Diffusion Wavelets on Connectome: Localizing the Sources of Diffusion Mediating Structure-Function Mapping Using Graph Diffusion Wavelets

The intricate link between brain functional connectivity (FC) and structural connectivity (SC) is explored through models performing diffusion on SC to derive FC, using varied methodologies from single to multiple graph diffusion kernels. However, existing studies have not correlated diffusion scales with specific brain regions of interest (RoIs), limiting the applicability of graph diffusion. We propose a novel approach using graph heat diffusion wavelets to learn the appropriate diffusion scale for each RoI to accurately estimate the SC-FC mapping. Using the open HCP dataset, we achieve an average Pearson's correlation value of 0.833, surpassing the state-of-the-art methods for prediction of FC. It is important to note that the proposed architecture is entirely linear, computationally efficient, and notably demonstrates the power-law distribution of diffusion scales. Our results show that the bilateral frontal pole, by virtue of it having large diffusion scale, forms a large community structure. The finding is in line with the current literature on the role of the frontal pole in resting-state networks. Overall, the results underscore the potential of graph diffusion wavelet framework for understanding how the brain structure leads to functional connectivity.