited for analyzing group-level differences in biomedical data, particu- larly in cases where capturing and analyzing individual growth trajectories is important.

Furthermore, for group comparisons, growth curve models alleviate the problem of mul- tiple comparisons as fitted-curve coefficients are compared, in contrast to traditional ap- proaches where multiple individual points along the curve are compared. In our case, the growth trajectories of graph metric values of a subject carry important information about the variance within the group, and so growth trajectories need to be incorporated in the model. The coefficients of growth curve models capture the baseline performance, instantaneous growth rate, and the acceleration of the variable of interest.

2.4.1.3 Regional topology

We identify the hub regions of large-scale brain networks in the two groups in Scale 3

(0.01 to 0.05 Hz), by using the procedure described in Section 2.2.3. We then qualitatively compare the hub regions in the two groups so that we can identify group differences, if any, in hub regions.

2.4.2 Comparing brain connectivity

In this section, we describe our methods to compare the connectivity of large-scale hu- man brain networks at the global, subnetwork, and regional level.

2.4.2.1 Global connectivity

To investigate differences in global brain connectivity, we examine the network connec- tivity patterns in the two groups. We use a supervised machine learning approach to CHAPTER 2. BACKGROUND AND METHODS 72

identify the global connectivity differences. The advantage of this approach is twofold.

First, it allows us to answer the question whether the global brain connectivity between the two groups is different, and to what extent. The second reason is more important: the classification model learned from this data-driven approach can be used as a quanti- tative image-based biomarker to distinguish a brain disorder from a healthy condition, if we apply the approach to such datasets.

Applying the machine learning approach, we use the brain connectivity patterns— the correlation values between each pair of brain regions belonging to the network—as the input (features) to a pattern-based classifier. The classifier distinguishes one group from another group by making classification decisions based on the learned model—value of the linear combination of these features. We use a widely used linear-classifier (the support vector machine) because it is best suited for our purpose of classification based on a large number of features but a small number of training samples, as is usually the case in brain imaging studies. We use Leave-one-out cross-validation (LOOCV) to measure the performance of the classifier in distinguishing one group from another group. In

LOOCV, one single observation is used for testing the classifier that is trained using the remaining observations. We repeat this process so that every observation is used once for testing purposes. We further explain this procedure with the help of the following example: Assume n1 and n2 is the number of subjects in the two groups that are being compared. Let, X (i) be the vector of features—correlation values between each pair of brain regions belonging to the network—of subject i. We measure the performance of the classifier in distinguishing one group from another, as follows: CHAPTER 2. BACKGROUND AND METHODS 73

1. Split the merged dataset consisting of N (= n1+n2) feature vectors into N disjoint

subsets—S1, S2,..SN

2. For i = 1 t o N,

(a) Train the classifier on S S S .. S S ..S . i.e train on all subsets 1 2 i 1 i+1 i+2 N ∪ ∪ − ∪ ∪ ∪

except Si , to learn the classification model Mi

(b) Test the performance of Mi on the subset Si .

3. Compute the performance of the classifier as the average of performance across all

the subsets.

2.4.2.2 Subnetwork connectivity

To characterize subnetwork brain connectivity differences, we compare the regional con- nectivity at the subnetwork level in the two groups, as follows:

First, we identify inter-regional pairs that show statistically significant (p < 0.01, FDR corrected) increased or decreased connectivity (as measured by inter-regional wavelet cor- relation) in one group compared to another group. Second, we count the number of in- creased (+1) or decreased (–1) connectivities for each of the 15 subnetwork-to-subnetwork pairs. For example, to identify differential connectivity between the association subnet- work and the subcortical subnetwork, we count the number of decreased or increased con- nectivities between all pairs of regions belonging to the association subnetwork and sub- cortical subnetwork. Third, since each subnetwork has a different number of regions, we CHAPTER 2. BACKGROUND AND METHODS 74

normalize the aggregated differential connectivity count by the number of possible con- nections between pairs of regions belonging to the two subnetworks under investigation.

Finally, we perform statistical inference (p < 0.01, FDR corrected) on the normalized counts to identify subnetwork pairs that exhibit between-group differential connectivity.

2.4.2.3 Regional connectivity

To examine differences in regional connectivity in the two groups, we first perform a z-transformation of the individual regional correlation values, followed by a centering of the distribution around a zero mean. We then compare these normalized correlation values between the two subject groups to identify region pairs that exhibit between-group statistically significant (p < 0.01, FDR corrected) differential connectivity.

2.5 Summary

In this chapter, we described in detail our methods for analyzing task-free fMRI and DTI data in order to quantitatively examine key aspects of brain architecture and function, highlighting their significance and novelty. More specifically, we provided algorithmic and implementation details, along with the necessary background information, of our methods for detecting large-scale human brain networks by analyzing task-free fMRI data, quantifying brain network topology at the global, subnetwork, and regional level by using a network analytical approach, assessing structure–function relationships in brain networks by combining task-free fMRI and DTI data, and comparing the brain network topology and connectivity between subject populations. Chapter 3

Large-Scale Brain Networks in

Alzheimer’s Disease

In this chapter, we present results of our work where we applied our methods to a brain imaging dataset consisting of task-free fMRI obtained from 21 subjects with Alzheimer’s disease (AD) and 18 age-matched healthy controls, in order to investigate whether global functional organization of the brain is disrupted in AD.

3.1 Abstract

Alzheimer’s disease (AD) is a brain disorder characterized by progressive impairment of episodic memory and other cognitive domains resulting in dementia and, ultimately, death. Functional neuroimaging studies have identified brain regions that show abnor- mal brain function in AD. Although there is converging evidence about the identity of

75 CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 76

these regions, it is not clear how this abnormality affects the global functional organiza- tion of the brain. In order to characterize the global functional organization of the brain, our approach uses quantitative graph-theoretic measures of global network topology and connectivity. Specifically, we used methods described in the previous chapter to compute the global topological measures of large-scale whole-brain networks, which are derived from task-free fMRI data obtained from AD participants and age-matched healthy con- trols. We observed that the AD participants had significantly lower regional connectivity, and showed disrupted global functional organization. Importantly, our results indicate that cognitive decline in Alzheimer’s disease patients is associated with disrupted func- tional connectivity in the entire brain. Our findings further suggest that quantitative graph-theoretic measures of global network topology may be useful as an imaging-based biomarker to distinguish AD from healthy aging.

More generally, the findings demonstrate the usefulness of our methods for character- izing and comparing the global topology of large-scale brain networks, and therefore the global functional organization of the brain, in healthy and diseased populations.

3.2 Introduction

Imaging studies in AD have begun a shift from studies of brain structure (Jack et al., 2000;

Pearlson et al., 1992) to more recent studies highlighting focal regions of abnormal brain function (Backman et al., 1999; Rombouts et al., 2000; Smith et al., 1999; Sperling et al.,

2003). Most recently, fMRI studies have moved beyond focal activation abnormalities to dysfunctional brain connectivity. CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 77

PET studies, restricted to across-subject connectivity measures, have shown that AD patients have decreased hippocampus connectivity with prefrontal cortex (Grady et al.,

2001) and posterior cingulate cortex (Heun et al., 2006) during memory tasks. Using fMRI, Greicius et al. demonstrated that AD patients performing a simple motor task had reduced intra-subject functional connectivity within a network of brain regions— termed the default-mode network—that includes posterior cingulate cortex, temporopari- etal junction, and hippocampus (Greicius et al., 2004). Bokde et al. reported abnormal- ities in fusiform gyrus connectivity during a face-matching task in subjects with mild cognitive impairment (MCI)—frequently a precursor to AD (Bokde et al., 2006). Three recent studies have reported reduced default-mode network deactivation in MCI and/or AD patients during encoding tasks (Celone et al., 2006; Rombouts et al., 2005) and dur- ing a semantic classification task (Lustig et al., 2003). Celone et al also reported increased default-mode network deactivation in a subset of “less impaired” MCI patients.

In addition to analyzing functional connectivity during task performance, functional connectivity has also been investigated during task-free conditions. Using this approach,

Wang et al. found disrupted functional connectivity between hippocampus and several neocortical regions in AD (Wang et al., 2006b). Similarly, Li et al. reported reduced intrahippocampal connectivity during task-free conditions (Li et al., 2002). Most recently

Sorg et al. (Sorg et al., 2007) reported reduced task-free functional connectivity in the default-mode network of MCI patients. Although evidence is accumulating that AD disrupts functional connections between brain regions (Delbeuck et al., 2003), it is not clear whether AD disrupts global functional brain organization. CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 78

Here, we use a graph-theoretic approach to examine the global functional organiza- tion of the brain in AD. More specifically, we examined the global functional organiza- tion of the brain in AD by (1) detecting large-scale whole-brain functional connectivity networks from task-free fMRI data, (2) characterizing the global organization of these networks using graph metrics of global topology, and (3) comparing these characteristics between AD patients and age-matched healthy controls. We hypothesized that global functional brain organization would be abnormal in AD. Further, given the need for a reliable, non-invasive clinical test for AD (Thal et al., 2006), we sought to determine whether a graph-theoretic measure of global organization of large-scale brain networks obtained from task-free fMRI data might provide a sensitive and specific biomarker in

AD.

3.3 Materials and Methods

Participants

Twenty one subjects with AD and eighteen age-matched healthy control subjects partic- ipated in this study after giving written, informed consent. For those AD patients who were unable to give informed consent, written, informed consent was obtained from their legal guardian. The study protocol was approved by the Stanford University Institutional

Review Board. The AD subjects (10 males, 11 females) ranged in age from 48 to 83 (mean age 63.97) with 12 to 22 years of education (mean years of education 15.89). The subjects were recruited from memory disorder clinics in Stanford University and the University CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 79

of California San Francisco (UCSF). All AD subjects met the NINDS-ADRDA criteria for probable AD (McKhann et al., 1984). One subject had a presenilin-1 mutation; a second subject’s mother had a presenilin-2 mutation (the subject herself did not wish to be tested). Diagnosis of three other subjects has since been confirmed at autopsy. ApoE status was known for 4 additional AD subjects: one was homozygous for the ApoE 4 allele and 3 were heterozygous for the ApoE 4 allele. The control subjects (10 males, 8 females) ranged in age from 37 to 77 (mean age 62.84) with 12 to 21 years of education

(mean years of education 16.53). Study subjects were recruited from several sources (part- ners of AD patients, participants in a longitudinal study of normal aging at UCSF, and

Stanford research staff). Control subjects denied any significant neuropsychiatric disease or memory trouble, were not taking any psychoactive medicines, and had to have a Mini

Mental State Examination (MMSE) score of 27 or more. 14 of 21 AD patients were tak- ing an acetylcholinesterase inhibitor. And, 12 of 21 AD patients were taking memantine, an NMDA-receptor anatagonist. The MMSE score of the AD group ranged from 12 to

29 (mean MMSE score 22.14) and the MMSE score of the control group ranged from 27 to 30 (mean MMSE score 29). Each subject underwent an MMSE, a structural MRI scan, and a task-free fMRI scan.

