Brain network eigenmodes provide a robust and compact representation of the structural connectome in health and disease

Integrative, segregative, and degenerate harmonics of the structural connectome

Unifying integration and segregation in the brain has been a fundamental puzzle in neuroscience ever since the conception of the "binding problem." Here, we introduce a framework that places integration and segregation within a continuum based on a fundamental property of the brain-its structural connectivity graph Laplacian harmonics and a new feature we term the gap-spectrum. This framework organizes harmonics into three regimes-integrative, segregative, and degenerate-that together account for various group-level properties. Integrative and segregative harmonics occupy the ends of the continuum, and they share properties such as reproducibility across individuals, stability to perturbation, and involve "bottom-up" sensory networks. Degenerate harmonics are in the middle of the continuum, and they are subject-specific, flexible, and involve "top-down" networks. The proposed framework accommodates inter-subject variation, sensitivity to changes, and structure-function coupling in ways that offer promising avenues for studying cognition and consciousness in the brain.

Edge Density Imaging Identifies White Matter Biomarkers of Late-Life Obesity and Cognition

Alzheimer disease (AD) and obesity are related to disruptions in the white matter (WM) connectome. We examined the link between the WM connectome and obesity and AD through edge-density imaging/index (EDI), a tractography-based method that characterizes the anatomical embedding of tractography connections. A total of 60 participants, 30 known to convert from normal cognition or mild-cognitive impairment to AD within a minimum of 24 months of follow up, were selected from the Alzheimer disease Neuroimaging Initiative (ADNI). Diffusion-weighted MR images from the baseline scans were used to extract fractional anisotropy (FA) and EDI maps that were subsequently averaged using deterministic WM tractography based on the Desikan-Killiany atlas. Multiple linear and logistic regression analysis were used to identify the weighted sum of tract-specific FA or EDI indices that maximized correlation to body-mass-index (BMI) or conversion to AD. Participants from the Open Access Series of Imaging Studies (OASIS) were used as an independent validation for the BMI findings. The edge-density rich, periventricular, commissural and projection fibers were among the most important WM tracts linking BMI to FA as well as to EDI. WM fibers that contributed significantly to the regression model related to BMI overlapped with those that predicted conversion; specifically in the frontopontine, corticostriatal, and optic radiation pathways. These results were replicated by testing the tract-specific coefficients found using ADNI in the OASIS-4 dataset. WM mapping with EDI enables identification of an abnormal connectome implicated in both obesity and conversion to AD.

Systematic evaluation of fMRI data-processing pipelines for consistent functional connectomics

Functional interactions between brain regions can be viewed as a network, enabling neuroscientists to investigate brain function through network science. Here, we systematically evaluate 768 data-processing pipelines for network reconstruction from resting-state functional MRI, evaluating the effect of brain parcellation, connectivity definition, and global signal regression. Our criteria seek pipelines that minimise motion confounds and spurious test-retest discrepancies of network topology, while being sensitive to both inter-subject differences and experimental effects of interest. We reveal vast and systematic variability across pipelines' suitability for functional connectomics. Inappropriate choice of data-processing pipeline can produce results that are not only misleading, but systematically so, with the majority of pipelines failing at least one criterion. However, a set of optimal pipelines consistently satisfy all criteria across different datasets, spanning minutes, weeks, and months. We provide a full breakdown of each pipeline's performance across criteria and datasets, to inform future best practices in functional connectomics.

Spectral graph model for fMRI: a biophysical, connectivity-based generative model for the analysis of frequency-resolved resting state fMRI

