# Diffusion wavelets on connectome: Localizing the sources of diffusion mediating structure-function mapping using graph diffusion wavelets

## TL;DR

This paper introduces a new method using graph diffusion wavelets to better understand how brain structure relates to function, achieving high accuracy in predicting functional connectivity.

## Contribution

The novel use of graph diffusion wavelets to assign region-specific diffusion scales for structure-function mapping.

## Key findings

- The proposed method achieves an average Pearson’s correlation of 0.833 in predicting functional connectivity.
- The frontal pole is associated with large diffusion scales, forming significant community structures.
- Diffusion scales follow a power-law distribution, indicating a scale-free process in the brain.

## Abstract

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 diffusion wavelets to learn the appropriate diffusion scale for each RoI to accurately estimate the SC-FC mapping. Using the open Human Connectome Project dataset, we achieve an average Pearson’s correlation value of 0.833, surpassing the state-of-the-art methods for the 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 FC.

In the network diffusion paradigm for brain structure-to-function mapping, we noticed limitations such as manually decided diffusion scales and the absence of region of interest–level analysis. We addressed this problem by independently developing the graph diffusion wavelets having multiscale and multiresolution property. Each brain region is associated with a diffusion scale that defines the extent of spatial communication. Using graph diffusion wavelets, we are able to predict the functional connectome with state-of-the-art results. We observe that the diffusion scales follow a power-law degree distribution, which is indicative of a scale-free process in the brain. The frontal pole is a dominant member of the various resting-state networks, and our model is able to associate higher diffusion scales to this region. The graph diffusion wavelet model is a novel method that not only excels in downstream task but also provides insights into the structure-function relation.