Data acquisition

For the task-free scan, subjects were instructed to keep their eyes closed and try not to move. The scan lasted for 6 minutes (rest1 scan). All the subjects (except for one control CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 80

subject and two AD subjects) also underwent another task-free scan that lasted for 6 min- utes (rest2 scan) and was acquired immediately after the first task-free scan. Functional images were acquired on a 3-T General Electric Signa scanner using a standard whole- head coil. Twenty-eight axial slices (4mm thick, 1mm skip) were acquired parallel to the plane connecting the anterior and posterior commissures and covering the whole brain using a T2* weighted gradient echo spiral in/out pulse sequence (TR = 2000 msec, TE

= 30 msec, flip angle = 80◦ and 1 interleave)(Glover & Law, 2001). To aid in the local- ization of functional data, a high resolution T1-weighted spoiled grass gradient recalled

(SPGR) 3D MRI sequence with the following parameters was used: 124 coronal slices

1.5mm thickness, no skip, TR = 11 ms, TE = 2 ms, and flip angle = 15◦. Data were acquired by Drs Bruce Miller and Gary Glover.

Data preprocessing

Data (rest1 and rest2 scans) were preprocessed using statistical parametric mapping (SPM2) software (http://fil.ion.ucl.ac.uk/spm). The first 8 image acquisitions of the task-free functional time series were discarded to allow for stabilization of the MR signal. Each of the remaining 172 volumes underwent the following preprocessing steps: realignment, normalization to the Montreal Neurological Institute (MNI) template, and smoothing carried out using a 4 mm full width half maximum Gaussian kernel to decrease spatial noise. Excessive motion, defined as greater than 3.5mm of translation or 3.5 degrees of rotation in any plane, was not present in any of the task-free scans. CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 81

Detecting large-scale brain networks in AD participants and age-matched healthy controls

The preprocessed task-free functional MRI datasets were analyzed for detecting large-scale networks at the whole-brain level. The analysis was performed, as follows:

Identifying nodes

The nodes were identified using anatomical criteria. More specifically, we parcellated the whole brain into 90 regions using the AAL anatomical templates defined by Tzourio-

Mazoyer et al. (Tzourio-Mazoyer et al., 2002). A task-free fMRI timeseries was computed for each of the 90 regions by averaging all voxels within each region at each time point in the time series, resulting in 172 time points for each of the 90 anatomical regions of interest. These regional fMRI time series were then used to identify edges in a 90 node large-scale whole-brain network for each subject.

Identifying edges

Wavelet analysis was used to construct correlation matrices from the regional fMRI time series data. These matrices described frequency-dependent correlations, a measure of functional connectivity, between spatially-distinct brain regions. For each subject, a 90- node, scale-specific, undirected graph of the brain network was constructed by thresh- olding the wavelet correlation matrix computed at that scale. In our analysis we defined three scales (frequency components of interest): scale 1 (0.13 to 0.25 Hz), scale 2 (0.06 to

0.12 Hz), and scale 3 (0.01 to 0.05 Hz). For more details on the wavelet-based analysis for CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 82

identifying edges, see Section 2.1.4 in Chapter 2.

Once a large-scale whole-brain network was detected from the task-free fMRI data, we characterized this network in terms of its global topological properties and connectivity.

Quantifying global topology of large-scale brain networks in AD par- ticipants and age-matched healthy controls

Clustering and path length

We computed the clustering coefficient (C ) and characteristic path length (L) of large- scale whole-brain networks detected from the task-free fMRI data obtained from 21 AD subjects and 18 age-matched healthy controls, by using the methods described in Section

2.2.1 in Chapter 2.

To evaluate the global topology of the brain network, we compared the clustering coefficient and the characteristic path length of the network with corresponding values

(Cran , Lran) obtained and averaged across 1000 random networks with the same number of nodes and degree distribution. Networks with an optimal balance between localized and distributed processing are characterized by high normalized clustering coefficient

γ (C /Cran) > 1 and low normalized characteristic path length λ (L/Lran) ˜ 1 compared to random networks. A cumulative metric σ—the ratio of normalized clustering coefficient

(γ) to the characteristic path length (λ)—is thus greater than 1 for such networks. CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 83

Global efficiency

The characteristic path length is not meaningful when the graph contains disconnected nodes. To address this issue, we ensured that only metrics computed on connected graphs were considered in our analysis. Specifically, the algorithm used to choose the correlation threshold (R) guaranteed that disconnected graphs were excluded from the analysis. Nev- ertheless, to further determine if our characteristic path length findings were robust and reliable, we computed global efficiency (E) of large-scale whole-brain networks detected from the task-free fMRI data obtained from 21 AD subjects and 18 age-matched healthy controls, by using the methods described in Section 2.2.1 in Chapter 2.

To evaluate the network for its global efficiency of parallel information processing, we compared the global efficiency of the network (E) with corresponding values (Eran) obtained and averaged across 1000 random networks with the same number of nodes and degree distribution. An efficient network with low clustering is characterized by global efficiency value that is lower than the random network–Eg l obal (E/Eran) < 1.

Comparing global topology of large-scale brain networks in AD par- ticipants and age-matched healthy controls

Clustering and path length

We compared the clustering coefficient γ (C /Cran) and path length λ ( L/Lran) values of large-scale brain networks in the two groups, by using the method described in Section

2.4.1.1 in Chapter 2.

We next compared clustering coefficient values of four anatomical regions of interest CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 84

in the two groups. These four regions included the left hippocampus, the right hippocam- pus, the left precentral gyrus, and the right precentral gyrus. These were chosen because we hypothesized significant differences in the hippocampus (a region targeted early in

AD), but not in the precentral gyrus (which is typically spared even in the advanced stages of AD) (Braak and Braak, 1991). This regional profiling analysis was performed on the clustering coefficient (and not the path length) because only the former differed significantly between the AD and control groups. Growth curve modeling, with an inter- cept (baseline), linear and quadratic terms, was used to compare the clustering coefficient values for threshold values from 0.1 to 0.6 in the two subject groups. We chose these thresholds because beyond 0.6 the network divides into disconnected subsets of nodes and global topological metrics are then no longer meaningful (Watts and Strogatz, 1998).

Global efficiency

We compared the global efficiency Eg l obal (E/Eran) values of large-scale brain networks in the two groups, by using the method described in Section 2.4.1.1 in Chapter 2.

Comparing regional connectivity of large-scale brain networks in AD participants and age-matched healthy controls

We then examined regional correlation values (connectivity) in the two groups. Wavelet correlation values of 4005 pairs of anatomical regions were first z-normalized and then compared between the two subject groups. T-test with a false discovery rate of 0.01 was used to test if the difference was significant. For the frequency range 0.01 to 0.05 Hz, CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 85

the correlation values of 108 pairs of anatomical regions out of a total 4005 pairs were significantly lower in the AD group as compared to the control group while only 42 correlation values showed a significant increase in the AD group (p < 0.01, corrected for multiple comparisons). To get an idea of average differences in the global functional orga- nization in the two groups, we investigated the regional connectivity at a coarser level of granularity. Ninety anatomical regions of our network were grouped into eight higher- level anatomical regions using the grouping defined by Tzourio-Mazoyer et al.(Tzourio-

Mazoyer et al., 2002). The prefrontal lobe region consists of the superior frontal gyrus

(dorsolateral, orbital, medial, medial orbital), the middle frontal gyrus (orbital), the in- ferior frontal gyrus (opercular, triangular, orbital), the olfactory gyrus, the gyrus rectus, and the anterior cingulate. The other parts of the frontal lobe region consist of the pre- central gyrus, the supplementary motor area, the median cingulate, and the rolandic operculum. The occipital lobe region consists of the calcarine fissure, the cuneus, the lingual gyrus, the superior occipital gyrus, the middle occipital gyrus, and the inferior occipital gyrus. The temporal lobe and the medial temporal region consists of the su- perior temporal gyrus, the temporal pole (superior, middle), the middle temporal gyrus, the inferior temporal gyrus, the heschl gyrus, the fusiform gyrus, the hippocampus, the parahippocampal gyrus, and the amygdala. The parietal lobe region consists of the post- central gyrus, the superior parietal lobule, the inferior parietal lobule, the supramarginal gyrus, the angular gyrus, the precuneus, the paracentral lobule, and the posterior cin- gulate gyrus. The corpus striatum region consists of the caudate nucleus, the putamen, and the pallidum. Each higher level anatomical region consists of regions from both the CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 86

Table 3.1: Demography and MMSE scores. MMSE scores are significantly different in AD patients compared with control subjects ( denotes significant differences between groups ∗ AD (n = 21) Controls (n = 18) Age 63.97 (range: 48 to 83) 62.84 (range: 37 to 77) Sex 10 males, 11 females 10 males, 8 females Years of Education 15.89 (range: 12 to 22) 16.53 (range: 12 to 21) MMSE 22.14* (range: 12 to 29) 29* (range: 27 to 30) hemispheres. Differences in mean correlation coefficients for 4005 pairs were aggregated into 32 pairs and the resulting differences were then normalized. In the aggregation step, the number of decreased (-1) or increased connectivities (+1) for each of the 32 pairs (=

(8 X 8) /2) was counted. For example, to identify differential connectivity between the prefrontal lobe region and the occipital lobe region the number of decreased or increased connectivities between all pairs of sub-regions belonging to the prefrontal lobe region and occipital lobe region was counted. Since each brain region has a different number of sub- regions, the aggregated differential connectivity count was normalized by the number of possible connections between pairs of sub regions belonging to the two brain regions under investigation.

3.4 Results

Demographic data are shown in Table 3.1. Subject groups did not differ significantly in age (p = 0.73), gender distribution (p = 0.62), or years of education (p = 0.58). The mean

MMSE was significantly lower (p < 0.0001) for the AD group (22.14) compared to the controls (29). CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 87

3.4.1 Comparison of global topology of large-scale brain networks

in AD participants and age-matched healthy controls

3.4.1.1 Clustering and path length

We first examined graph metrics obtained for the large-scale brain networks constructed by thresholding (threshold values ranged from 0.01 to 0.99 with increments of 0.01) the wavelet correlation matrix computed at three scales (frequencies in the range from 0.01 to 0.25 Hz) for the AD group and the control group (see Figure 3.1, Figure 3.4A).

Functional brain connectivity and global topological properties were salient at lower- frequencies (0.01 to 0.05 Hz) for the AD group and the control group. This result pro- vides further evidence that meaningful task-free signal is subtended by lower-frequencies.

Therefore, we only report results for this frequency interval in subsequent analyses.

In the frequency interval between 0.01 to 0.05 Hz, we examined λ, γ, and σ values in the two groups. Mean λ, mean γ, and mean σ values for the networks of the AD group and control group were derived by thresholding the correlation matrices such that the network has K0 (= 40) edges. Results (shown in Figure 3.2) were: (i) No significant differences in the mean λ values were observed. (ii) Mean γ values in the AD group were significantly lower than in the control group (p < 0.01) and (iii) Mean σ values in the AD group were significantly lower than in the control group (p < 0.01) .

