Voxel-wise function-structure coupling with diffusion-weighted and functional MRI

Function-structure coupling methods often compare functional connectivity with regional structural connectomes derived from diffusion MRI tractography. Such regional representation can obscure spatially extended, indirect, or crossing-fibre structural support between functionally connected regions. This work proposes a voxel-wise function-structure coupling using a constrained-Laplacian framework that imposes observed fMRI-derived functional connectivity values on voxel-wise structural graphs derived from fibre orientation distributions (FODs) of individual subjects. The method produces graph potentials, voxel-edge current fields, and voxel-wise support maps that describe how functional relationships are accommodated by local diffusion-derived structural architecture. Evaluation consists of an in-silico diffusion phantom, inspection of local graph construction in coherent and crossing-fibre regions, seven resting-state fMRI network demonstrations in three Human Connectome Project subjects, test-retest analyses of the subjects, and a network parcellation scale analysis. A permutation analysis was used to investigate how much of each network can be explained by a common white matter structure and variation from this common backbone. Across subjects, median observed-null resemblance ranged from 0.578 to 0.630 for whole-map Pearson correlation and from 0.287 to 0.328 for top-5% Dice overlap. These findings support a conservative interpretation of voxel-wise FSC providing a spatially resolved quantitative representation of functional constraints on a diffusion-derived graph. Yet, the present experiments do not establish anatomical network specificity.