Analyzing Brain Tumor Connectomics using Graphs and Persistent Homology

TL;DR

This study addresses differentiating brain tumor origins by analyzing whole-brain connectomes derived from diffusion-weighted MRI using a dual approach: persistent homology ($H_0$ birth/death of components and $H_1$ loops via extended filtration) and graph-theoretic features to capture global and local connectivity patterns. It integrates anatomically constrained tractography, 84 Desikan–Killiany atlas regions, and the Brain Connectivity Toolbox to extract discriminative topological and local-global network measures, with Wasserstein distances used to quantify diagram differences and leave-one-out cross-validated classifiers achieving up to $88\%$ accuracy for HC vs Meningioma and $80\%$ for HC vs Glioma, plus $80\%$ for Meningioma vs Glioma. The results demonstrate that topological signatures complement conventional graph metrics in detecting tumor-type–specific structural alterations, offering potential biomarkers for diagnostic differentiation and informing clinical decision-making, though they require validation in larger cohorts. The work highlights the value of combining persistent homology with connectome-based graph analysis to advance personalized assessment of brain tumor effects on structural connectivity.

Abstract

Recent advances in molecular and genetic research have identified a diverse range of brain tumor sub-types, shedding light on differences in their molecular mechanisms, heterogeneity, and origins. The present study performs whole-brain connectome analysis using diffusionweighted images. To achieve this, both graph theory and persistent homology - a prominent approach in topological data analysis are employed in order to quantify changes in the structural connectivity of the wholebrain connectome in subjects with brain tumors. Probabilistic tractography is used to map the number of streamlines connecting 84 distinct brain regions, as delineated by the Desikan-Killiany atlas from FreeSurfer. These streamline mappings form the connectome matrix, on which persistent homology based analysis and graph theoretical analysis are executed to evaluate the discriminatory power between tumor sub-types that include meningioma and glioma. A detailed statistical analysis is conducted on persistent homology-derived topological features and graphical features to identify the brain regions where differences between study groups are statistically significant (p < 0.05). For classification purpose, graph-based local features are utilized, achieving a highest accuracy of 88%. In classifying tumor sub-types, an accuracy of 80% is attained. The findings obtained from this study underscore the potential of persistent homology and graph theoretical analysis of the whole-brain connectome in detecting alterations in structural connectivity patterns specific to different types of brain tumors.

Figures (7)

• Figure 1: Block schematic of the proposed study
• Figure 2: Visualization of generated streamlines is showed in three MRI planes for one healthy subject: Fig.(A) and one subject diagnosed with meningioma: Fig.(B). As seen from Fig.(B), no streamlines are observed within the region affected by the meningioma. Fig.(C) shows the resultant connectome as obtained from streamlines of one healthy subject. Enhanced structural connectivity within each hemisphere is evident, represented by the prominent diagonal boxes. Increased structural connectivity between homologous regions of the left and right hemisphere is depicted by brighter spots in the off-diagonal boxes.
• Figure 3: The persistence diagram in dimension-0 (top row in left panel) and dimension-1 (bottom row in left panel) as obtained from whole brain connectome, for one representative subject of control (first column), glioma (second column) and meningioma (third column). The kernel density estimate (KDE) plot and the corresponding histogram for the dimension-1 persistence diagram is shown at the right panel.
• Figure 4: Illustration of the effect of sparsity with synethetic dataset: There is a noticeable increase in the alignment of points along both vertical and horizontal axes in persistence diagram as the level of sparsity is decreased [Fig. (A) to Fig (C)]. The leftmost matrix contains 200 random edge connectivity values (c=200), making it highly sparse. The corresponding persistence diagram is highly scattered, indicating that in a sparse matrix, many features are created and die over a wide range of filtration values. As the sparsity decreases (middle column with c=400), the corresponding persistence diagram shows less scattering compared to the sparse matrix but still maintains a degree of spread. There is a noticeable increase in the alignment of points along both the vertical and horizontal axes as When the sparsity is further decreased, resulting in a denser matrix (right column with c=1000), the corresponding persistence diagram shows many points aligned both horizontally and vertically. This alignment indicates that many features in the topological filtration are born and die at the same or similar filtration values.
• Figure 5: Visualization of Wasserstein distance and the corresponding violin plot for dimension-0 (first and second column) and -1 (third and fourth column), across all subjects to find the statistical significance($p<0.05$) across study groups.