To further examine differences in clustering coefficient (γ) values between the two groups, we examined node level γ values. Figure 3.3 shows a plot of γ for each of the four regions (left hippocampus, right hippocampus, left precentral gyrus, right precentral gyrus), for the AD group and the control group as a function of the correlation threshold. CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 88

Figure 3.1: Global organization of large-scale brain networks in AD participants and controls, at three frequency intervals of interest. Graph metrics—degree, normalized characteristic path length λ (L/Lran), normalized clustering coefficient γ (C /Cran), σ (γ/λ), for the AD group (o) and the control group ( ) at three frequency intervals—0.01 to 005 Hz (green), 0.06 to 0.12 Hz (blue), and 0.13 to4 0.25 Hz (red).(a) For both groups, the mean degree—a measure of network connectivity is highest at Scale 3 for a wide range of correlation thresholds (0.01 < R < 0.7), (b) The mean characteristic path length (λ) is low (1 < λ < 1.27) and shows similar trends at all the scales, (c) The clustering coefficient (γ) for both groups is highest at Scale 3, (d) Due to higher mean γ values, the σ (γ /λ) is highest at Scale 3 for both groups. σ showed a linear increase as the threshold increased (degree decreased). σ values for higher correlation thresholds are hard to interpret as at higher threshold values graphs of functional brain networks have fewer edges (smaller degree) and tend to split into isolated sub-graphs. CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 89

Figure 3.2: Global organization of large-scale brain networks in AD participants and controls, at the low frequency interval. Global topological properties—normalized char- acteristic path length λ (L/Lran), normalized clustering coefficient γ (C /Cran), σ (γ/λ)— for networks derived by thresholding the correlation matrices such that the network has K0 edges.Error bars represent values two standard deviations from the mean. (A) Mean λ values for the AD group and the control group. No significant differences in the mean λ values are observed. (B) Mean γ values for the AD group and the control group. γ values in AD group were significantly lower (indicated by *) than that in the control group (p < 0.01). (C) Mean σ values for the AD group and the control group. σ values in AD group were significantly lower (indicated by *) than that in the control group (p < 0.01). CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 90

In the left and the right hippocampus, the fitted growth curve was significantly lower (p

< 0.01) in the AD group, compared to the control group, reflecting lower clustering coefficient values for a range of threshold values from 0.1 to 0.6. A similar analysis in the left and right precentral gyrus, revealed no significant differences in the clustering coefficient values. Across the four regions, no significant differences in the clustering coefficient values were observed for correlation threshold values > 0.6, mainly due to the large variance observed at higher threshold values.

To determine whether the differences observed in γ values reflect true differences and not artifacts of different average correlation values, we repeated our analysis by comput- ing γ values as a function of the number of edges in the graph. Mean γ values of four anatomical regions of interest for the AD group and the control group for networks de- rived by thresholding the individual correlation matrices such that the network has K0 edges were computed and compared. Results were consistent with the initial analysis – significantly lower clustering coefficient values (p < 0.01) in the left and right hippocam- pus in AD, and no significant differences in the left and right precentral gyrus.

3.4.1.2 Global efficiency

In the frequency interval between 0.01 to 0.05 Hz, we examined Eg l obal values in the two groups. Mean Eg l obal values for the networks of the AD group and control group were derived by thresholding the correlation matrices such that the network has K0 (=

40) edges. No significant differences in the mean Eg l obal values were observed (shown in Figure 3.4B). CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 91

Figure 3.3: Regional organization of large-scale brain networks in AD participants and controls.γ (C /Cran), the normalized clustering coefficient, for four regions of interest – left hippocampus (Hippocampus - Left), right hippocampus (Hippocampus - Right), left precentral gyrus (Precentral Gyrus - Left), right precentral gyrus (Precentral Gyrus - Right) – for the AD group (red) and the control group (blue) as a function of the corre- lation threshold. In the left and the right hippocampus, for threshold values from 0.1 to 0.6, the clustering coefficient values in the AD group were significantly lower (p < 0.01) than in the control group, while for the left and the right precentral gyrus, no significant differences in the clustering coefficient values were observed at any correlation threshold. CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 92

Figure 3.4: Global efficiency of large-scale brain networks in AD participants and con- trols.(A) Global efficiency measure (Eg l obal ), for the AD group (o) and the control group ( ) at three frequency intervals—0.01 to 005 Hz (green), 0.06 to 0.12 Hz (blue), and 0.13 4 to 0.25 Hz (red). The mean Eg l obal value is low (0.78 < λ < 1) and shows similar trends at all the scales (B) For the frequency interval 0.01 to 005 Hz (green)—mean Eg l obal val- ues for the AD group and the control group for networks derived by thresholding the correlation matrices such that the network has K0 edges. No significant differences in the mean Eg l obal values were observed. Error bars represent values two standard deviations from the mean. CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 93

3.4.2 Specificity and sensitivity of global topological metrics in dis-

tinguishing AD participants from age-matched healthy con-

trols

Here, we examined whether a global topological metric—γ (normalized clustering coefficient)— might prove sufficiently sensitive and specific to serve as a biomarker for AD. Using the cut-off value (γ = 1.57) that maximizes sensitivity and specificity, γ correctly classified 14 out of 18 controls and 15 of 21 AD subjects, yielding 72% sensitivity and 78% specificity respectively. A receiver operating characteristic curve for various cut-off values is shown in Figure 3.5. The Area Under the Curve for the ROC was 0.754 (95% CI Area 0.602 to

0.906).

3.4.3 Comparison of regional connectivity of large-scale brain net-

works in AD participants and age-matched healthy controls

We next examined regional correlation values (connectivity) in the two groups. Results show that compared to the control group, the AD group had decreased correlation values

(1) within the temporal lobe, (2) between the temporal lobe and thalamus, (3) between the temporal lobe and corpus striatum, (4) between the thalamus and occipital lobe, and

(5) between the thalamus and other parts of the frontal lobe, but increased correlations

(1) within the prefrontal areas, (2) within other parts of frontal lobe, (3) between the prefrontal areas and other parts of the frontal lobe, and (4) between other parts of frontal lobe and the corpus striatum. CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 94

Figure 3.5: Specificity and sensitivity of quantitative metrics of global organization of large-scale brain networks in distinguishing AD participants from controls. Receiver operating characteristic curve, plot of the sensitivity vs. (1-specificity) for distinguishing AD participants from controls as a function of varying normalized clustering coefficient (γ) threshold.Using a cut-off value of 1.57, γ correctly classified 14 out of 18 controls and 15 of 21 AD subjects yielding 72% sensitivity and 78% specificity. The Area under the curve was 0.754 (95% CI Area 0.602 to 0.906). CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 95

3.4.4 Reproducibility of findings

To determine if our findings were robust—reproducible across datasets—we repeated our entire analysis on a second task-free fMRI dataset (rest2 scans) acquired from the same set of subjects. Results were consistent with previous analysis (performed on data from rest1 scan): (i) Functional brain connectivity and global topological metrics including the global efficiency were salient in the low frequency interval—0.01 to 0.05 Hz (Scale 3), (ii)

No significant differences in the mean λ values were observed, (iii) Mean γ values in the

AD group were significantly lower than in the control group (p < 0.01), (iv) Mean σ val- ues in the AD group were significantly lower than that in the control group (p < 0.01), (v)

No significant differences in the mean Eg l obal values were observed, and (vi) significantly lower clustering coefficient values were found in the left and right hippocampus in AD, with no significant differences in the left and right precentral gyrus.

3.5 Discussion

In this work, we investigated whether global functional brain organization is disrupted in

AD. To our knowledge, this is the first work to examine alterations in global functional organization and connectivity in AD patients using fMRI data. Graph-based metrics of global network topology—clustering coefficient and characteristic path length—were used to measure and characterize global functional organization in the brain. The main

finding is that functional large-scale whole-brain networks in AD consistently showed CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 96

lower clustering but similar characteristic path lengths compared to controls, which sug- gests disrupted global functional organization in AD. Our findings also suggest that met- rics of global network topology might be useful as an imaging biomarker for AD.

The characteristic path lengths were low (λ ˜1) and showed no significant differences between the AD group and the control group, suggesting short distances between distinct brain regions in both groups. This finding suggests an organization consisting of multiple short alternative paths between nodes in functional brain networks in both groups.

The most interesting finding of our work was the lower levels of clustering observed in the AD group. Clustering coefficient is a measure of the extent of localized processing in a network (Strogatz, 2001). The difference in clustering coefficients in the AD group as compared to the control group was observed at a correlation threshold at or near a sub- ject’s average correlation (to ensure an equivalent number of edges across subjects), and the clustering coefficient was significantly lower in the AD group, suggesting decreased localized processing in AD.

The global efficiency (Eg l obal ) were high and showed no significant differences be- tween the AD group and the control group, suggesting high efficiency in parallel in- formation processing in brain networks in both groups. This finding parallels results obtained with measures of characteristic path length.

Node level analysis of differences in clustering coefficients as a function of correlation threshold showed that the left and the right hippocampal regions differed significantly between groups. In contrast, the clustering coefficient of the precentral gyrus did not differ between groups. This suggests disrupted connectivity from the hippocampus to CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 97

other regions of the brain in AD. This finding is consistent with the study by Greicius et al. (Greicius et al., 2004) showing reduced functional connectivity of the hippocampus within a specific network of regions—the default mode network (Greicius, 2003; Raichle et al., 2001) that includes the posterior cingulate and lateral temporoparietal cortices, in AD. It is also consistent with the study by Wang et al. (Wang et al., 2006b) showing altered hippocampal connectivity to several neocortical regions in the early stages of AD.

Other studies have reported decreased intrahippocampal synchrony of low frequency

BOLD fluctuations (Li et al., 2002) during a task-free scan. Taken together, these findings point to significantly altered local and global hippocampal network connectivity in AD.

Analysis of the group differences in the regional connectivity across several broadly defined anatomical regions demonstrate that AD patients not only showed decreased in- tratemporal, temporo-thalamus, temporo-corpus striatum, thalamo-occipital and thalamo- frontal connectivity but, surprisingly, also showed increased intrafrontal, frontal-prefrontal, and fronto-corpus striatum connectivity. These findings are in line with the recent study by Wang et al. (Wang et al., 2006a) which not only reported decreased connectivity be- tween a number of regions, but also increased prefrontal connectivity in AD. As sug- gested by fMRI studies showing increased prefrontal activation in AD during task per- formance (Gould et al., 2006), these findings suggest that patients with AD may rely on increased prefrontal connectivity to compensate for reduced temporal connectivity. An intriguing (and testable) hypothesis is that the ability to make such compensatory changes in frontal lobe connectivity may account in part for the “cognitive reserve” phenomenon

(Stern, 2006) that allows some patients to perform better than others despite equivalent CHAPTER 3. BRAIN NETWORKS IN ALZHEIMER’S DISEASE 98

pathological burdens.

To address the extent to which global topological metrics serve as a sensitive biomarker to distinguish AD from healthy aging, we examined γ values in the two subject groups.

The clustering coefficient is a measure of efficiency in network connectivity. It distin- guished AD subjects from controls with a sensitivity of 72% and specificity of 78%.

These values approach the sensitivity and specificity reported for other imaging biomark- ers (Greicius et al., 2004; Klunk et al., 2004; Rabinovici et al., 2007; Ramani et al., 2006) and are close to the range considered clinically relevant by a recent Working Group on biomarkers in AD (Ramani et al., 2006). With some improvements in the technique— decreasing the number of nodes in the network for example—the clustering coefficient may therefore prove to be an effective biomarker for AD, though prospective studies will be required to validate its effectiveness. In addition to its promise as a diagnostic aid, the clustering coefficient merits investigation as a functional marker of response to treatment.

In conclusion, we have demonstrated that fMRI-derived functional large-scale whole- brain networks in AD show lower levels of clustering. Our findings suggest that cognitive decline in AD is associated with disrupted global functional organization in the brain.

