Tau pathology, a hallmark of Alzheimer’s disease (AD), is thought to spread cell-to-cell via axonal connections, beginning focally before expanding throughout the brain. This study uses computational models to investigate the interplay between network spread and regional vulnerability in influencing tau spread, focusing specifically on MAPT and APOE genes, and Aβ plaques. 66 regional (Desikan-Killiany atlas) tau-PET standardized uptake value ratio (SUVR) values were extracted from participants in the Swedish BioFINDER-2 study: 429 cognitively normal (CN), 91 subjective cognitive decline (SCD), 168 mild cognitive impairment (MCI), and 182 AD. Values were adjusted for mean choroid plexus signal and converted to tau-positive probabilities using two-component Gaussian mixture models. The Susceptible-Infectious-Recovered (SIR) model (Fig. 1A) was employed to simulate tau spread through brain networks measured using structural connectivity from young individuals. We examined the roles of MAPT, APOE, and Aβ in tau propagation by parameterizing them regionally to influence tau synthesis, clearance, spreading, or misfolding. Regional MAPT and APOE were extracted from Allen Brain Atlas, and Aβ from Aβ-PET. Performance of both baseline models (connectivity-only) and models incorporating regional biological information were evaluated based on their ability to reconstruct observed regional tau levels. Performance was evaluated across the whole sample and groups based on diagnosis, APOE e4 carriage and Aβ positivity. The SIR model recapitulates observed tau patterns, suggesting connectivity-based propagation in early-stage regions (Fig. 1B, C). Allowing regional MAPT to moderate normal tau synthesis improved the model fit overall, and for all groups except CN or Aβ- participants (Fig. 2,3). Regional APOE or Aβ information did not enhance the model performance overall (Fig. 2B, C). However, allowing regional APOE to moderate tau clearance showed better performance in APOE e4 carriers vs. non-carriers, and allowing regional Aβ to moderate tau spread improved performance compared to baseline model among Aβ+ individuals (Fig. 3). Our results suggest that brain connectivity explains early temporal lobe tau spread patterns, while regional intrinsic (MAPT) and disease-related (Aβ) susceptibility may influence spread of tau into other regions at later stages. Future work will test other hypotheses of tau spread by refining this model with additional biological information.

Understanding the interplay between human brain structure and function is crucial to discern neural dynamics. This study explores the relation between brain structure and macroscale functional activity using subject-specific structural connectome eigenmodes, complementing prior work that focused on group-level models and geometry. Leveraging data from the Human Connectome Project, we assess accuracy in reconstructing various functional MRI-based cortical maps using individualised eigenmodes, specifically, across a range of connectome construction parameters. Our results show only minor differences in performance between surface geometric eigen-modes, a local neighborhood graph, a highly smoothed null model, and individual and group-level connectomes at modest smoothing and density levels. Furthermore, our results suggest that spatially smooth eigenmodes best explain functional data. The absence of improvement of individual connectomes and surface geometry over smoothed null models calls for further methodological innovation to better quantify and understand the degree to which brain structure constrains brain function.

Background:Accurate classification of electroencephalogram (EEG) signals is challenging given the nonlinear and nonstationary nature of the data as well as subject-dependent variations. Graph signal processing (GSP) has shown promising results in the analysis of brain imaging data. Methods:In this article, a GSP-based approach is presented that exploits instantaneous amplitude and phase coupling between EEG time series to decode motor imagery (MI) tasks. A graph spectral representation of the Hilbert-transformed EEG signals is obtained, in which simultaneous diagonalization of covariance matrices provides the basis of a subspace that differentiates two classes of right hand and right foot MI tasks. To determine the most discriminative subspace, an exploratory analysis was conducted in the spectral domain of the graphs by ranking the graph frequency components using a feature selection method. The selected features are fed into a binary support vector machine that predicts the label of the test trials. Results:The performance of the proposed approach was evaluated on brain-computer interface competition III (IVa) dataset. Conclusions:Experimental results reflect that brain functional connectivity graphs derived using the instantaneous amplitude and phase of the EEG signals show comparable performance with the best results reported on these data in the literature, indicating the efficiency of the proposed method compared to the state-of-the-art methods.

