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Conventionally, as a preprocessing step, functional MRI (fMRI) data are spatially smoothed before further analysis, be it for activation mapping on task-based fMRI or functional connectivity analysis on resting-state fMRI data. When images are smoothed volumetrically, however, isotropic Gaussian kernels are generally used, which do not adapt to the underlying brain structure. Alternatively, cortical surface smoothing procedures provide the benefit of adapting the smoothing process to the underlying morphology, but require projecting volumetric data on to the surface. In this paper, leveraging principles from graph signal processing, we propose a volumetric spatial smoothing method that takes advantage of the gray-white and pial cortical surfaces, and as such, adapts the filtering process to the underlying morphological details at each point in the cortex.

Heschl’s Gyrus (HG), which hosts the primary auditory cortex, exhibits large variability not only in size but also in its gyrification patterns, within (i.e., between hemispheres) and between individuals. Conventional structural measures such as volume, surface area and thickness do not capture the full morphological complexity of HG, in particular, with regards to its shape. We present a method for characterizing the morphology of HG in terms of Laplacian eigenmodes of surface-based and volume-based graph representations of its structure, and derive a set of spectral graph features that can be used to discriminate HG subtypes. We applied this method to a dataset of 177 adults previously shown to display considerable variability in the shape of their HG, including data from amateur and professional musicians, as well as non-musicians. Results show the superiority of the proposed spectral graph features over conventional ones in differentiating HG subtypes, in particular, single HG versus Common Stem Duplications (CSDs). We anticipate the proposed shape features to be found beneficial in the domains of language, music and associated pathologies, in which variability of HG morphology has previously been established.

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 fMRI data in WM that accounts for known spatial constraints on the BOLD signal in WM. In particular, the spatial correlation structure of the BOLD signal in WM 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 BOLD signal in WM. The fundamental element in the proposed method is a graph-based description of WM that encodes the underlying anisotropy observed across WM, derived from diffusion-weighted 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 fMRI data in WM, as an alternative to the conventional practice of using isotropic Gaussian filters. We test the proposed filtering approach on two sets of simulated 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 that the proposed method enables the detection of streamline-like activations within axonal bundles. Funding: McDonnell Center for Systems Neuroscience at Washington University; Swedish Research CouncilSwedish Research CouncilEuropean Commission [2017-04889, 2018-06689]; Royal Physiographic Society of Lund; Thorsten and Elsa Segerfalk Foundation; Hans Werthen Foundation; ITEA3/VINNOVA; Center for Industrial Information Technology (CENIIT) at Linkoping University; BrightFocus FoundationBrightFocus Foundation [A2016172S]; NIHUnited States Department of Health & Human ServicesNational Institutes of Health (NIH) - USA; National Institute of Diabetes and Digestive and Kidney DiseasesUnited States Department of Health & Human ServicesNational Institutes of Health (NIH) - USANIH National Institute of Diabetes & Digestive & Kidney Diseases (NIDDK) [K01DK101631]; National Institute on AgingUnited States Department of Health & Human ServicesNational Institutes of Health (NIH) - USANIH National Institute on Aging (NIA) [R56AG068261]; [1U54MH091657]

In this work, we leverage the Laplacian eigenbasis of voxelwise white matter (WM) graphs derived from diffusionweighted MRI data, dubbed WM harmonics, to characterize the spatial structure of WM fMRI data. Our motivation for such a characterization is based on studies that show WM fMRI data exhibit a spatial correlational anisotropy that coincides with underlying fiber patterns. By quantifying the energy content of WM fMRI data associated with subsets of WM harmonics across multiple spectral bands, we show that the data exhibits notable subtle spatial modulations under functional load that are not manifested during rest. WM harmonics provide a novel means to study the spatial dynamics of WM fMRI data, in such way that the analysis is informed by the underlying anatomical structure. Funding: Swedish Research CouncilSwedish Research CouncilEuropean Commission [2017-04889]; Royal Physiographic Society of Lund; Thorsten and Elsa Segerfalk Foundation; BrightFocus FoundationBrightFocus Foundation [A2016172S]; NIHUnited States Department of Health & Human ServicesNational Institutes of Health (NIH) - USA [K01DK101631, R56AG068261, P41EB015902, R01MH074794]; ITEA3/VINNOVA funded project Intelligence based iMprovement of Personalized treatment And Clinical workflow supporT (IMPACT); Center for Industrial Information Technology (CENIIT) at Linkoping University; Hans Werth en Foundation; SwedenAmerica Foundation

In this work, we leverage the Laplacian eigenbasis of voxelwise white matter (WM) graphs derived from diffusion-weighted MRI data, dubbed WM harmonics, to characterize the spatial structure of WM fMRI data. Our motivation for such a characterization is based on studies that show WM fMRI data exhibit a spatial correlational anisotropy that coincides with underlying fiber patterns. By quantifying the energy content of WM fMRI data associated with subsets of WM harmonics across multiple spectral bands, we show that the data exhibits notable subtle spatial modulations under functional load that are not manifested during rest. WM harmonics provide a novel means to study the spatial dynamics of WM fMRI data, in such way that the analysis is informed by the underlying anatomical structure.