Resting state functional MRI (rs-fMRI) is a popular and widely used technique to explore the brain's functional organization and to examine if it is altered in neurological or mental disorders. The most common approach for its analysis targets the measurement of the synchronized fluctuations between brain regions, characterized as functional connectivity (FC), typically relying on pairwise correlations in activity across different brain regions. While hugely successful in exploring state- and disease-dependent network alterations, these statistical graph theory tools suffer from two key limitations. First, they discard useful information about the rich frequency content of the fMRI signal. The rich spectral information now achievable from advances in fast multiband acquisitions is consequently being under-utilized. Second, the analyzed FCs are phenomenological without a direct neurobiological underpinning in the underlying structures and processes in the brain. There does not currently exist a complete generative model framework for whole brain resting fMRI that is informed by its underlying biological basis in the structural connectome. Here we propose that a different approach can solve both challenges at once: the use of an appropriately realistic yet parsimonious biophysical signal generation model followed by graph spectral (i.e. eigen) decomposition. We call this model a Spectral Graph Model (SGM) for fMRI, using which we can not only quantify the structure-function relationship in individual subjects, but also condense the variable and individual-specific repertoire of fMRI signal's spectral and spatial features into a small number of biophysically-interpretable parameters. We expect this model-based inference of rs-fMRI that seamlessly integrates with structure can be used to examine state and trait characteristics of structure-function relations in a variety of brain disorders.

Impact of white matter hyperintensities on structural connectivity and cognition in cognitively intact ADNI participants

We used indirect brain mapping with virtual lesion tractography to test the hypothesis that the extent of white matter tract disconnection due to white matter hyperintensities (WMH) is associated with corresponding tract-specific cognitive performance decrements. To estimate tract disconnection, WMH masks were extracted from FLAIR MRI data of 481 cognitively intact participants in the Alzheimer's Disease Neuroimaging Initiative (ADNI) and used as regions of avoidance for fiber tracking in diffusion MRI data from 50 healthy young participants from the Human Connectome Project. Estimated tract disconnection in the right inferior fronto-occipital fasciculus, right frontal aslant tract, and right superior longitudinal fasciculus mediated the effects of WMH volume on executive function. Estimated tract disconnection in the left uncinate fasciculus mediated the effects of WMH volume on memory and in the right frontal aslant tract on language. In a subset of ADNI control participants with amyloid data, positive status increased the probability of periventricular WMH and moderated the relationship between WMH burden and tract disconnection in executive function performance.

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

Voxel-based morphometry (VBM) and surface-based morphometry (SBM) are two widely used neuroimaging techniques for investigating brain anatomy. These techniques rely on statistical inferences at individual points (voxels or vertices), clusters of points, or a priori regions-of-interest. They are powerful tools for describing brain anatomy, but offer little insights into the generative processes that shape a particular set of findings. Moreover, they are restricted to a single spatial resolution scale, precluding the opportunity to distinguish anatomical variations that are expressed across multiple scales. Drawing on concepts from classical physics, here we develop an approach, called mode-based morphometry (MBM), that can describe any empirical map of anatomical variations in terms of the fundamental, resonant modes-eigenmodes-of brain anatomy, each tied to a specific spatial scale. Hence, MBM naturally yields a multiscale characterization of the empirical map, affording new opportunities for investigating the spatial frequency content of neuroanatomical variability. Using simulated and empirical data, we show that the validity and reliability of MBM are either comparable or superior to classical vertex-based SBM for capturing differences in cortical thickness maps between two experimental groups. Our approach thus offers a robust, accurate, and informative method for characterizing empirical maps of neuroanatomical variability that can be directly linked to a generative physical process.

Default Mode Network Hypoalignment of Function to Structure Correlates With Depression and Rumination

BACKGROUND

Recent studies have begun to examine how signals in the brain correspond to the underlying white matter structure using tools from the field of graph signal processing to quantify brain function alignment to brain network topology. Here, we applied this framework for the first time toward a transdiagnostic cohort of individuals with internalizing psychopathologies, including mood and anxiety disorders, to uncover how such alignment within the default mode network (DMN) is related to depression and rumination symptoms.

METHODS

Both diffusion-weighted and resting-state functional magnetic resonance imaging were obtained from participants at baseline (n = 60 patients, n = 19 healthy control participants). Patients were randomized to 12 weeks of treatment with either a selective serotonin reuptake inhibitor or cognitive behavioral therapy, and symptom scales were readministered posttreatment (n = 46 patients at follow-up). Using graph signal processing methodology, we quantified the alignment of functional signals to their underlying white matter structural networks.

