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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 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 eigen-modes 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 that brain activity can be well approximated by a small subset of low-frequency components. 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.

Childhood is a period of extensive cortical and neural development. Among other things, axons in the brain gradually become more myelinated, promoting the propagation of electrical signals between different parts of the brain, which in turn may facilitate skill development. Myelin is difficult to assess in vivo, and measurement techniques are only just beginning to make their way into standard imaging protocols in human cognitive neuroscience. An approach that has been proposed as an indirect measure of cortical myelin is the T1w/T2w ratio, a contrast that is based on the intensities of two standard structural magnetic resonance images. Although not initially intended as such, researchers have recently started to use the T1w/T2w contrast for between-subject comparisons of cortical data with various behavioral and cognitive indices. As a complement to these earlier findings, we computed individual cortical T1w/T2w maps using data from the Adolescent Brain Cognitive Development study (N = 960; 449 females; aged 8.9 to 11.0 years) and related the T1w/T2w maps to indices of cognitive ability; in contrast to previous work, we did not find significant relationships between T1w/T2w values and cognitive performance after correcting for multiple testing. These findings reinforce existent skepticism about the applicability of T1w/T2w ratio for inter-individual comparisons.

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 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.

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

The analysis of signals on complex topologies modeled by graphs is a topic of increasing importance. Decompositions play a crucial role in the representation and processing of such information. Here, we propose a new tight frame design that is adapted to a class of signals on a graph. The construction starts from a prototype Meyer-type system of kernels with uniform subbands. The ensemble energy spectral density is then defined for a given set of signals defined on the graph. The prototype design is then warped such that the resulting subbands capture the same amount of energy for the signal class. This approach accounts at the same time for graph topology and signal features. The proposed frames are constructed for three different graph signal sets and are compared with non-signal-adapted frames. Vertex localization of a set of resulting atoms is studied. The frames are then used to decompose a set of real graph signals and are also used in a setting of signal denoising. The results illustrate the superiority of the designed signal-adapted frames, over frames blind to signal characteristics, in representing data and in denoising.

The human brain cortical layer has a convoluted morphology that is unique to each individual. Characterization of the cortical morphology is necessary in longitudinal studies of structural brain change, as well as in discriminating individuals in health and disease. A method for encoding the cortical morphology in the form of a graph is presented. The design of graphs that encode the global cerebral hemisphere cortices as well as localized cortical regions is proposed. Spectral metrics derived from these graphs are then studied and proposed as descriptors of cortical morphology. As proof-of-concept of their applicability in characterizing cortical morphology, the metrics are studied in the context of hemispheric asymmetry as well as gender dependent discrimination of cortical morphology., Comment: arXiv admin note: substantial text overlap with arXiv:1810.10339

Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph signals based on notions of scale (e.g., coarse to fine). The graph spectrum is more irregular than for conventional domains; i.e., it is influenced by graph topology, and, therefore, assumptions about spectral representations of graph signals are not easy to make. Here, we propose a tight frame design that is adapted to the graph Laplacian spectral content of a given class of graph signals. The design exploits the ensemble energy spectral density, a notion of spectral content of the given signal set that we determine either directly using the graph Fourier transform or indirectly through approximation using a decomposition scheme. The approximation scheme has the benefit that (i) it does not require diagonalization of the Laplacian matrix, and (ii) it leads to a smooth estimate of the spectral content. A prototype system of spectral kernels each capturing an equal amount of energy is defined. The prototype design is then warped using the signal set’s ensemble energy spectral density such that the resulting subbands each capture an equal amount of ensemble energy. This approach accounts at the same time for graph topology and signal features, and it provides a meaningful interpretation of subbands in terms of coarse-to-fine representations.

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.

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.