More generally, the findings demonstrate the usefulness of our methods for characterizing and comparing the global topology of large-scale brain networks, and therefore the global functional organization of the brain, in healthy and diseased populations Chapter 4

Development of Large-Scale Brain

Networks in Children

The results described in the previous chapter demonstrate the usefulness of our methods in quantitatively examining and comparing global functional organization of the human brain. In this chapter, we present results of our work where we applied our methods to a brain imaging dataset consisting of task-free fMRI and DTI data obtained from 23 children and 22 young-adults, in order to examine changes in the global, subnetwork, and regional functional organization of the human brain, as well as in the structure–function relationships within the brain, with development.

99 CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 100

4.1 Abstract

The ontogeny of functional organization of the human brain is not well understood.

To gain insight into how normal brain organization develops, we detected large-scale brain networks in children and young-adults, and used a network-analytical approach to characterize and compare the organization of brain networks at multiple levels of gran- ularity. Comparison of network properties, revealed that although children and young- adults’ brain have similar robust and efficient organization at the global level, they differ significantly in subnetwork organization and connectivity. We found that subcortical subnetwork was more strongly connected with primary sensory, association, and par- alimbic subnetworks in children, whereas young-adults showed stronger connectivity between paralimbic, limbic, and association subnetworks. Further, combined analysis of functional connectivity with wiring distance and structural connectivity measures de- rived from DTI-based white-matter fiber tracking revealed that the development of large- scale brain networks is characterized by weakening of short-range functional connectiv- ity and strengthening of long-range functional connectivity. Additionally, we found that structure–function relationships within large-scale brain networks become more mature with development. Importantly, our findings show that the dynamic process of over- connectivity followed by pruning, which rewires connectivity at the neuronal level, also operates at the systems level, helping to reconfigure and rebalance subcortical and par- alimbic connectivity in the developing brain. Our results show how our approach of network analyses of multimodal brain connectivity allows us to elucidate key principles underlying functional brain maturation, suggesting new avenues for future research on CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 101

neurodevelopmental disorders such as autism.

More generally, our methods provide a quantitative framework for a detailed inves- tigation of large-scale brain networks and their organization, in developing healthy and diseased brain.

4.2 Introduction

Understanding the development of human brain organization is critical for gaining in- sight into brain organization and functions in adulthood as well as for investigating dis- orders such as autism spectrum disorders (ASD) and attention-deficit/hyperactivity dis- order (ADHD), where normal developmental processes are disrupted. Neuroimaging studies of development have primarily focused on structural changes from childhood, to adolescence, and into adulthood. These studies have reported age-related changes in

(1) overall brain volumes (Giedd et al., 1999; Good et al., 2001), (2) volumes of individ- ual brain areas (Pujol et al., 1993; Thompson et al., 2000), (3) regional cortical thickness

(Shaw et al., 2008; Sowell et al., 2004), as well as (4) regional and global grey-matter and white-matter densities (Gogtay et al., 2004; Paus et al., 1999; Thompson et al., 2005).

Collectively these studies have suggested that the human brain undergoes vast develop- mental changes in grey and white matter structure between childhood and adulthood.

These changes are thought to reflect synaptic pruning and myelination observed at the neuronal level (Gogtay et al., 2004; Thompson et al., 2005). In spite of growing evidence from these studies for patterned brain development, the functional organization of the human brain in childhood is not well understood and it is also not clear how the above CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 102

structural changes translate to differences in functional brain organization between chil- dren and adults.

Task-free fMRI is a useful technique for investigating the functional organization of the human brain. This method detects interregional correlations in spontaneous blood oxygen level-dependent (BOLD) signal fluctuations (Biswal et al., 1995; Fox and Raichle,

2007), and has been used to investigate brain networks involved in motor (Biswal et al.,

1995), sensory (De Luca et al., 2005), attention (Fox et al., 2006), cognitive control (Seeley et al., 2007), and memory (Greicius et al., 2003; Vincent et al., 2006) systems. However, only a small number of studies have examined developmental changes in functional brain organization. A few recent studies have examined developmental changes in functional connectivity of brain regions involved in attention and cognitive control (Fair et al.,

2007)and the default mode network (Fair et al., 2008), as well as in functional connectiv- ity of anatomical structures such as the anterior cingulate cortex (Kelly et al., 2008). To our knowledge, the developmental changes in the functional organization of large-scale networks at the whole-brain level have not yet been investigated.

Here we first examined developmental changes in the functional organization of large- scale whole-brain networks by (1) detecting large-scale whole-brain functional connec- tivity networks from task-free fMRI data, (2) characterizing the organization of these networks using metrics of global and regional topology and connectivity, and (3) com- paring these metrics of global and regional brain organization between healthy children

(ages 7 to 9) and young-adults (ages 19 to 22). The results described in the previous chap- ter suggest that in older adults (age 40 and above) large-scale brain networks have high CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 103

clustering and short path—a small-world architecture—that reflects a robust and efficient, non-random, functional organization. Whether children and younger adults have a sim- ilar functional brain organization is currently not known. This question is important from a developmental perspective because the brain undergoes vast changes in structural connectivity during adolescence (Gogtay et al., 2004). We hypothesized that the global functional organization of brain networks would be characterized by non-random, ef-

ficient, small-world characteristics in both subject groups, but that young-adults would show higher efficiency compared to children, based on previous neurobiological studies in humans and animals suggesting that developmental changes improve efficiency of in- formation processing in the brain (Changeux and Danchin, 1976; Goldman-Rakic, 1987;

Huttenlocher, 1990). We further predicted that regional organization patterns would be significantly different in children, reflecting a process of continuing structural maturation during the period between childhood and young adolescence. To further characterize developmental changes in the global and regional functional organization of brain net- works, we examined functional organization in five subnetworks—primary sensory, sub- cortical, limbic, paralimbic and association. Additionally, developmental changes in the connectivity between these subnetworks were examined. Next, to characterize the under- lying developmental processes that produce these changes in the global, regional and sub- network functional organization of large-scale brain networks, we examined changes in functional connectivity as a function of DTI-based wiring distance between distinct brain regions. The formation of brain networks during development is thought to arise from a dual process of integration and segregation (Fair et al., 2007; Johnson and Munakata, CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 104

2005; Miltner et al., 1999; Salinas and Sejnowski, 2001; Varela et al., 2001). Accordingly, we investigated whether there is in vivo developmental evidence for the emergence of functional segregation and integration in large-scale brain networks. Lastly, we investi- gated how the functional connectivity within large-scale brain networks emerges from the underlying brain structure in children and young-adults. To this end, we assessed the relationships between network functional and structural connectivity. The struc- tural connectivity between network nodes was measured by detecting white-matter fiber pathways connecting the nodes, using DTI-based tractography. We hypothesized that structural connectivity would be a good predictor of functional connectivity in both the groups, and that this structure–function relationship will become more mature with age.

4.3 Materials and Methods

Participants

Twenty-three children and twenty-two IQ-matched young-adult subjects participated af- ter giving written, informed consent. For those subjects who were unable to give in- formed consent, written, informed consent was obtained from their legal guardian. The protocol was approved by the Stanford University Institutional Review Board. The chil- dren subjects (10 males, 13 females) ranged in age from 7 to 9 (mean age 7.95) with an IQ range of 88 to 137 (mean IQ: 112); the young-adult subjects (11 males, 11 females) ranged in age from 19 to 22 (mean age 20.4) with an IQ range of 97 to 137 (mean IQ: 112). The CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 105

subjects were recruited locally—children from local schools and young-adults from Stan- ford University and neighboring community colleges. 11 of 23 children subjects were

2nd graders and rest of the children subjects were 3rd graders; the young-adult subjects had 13 to 16 years of education (mean years of education 14.5).

Data acquisition

For the task-free scan, subjects were instructed to keep their eyes closed and try not to move for the duration of the 8 minute scan. Functional images were acquired on a 3T GE

Signa scanner (General Electric, Milwaukee, WI) using a custom-built head coil. Head movement was minimized during scanning by a comfortable custom-built restraint. A total of 29 axial slices (4.0mm thickness, 0.5mm skip) parallel to the AC-PC line and covering the whole brain were imaged with a temporal resolution of 2 seconds using a

T2* weighted gradient echo spiral in-out pulse sequence (Glover and Law, 2001) with the following parameters: TR = 2000msec, TE = 30msec, flip angle = 80◦, 1 interleave. The field of view was 20 cm, and the matrix size was 64x64, providing an in-plane spatial resolution of 3.125 mm. To reduce blurring and signal loss arising from field inhomo- geneities, an automated high-order shimming method based on spiral acquisitions was used before acquiring functional MRI scans. A high resolution T1-weighted spoiled grass gradient recalled (SPGR) inversion recovery 3D MRI sequence was acquired. The follow- ing parameters were used: TI = 300 msec, TR = 8.4 msec; TE = 1.8 msec; flip angle = 15o; 22 cm field of view; 132 slices in coronal plane; 256 x 192 matrix; 2 NEX, acquired resolution = 1.5 x 0.9 x 1.1 mm. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 106

For the DTI scan, the pulse sequence was a diffusion-weighted single-shot spin-echo, echo planar imaging sequence (TE = 70.8 ms; TR = 8.6 s; field of view = 220 mm; matrix size = 128 x 128; bandwidth = 110kHz; partial k-space acquisition). We acquired 63 ± axial, 2-mm thick slices (no skip) for 2 b values, b = 0 and b = approximately 850 s/mm2. The high b value was obtained by applying gradients along 23 different diffusion direc- tions. Two gradient axes were energized simultaneously to minimize TE. The polarity of the effective diffusion-weighting gradients was reversed for odd repetitions to reduce cross-terms between diffusion gradients and imaging and background gradients.

Data were acquired by Leeza Kondos, Katherine Prater, and Jose Anguiano.

Data preprocessing

Task-free fMRI data were preprocessed using statistical parametric mapping (SPM5) soft- ware (http://fil.ion.ucl.ac.uk/spm). The first 8 image acquisitions of the task-free func- tional time series were discarded to allow for stabilization of the MR signal. Each of the remaining 232 volumes underwent the following preprocessing steps: realignment, normalization to the Montreal Neurological Institute (MNI) template, and smoothing carried out using a 4 mm full width half maximum Gaussian kernel to decrease spatial noise. Excessive motion, defined as greater than 3.5mm of translation or 3.5 degrees of rotation in any plane, was not present in any of the task-free scans. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 107

Detecting large-scale brain networks in children and young-adults

The preprocessed task-free fMRI datasets were analyzed for detecting large-scale networks at the whole-brain level. The analysis was performed, as follows:

Identifying nodes

The nodes were identified using anatomical criteria. More specifically, we parcellated the whole brain into 90 regions using the AAL anatomical templates defined by Tzourio-

Mazoyer et al. (Tzourio-Mazoyer et al., 2002). A task-free fMRI timeseries was computed for each of the 90 regions by averaging all voxels within each region at each time point in the time series, resulting in 232 time points for each of the 90 anatomical regions of interest. These regional fMRI time series were then used to identify edges in a 90 node large-scale whole-brain network for each subject.

Identifying edges

Wavelet analysis was used to construct correlation matrices from the regional fMRI time series data. These matrices described frequency-dependent correlations, a measure of functional connectivity, between spatially-distinct brain regions. For each subject, a 90- node, scale-specific, undirected graph of the brain network was constructed by thresh- olding the wavelet correlation matrix computed at that scale. In our analysis we defined three scales (frequency components of interest): scale 1 (0.13 to 0.25 Hz), scale 2 (0.06 to

0.12 Hz), and scale 3 (0.01 to 0.05 Hz). For more details on the wavelet-based analysis for identifying edges, see Section 2.1.4 in Chapter 2. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 108

Once a large-scale whole-brain network was detected from the task-free fMRI data, we characterized this network in terms of its multilevel topological properties, connectivity, and relationship to the underlying brain anatomy.