RESULTS

We found that signal alignment within the posterior DMN was decreased in patients with internalizing psychopathologies compared with healthy control participants and was inversely (negatively) correlated with baseline depression and rumination scales. Signal alignment within the posterior DMN was also correlated with the ratio of total within-DMN to extra-DMN functional connectivity for these regions.

CONCLUSIONS

These findings are consistent with previous literature regarding pathological promiscuity of posterior DMN connectivity and provide the first graph signal processing-based analyses in a transdiagnostic cohort of patients with internalizing psychopathologies.

Eigenmode-based approach reveals a decline in brain structure-function liberality across the human lifespan

While brain function is supported and constrained by the underlying structure, the connectome-based link estimated by current approaches is either relatively moderate or accompanied by high model complexity, with the essential principles underlying structure-function coupling remaining elusive. Here, by proposing a mapping method based on network eigendecomposition, we present a concise and strong correspondence between structure and function. We show that the explanation of functional connectivity can be significantly improved by incorporating interactions between different structural eigenmodes. We also demonstrate the pronounced advantage of the present mapping in capturing individual-specific information with simple implementation. Applying our methodology to the human lifespan, we find that functional diversity decreases with age, with functional interactions increasingly dominated by the leading functional mode. We also find that structure-function liberality weakens with age, which is driven by the decreases in functional components that are less constrained by anatomy, while the magnitude of structure-aligned components is preserved. Overall, our work enhances the understanding of structure-function coupling from a collective, connectome-oriented perspective and promotes a more refined identification of functional portions relevant to human aging, holding great potential for mechanistic insights into individual differences associated with cognition, development, and neurological disorders.

Enhanced brain structure-function tethering in transmodal cortex revealed by high-frequency eigenmodes

While the link between brain structure and function remains an ongoing challenge, the prevailing hypothesis is that the structure-function relationship may itself be gradually decoupling from unimodal to transmodal cortex. However, this hypothesis is constrained by the underlying models which may neglect requisite information. Here we relate structural and functional connectivity derived from diffusion and functional MRI through orthogonal eigenmodes governing frequency-specific diffusion patterns. We find that low-frequency eigenmodes contribute little to functional interactions in transmodal cortex, resulting in divergent structure-function relationships. Conversely, high-frequency eigenmodes predominantly support neuronal coactivation patterns in these areas, inducing structure-function convergence along a unimodal-transmodal hierarchy. High-frequency information, although weak and scattered, could enhance the structure-function tethering, especially in transmodal association cortices. Our findings suggest that the structure-function decoupling may not be an intrinsic property of brain organization, but can be narrowed through multiplexed and regionally specialized spatiotemporal propagation regimes.

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

Voxel-based morphometry (VBM) and surface-based morphometry (SBM) are two widely used neuroimaging techniques for investigating brain anatomy. These techniques rely on statistical inferences at individual points (voxels or vertices), clusters of points, or a priori regions-of-interest. They are powerful tools for describing brain anatomy, but offer little insights into the generative processes that shape a particular set of findings. Moreover, they are restricted to a single spatial resolution scale, precluding the opportunity to distinguish anatomical variations that are expressed across multiple scales. Drawing on concepts from classical physics, here we develop an approach, called mode-based morphometry (MBM), that can describe any empirical map of anatomical variations in terms of the fundamental, resonant modes--eigenmodes--of brain anatomy, each tied to a specific spatial scale. Hence, MBM naturally yields a multiscale characterization of the empirical map, affording new opportunities for investigating the spatial frequency content of neuroanatomical variability. Using simulated and empirical data, we show that the validity and reliability of MBM are either comparable or superior to classical vertex-based SBM for capturing differences in cortical thickness maps between two experimental groups. Our approach thus offers a robust, accurate, and informative method for characterizing empirical maps of neuroanatomical variability that can be directly linked to a generative physical process.

