Using Hierarchical Random Graphs (HRGs) to Model Brain Networks Open Access

Abstract

The human cerebral cortex is functionally segregated with coactivating regions. These areas have been shown in literature to be organized across hierarchies from local to global networks11. Using fMRI to characterize whole brain activity, previous studies have shown the utility of functional connectivity graphs that represent the cross-correlation matrix of the fMRI activity at different brain regions as a measure to study network hierarchy13..However, functional connectivity estimates are known to be noisy- often requiring long timeseries to converge to a final value. We propose the utility of sampling the functional connectivity (FC) matrices from fMRIs and modelling the data as hierarchical random graphs (HRGs) that represent real data as dendrograms, since the hierarchical organization is theoretically independent of the noise. The HRG approach models the structure of the brain by clustering more connected brain regions together across increasing scales.We show that the random noise that exists in each individual scan as compared to the group average does not translate into this hierarchical representation and thus it can meaningfully predict missing edges from the ground truth more accurately than classical statistical methods can. By validating the use of HRGs through harnessing the hierarchical nature of brain networks to make predictions between FC matrices with known differences, we argue that this is a powerful approach to modelling the brain network since it can be translated to study unknown differences in varying populations including healthy versus disease brain studies.

Table of Contents

TABLE OF CONTENTS

LIST OF FIGURES

1

INTRODUCTION

3

1.1 Functional Architecture of the Brain  

3

1.2 Functional Connectivity

4

1.3 Motivation for the Experiment

5

1.4 Networks and Hierarchies

6

METHODS

9

2.1 Experimental Paradigm

9

2.1.1 Preliminary Test  

9

2.1.2 Optimizing Parameters  

10

2.1.3 Analysis on Real Data  

12

2.2 Dataset and Processing

14

2.3 Sampling Function

15

2.4 The Algorithm

17

RESULTS

22

3.1 Preliminary Test of the Algorithm  

22

3.2 Positive and Negative Edges

24

3.3 Functional Connectivity graphs

25

3.4 Scanning Parameters

27

3.5 Comparing the Two Algorithms

34

DISCUSSION

36

4.1 Functional Connectivity Matrices

36

4.2 Positive and Negative Edges

37

4.3 Sampling Thresholds   

38

4.4 Comparing the Methods  

39

4.4.1 Missing Edges

39

4.4.2 Predicting Missing Edges   

40

CONCLUSION

41

REFERENCES

43

About this Honors Thesis

Rights statement

• Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.

School	Emory College
Department	Physics
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Biology, Neuroscience Statistics Engineering, Biomedical
Keyword	fMRI Neuroscience Physics Functional Connectivity Monte Carlo Markov Chain Biomedical Engineering
Committee Chair / Thesis Advisor	Shella Keilholz, Emory University/Georgia Tech
Committee Members	Ilya Nemenman, Emory University Stefan Boettcher, Emory University

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