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. We define the strength of local voxel-to-voxel connections using diffusion tensors and orientation distribution functions derived from diffusion-weighted 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. 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 low-frequency graph Laplacian eigenmodes, we show, firstly, that brain activity can be well approximated by a small subset of low-frequency components, and secondly, that spectral graph energy profiles differ under different functional loads. 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.

Spectral Representation of EEG Data using Learned Graphs with Application to Motor Imagery Decoding

“…The fundamental idea in GSP is to apply signal processing procedures to data that reside on an irregular domain described by a graph, a construct consisting of a set of vertices and edges. GSP has in particular been adopted in a steadily increasing number of studies for characterization and processing of functional MRI data (Huang et al, 2018; Atasoy et al, 2017; Preti and Van De Ville, 2019; Abramian et al, 2021; Luppi et al, 2022; Behjat et al, 2015, 2022). For EEG data, a number of studies have shown promising results, namely, for dimensionality reduction (Tanaka et al, 2016; Kalantar et al, 2017), signal denoising (Cattai et al, 2021), and motor imagery (MI) decoding (Georgiadis et al, 2021; Cattai et al, 2022).…”

Mode‐based morphometry: A multiscale approach to mapping human neuroanatomy

“…Eigenmodes correspond to the natural, resonant modes of the system and represent an orthogonal basis set that can describe any spatial pattern expressed by the system, much like the basis set of sines and cosines used to understand the frequency content of signals in Fourier analysis (Felippa et al, 2001; Melrose & McPhedran, 1991). Recent work has shown that eigenmodes derived either from a model of brain geometry, termed geometric eigenmodes , or from a graph‐based model of the structural connectome based on diffusion MRI, termed connectome eigenmodes , can be used as a basis set for reconstructing diverse aspects of brain activity (Atasoy et al, 2016; Behjat et al, 2022; Cummings et al, 2022; Gabay et al, 2018; Ghosh et al, 2022; Henderson et al, 2022; Mukta et al, 2020; Naze et al, 2021; Pang et al, 2023; Robinson et al, 2021; Rué‐Queralt et al, 2021), for quantifying structure–function coupling in the brain (Griffa et al, 2022; Liu et al, 2022; Preti & Van De Ville, 2019), and for understanding atrophy patterns in neurodegeneration (Abdelnour et al, 2015; Abdelnour et al, 2016; Abdelnour et al, 2021) and other conditions (Orrù et al, 2021; Wang et al, 2017). In each of these cases, empirical spatial brain maps can be viewed as resulting from the preferential involvement, or excitation, of specific resonant modes of brain structure, thus offering insights into the generative physical mechanisms that shape the observed spatial pattern, much like the musical notes of a violin string are due to excitations of its resonant modes.…”

Mode-based morphometry: A multiscale approach to mapping human neuroanatomy

“…Eigenmodes correspond to the natural, resonant modes of the system and represent an orthogonal basis set that can describe any spatial pattern expressed by the system, much like the basis set of sines and cosines used to understand the frequency content of signals in Fourier analysis [20,22]. Recent work has shown that eigenmodes derived either from a model of brain geometry, termed geometric eigenmodes, or from a graph-based model of the structural connectome based on diffusion MRI, termed connectome eigenmodes, can be used as a basis set for reconstructing diverse aspects of brain activity [23,24,25,26,27,28,15,29,30,31,32], for quantifying structure-function coupling in the brain [33,34,35], and for understanding atrophy patterns in neurodegeneration [36,37,38] and other conditions [39,40]. In each of these cases, empirical spatial brain maps can be viewed as resulting from the preferential involvement, or excitation, of specific resonant modes of brain structure, thus offering insights into the generative physical mechanisms that shape the observed spatial pattern.…”