Distributed harmonic patterns of structure-function dependence orchestrate human consciousness

A central question in neuroscience is how consciousness arises from the dynamic interplay of brain structure and function. Here we decompose functional MRI signals from pathological and pharmacologically-induced perturbations of consciousness into distributed patterns of structure-function dependence across scales: the harmonic modes of the human structural connectome. We show that structure-function coupling is a generalisable indicator of consciousness that is under bi-directional neuromodulatory control. We find increased structure-function coupling across scales during loss of consciousness, whether due to anaesthesia or brain injury, capable of discriminating between behaviourally indistinguishable sub-categories of brain-injured patients, tracking the presence of covert consciousness. The opposite harmonic signature characterises the altered state induced by LSD or ketamine, reflecting psychedelic-induced decoupling of brain function from structure and correlating with physiological and subjective scores. Overall, connectome harmonic decomposition reveals how neuromodulation and the network architecture of the human connectome jointly shape consciousness and distributed functional activation across scales.

Predicting time-resolved electrophysiological brain networks from structural eigenmodes

How temporal modulations in functional interactions are shaped by the underlying anatomical connections remains an open question. Here, we analyse the role of structural eigenmodes, in the formation and dissolution of temporally evolving functional brain networks using resting-state magnetoencephalography and diffusion magnetic resonance imaging data at the individual subject level. Our results show that even at short timescales, phase and amplitude connectivity can partly be expressed by structural eigenmodes, but hardly by direct structural connections. Albeit a stronger relationship was found between structural eigenmodes and time-resolved amplitude connectivity. Time-resolved connectivity for both phase and amplitude was mostly characterised by a stationary process, superimposed with very brief periods that showed deviations from this stationary process. For these brief periods, dynamic network states were extracted that showed different expressions of eigenmodes. Furthermore, the eigenmode expression was related to overall cognitive performance and co-occurred with fluctuations in community structure of functional networks. These results implicate that ongoing time-resolved resting-state networks, even at short timescales, can to some extent be understood in terms of activation and deactivation of structural eigenmodes and that these eigenmodes play a role in the dynamic integration and segregation of information across the cortex, subserving cognitive functions.

A Riemannian approach to predicting brain function from the structural connectome

Ongoing brain function is largely determined by the underlying wiring of the brain, but the specific rules governing this relationship remain unknown. Emerging literature has suggested that functional interactions between brain regions emerge from the structural connections through mono- as well as polysynaptic mechanisms. Here, we propose a novel approach based on diffusion maps and Riemannian optimization to emulate this dynamic mechanism in the form of random walks on the structural connectome and predict functional interactions as a weighted combination of these random walks. Our proposed approach was evaluated in two different cohorts of healthy adults (Human Connectome Project, HCP; Microstructure-Informed Connectomics, MICs). Our approach outperformed existing approaches and showed that performance plateaus approximately around the third random walk. At macroscale, we found that the largest number of walks was required in nodes of the default mode and frontoparietal networks, underscoring an increasing relevance of polysynaptic communication mechanisms in transmodal cortical networks compared to primary and unimodal systems.

A Riemannian Revisiting of Structure-Function Mapping Based on Eigenmodes

Understanding the link between brain structure and function may not only improve our knowledge of brain organization, but also lead to better quantification of pathology. To quantify this link, recent studies have attempted to predict the brain's functional connectivity from its structural connectivity. However, functional connectivity matrices live in the Riemannian manifold of the symmetric positive definite space and a specific attention must be paid to operate on this appropriate space. In this work we investigated the implications of using a distance based on an affine invariant Riemannian metric in the context of structure-function mapping. Specifically, we revisit previously proposed structure-function mappings based on eigendecomposition and test them on 100 healthy subjects from the Human Connectome Project using this adapted notion of distance. First, we show that using this Riemannian distance significantly alters the notion of similarity between subjects from a functional point of view. We also show that using this distance improves the correlation between the structural and functional similarity of different subjects. Finally, by using a distance appropriate to this manifold, we demonstrate the importance of mapping function from structure under the Riemannian manifold and show in particular that it is possible to outperform the group average and the so-called glass ceiling on the performance of mappings based on eigenmodes.