Goal: 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 low-frequency graph Laplacian eigenmodes, we show that brain activity can be well approximated by a small subset of low-frequency 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.

Hemispheric asymmetry is a universal property of brain organization with wide implications into brain function and structure, and diseases. This study presents a laterality index for characterizing hemispheric asymmetries that underlie cortical maps using geometric eigenmodes derived from human cortical surfaces. We develop a generalized design to quantify asymmetries across various cortical spatial scales. While the design is individual-specific, we implement normalization steps to enable unbiased comparisons across individuals. As a proof of concept, we validated the method on cortical maps of 545 subjects across two datasets, using fMRI maps of healthy individuals and tau-PET maps of patients across the Alzheimer's disease continuum. Our results reveal that cortical regions in different canonical functional networks have connectivity patterns that entail different degrees of hemispheric asymmetry. Moreover, aggregates of the pathological tau protein manifest subtle asymmetries at varying spatial scales along the disease continuum.

Eigenmodes can be derived from various structural brain properties, including cortical surface geometry[1][1] and interareal axonal connections comprising an organism’s connectome[2][2]. Pang and colleagues map geometric and connectome eigenmodes to spatial patterns of human brain activity, assessing whether brain connectivity or geometry provide greater explanatory power of brain function[3][3]. The authors find that geometric eigenmodes are superior predictors of cortical activity compared to connectome eigenmodes. They conclude that this supports the predictions of neural field theory (NFT)[4][4], in that “brain activity is best represented in terms of eigenmodes derived directly from the shape of the cortex, thus emphasizing a fundamental role of geometry in constraining dynamics”. The experimental comparisons favoring geometric eigenmodes over connectome eigenmodes, in conjunction with specific statements regarding the relative efficacy of geometry in representing brain activity, have been widely interpreted to mean that geometry imposes stronger constraints on cortical dynamics than connectivity[5][5]–[9][6]. Here, we reconsider the comparative experimental evidence focusing on the impact of connectome mapping methodology. Utilizing established methods to mitigate connectome construction limitations, we map new connectomes for the same dataset, finding that eigenmodes derived from these connectomes reach comparable accuracy in explaining brain activity to that of geometric eigenmodes. We conclude that the evidence presented to support the comparative proposition that “eigenmodes derived from brain geometry represent a more fundamental anatomical constraint on dynamics than the connectome” may require reconsideration in light of our findings. Pang and colleagues present compelling evidence for the important role of geometric constraints on brain function, but their findings should not be interpreted to mean that geometry has superior explanatory power over the connectome. ### Competing Interest Statement The authors have declared no competing interest. [1]: #ref-1 [2]: #ref-2 [3]: #ref-3 [4]: #ref-4 [5]: #ref-5 [6]: #ref-9

Electroencephalography (EEG) data entail a complex spatiotemporal structure that reflects ongoing organization of brain activity. Characterization of the spatial patterns is an indispensable step in numerous EEG processing pipelines. We present a novel method for transforming EEG data into a spectral representation. First, we learn subject-specific graphs from each subject’s EEG data. Second, by eigendecomposition of the normalized Laplacian matrix of each subject’s graph, an orthonormal basis is obtained using which any given EEG map of the subject can be decomposed, providing a spectral representation of the data. We show that energy of EEG maps is strongly associated with low frequency components of the learned basis, reflecting the smooth topography of EEG maps. As a proof-of-concept for this alternative view of EEG data, we consider the task of decoding two-class motor imagery (MI) data. To this aim, the spectral representations are first mapped into a discriminative subspace for differentiating two-class data using a projection matrix obtained by the Fukunaga–Koontz transform (FKT). An SVM classifier is then trained and tested on the resulting features to differentiate MI classes. The method is benchmarked against features extracted from a subject-specific functional connectivity matrix as well as four alternative MI-decoding methods on Dataset IVa of BCI Competition III. Experimental results show the superiority of the proposed method over alternative approaches in differentiating MI classes, reflecting the added benefit of (i) decomposing EEG data using data-driven, subject-specific harmonic bases, and (ii) accounting for class-specific temporal variations in spectral profiles.

