UC San Diego

In human brain imaging studies, researchers have predominantly used the correlation method to estimate the “functional connectivity”. However, spurious correlations can be measured between two brain regions without even having direct connection or interaction between them. This high correlation can be due to the strong interactions of the two brain regions with common input from a third region which may or may not be observed. One previously proposed solution to this problem is to use a sparse-regularized inverse covariance matrix or precision matrix (SRPM) when all the regions are observed. The SRPM method yields partial correlations to measure strong direct interactions between pairs of observed regions while simultaneously removing the influence of the rest of the observed regions thus identifying observed regions that are conditionally independent. However, in most brain studies, especially in electrocorticography (ECoG), simultaneously recording all brain regions is a near impossible task using existing imaging technologies. Hence researchers have recently proposed to use a sparse-plus-latent-regularized precision matrix (SLRPM) when there are unobserved or latent regions interacting with the observed regions. The SLRPM method yields partial correlations of the conditional statistics of the observed regions given the latent regions thus identifying observed regions that are conditionally independent of both the observed and latent regions.

In the first contribution of the thesis, we evaluate the performance of the SRPM and SLRPM methods using simple artificial networks. In the second contribution of the thesis, we demonstrate the application of the SRPM method for estimating brain connectivity during

stage 2 sleep spindles from human ECoG recordings from a patient with complex partial epilepsy. We only consider sleep spindles occurring in long seizure-free periods. Sleep spindles are automatically detected using delay-differential analysis (DDA), then analyzed

with SRPM and the Louvain method for community detection (LMCD). The performance of the SLRPM method is found to be similar to that of the SRPM method for this application. In the third contribution of the thesis, we demonstrate the application of the SLRPM method to estimate brain connectivity during epileptic seizures from human ECoG recordings. Seizures from 12 patients having complex partial epilepsy were analyzed using SLRPM and brain connectivity has been quantified using modularity index (MI), clustering coefficient (CC), and eigenvector centrality (EC). These applications will enhance our understanding of the global connectivity pattern of the human brain and may help us in finding better treatments in epilepsy.