Network Diffusion Embedding Reveals Transdiagnostic Subnetwork Disruption and Potential Treatment Targets in Internalizing Psychopathologies

Network diffusion models are a common and powerful way to study the propagation of information through a complex system and they offer straightforward approaches for studying multimodal brain network data. We developed an analytic framework to identify brain subnetworks with perturbed information diffusion capacity using the structural basis that best maps to resting state functional connectivity and applied it towards a heterogeneous dataset of internalizing psychopathologies (IPs), a set of psychiatric conditions in which similar brain network deficits are found across the swath of the disorders, but a unifying neuropathological substrate for transdiagnostic symptom expression is currently unknown. This research provides preliminary evidence of a transdiagnostic brain subnetwork deficit characterized by information diffusion impairment of the right area 8BM, a key brain region involved in organizing a broad spectrum of cognitive tasks, which may underlie previously reported dysfunction of multiple brain circuits in the IPs. We also demonstrate that models of neuromodulation involving targeting this brain region normalize IP diffusion dynamics towards those of healthy controls. These analyses provide a framework for multimodal methods that identify both brain subnetworks with disrupted information diffusion and potential targets of these subnetworks for therapeutic neuromodulatory intervention based on previously well-characterized methodology.

Alpha blocking and 1/fβ spectral scaling in resting EEG can be accounted for by a sum of damped alpha band oscillatory processes

The dynamical and physiological basis of alpha band activity and 1/f^β noise in the EEG are the subject of continued speculation. Here we conjecture, on the basis of empirical data analysis, that both of these features may be economically accounted for through a single process if the resting EEG is conceived of being the sum of multiple stochastically perturbed alpha band damped linear oscillators with a distribution of dampings (relaxation rates). The modulation of alpha-band and 1/f^β noise activity by changes in damping is explored in eyes closed (EC) and eyes open (EO) resting state EEG. We aim to estimate the distribution of dampings by solving an inverse problem applied to EEG power spectra. The characteristics of the damping distribution are examined across subjects, sensors and recording condition (EC/EO). We find that there are robust changes in the damping distribution between EC and EO recording conditions across participants. The estimated damping distributions are found to be predominantly bimodal, with the number and position of the modes related to the sharpness of the alpha resonance and the scaling (β) of the power spectrum (1/f^β). The results suggest that there exists an intimate relationship between resting state alpha activity and 1/f^β noise with changes in both governed by changes to the damping of the underlying alpha oscillatory processes. In particular, alpha-blocking is observed to be the result of the most weakly damped distribution mode becoming more heavily damped. The results suggest a novel way of characterizing resting EEG power spectra and provides new insight into the central role that damped alpha-band activity may play in characterising the spatio-temporal features of resting state EEG.

The resting human electroencephalogram (EEG) exhibits two dominant spectral features: the alpha rhythm (8–13 Hz) and its associated attenuation between eyes-closed and eyes-open resting state (alpha blocking), and the 1/f^β scaling of the power spectrum. While these phenomena are well studied a thorough understanding of their respective generative processes remains elusive. By employing a theoretical approach that follows from neural population models of EEG we demonstrate that it is possible to economically account for both of these phenomena using a singular mechanistic framework: resting EEG is assumed to arise from the summed activity of multiple uncorrelated, stochastically driven, damped alpha band linear oscillatory processes having a distribution of relaxation rates or dampings. By numerically estimating these damping distributions from eyes-closed and eyes-open EEG data, in a total of 136 participants, it is found that such damping distributions are predominantly bimodal in shape. The most weakly damped mode is found to account for alpha band power, with alpha blocking being driven by an increase in the damping of this weakly damped mode, whereas the second, and more heavily damped mode, is able to explain 1/f^β scaling present in the resting state EEG spectra.