The human cortical layer exhibits a convoluted morphology that is unique to each individual. Conventional volumetric fMRI processing schemes take for granted the rich information provided by the underlying anatomy. We present a method to study fMRI data on subject-specific cerebral hemisphere cortex (CHC) graphs, which encode the cortical morphology at the resolution of voxels in 3-D. We study graph spectral energy metrics associated to fMRI data of 100 subjects from the Human Connectome Project database, across seven tasks. Experimental results signify the strength of CHC graphs' Laplacian eigenvector bases in capturing subtle spatial patterns specific to different functional loads as well as experimental conditions within each task., Comment: Fixed two typos in the equations; (1) definition of L in section 2.1, paragraph 1. (2) signal de-meaning and normalization in section 2.4, paragraph 1

Brain activation mapping using functional MRI (fMRI) based on blood oxygenation level-dependent (BOLD) contrast has been conventionally focused on probing gray matter, the BOLD contrast in white matter having been generally disregarded. Recent results have provided evidence of the functional significance of the white matter BOLD signal, showing at the same time that its correlation structure is highly anisotropic, and related to the diffusion tensor in shape and orientation. This evidence suggests that conventional isotropic Gaussian filters are inadequate for denoising white matter fMRI data, since they are incapable of adapting to the complex anisotropic domain of white matter axonal connections. In this paper we explore a graph-based description of the white matter developed from diffusion MRI data, which is capable of encoding the anisotropy of the domain. Based on this representation we design localized spatial filters that adapt to white matter structure by leveraging graph signal processing principles. The performance of the proposed filtering technique is evaluated on semi-synthetic data, where it shows potential for greater sensitivity and specificity in white matter activation mapping, compared to isotropic filtering. Funding agencies: Swedish Research CouncilSwedish Research Council [2018-06689, 2017-04889]; Center for Industrial Information Technology (CENIIT) at Linkoping University; Wallenberg AI, Autonomous Systems and Software Program (WASP) - Knut and Alice Wallenberg Foundation

A graph based framework for fMRI brain activation mapping is presented. The approach exploits the spectral graphwavelet transform (SGWT) for the purpose of defining an advanced multi-resolutional spatial transformation for fMRI data. The framework extends wavelet based SPM (WSPM), which is an alternative to the conventional approach of statistical parametric mapping (SPM), and is developed specifically for group-level analysis. We present a novel procedure for constructing brain graphs, with subgraphs that separately encode the structural connectivity of the cerebral and cerebellar gray matter (GM), and address the inter-subject GM variability by the use of template GM representations. Graph wavelets tailored to the convoluted boundaries of GM are then constructed as a means to implement a GM-based spatial transformation on fMRI data. The proposed approach is evaluated using real as well as semi-synthetic multi-subject data. Compared to SPM and WSPM using classical wavelets, the proposed approach shows superior type-I error control. The results on real data suggest a higher detection sensitivity as well as the capability to capture subtle, connected patterns of brain activity. (C) 2015 Elsevier Inc. All rights reserved.

Wavelet-based statistical parametric mapping (WSPM) is an extension of the classical approach in fMRI activation mapping that combines wavelet processing with voxel-wise statistical testing. We recently showed how WSPM, using graph wavelets tailored to the full gray-matter (GM) structure of each individual’s brain, can improve brain activity detection compared to using the classical wavelets that are only suited for the Euclidian grid. However, in order to perform analysis on a subject-invariant graph, canonical graph wavelets should be designed in normalized brain space. We here introduce an approach to define a fixed template graph of the cerebellum, an essential component of the brain, using the SUIT cerebellar template. We construct a corresponding set of canonical cerebellar graph wavelets, and adopt them in the analysis of both synthetic and real data. Compared to classical SPM, WSPM using cerebellar graph wavelets shows superior type-I error control, an empirical higher sensitivity on real data, as well as the potential to capture subtle patterns of cerebellar activity.

Wavelet approaches have been successfully applied to the detection of brain activity in fMRI data. Spatial activation patterns have a compact representation in the wavelet domain. However classical wavelets designed for regular Euclidean spaces are not optimal for the topologically complicated gray matter (GM) domain where activation is expected. We hypothesized that wavelet bases that are adapted to the structure of the GM would be more powerful in detecting brain activity. We therefore combine (1) a GM based graph wavelet transform as an advanced spatial transformation for fMRI data with (2) the wavelet based statistical parametric mapping framework (WSPM). We introduce suitable design choices for the graph wavelet transform and evaluate the performance of the proposed approach both on simulated and real fMRI data. Compared to SPM and conventional WSPM the graph based WSPM shows improved detection of finely 3D structured brain activity. © 2013 IEEE.

Non-invasive characterization of brain structure has been made possible by the introduction of magnetic resonance imaging (MRI). Graph modeling of structural connectivity has been useful, but is often limited to defining nodes as regions from a brain atlas. Here, we propose two methods for encoding structural connectivity in a huge brain graph at the voxel-level resolution (i.e., 850’000 voxels) based on diffusion tensor imaging (DTI) and the orientation density functions (ODF), respectively. The eigendecomposition of the brain graph’s Laplacian operator is then showing highly-resolved eigenmodes that reflect distributed structural features which are in good correspondence with major white matter tracks. To investigate the intrinsic dimensionality of eigenspace across subjects, we used a Procrustes validation that characterizes inter-subject variability. We found that the ODF approach using 3-neighborhood captures the most in-formation from the diffusion-weighted MRI. The proposed methods open a wide range of possibilities for new research avenues, especially in the field of graph signal processing applied to functional brain imaging.