Functional connectivity (FC) between brain regions as manifested via fMRI entails signatures that can be used to differentiate individuals and decode cognitive tasks. In this work, we use methods from graph structure inference to estimate FC, which is in contrast to the conventional approach of deriving FC via correlation. Moreover, we infer FC graphs from seed-based co-activation patterns instead of raw fMRI data. We also propose a multi-task neural network architecture to jointly perform subject-identification and task-decoding from inferred functional brain graphs. We validate the developed model on data from the Human Connectome Project across eight fMRI tasks. Most importantly, our results show the superior task-decoding performance of FC graphs inferred from seed-based activity maps over graphs inferred from raw fMRI data. Furthermore, via gradient-based back-projection, we derive a significance score for inputs to the neural network, and present results showing the differential role of brain connections in subject-identification and task-decoding.

A growing body of research in the past decade has revealed that functional interaction between brain regions entail subject-specific idiosyncrasies that are highly replicable. As such, functional connectivity patterns can be seen as an individual's brain fingerprint, enabling their identification within a population, in health and disease. The conventional method involves constructing the functional connectome by treating brain regions as vertices and utilizing pairwise measures of statistical dependence, such as Pearson's correlation coefficient, between the regional time-courses as edge weights. However, by focusing on EEG data in our study, we propose an alternative approach to learn a sparse graph structure from an individual's EEG data using principles from graph signal processing. The inferred subject-specific graphs encode subtle instantaneous spatial relations between the ensemble set of EEG electrodes in such way that EEG maps are seen as smooth functions residing on the graph. We validated the inferred graphs on two publicly available EEG datasets, demonstrating that the learned graphs outperform correlation-based functional connectomes in fingerprinting performance. This talk provides an overview of our proposed method and related results, which was presented at the 2023 European Signal Processing Conference in Helsinki, Finland. The work was selected as the second-best student paper; aside from the talk, a poster was presented as part of the contest, segments of which can be found as figures in the present article.

A growing number of resting-state fMRI (rs-fMRI) studies report changes in network activity to be a frequent and often early pathological feature in many neurodegenerative conditions. The majority of studies have primarily focused on changes in group averages, failing to account for individual functional connectivity (FC) idiosyncrasies that have been shown to provide a unique identifier or “fingerprint” in healthy individuals (Finn et al., 2015). It thus remains unclear to what extent FC-signatures are stable in the context of cognitive decline and Alzheimer’s Disease (AD) pathology (e.g., β-amyloid [Aβ] and tau). We studied the robustness of subject-specific FC in a longitudinal cohort covering the AD spectrum. 275 participants with longitudinal rs-fMRI data—baseline plus a follow up after approximately two-years—were selected from the Swedish BioFINDER-2 cohort, split into six groups: cognitively normal (CN) Aβ-, subjective cognitive decline (SCD) Aβ-, SCD Aβ+, mild cognitive decline (MCI) Aβ-, MCI Aβ+, and AD Aβ+. FC matrices were derived from each subject rs-fMRI session using the Schaefer cortical parcellation (200 and 400 ROIs), and consequently, a 275×275 identifiability matrix (IM) was derived; see Fig. 1B. For each subject, two fingerprinting measures were extracted from the IM: self identifiability (I-self) and differential identifiability (I-diff); see Fig.1B. I-self and I-diff show varied distributions across the six groups, but values remain notably high even within the AD Aβ+ (Fig.2A). Both I-self and I-diff show significant differences between CN Aβ- and AD Aβ+ (Fig.2B). SCD Aβ- not only show a greater difference to AD Aβ+, but also to SCD Aβ+ and MCI Aβ+; see Fig.2B. Baseline tau-PET was associated with I-self (r = -0.1928,p = 0.0014) and to a lesser degree with I-diff (r = -0.1293, p = 0.0334), whereas baseline MMSE was only found associated to I-self (r = 0.1671,p = 0.0055); neither I-self nor I-diff were associated with age (Fig.3). Our results suggest that resting-state FC is mostly stable under cognitive decline and presence of AD pathology. FC was most notably differentiable for SCD Aβ-, suggesting it as a potential signature to decipher underlying cognitive status and to predict likelihood of future conversion to AD.