Deep brain stimulation for parkinson's disease induces spontaneous cortical hypersynchrony in extended motor and cognitive networks

The mechanism of action of deep brain stimulation (DBS) to the basal ganglia for Parkinson's disease remains unclear. Studies have shown that DBS decreases pathological beta hypersynchrony between the basal ganglia and motor cortex. However, little is known about DBS's effects on long range corticocortical synchronization. Here, we use machine learning combined with graph theory to compare resting-state cortical connectivity between the off and on-stimulation states and to healthy controls. We found that turning DBS on increased high beta and gamma band synchrony (26 to 50 Hz) in a cortical circuit spanning the motor, occipitoparietal, middle temporal, and prefrontal cortices. The synchrony in this network was greater in DBS on relative to both DBS off and controls, with no significant difference between DBS off and controls. Turning DBS on also increased network efficiency and strength and subnetwork modularity relative to both DBS off and controls in the beta and gamma band. Thus, unlike DBS's subcortical normalization of pathological basal ganglia activity, it introduces greater synchrony relative to healthy controls in cortical circuitry that includes both motor and non-motor systems. This increased high beta/gamma synchronization may reflect compensatory mechanisms related to DBS's clinical benefits, as well as undesirable non-motor side effects.

Discrete spectral eigenmode-resonance network of brain dynamics and connectivity

The problem of finding a compact natural representation of brain dynamics and connectivity is addressed using an expansion in terms of physical spatial eigenmodes and their frequency resonances. It is demonstrated that this discrete expansion via the system transfer function enables linear and nonlinear dynamics to be analyzed in compact form in terms of natural dynamic "atoms," each of which is a frequency resonance of an eigenmode. Because these modal resonances are determined by the system dynamics, not the investigator, they are privileged over widely used phenomenological patterns, and obviate the need for artificial discretizations and thresholding in coordinate space. It is shown that modal resonances participate as nodes of a discrete spectral network, are noninteracting in the linear regime, but are linked nonlinearly by wave-wave coalescence and decay processes. The modal resonance formulation is shown to be capable of speeding numerical calculations of strongly nonlinear interactions. Recent work in brain dynamics, especially based on neural field theory (NFT) approaches, allows eigenmodes and their resonances to be estimated from data without assuming a specific brain model. This means that dynamic equations can be inferred using system identification methods from control theory, rather than being assumed, and resonances can be interpreted as control-systems data filters. The results link brain activity and connectivity with control-systems functions such as prediction and attention via gain control and can also be linked to specific NFT predictions if desired, thereby providing a convenient bridge between physiologically based theories and experiment. Amplitudes of modes and resonances can also be tracked to provide a more direct and temporally localized representation of the dynamics than correlations and covariances, which are widely used in the field. By synthesizing many different lines of research, this work provides a way to link quantitative electrophysiological and imaging measurements, connectivity, brain dynamics, and function. This underlines the need to move between coordinate and spectral representations as required. Moreover, standard theoretical-physics approaches and mathematical methods can be used in place of ad hoc statistical measures such as those based on graph theory of artificially discretized and decimated networks, which are highly prone to selection effects and artifacts.

Predicted disconnectome associated with progressive periventricular white matter ischemia

We used a virtual lesion DTI fiber tracking approach with healthy subject DTI data and simulated periventricular white matter (PVWM) lesion masks to predict the sequence of connectivity changes associated with progressive PVWM ischemia. We found that the optic radiations, inferior fronto-occipital fasciculus, inferior longitudinal fasciculus, corpus callosum, temporopontine tract and fornix were affected in early simulated ischemic injury, and that the connectivity of subcortical, cerebellar, and visual regions were significantly disrupted with increasing simulated lesion severity. The results of this study provide insights into the spatial-temporal changes of the brain structural connectome under progressive PVWM ischemia. The virtual lesion approach provides a meaningful proxy to the spatial-temporal changes of the brain's structural connectome and can be used to further characterize the cognitive sequelae of progressive PVWM ischemia in both normal aging and dementia.

