Diffusion-Informed Spatial Smoothing of fMRI Data in White Matter Using Spectral Graph Filters

Abstract

Brain activation mapping using functional magnetic resonance imaging (fMRI) has been extensively studied in brain gray matter (GM), whereas in large disregarded for probing white matter (WM). This unbalanced treatment has been in part due to controversies in relation to the nature of the blood oxygenation level-dependent (BOLD) contrast in WM and its detachability. However, an accumulating body of studies has provided solid evidence of the functional significance of the BOLD signal in WM and has revealed that it exhibits anisotropic spatio-temporal correlations and structure-specific fluctuations concomitant with those of the cortical BOLD signal. In this work, we present an anisotropic spatial filtering scheme for smoothing WM fMRI data that accounts for known spatial constraints on the BOLD signal in WM. In particular, the spatial correlation structure of the WM BOLD signal is highly anisotropic and closely linked to local axonal structure in terms of shape and orientation, suggesting that isotropic Gaussian filters conventionally used for smoothing fMRI data are inadequate for denoising the WM BOLD signal as they are incapable of adapting to the underlying domain of the BOLD signal in white matter. The fundamental element in the proposed method is a graph-based description of the WM that encodes the underlying anisotropy observed across WM, derived from diffusion MRI data. Based on this representation, and leveraging graph signal processing principles, we design subject-specific spatial filters that adapt to a subject's unique WM structure at each position in the WM that they are applied at. We use the proposed filters to spatially smooth WM fMRI data, as an alternative to the conventional practice of using isotropic Gaussian filters. We test the proposed filtering approach on two sets of phantoms, showcasing its greater sensitivity and specificity for the detection of slender anisotropic activations, compared to that achieved with isotropic Gaussian filters. We also present WM activation mapping results on the Human Connectome Project's 100-unrelated subject dataset, across seven functional tasks, showing the capacity of the proposed method for detecting streamline-like activations within axonal bundles.

Characterization of spatial dynamics of fMRI data in white matter using diffusion-informed white matter harmonics

“…microvascular structure as well as the body of recent reports on the anisotropic spatial structure of such data. Recent work implementing spatial smoothing on diffusion-informed WM graphs has shown the benefit of using anisotropic filters that adapt to the underlying diffusion structure in WM [10,11]. The present work builds on the benefits of subject-specific, voxel-wise WM graphs, showing that their Laplacian eigenbasis, dubbed WM harmonics, can provide a novel means for characterizing the spatial structure in WM fMRI data.…”

“…To characterize the underlying domain of WM fMRI data, we leveraged diffusion-weighted MRI data to construct voxelresolution graphs based on the method proposed in [11]. In particular, for each subject, and each hemisphere, we constructed a graph, wherein each WM voxel is represented as a graph vertex, and the relation between neighboring voxels is defined based the extent of coherence between their associated diffusion ODFs: two vertices whose associated voxels are adjacent are connected through an edge with a high weight if their associated ODFs are well aligned with the edge connecting them, and vice versa.…”

“…In particular, for each subject, and each hemisphere, we constructed a graph, wherein each WM voxel is represented as a graph vertex, and the relation between neighboring voxels is defined based the extent of coherence between their associated diffusion ODFs: two vertices whose associated voxels are adjacent are connected through an edge with a high weight if their associated ODFs are well aligned with the edge connecting them, and vice versa. For further details on the design we refer to [11]. As previously mentioned, we refer to the Laplacian eigenmodes of the resulting WM graphs as WM harmonics.…”

“…Recent work implementing spatial smoothing on diffusioninformed WM graphs has shown the benefit of using anisotropic filters that adapt to the underlying diffusion structure in WM [10,11]. Such WM graphs have also been found beneficial in showing the collective mediation of WM pathways based on functional activity in gray matter [12].…”

Cortical Surface-Informed Volumetric Spatial Smoothing of fMRI Data via Graph Signal Processing

“…[7], [8], [9], [10], [11]-and volume-based-see e.g. [12], [13], [14], [15]-methods, which differ from methods such as [16], [17], [18], [19] in that they leverage an independent contrast image-different from the data to be smoothedthat confines the spatial profile of the filters.…”