Using a Brain Network Model to Predict Brain Structure from Function Open Access

Green, Nicholas (Spring 2019)

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Brain network models have become a promising theoretical framework in simulating signals that are representative of whole brain activity such as resting state functional-MRI (rs-fMRI). Brain network models use the structural connectivity of the brain as an input and, using a set of differential equations to describe the dynamics, they can be used to simulate brain activity starting from a randomly initialized signal. Previous studies have shown that these models can simulate brain activity that are functionally coordinated as measured through averaged functional connectivity with a high degree of similarity to empirical rs-fMRI data. In this study, we address the inverse problem: by utilizing measured rs-fMRI and treating brain structure as a variable, we formulate and solve the constrained convex optimization problem for the sparsest structural connectivity that, for a given set of dynamics, explains the measured brain activity. We solve the constraint problem with machine learning, using gradient descent on our loss function. In this experiment, three different models are used in order to explore what level of complexity in the model constraints leads to the more accurate solution. These models are based around intuition about the brain and grew in complexity, first penalizing large weights, then penalizing large weights and large tract lengths, and finally using these penalties but with two weight matrices, one being a term that synchronizes brain regions and the other being a term that pushes them apart. We found that the more complex the model, the better the solution, with higher correlation with actual structural connectivity. When only considering within-hemispheric connections, since connections between hemispheres are not as well known, correlations were even higher, going from 0.353 to 0.437 to 0.569 as the model complexity increased. In previous studies that worked on similar generative models, the simulated connectomes had correlations in the range of 0.3 to 0.5. So, the solutions generated here are quite promising. This experiment shows that we can predict structure from function just as well as function from structure using brain network models. These results open up new avenues to explore with brain network models and possible new models to implement.  

Table of Contents

Introduction - 1

Methods - 6

Data - 6

Tractography - 8

rs-fMRI Prerocessing - 10

Brain Network Model Equation - 12

Optimization Method - 13

Regularization and Length Penalty - 15

Separated Weight Matrices - 16

Analysis - 16

Results - 17

No Model: Initial matrix analysis - 17

Model Using Single Matrix with Weight Penalty (Model 1) - 17

Model Using Single Matrix with Weight and Length Penalty (Model 2) - 19

Model Using Two Matrices with Length Penalty (Model 3) - 20

Summary of Results - 22

Discussion - 22

Model Performance - 22

Limitations - 25

Future Directions - 26

Conclusion - 27

Appendix: Python Code - 28

Model 1 - 28

Model 2 - 29

Model 3 - 31

References - 34

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