Quantifying global topology of large-scale brain networks in children and young-adults

Clustering and path length

We computed the clustering coefficient (C ) and characteristic path length (L) of large- scale whole-brain networks detected from the task-free fMRI data obtained from 23 chil- dren and 22 young-adults, by using the methods described in Section 2.2.1 in Chapter

2.

To evaluate the global topology of the brain network, we compared the clustering coefficient and the characteristic path length of the network with corresponding values

(Cran , Lran) obtained and averaged across 1000 random networks with the same number of nodes and degree distribution. Networks with an optimal balance between localized and distributed processing are characterized by high normalized clustering coefficient

γ (C /Cran) > 1 and low normalized characteristic path length λ (L/Lran) ˜ 1 compared to random networks. A cumulative metric σ—the ratio of normalized clustering coefficient

(γ) to the characteristic path length (λ)—of such networks is thus greater than 1. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 109

Global efficiency

The characteristic path length is not meaningful when the graph contains disconnected nodes. To address this issue, we ensured that only metrics computed on connected graphs were considered in our analysis. Specifically, the algorithm used to choose the correlation threshold (R) guaranteed that disconnected graphs were excluded from the analysis. Nev- ertheless, to further determine if our characteristic path length findings were robust and reliable, we computed global efficiency (E) of large-scale whole-brain networks detected from the task-free fMRI data obtained from 23 children and 22 young-adults, by using the method described in Section 2.2.1 in Chapter 2.

To evaluate the brain network for its global efficiency of parallel information pro- cessing, we compared the global efficiency of the network (E) with corresponding values

(Eran) obtained and averaged across 1000 random networks with the same number of nodes and degree distribution. An efficient network with low clustering is characterized by global efficiency value that is lower than the random network–Eg l obal (E/Eran) < 1.

Hierarchy

To evaluate the hierarchical nature of the brain network, we used the β parameter (Ravasz and Barabasi, 2003). We computed β parameter of large-scale whole-brain networks de- tected from the task-free fMRI data obtained from 23 children and 22 young-adults. β measures the extent of the power-law relationship between the clustering coefficient (C )

β and the degree (k): C = k− . The clustering coefficient (Ci ) and the degree (ki ) of every node was computed; β of the network was calculated by fitting a linear regression line to CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 110

the plot of log(C ) versus log(k). See Section 2.2.1 in Chapter 2, for details.

Comparing global topology of large-scale brain networks in children and young-adults

We compared the clustering coefficient γ (C /Cran), path length λ ( L/Lran), global effi- ciency Eg l obal (E/Eran), and hierarchy (β/βran) values of large-scale brain networks in the two groups, by using the methods described in Section 2.4.1.1 in Chapter 2.

Comparing global connectivity of large-scale brain networks in chil- dren and young-adults

To investigate developmental differences in global connectivity of large-scale brain net- works, we examined the whole-brain functional connectivity patterns in the two groups by using a data-driven supervised learning approach. The functional connectivity patterns— the correlation values of 4005 pairs of anatomical regions—were used as the input (fea- tures) to a pattern-based classifier. The classifier distinguishes young-adults from children by making classification decision based on value of the linear combination of these fea- tures. A widely used linear-classifier (support vector machine) that was best suited for our purpose of classification based on large number of features (4005) but a small number of training samples (45), was used in our analysis. Leave-one-out cross-validation (LOOCV) was used to measure the performance of the classifier in distinguishing young-adults from children. See Section 2.4.2.1 in Chapter 2, for details. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 111

Quantifying subnetwork topology of large-scale brain networks in children and young-adults

The human brain can be divided into five subnetworks—association, limbic, paralimbic, primary, and subcortical—each of them having a distinct function (Mesulam, 2000a). We assessed the network organization of these subnetworks by examining the profile of met- rics (γ, λ, Eg l obal , and degree) at the subnetwork level. The nodes of the network were grouped into these five subnetworks. The graph metrics (γ, λ, Eg l obal , and degree) of the network nodes were aggregated into five subnetworks. See Section 2.2.2 in Chapter 2, for details.

Comparing subnetwork topology of large-scale brain networks in chil- dren and young-adults

We compared the aggregated topology metrics— γ, λ, Eg l obal , and degree—for each of the five subnetworks, in the two subject groups by using growth curve modeling, with an intercept, linear and quadratic terms. See Section 2.4.1.2 in Chapter 2, for details.

Comparing subnetwork connectivity of large-scale brain networks in children and young-adults

To further characterize subnetwork level differences in network organization, we ex- amined the subnetwork connectivity in the two groups, as follows. First, inter-regional pairs that showed statistically significant (p < 0.01, FDR corrected) increased or decreased CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 112

functional connectivity in young-adults group compared to child group were identified as

(+1) or (-1) respectively. Second, the number of decreased (-1) or increased connectivities

(+1) for each of the 15 pairs was counted. Third, since each subnetwork has a differ- ent number of regions, the aggregated differential connectivity count was normalized by the number of possible connections between pairs of regions belonging to the two sub- networks under investigation. Finally, we perform statistical inference (p < 0.01, FDR corrected) on the normalized counts to identify subnetwork pairs that exhibit between- group differential connectivity. See Section 2.4.2.2 in Chapter 2, for details.

Quantifying regional topology of large-scale brain networks in chil- dren and young-adults

To elucidate the role of brain regions in network operation, we used graph metrics: de- gree, betweenness centrality, closeness centrality, and eigenvector centrality. We com- puted these metrics for each region of the large-scale brain network, for each subject.

We identify the important hub regions of the network as those whose value, for one of the four graph metrics, is at least two standard deviations greater than the mean over all regions in the network. See Section 2.2.3 in Chapter 2, for details.

Comparing regional topology of large-scale brain networks in chil- dren and young-adults

We then qualitatively compared the hub regions in the two groups so we can identify group differences, if any, in hub regions. See Section 2.4.1.3 in Chapter 2, for details. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 113

Comparing regional connectivity of large-scale brain networks in chil- dren and young-adults

Next we examined regional connectivity in the two groups. We compared regional cor- relation values aggregated across the 4005 pairs of anatomical regions in the two groups.

No significant between-group differences in the aggregated correlation values were ob- served. Based on this observation, subsequently, individual regional correlation values were z-transformed followed by centering of the distribution around zero mean. These normalized correlation values were compared between the two subject groups. T-test with a false discovery rate of 0.005 was used to test for significant differences. See Section

2.4.2.3 in Chapter 2, for details.

Analysis of developmental changes in regional connectivity with wiring distance

We examined the relationship between differences in regional connectivity in the two groups and the inter-regional wiring distance as determined using DTI. The wiring dis- tance between two regions was computed by measuring the average length of the white- matter fiber pathways connecting those regions, by using the method described in Section

2.3.1.2 in Chapter 2. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 114

Comparing structure–function relationships within large-scale brain networks in children and young-adults

We next examined the relationship between regional connectivity assessed using func- tional correlation and structural connectivity assessed using DTI-based fiber density, in the two groups. The fiber density between two regions was computed by measuring the number of white-matter fiber pathways per unit area connecting those regions, by us- ing the method described in Section 2.3.1.2 in Chapter 2. Additionally, mean fractional anisotropy (FA) of the white-matter fiber pathway was computed by averaging the FA value along the fiber pathways. Mean FA is a measure of structural integrity of a white- matter pathway. We used mean FA as an alternative measure of structural connectivity.

Analysis of development of large-scale brain networks consisting of functionally-defined nodes

The analyses described above allow us to examine developmental changes in the func- tional organization of large-scale brain networks consisting of anatomically-defined nodes.

In complement to the anatomy-based parcellation, the human brain can be subdivided into functionally separable areas. Brain networks consisting of functionally-defined nodes provide insights into network operation that are complementary to those obtained from networks consisting of anatomically-defined nodes (Mesulam, 2000a). We next examined developmental changes in large-scale brain networks consisting of functionally-defined nodes. We first identified network nodes by using the ICA-based method described in CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 115

Table 4.1: Demographic and cognitive profile. Age and years of education, but not IQ nor gender, are significantly different in young-adults compared with children (** denotes significant differences between groups). Children (n = 23) Young-adults (n = 22) Age 7.95** (range: 7 to 9) 20.40** (range: 19 to 22) Gender 10 males, 13 females 11 males, 11 females IQ 112 (range: 88 to 137) 112 (range:97 to 137) Years of education 2.52** (range: 2 to 3) 14.5** (range: 13 to 16)

Section 2.1.3.3 in Chapter 2, resulting in parcellation of the whole-brain into 33 func- tionally homogeneous regions. A task-free fMRI timeseries was computed for each of the 33 regions by averaging all voxels within each region at each time point in the time- series. These regional fMRI time series were then used to identify edges in a 33 node large-scale brain network for each subject. We identified edges by using the wavelet-based method described in Section 2.1.4 in Chapter 2. Once a large-scale brain network con- sisting of functionally-defined nodes was detected from task-free fMRI data, we charac- terized the network in terms of its multilevel topological properties, connectivity, and relationship to the underlying brain anatomy, and then compared these characteristics between children and young-adults, by repeating our entire analysis (described above) on the functionally-defined brain networks.

4.4 Results

Demographic and cognitive profile data for the child and young-adult groups is shown in Table 4.1. The two groups were well-matched and did not differ in IQ (p = 0.93) or gender (p = 0.75). CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 116

4.4.1 Comparison of global topology of large-scale brain networks

in children and young-adults

4.4.1.1 Clustering and path length

We first examined graph metrics obtained for the large-scale brain networks constructed by thresholding (threshold values ranged from 0.01 to 0.99 with increments of 0.01) the wavelet correlation matrix computed at three scales (frequencies in the range from 0.01 to 0.25 Hz) for the children group and the young-adults group (Figure 4.1).

Functional brain connectivity and global topological properties were salient at lower- frequencies (0.01 to 0.05 Hz) for both the children and young-adult groups. This re- sult provides further evidence that meaningful task-free signal is subtended by lower- frequencies, consistent with evidence from the previous chapter. Therefore, we only report results for this frequency interval in subsequent analyses.

In the frequency interval between 0.01 to 0.05 Hz, we examined λ, γ, and σ values in the two groups. Mean λ, mean γ, and mean σ values for the networks of each group were derived by thresholding the correlation matrices such that the network has on average K0

(= 48) edges per node. Using this approach, no significant differences in the mean λ, γ, and σ values were observed between children and young-adults.

4.4.1.2 Global efficiency

In the frequency interval between 0.01 to 0.05 Hz, we examined Eg l obal values in the two groups. Mean Eg l obal values for the networks of each group were derived by thresholding the correlation matrices such that the network has on average K0 (= 48) edges per node. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 117

Figure 4.1: Developmental changes in global organization of large-scale brain networks. Graph metrics—degree, path length (λ), clustering coefficient (γ),σ (γ /λ)—for children ( ) and young-adults (o) at three frequency intervals. (A) For both groups, the mean degree—a4 measure of network connectivity—is highest at Scale 3 for a wide range of cor- relation thresholds (0.01 < R < 0.8). (B) The mean characteristic path length (λ) is low (1 < λ < 1.57) and shows similar trends at all the scales. (C) The clustering coefficient (γ) for both groups is highest at Scale 3. (D) Due to higher mean γ values, σ is highest at Scale 3 for both groups. σ showed a linear increase as the threshold increased and the degree decreased. σ values for higher correlation thresholds are hard to interpret as at higher threshold values graphs of functional brain networks have fewer edges (smaller de- gree) and tend to split into isolated sub-graphs. At each of the three scales, no significant differences in the degree, λ, γ and σ values, for a range of correlation thresholds, were observed between children and young-adults. Scale 1 (0.13 to 0.25 Hz) is shown in red, Scale 2 (0.06 to 0.12 Hz) is in blue and Scale 3 (0.01 to 0.05 Hz) is in green. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 118

No significant differences in the mean Eg l obal values were observed.

