Doctor of Philosophy
Understanding a system as complex as the human brain is a very demanding task. Directly working with structural and functional neuroimaging data has led to most of the understanding we have gained about the human brain. However, performing only the direct statistical comparisons on the empirical function and the structure does not fully explain the observed long-range functional correlations. Therefore, implementations of mathematical models to gain further understanding of the relationship between the structure and function of the brain is critical. Additionally, spontaneous functions of the brain can only be predicted using computer simulated models; which will be pivotal for studying the patients with accidental brain injuries. Therefore, this research aims to present an optimized computer simulated model not only to further understand the structure-function relationship of the brain but also to predict the functional changes when anatomy is altered.
Based on prior work, 2-dimensional classical Ising model stands out among the other models in modeling the functions of the brain due to its simplicity. Hence, a 2-dimensional Ising model was simulated on a structural connectome (generalized Ising model) that acts as a proxy for the anatomical connectivity in the brain. Simulations allowed the prediction of functional connectivity using the structure, at criticality. It also enabled the introduction of a novel methodology to calculate the ”dimensionality” of the brain. Our results showed the dimensionality of a healthy brain is two when it is defined using the information flow in the brain. Further research illustrated the dependency of dimensionality on the diffusion tractography method used to obtain the structural connectome. It was also concluded that an optimized generalized Ising model has to be simulated using a structural connectome generated by deterministic tractography to acquire the best predictions of empirical function. Additional investigations into a more generalized version of the Ising model—Potts model with different number of spin states—illustrated that increasing the number of spin states does not increase the predictability. It also supported the hypothesis that the model could be simulating the digital nature of direct neural activity rather than the indirect activity measured by brain imaging.
Abeyasinghe, Pubuditha M., "Calculating the Dimensionality of the Brain, and Other Applications of an Optimized Generalized Ising Model in Predicting Brain's Spontaneous Functions" (2019). Electronic Thesis and Dissertation Repository. 6124.
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