Voxel-Wise Brain Graphs From Diffusion MRI: Intrinsic Eigenspace Dimensionality and Application to Functional MRI

Abstract

Structural brain graphs are conventionally limited to defining nodes as gray matter regions from an atlas, with edges reflecting the density of axonal projections between pairs of nodes. Here we explicitly model the entire set of voxels within a brain mask as nodes of high-resolution, subject-specific graphs. Methods: We define the strength of local voxel-to-voxel connections using diffusion tensors and orientation distribution functions derived from diffusion MRI data. We study the graphs' Laplacian spectral properties on data from the Human Connectome Project. We then assess the extent of inter-subject variability of the Laplacian eigenmodes via a procrustes validation scheme. Finally, we demonstrate the extent to which functional MRI data are shaped by the underlying anatomical structure via graph signal processing. Results: The graph Laplacian eigenmodes manifest highly resolved spatial profiles, reflecting distributed patterns that correspond to major white matter pathways. We show that the intrinsic dimensionality of the eigenspace of such high-resolution graphs is only a mere fraction of the graph dimensions. By projecting task and resting-state data on lowfrequency graph Laplacian eigenmodes, we show that brain activity can be well approximated by a small subset of lowfrequency components. Conclusions: The proposed graphs open new avenues in studying the brain, be it, by exploring their organisational properties via graph or spectral graph theory, or by treating them as the scaffold on which brain function is observed at the individual level.

Integrative, Segregative, and Degenerate Harmonics of the Structural Connectome

“…Qualitatively, we found that the lowest harmonics in the consensus SC matched with those previously reported [61, 33, 5] (Figure 1A). Quantitatively, we investigated how SC harmonics related to spatial frequency properties; namely sparsity, zero-cross rate, network zero-crossings [23], and roughness.…”

“…Note that others have recently performed eigenvector alignment using Procrustes [5]; however, we refrained from this approach to preserve as much of the subject-specific features in the harmonics as possible, since understanding the subtle harmonic variation across subjects is a key question evaluated in this work.…”

“…Where |•| denotes an absolute value, and u p(i) is the column in U corresponding to the i th index in the permutation p. By matching individual subjects to the consensus SC, we retain an ordering of ascending eigenvalues with respect to the consensus SC. Note that others have recently performed eigenvector alignment using Procrustes [40] ; however, we refrained from this approach to preserve as much of the subject-specific features in the harmonics as possible, since understanding the subtle harmonic variation across subjects is a key question evaluated in this work.…”

Joint subject-identification and task-decoding from inferred functional brain graphs via a multi-task neural network

“…Through a series of experiments, we show the superiority of the proposed method over conventional strategies of performing classification based on correlation-based FC. Our promising results suggest the potential to further expand the proposed MTNN architecture, to take as input higher resolution FC graphs [23] or fMRI spectral features extracted on atlas-based [24] or high resolution [25,26] structural brain graphs. Lastly, a detailed analysis of the significance of intra/inter network connections in the performance of the trained models is a fertile avenue for future research.…”

Eigenmodes of the brain: revisiting connectomics and geometry

“…To this end, we used the Procrustes transform (PT) 36 , which finds the optimal rotation to match two linear subspaces. This method has been previously used in related work 37 , albeit with a different goal, to quantify the degree of inter-subject variability of eigenmodes of voxel-wise brain graphs. Given two sets of K eigenmodes, PT optimally transforms one set to match the other set.…”