4.4.1.3 Hierarchy

Hierarchy (β) is a measure of the relationship between the clustering coefficient and node-level connectivity in the network. Networks with higher hierarchy values are characterized by high degree nodes which exhibit low clustering, and vice versa. Mean

βvalues for the networks of the children group and young-adults group were derived by thresholding the correlation matrices such that the network has on average K0 (= 48) edges per node. The mean β values in the young-adult group were significantly higher than in the children group (p < 0.01), as shown in Figure 4.2.

4.4.2 Comparison of global connectivity of large-scale brain networks

in children and young-adults

We examined differences in global connectivity patterns between children and young- adults. The connectivity patterns—correlation values of 4005 pairs of anatomical regions— were used as features in a support vector machine (SVM) classifier. We found that connec- tivity patterns in children could be distinguished from those in young-adults with 91% accuracy. This suggests that functional connectivity patterns at the whole-brain level in children are significantly different from those in young-adults. We report below the nature of these developmental changes in the context of subnetwork and regional organi- zation of brain connectivity. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 119

Figure 4.2: Developmental changes in hierarchical organization of large-scale brain net- works. Hierarchy measure (β) values were significantly higher in young-adults (indicated by **) compared to children (p < 0.01). Error bars represent standard error. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 120

4.4.3 Comparison of subnetwork topology of large-scale brain net-

works in children and young-adults

We then examined differences in organization of five major subnetworks—association, limbic, paralimbic, primary, and subcortical (Mesulam, 2000a). Figure 4.3 shows a plot of degree, path length (λ), efficiency, and clustering coefficient (γ) values for each of the five subnetworks, for children and young-adults, as a function of the correlation threshold.

In the subcortical subnetwork, the fitted growth curve of degree and efficiency values was significantly higher (p<0.01) while the curve of λ values was significantly lower (p<0.01) in children, compared to young-adults, reflecting higher connectivity, higher efficiency values, and lower path length for a range of threshold values from 0.1 to 0.6. A similar analysis in the association, limbic, paralimbic, and primary sensory areas, revealed no significant differences in the degree, λ, efficiency, and γ values. Across the five subnet- works, no significant differences in the degree, λ, efficiency, and γ values were observed for correlation threshold values >0.6, mainly due to the large variance observed at higher threshold values.

We next examined the degree, λ, efficiency, and γ values for each of the 90 regions, for the two groups. Consistent with the above findings, a significant number of subcortical regions (6 out of 8; p < 0.01) showed differences between the two groups in at least one of the four metrics (degree, λ, efficiency, and γ), whereas only 2 out of 8 regions in the primary sensory, 17 out of 44 regions in association, 3 out of 6 regions in limbic, and 12 out of 24 regions in the paralimbic areas, showed differences. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 121

Figure 4.3: Developmental changes in subnetwork organization of large-scale brain net- works. Graph metrics—degree, path length (λ), efficiency, clustering coefficient (γ)— within each of the five subnetworks – association, limbic, paralimbic, primary, and subcortical—are shown for children (blue) and young-adults (red), as a function of the correlation threshold. In the subcortical subnetwork, for threshold values from 0.1 to 0.6, degree and efficiency values were significantly higher and λ values significantly lower in children, compared to young-adults (p < 0.01, indicated by **), while for the asso- ciation, limbic, paralimbic, and primary sensory areas, no significant differences in the degree,λ, efficiency, and γ values were observed at any correlation threshold. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 122

4.4.4 Comparison of subnetwork connectivity of large-scale brain

networks in children and young-adults

To further investigate differences in subnetwork organization, we examined subnetwork connectivity differences between the two groups. We found that the subcortical subnet- work had increased connectivity with the primary sensory, association and paralimbic subnetworks in children, compared to young-adults. Young-adults, on the other hand, had increased connectivity between paralimbic and association subnetworks, between paralimbic and limbic subnetworks, and between limbic and association subnetworks (p

< 0.001; FDR-corrected for multiple comparisons) (Figure 4.4A). Figure 4.4B shows a graphical representation of developmental differences in functional connectivity along the posterior-anterior and ventral-dorsal axes, highlighting greater subcortical connectiv- ity in children and greater paralimbic connectivity in young-adults.

4.4.5 Comparison of regional topology of large-scale brain networks

in children and young-adults

Large-scale brain networks in both children and young-adults showed hierarchical orga- nization with children showing lower-levels of hierarchy compared to young-adults. Hi- erarchical networks are characterized by hubs that are connected to nodes not otherwise connected to each other. To further characterize the observed differences in hierarchical organization, we examined hub regions in the two groups. In the young-adults group, regions of the bilateral middle cingulate gyrus, the left middle frontal gyrus, right supe- rior frontal gyrus, and the bilateral inferior temporal gyrus were identified as network CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 123

Figure 4.4: Developmental changes in subnetwork connectivity of large-scale brain net- works. (A) Children had significantly greater subcortical-primary sensory, subcortical- association, subcortical-paralimbic, and lower paralimbic-association, paralimbic-limbic, association-limbic subnetwork connectivity than young-adults (p < 0.01, indicated by **). Error bars represent standard error. (B) Graphical representation of developmental changes in connectivity along the posterior-anterior and ventral-dorsal axes, highlight- ing higher subcortical connectivity (subcortical nodes are shown in green) and lower paralimbic connectivity (paralimbic nodes are shown in gold) in children, compared to young-adults. Brain regions are plotted using the y and z coordinates of their centroids (in mm) in MNI space. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 124

hubs by atleast one of the four parameters considered. Whereas in the children group, re- gions of the bilateral middle cingulate gyrus, the bilateral orbitofrontal cortex, the right fusiform gyrus, the right precentral gyrus, the right inferior temporal gyrus, and the right middle temporal gyrus were identified as network hubs (Table 4.2).

4.4.6 Comparison of regional connectivity of large-scale brain net-

works in children and young-adults

Figure 4.5 shows separate group-averaged regional connectivity matrices for children and young-adults. Inter-subject variability in these correlation values was low in both the groups. Specifically, correlation values in the young-adult group showed inter-subject variance of 0.046 while the correlation values in the child group showed inter-subject variance of 0.036. Between group comparison revealed higher inter-subject variance in the young-adults compared to children (p < 0.01). 430 pairs of anatomical regions showed significantly higher correlations in children and 321 pairs showed significantly higher correlations in young-adults (p < 0.005, FDR corrected).

4.4.7 Developmental changes in regional connectivity with wiring

distance

We next investigated whether development is associated with simultaneous emergence of functional segregation and integration at the whole-brain level. For each pair of regions we first computed the wiring distance using DTI-based fiber tracking. We then examined CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 125

Table 4.2: Brain regions identified as network hubs in children and young-adults. Regions were identified as network hubs as those whose value, for one of the four metric—degree, betweenness centrality, closeness centrality, eigen centrality—is atleast two standard de- viations greater than the mean over all regions of the network (denoted by *). Brain region Degree Betweenness Closeness Eigen central- centrality centrality ity

Children Young- Children Young- Children Young- Children Young- adults adults adults adults Middle cin- * * * * * * gulate gyrus, Left Middle cin- * * gulate gyrus, Right Orbitofrontal * cortex (infe- rior), Left Orbitofrontal * cortex (infe- rior), Right Middle frontal * gyrus, Left Superior * frontal gyrus, Right Fusiform * gyrus, Right Precentral * * gyrus, Right Inferior tem- * poral gyrus, Left Inferior tem- * * * * * poral gyrus, Right Middle tem- * poral gyrus, Right CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 126

Figure 4.5: Regional connectivity in children and young-adults. Group averaged func- tional connectivity matrices for children and young-adults. Value of the (i,j)th element of the connectivity matrix corresponds to group averaged scale 3 wavelet correlation be- tween the resting-state timeseries of brain region i and region j. Low correlation values are shown in darker color while high correlation values are shown in lighter color. Qual- itatively, children, compared to young-adults, showed higher connectivity between the subcortical (caudate, globus pallidus, putamen, thalamus) and the cortical regions, and lower connectivity between the paralimbic (cingulate gyrus, orbitofrontal cortex, insula, parahippocampus gyrus, rectus gyrus, temporal pole) and the cortical regions. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 127

developmental changes in regional connectivity in relation to the wiring distance be- tween them. We found that functional connectivity between more proximal anatomical regions were significantly higher in children, whereas functional connectivity between more distal anatomical regions were significantly higher in young-adults (p < 0.0001), as shown in Figure 4.6. This suggests a pattern of higher short-range functional segregation in children and higher long-range functional integration in young-adults.

4.4.8 Comparison of structure–function relationships within large-

scale brain networks in children and young-adults

Next, we examined the relationship between functional and structural connectivity within large-scale brain networks. We found that functional connectivity and fiber density be- tween the network nodes were significantly positively correlated in both the groups; the correlation value higher in young-adults (r = 0.3; p < 0.001), compared to children (r =

0.11; p < 0.001), as shown in Figure 4.7.

A similar relationship between network functional connectivity and structural con- nectivity was observed when mean fractional anisotropy (FA) was used as a measure of structural connectivity instead of fiber density. Specifically, we found that functional connectivity and mean FA between the network nodes were significantly positively cor- related in both the groups; the correlation value higher in young-adults (r = 0.23; p <

0.001), compared to children (r = 0.1; p < 0.001) CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 128

Figure 4.6: Developmental changes in regional connectivity with DTI-based wiring dis- tance. The wiring distance (d) of all connections which differed significantly between the children and young-adults is plotted against developmental change in correlation values ( r) of those connections. Correlation values that were higher in children, compared to4 young-adults, are displayed in red, and the values that were higher in young-adults, compared to children, are displayed in blue. The mean wiring distance of the connec- tions that showed higher correlation values in children (mean r = -0.2), compared to young-adults, was 54.12 mm; the mean wiring distance of the connections4 that showed higher correlation values in young-adults (mean r = 0.1), compared to children, was 63.09 mm. The correlation values of short-range4 connections were significantly greater in children whereas young-adults showed stronger long-range connectivity (p < 0.0001). Wiring distances were computed using DTI-based fiber tracking. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 129

Figure 4.7: Structure–function relationships within large-scale brain networks in chil- dren and young-adults. Functional connectivity, assessed using correlations between the network nodes, and structural connectivity, assessed using DTI-based measures of fiber density showed significant positive correlation in both children(r = 0.11; p < 0.001) and young-adults (r = 0.3; p < 0.001). CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 130

4.4.9 Comparison of large-scale brain networks consisting of functionally-

defined nodes in children and young-adults

Lastly, we investigated developmental changes in large-scale brain networks consisting of functionally-defined nodes. Results from this analysis were largely similar with the previous analysis (performed on large-scale brain networks consisting of anatomically defined nodes), namely: (1) No significant differences in the values of global topological measures—λ, γ, σ and Eg l obal —were observed between children and young-adults. (2)