Taking advantage of the human brain functional connectome as an individual's fingerprint has attracted great research in recent years. Conventionally, Pearson correlation between regional time-courses is used as a pairwise measure for each edge weight of the connectome. Building upon recent advances in graph signal processing, we propose here to estimate the graph structure as a whole by considering all time-courses at once. Using data from two publicly available datasets, we show the superior performance of such learned brain graphs over correlation-based functional connectomes in characterizing an individual.

Resting-state fMRI has proven to entail subject-specific signatures that can serve as a fingerprint to identify individuals. Conventional methods are based on building a connectivity matrix based on correlation between the average time course of pairs of brain regions. This approach, first, disregards the exquisite spatial detail manifested by fMRI due to working on average regional activities, second, cannot disentangle correlations associated to cognitive activity and underlying noise, and third, does not account for cortical morphology that spatially constraints function. Here we propose a method to address these shortcomings via leveraging principles from graph signal processing. We build high spatial resolution cortical graphs that encode each individual’s cortical morphology and treat region-specific, whole-hemisphere fMRI maps as signals that reside on the graphs. fMRI graph signals are then decomposed using systems of graph spectral kernels to extract structure-informed functional signatures, which are in turn used for fingerprinting. Results on 100 subjects showed the overall superior subject differentiation power of the proposed signatures over the conventional method. Moreover, placement of the signatures within canonical functional brain networks revealed the greater contribution of high-level cognitive networks in subject identification.

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.

Dealing with irregular domains, graph signal processing (GSP) has attracted much attention especially in brain imaging analysis. Motor imagery tasks are extensively utilized in brain-computer interface (BCI) systems that perform classification using features extracted from Electroencephalogram signals. In this paper, a GSP-based approach is presented for two-class motor imagery tasks classification. The proposed method exploits simultaneous diagonalization of two matrices that quantify the covariance structure of graph spectral representation of data from each class, providing a discriminative subspace where distinctive features are extracted from the data. The performance of the proposed method was evaluated on Dataset IVa from BCI Competition III. Experimental results show that the proposed method outperforms two state-of-the-art alternative methods.

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.

In this work, we leverage the Laplacian eigenbasis of voxel-wise 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 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 detectability. 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.

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.

Understanding how the anatomy of the human brain constrains and influences the formation of large-scale functional networks remains a fundamental question in neuroscience. Here, given measured brain activity in gray matter, we interpolate these functional signals into the white matter on a structurally-informed high-resolution voxel-level brain grid. The interpolated volumes reflect the underlying anatomical information, revealing white matter structures that mediate the interaction between temporally coherent gray matter regions. Functional connectivity analyses of the interpolated volumes reveal an enriched picture of the default mode network (DMN) and its subcomponents, including the different white matter bundles that are implicated in their formation, thus extending currently known spatial patterns that are limited within the gray matter only. These subcomponents have distinct structure-function patterns, each of which are differentially observed during tasks, demonstrating plausible structural mechanisms for functional switching between task-positive and -negative components. This work opens new avenues for the integration of brain structure and function, and demonstrates the collective mediation of white matter pathways across short and long-distance functional connections.

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. Using graph signal processing principles, we study spectral energy metrics associated to fMRI data, on 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 to sets of experimental conditions within each task.