Unified topological inference for brain networks in temporal lobe epilepsy using the Wasserstein distance.

Persistent homology offers a powerful tool for extracting hidden topological signals from brain networks. It captures the evolution of topological structures across multiple scales, known as filtrations, thereby revealing topological features that persist over these scales. These features are summarized in persistence diagrams, and their dissimilarity is quantified using the Wasserstein distance. However, the Wasserstein distance does not follow a known distribution, posing challenges for the application of existing parametric statistical models. To tackle this issue, we introduce a unified topological inference framework centered on the Wasserstein distance. Our approach has no explicit model and distributional assumptions. The inference is performed in a completely data driven fashion. We apply this method to resting-state functional magnetic resonance images (rs-fMRI) of temporal lobe epilepsy patients collected from two different sites: the University of Wisconsin-Madison and the Medical College of Wisconsin. Importantly, our topological method is robust to variations due to sex and image acquisition, obviating the need to account for these variables as nuisance covariates. We successfully localize the brain regions that contribute the most to topological differences. A MATLAB package used for all analyses in this study is available at https://github.com/laplcebeltrami/PH-STAT.

Topological Embedding of Human Brain Networks with Applications to Dynamics of Temporal Lobe Epilepsy.

We introduce a novel, data-driven topological data analysis (TDA) approach for embedding brain networks into a lower-dimensional space in quantifying the dynamics of temporal lobe epilepsy (TLE) obtained from resting-state functional magnetic resonance imaging (rs-fMRI). This embedding facilitates the orthogonal projection of 0D and 1D topological features, allowing for the visualization and modeling of the dynamics of functional human brain networks in a resting state. We then quantify the topological disparities between networks to determine the coordinates for embedding. This framework enables us to conduct a coherent statistical inference within the embedded space. Our results indicate that brain network topology in TLE patients exhibits increased rigidity in 0D topology but more rapid flections compared to that of normal controls in 1D topology.

Unified Topological Inference for Brain Networks in Temporal Lobe Epilepsy Using the Wasserstein Distance.

Persistent homology offers a powerful tool for extracting hidden topological signals from brain networks. It captures the evolution of topological structures across multiple scales, known as filtrations, thereby revealing topological features that persist over these scales. These features are summarized in persistence diagrams, and their dissimilarity is quantified using the Wasserstein distance. However, the Wasserstein distance does not follow a known distribution, posing challenges for the application of existing parametric statistical models. To tackle this issue, we introduce a unified topological inference framework centered on the Wasserstein distance. Our approach has no explicit model and distributional assumptions. The inference is performed in a completely data driven fashion. We apply this method to resting-state functional magnetic resonance images (rs-fMRI) of temporal lobe epilepsy patients collected from two different sites: the University of Wisconsin-Madison and the Medical College of Wisconsin. Importantly, our topological method is robust to variations due to sex and image acquisition, obviating the need to account for these variables as nuisance covariates. We successfully localize the brain regions that contribute the most to topological differences. A MATLAB package used for all analyses in this study is available at https://github.com/laplcebeltrami/PH-STAT.

Regional homogeneity (ReHo) changes in new onset versus chronic benign epilepsy of childhood with centrotemporal spikes (BECTS): A resting state fMRI study.

OBJECTIVE: The purpose of this study was to investigate regional homogeneity (ReHo) in children with new-onset drug-naïve Benign Epilepsy with Centrotemporal Spikes (BECTS), chronic BECTS and healthy controls (HC) using the Regional Homogeneity (ReHo) method applied to resting state fMRI data. METHODS: Resting state fMRI data was collected from three groups of children aged 6-13, including new onset drug naïve BECTS, chronic BECTS with medication, and HC; the data analyzed by ReHo method. Mandarin school exams scores were acquired and compared across groups. RESULTS: There were three main findings. Firstly, compared with HC, abnormally increased ReHo was observed in bilateral sensorimotor regions in new onset BECTS which normalized or even reversed in the chronic BECTS group. Secondly, enhanced ReHo was found in the left frontal language region in the two BECTS groups, with even higher ReHo value in the chronic group. Lastly, decreased ReHo was found in regions of the default mode network (DMN), bilateral occipital lobes and cerebellum in both the new onset and chronic BECTS groups, lower in chronic BECTS. Behavioral analyses of school scores showed the chronic BECTS group presented significantly lower scores compared to HC (p<.05). SIGNIFICANCE: The coherence of low frequency fluctuations is disrupted in sensorimotor, language and DMN-related regions in new-onset BECTS. Some of these effects seem to be selectively normalized in chronic BECTS, thus allowing us to explore possible chronicity and AED-induced effects on BECTS. Abnormal ReHo in left language and DMN regions could be responsible for impairments of cognitive function.