The hierarchy measure β value for the two groups was significantly higher in young- adults than in children. (3) Global Connectivity patterns in children could be distin- guished from those in young-adults with 91.11% accuracy. (4) 40 pairs of network nodes showed significantly higher correlations in children and 37 pairs showed significantly higher correlations in young-adults (p < 0.005; FDR corrected). (5) The mean wiring distance of the connections that showed higher correlation values in children (mean r 4 = -0.12), compared to young-adults, was 69.31 mm; the mean wiring distance of the connections that showed higher correlation values in young-adults (mean r = 0.23), 4 compared to children, was 74.47 mm. The correlation values of short-range connections were significantly greater in children whereas young-adults showed stronger long-range connectivity (p < 0.01). (6) The functional connectivity and the fiber density between the network nodes were significantly positively correlated in both the groups; the corre- lation value was higher in young-adults (r = 0.21; p < 0.01 ), compared to children (r =

0.09; p < 0.01 ). CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 131

4.5 Discussion

This work is, to our knowledge, the first to characterize the organization and devel- opment of large-scale human brain networks in children. To this end, we developed methods for characterizing and comparing organization of large-scale brain networks at multiple levels of granularity. Additionally, we developed methods combining structural and functional brain imaging data to quantitatively assess structure–function relation- ships within large-scale brain networks. Application of these methods to task-free fMRI and DTI data obtained from healthy children (ages 7-9y) and young-adults (ages 19-22y) revealed that: (1) large-scale brain networks in 7-9 year old children showed similar small- world, non-random, functional organization at the global level, as young-adults, (2) com- pared to young-adults, functional brain networks in children showed significantly lower levels of hierarchical organization, (3) children and young-adults had significantly dif- ferent subnetwork connectivity patterns, more specifically stronger subcortical-cortical and weaker cortico-cortical connectivity in children, (4) the development of large-scale brain connectivity involves functional segregation and integration, characterized by a shift from stronger short-range connections in children to stronger long-range connec- tions in young-adults, and (5) structure–function relationships within large-scale brain networks become more mature with development. Collectively, these and other findings reported here provide new insights into the development of large-scale brain organization in children. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 132

Key aspects of global functional brain organization are conserved throughout de- velopment

Functional brain networks in both children and young-adults showed high clustering coefficient, a low characteristic path length, and high efficiency, suggesting the presence of sub-networks of densely connected nodes, mostly connected by a short path. Such a small-world like architecture is thought to assist in robust and dynamic information processing.

Our finding that large-scale brain networks in children showed small-world properties that were very similar to young-adults, together with the result described in the previous chapter that brain networks in older adults’ (ages > 40y) have similar global functional organization, suggests that key aspects of functional brain organization are conserved throughout the developmental process—from early childhood to young adulthood and into older adulthood. Critically, despite the fact that the brain undergoes vast structural reorganization at the neuronal level in the form of myelination and synaptic pruning throughout development, key global properties of functional organization appear to be conserved.

Global functional brain connectivity patterns in children and young-adults are sig- nificantly different

Notwithstanding similarities in global network properties, global functional connectiv- ity patterns in children were significantly different from those in young-adults. Support vector machine based pattern classification analysis showed that connectivity patterns CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 133

in children could be distinguished from those in young-adults with an accuracy of 91%, suggesting developmental changes in functional connectivity. We discuss below the na- ture of developmental changes in the context of hierarchical, subnetwork, and regional organization of brain connectivity.

Development of functional hierarchical organization

Our data provides new evidence that large-scale brain networks in children and young- adults differ in their hierarchical organization. Children showed significantly lower (p<0.001) levels of hierarchical organization than young-adults. Hierarchical networks are char- acterized by the presence of small densely-connected clusters; these clusters combine to form large less-interconnected clusters, which combine again to form larger lesser- interconnected clusters (Ravasz and Barabasi, 2003). Hierarchical organization has been discovered in the world-wide-web and several biological networks (Bassett et al., 2008;

Ravasz and Barabasi, 2003; Sales-Pardo et al., 2007). Hierarchical networks are optimally connected to support top-down relationships between nodes and minimize wiring costs, but are vulnerable to attack on hubs (Ravasz and Barabasi, 2003). The presence of hi- erarchical organization in the large-scale brain networks of children and young-adults suggests efficient functional connectivity patterns within these networks at the expense of higher vulnerability to attacks. Lower levels of hierarchical organization in children may therefore be protective to such vulnerability, allowing for more flexibility in net- work reconfiguration based on individual differences in cognitive experience and reserve.

This postulation is further supported by our finding that quantitatively there were fewer CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 134

hub regions in children, compared to young-adults. Moreover, the hub regions were dif- ferent in the two groups: in the children group, regions of the temporal and cingulate gyri were identified as network hubs; whereas, in the young-adults group, regions of the frontal and cingulated gyri, were identified as hubs. How hierarchy and hubs emerge in functionally meaningful ways is an important topic for future research, but the impor- tant finding here is that quantitative measures of hierarchy can be used to examine the emergence of functional hierarchy in the developing brain.

Development of functional subnetwork organization and connectivity

We examined developmental changes in the organization and connectivity of five func- tional subnetworks of the human brain. Briefly, the primary sensory subnetwork con- sists of unimodal regions for processing visual, auditory, somatosensory, olfactory and gustatory signals. The subcortical subnetwork includes deep brain nuclei, notably the basal ganglia and thalamus, and the association subnetwork comprises higher order mul- timodal regions, including the lateral prefrontal, parietal and temporal cortices. The par- alimbic subnetwork consists of the insula, anterior cingulate cortex, posterior cingulate cortex and the orbitofrontal cortex and the limbic subnetwork includes the amygdala and hippocampus. Together, these subnetworks map the external world into brains’ internal sensory, attentional, mnemonic, emotional and motivational systems (Mesulam, 1998).

Graph-theoretical analysis identified subcortical regions as a major locus of between- group differences in brain connectivity. More specifically, subcortical connectivity was characterized by higher degree, lower path length and higher efficiency in children (Fig- ure 4.3). Node wise analysis showed that the caudate, putamen and thalamus all showed CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 135

higher degree, lower path length and higher efficiency in children. The globus pallidus was the only subcortical region that did not differ in these network metrics between chil- dren and young-adults. Further analysis of functional connectivity with the other four subnetworks revealed that subcortical areas were more strongly correlated with primary sensory, association and paralimbic areas in children, as shown in Figure 4.4A. These re- sults suggest that subcortical-cortical connections are both more profuse and stronger in children and that the functional development of subcortical connectivity is characterized by both changes in wiring and strength of connections.

We also detected significant differences in cortical connectivity but in this case the pat- tern of age-related differences was reversed, with children showing significantly weaker connectivity between paralimbic, association and limbic areas (Figure 4.4A). Graph-theoretical measures of degree, efficiency, and path length of the four cortical subnetworks did not differ between the two groups (Figure 4.3). This suggests that key aspects of cortico- cortical wiring are similar in children and young-adults but the strength of the connec- tions is weaker in children.

These developmental changes converge on and extend findings from structural neu- roimaging studies that have shown protracted age-related structural differences in the regional gray- and white-matter (Gogtay et al., 2004; Lebel et al., 2008; Paus et al., 1999;

Shaw et al., 2008; Thompson et al., 2005). Our findings of differences in subcortical con- nectivity is consistent with reports that these areas undergo massive structural rewiring CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 136

characterized by progressive myelination of axons that emanate from these regions fol- lowed by extension of these myelinated axons into the cortex during development (Barnea-

Goraly et al., 2005; Lebel et al., 2008). The later teen years, which span an interval in be- tween childhood and young-adulthood is a period of significant brain maturation (Paus,

2005). In particular, caudate, putamen, and thalamus regions of the subcortical subnet- work show some of the largest changes in fractional anisotropy of white-matter tracts, in- creasing almost 30% to 50% from 5 to 25 years of age. In contrast, major cortico-cortico tracts show a more modest increase of 8 to 20% (Lebel et al., 2008). Taken together, these results suggest that changes in subnetwork functional connectivity parallel changes in maturation of white-matter tracts between childhood and young-adulthood. Critically, our data provide novel evidence for a process of rewiring and pruning of subcortical- cortical connectivity accompanied by increased cortico-cortical connectivity at the func- tional level.

Subcortical areas, comprising the basal ganglia and the thalamus, are important for adaptive processing of distributed information in a manner that facilitates the transfor- mation of sensory input and cognitive operations into behavior (Graybiel, 2004). More specifically, the basal ganglia link signals in distinct functional networks during differ- ent phases of cognitive information processing (Chang et al., 2007). Neurophysiological models and anatomical tracing studies have provided evidence for parallel motor, limbic and prefrontal cortico-basal-ganglia loops (Alexander and Crutcher, 1990; Middleton and

Strick, 2002) which funnel large-scale cortical activity into behaviorally relevant motor CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 137

output. In humans, these circuits are characterized by segregated and overlapping connec- tivity patterns and a complex pattern of hierarchically organized frontal inputs (Dragan- ski et al., 2008; Haber, 2003). These patterns support the parallel flow of cortical signals inputs into the basal ganglia, where multiple reward related signals are integrated in ways that facilitate incentive learning over short time scales and habit formation over long time scales (Graybiel, 2008; Haber et al., 2006). There have been few studies of how these loops develop in children, but the pattern of changes in subcortical-cortical functional connectivity observed in our work suggest a process of pruning at the systems-level. This form of pruning is characterized by weakening of specific subcortical links, leading to longer path lengths similar to those seen in young-adults. Exactly how these links re- sult in the formation of parallel and integrative loops, which support large-scale neuronal networks for learning and memory (Chang et al., 2007; Cummings, 1993) remains to be investigated.

Changes in paralimbic connectivity were the cornerstone of developing cortico-cortico connectivity. Paralimbic areas play a major role in detection of salient environmental events (Sridharan et al., 2008), in facilitating flexible behaviors in response to risk, re- ward and punishment (Bechara et al., 2000; Wallis, 2007), and in goal directed behavior

(Laurens et al., 2005). Converging evidence from a number of brain imaging studies across several task domains suggests that the insula and the anterior cingulate cortex re- spond to the degree of subjective salience, whether cognitive, homeostatic, or emotional

(Bud Craig, 2009; Seeley et al., 2007). These paralimbic areas play a causal role in acti- vating attentional and memory systems within association areas to facilitate controlled CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 138

processing of stimuli during cognitively demanding tasks (Sridharan et al., 2008). Paral- imbic and association areas also moderate emotional reactivity to stimuli in limbic areas

(Egner et al., 2008; Wager et al., 2008). These core motivational and regulatory processes are known to undergo significant changes during adolescence (Crone and van der Molen,

2004), a time when coordinated interaction of emotion, reasoning and decision-making becomes increasingly important (Paus et al., 2008; Steinberg, 2005). The tighter integra- tion of paralimbic with association and limbic areas revealed by our work may underlie the large-scale functional changes that facilitate this critical developmental process.

Short- and long-range functional connectivity in children compared to young-adults

Our analysis of functional connectivity changes with wiring distance provides strong ev- idence that development is characterized by simultaneous reduction of short-range con- nectivity and strengthening of long-range connectivity. This suggests a process of greater functional segregation in children and greater functional integration in young-adults at the whole-brain level, not just in circumscribed nodes of the attentional control (Fair et al., 2007) and default node networks (Fair et al., 2008). Methodologically, our work is an improvement over prior studies (Fair et al., 2007, 2008) because we used actual anatomical (physical) distance, derived from diffusion tensor imaging data, rather than the Euclidean distance, between nodes. Our findings provide new and more direct ev- idence that dual changes in functional integration and segregation with wiring distance reflects a general developmental principle that operates at the level of the whole brain. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 139

Two neurobiological processes are likely to contribute directly to these observed ef- fects. One, systematic pruning of local connections with age are likely to result in weak- ening of local connections and formation of more localized and specialized processing nodes. These changes are known to occur prenatally, in childhood and in adolescence

(Huttenlocher et al., 1982). In parallel, increased myelination of axonal fiber tracks with age, also contribute to strengthening of long-range connectivity (Fornari et al., 2007).

Maturation of structure–function relationships within brain networks

It is fundamentally important to understand how functional brain connectivity emerges from underlying brain structure. Recent studies have reported that functional connectiv- ity observed in the human brain reflect anatomical structure (Damoiseaux and Greicius,

2009), in older adults. Our analysis of functional and structural connectivity within large-scale brain networks provides new evidence regarding the existence of strong rela- tionships between inter-regional functional connectivity and structural connectivity at the whole-brain level, in younger adults as well as in children. Specifically, functional connectivity, as assessed using correlations, was significantly correlated with structural connectivity, as assessed using fiber density and mean FA, in both the groups.

More importantly, our findings critically inform our understanding of how structure– function relations evolve with development. We observe that structure–function associa- tion is stronger in young-adults, compared to children. The stronger association may be due to the selective synaptic pruning and myelination of structural connections with age.

This selective strengthening and weakening of anatomical wiring is thought to increase the efficiency of functional information processing. Thereby, with development, the CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 140

emergent functional interactions between brain regions are more likely to occur through direct monosynaptic structural connections between the regions rather than through in- direct polysynaptic connections.

Taken together, these findings suggest that the development of large-scale functional connectivity is related to ongoing developmental changes in structural connectivity, and that these structure–function relationships become more mature with age.

Development of large-scale brain networks consisting of functionally-defined nodes

Our analysis of large-scale brain networks consisting of functionally-defined nodes in children and young-adults revealed developmental pattern that was largely similar to the one described above (obtained by analyzing networks consisting of anatomically- defined nodes). More specifically, we found that functionally-defined networks in both children and young-adults had small-world, functional organization at the global level; compared to young-adults, children exhibited lower levels of hierarchical organization; the development of brain connectivity involves functional segregation and integration; and structure–function relationships within functionally-defined brain networks become more mature with development. These findings suggest that inferences about develop- mental differences in topological properties of brain networks are robust to the type of parcellation scheme employed. Furthermore, our findings provide evidence that the prin- ciples governing the functional development of the brain at the systems level are common across brain networks consisting of either anatomically- or functionally-defined nodes. CHAPTER 4. DEVELOPMENT OF BRAIN NETWORKS 141

Conclusion

Our findings suggest that large-scale brain networks derived from task-free fMRI have a robust functional organization in 7 to 9 year old children. Importantly, we show that the dynamic process of over-connectivity followed by pruning, which rewires connectivity at the neuronal level, also operates at the systems level and helps reconfigure and rebalance subcortical and paralimbic connectivity in the developing brain. We further show that this dynamic developmental process is shaped by ongoing developmental changes in brain structure.

Our work demonstrates the usefulness of network analysis of functional connectivity in elucidating the principles underlying brain maturation. Furthermore, our work shows how quantitative analysis of anatomical connectivity, and in particular the computation of wiring distance and fiber density between brain regions, allows us to link changes in functional networks to the maturation of white-matter anatomy. Such quantitative mul- timodal analysis of structural and functional brain connectivity will prove useful in help- ing us better understand the network architecture that shapes and constrains cognitive development. More generally, our methods provide a quantitative framework for a de- tailed investigation of large-scale networks and their organization, in developing healthy and diseased brain. Chapter 5

Conclusions and Future Directions

5.1 Conclusions

Understanding human brain function is one of the most important endeavors in mod- ern science. There is growing evidence that cognitive functions are executed by large- scale networks, comprising multiple interacting anatomically-connected brain areas. Al- though considerable progress has been made in understanding which specific brain areas are involved in particular cognitive functions, very little is known about the integrative functioning of large-scale brain networks. More specifically, less is known about how the large-scale network interactions are organized and how these interactions emerge from the underlying brain structure. This is partly due to a lack of neural measurement tech- niques and accompanying methods that are sophisticated enough to pursue this line of research. Recent technological advances in neural measurement techniques such as task- free fMRI and DTI have provided researchers with the unique opportunity to use brain

142 CHAPTER 5. CONCLUSIONS AND FUTURE DIRECTIONS 143

imaging data to investigate large-scale interactions and structural connections, between distributed brain regions.

In this work, we developed computational methods for analyzing task-free fMRI and

DTI data in order to quantitatively examine key aspects of large-scale human brain orga- nization and its relation to the underlying structure. Our approach was as follows: First, we developed methods to detect large-scale human brain networks, by using task-free fMRI data. We then implemented a graph theory-based approach, combined with net- work partitioning, that allowed us to quantify topology of the large-scale human brain networks at the global, subnetwork, and regional level. The analysis of network topology makes it possible for us to quantitatively examine the large-scale functional organization of the human brain at multiple levels of granularity. Next, we developed a multimodal imaging approach. We used it to combine task-free fMRI and DTI data, and then assess structure–function relationships in large-scale human brain networks so we could exam- ine how the large-scale functional organization of the human brain emerges from the underlying brain structure. Finally, we developed methods for comparing the topology and connectivity of large-scale human brain networks between subject populations in or- der to examine how the functional organization of the human brain changes, across the human lifespan.

Application of our methods to task-free fMRI and DTI data collected from subject populations including children, young-adults, and the elderly, provided new insights into how brain networks develop, mature, and become disrupted in disease states, and pointed to promising avenues of future work. Apart from the neuroscientific insights our studies CHAPTER 5. CONCLUSIONS AND FUTURE DIRECTIONS 144

provided, this work demonstrates that systematic network analysis of multimodal brain connectivity can be used to investigate specific neuroscientific questions. The questions of differences in brain connectivity are generic and are applicable to investigations be- yond the specific ones described in this work. For example, brain connectivity topology can be compared between relevant diseased and control groups to investigate disruptions in brain organization in disorders such as autism and ADHD, that are thought to be characterized by disruptions in synaptic pruning and myelination at the neuronal level

(Carper et al., 2002; Saitoh and Courchesne, 1998; Shaw et al., 2007). Additionally, quan- titative measures of changes in brain connectivity can be related to cognitive measures to investigate how cognitive functions emerge from brain networks. Notably, as suggested by our Alzheimer’s disease findings, application of our network-analytic approach may provide a sufficiently accurate, quantitative imaging-based biomarker of a brain disorder.

Such a biomarker would be extremely valuable: First, clinicians may use it as an objec- tive clinical test to more accurately diagnose a psychiatric or neurological disorder. This is a significant advantage considering that most brain disorders are currently diagnosed using subjective clinical tests such as questionnaires, which have very poor sensitivity and specificity in detecting the disease particularly at the early stages of the pathology. Lastly, a quantitative imaging-based biomarker of a brain disorder may serve as a functional marker of response to treatment. This would enable rapid and more accurate evaluation of experimental drugs thus accelerating drug development.

In addition to providing means to quantitatively examine key aspects of human brain organization, our methods collectively provide a unified approach to investigate cognitive CHAPTER 5. CONCLUSIONS AND FUTURE DIRECTIONS 145

function. In recent years, imaging studies of cognitive function have begun a shift from studies identifying regions involved in a particular function to more recent studies high- lighting brain network that supports the execution of a particular function. This newer trend, however, is likely to produce a catalog of brain networks–one network for one function. Such a fragmented network phrenological approach is less likely to provide sig- nificant insights into the complex functioning of the brain. Our unified approach enables the examination of cognitive function as a byproduct of interactions between regions of a core set of brain subnetworks detected using our methods. Thus, applying our methods a complex cognitive function could potentially be systematically studied by examining the interactions between components of brain subnetworks along with the relevant context.

More generally, the methods developed and the principles gleaned from our work can be applied to investigate other complex systems such as biological networks, where it is de- sirable to characterize and compare the multiscale, multilevel organization and dynamics of the embedded system.

In conclusion, this work provides a quantitative framework for the in vivo investiga- tion of how human brain systems operate in health and illness, and will ultimately help us to attain a more complete understanding of brain architecture and function.

5.2 Future directions

Future advancements in our understanding of human brain function will be contingent on the development of better techniques that reliably measure brain connectivity at a high spatiotemporal resolution, and the development of accompanying new analytical CHAPTER 5. CONCLUSIONS AND FUTURE DIRECTIONS 146

and informatics methods and tools. In the following text, we discuss some potential directions for future research.

As described earlier, networked brain regions interact during brain function at multi- ple time scales. Interactions at each time scale encode distinct information that is critical for the overall execution of brain function. To capture these multi-resolution brain dy- namics, new methods need to be developed that incorporate high temporal resolution data such as EEG, MEG, or optical imaging with the interactional information obtained, using our methods, from the slow-time-scale fMRI data. These new methods will allow us to better understand the integrative functioning of brain networks; specifically, how distributed brain areas act in concert with one another, at varying time scales, to perform complex mental functions.

A related direction for future research is to develop methods for linking brain connec- tivity data across multiple spatial resolutions that have been obtained by using different imaging modalities. We believe that computational models are vital for these purposes.

Recent computational work has shown much progress in developing high-fidelity models that generate in silico regional brain activity data that match well with the observed exper- imental data, at the macroscopic level (Honey et al., 2007, 2009; Izhikevich and Edelman,

2008). As the microscopic level data will be more readily available, these models could be extended to link the neuronal data to the regional brain data. The computational models will not only allow linking of microscopic to macroscopic-level brain data, but will also allow the investigation of how brain function emerges from the underlying structural substrate at multiple levels of the human brain architecture. CHAPTER 5. CONCLUSIONS AND FUTURE DIRECTIONS 147

The quantitative investigations of the human brain architecture and function will greatly benefit from the development of new statistical methods so we can quantify dy- namical aspects of brain organization that include, but are not limited to, dynamical hierarchies and context-dependent information flow. We will then be able to relate the results to cognitive measures so we can better understand how brain organization dynam- ics influence cognition.

Another direction for future research would consist of combining the brain connec- tivity data with genomic information. This will allow researchers to quantitatively as- sess genetic influences on network topology, connectivity, and dynamics. More impor- tantly, such integrative analysis of data obtained from diseased populations could help researchers derive quantitative multimodal biomarkers that would have a better diagnos- tic accuracy than that of modality specific biomarkers.

Lastly, as brain connectivity data is increasingly collected in brain imaging studies, it is imperative that such datasets be accessible to other researchers in order to acceler- ate neuroscientific progress (Biswal et al., 2009) . To this end, there is an urgent need to develop new informatics solutions for systematic management, and sharing, of brain data. Such solutions could entail development of multimodal ontology-based atlases that integrate brain connectivity data with canonical knowledge about neuroanatomy and function, obtained from neuroontologies such as NeuroLex and the foundational model of anatomy (FMA). The atlas framework will enable comprehensive data-driven analysis of brain connectivity across subject populations and cognitive conditions, which in turn will facilitate neuroscientific discovery and hypothesis formulation. Bibliography

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