Graph Models of Pathology Spread in Alzheimer's Disease: An Alternative to Conventional Graph Theoretic Analysis

Background: Graph theory and connectomics are new techniques for uncovering disease-induced changes in the brain's structural network. Most prior studied have focused on network statistics as biomarkers of disease. However, an emerging body of work involves exploring how the network serves as a conduit for the propagation of disease factors in the brain and has successfully mapped the functional and pathological consequences of disease propagation. In Alzheimer's disease (AD), progressive deposition of misfolded proteins amyloid and tau is well-known to follow fiber projections, under a "prion-like" trans-neuronal transmission mechanism, through which misfolded proteins cascade along neuronal pathways, giving rise to network spread. Methods: In this review, we survey the state of the art in mathematical modeling of connectome-mediated pathology spread in AD. Then we address several open questions that are amenable to mathematically precise parsimonious modeling of pathophysiological processes, extrapolated to the whole brain. We specifically identify current formal models of how misfolded proteins are produced, aggregate, and disseminate in brain circuits, and attempt to understand how this process leads to stereotyped progression in Alzheimer's and other related diseases. Conclusion: This review serves to unify current efforts in modeling of AD progression that together have the potential to explain observed phenomena and serve as a test-bed for future hypothesis generation and testing in silico. Impact statement Graph theory is a powerful new approach that is transforming the study of brain processes. There do not exist many focused reviews of the subfield of graph modeling of how Alzheimer's and other dementias propagate within the brain network, and how these processes can be mapped mathematically. By providing timely and topical review of this subfield, we fill a critical gap in the community and present a unified view that can serve as an in silico test-bed for future hypothesis generation and testing. We also point to several open and unaddressed questions and controversies that future practitioners can tackle.

Cognitive impairment after focal brain lesions is better predicted by damage to structural than functional network hubs

Hubs are highly connected brain regions important for coordinating processing in brain networks. It is unclear, however, which measures of network "hubness" are most useful in identifying brain regions critical to human cognition. We tested how closely two measures of hubness-edge density and participation coefficient, derived from white and gray matter, respectively-were associated with general cognitive impairment after brain damage in two large cohorts of patients with focal brain lesions (N = 402 and 102, respectively) using cognitive tests spanning multiple cognitive domains. Lesions disrupting white matter regions with high edge density were associated with cognitive impairment, whereas lesions damaging gray matter regions with high participation coefficient had a weaker, less consistent association with cognitive outcomes. Similar results were observed with six other gray matter hubness measures. This suggests that damage to densely connected white matter regions is more cognitively impairing than similar damage to gray matter hubs, helping to explain interindividual differences in cognitive outcomes after brain damage.

Gradients of connectivity as graph Fourier bases of brain activity

The application of graph theory to model the complex structure and function of the brain has shed new light on its organization, prompting the emergence of network neuroscience. Despite the tremendous progress that has been achieved in this field, still relatively few methods exploit the topology of brain networks to analyze brain activity. Recent attempts in this direction have leveraged on the one hand graph spectral analysis (to decompose brain connectivity into eigenmodes or gradients) and the other graph signal processing (to decompose brain activity "coupled to" an underlying network in graph Fourier modes). These studies have used a variety of imaging techniques (e.g., fMRI, electroencephalography, diffusion-weighted and myelin-sensitive imaging) and connectivity estimators to model brain networks. Results are promising in terms of interpretability and functional relevance, but methodologies and terminology are variable. The goals of this paper are twofold. First, we summarize recent contributions related to connectivity gradients and graph signal processing, and attempt a clarification of the terminology and methods used in the field, while pointing out current methodological limitations. Second, we discuss the perspective that the functional relevance of connectivity gradients could be fruitfully exploited by considering them as graph Fourier bases of brain activity.

Network model of pathology spread recapitulates neurodegeneration and selective vulnerability in Huntington's Disease

Huntington's Disease (HD), an autosomal dominant genetic disorder caused by a mutation in the Huntingtin gene (HTT), displays a stereotyped topography in the human brain and a stereotyped progression, initially appearing in the striatum. Like other degenerative diseases, spatial topography of HD is divorced from where implicated genes are expressed, a dissociation whose mechanistic underpinning is not currently understood. Cell autonomous molecular factors characterized by gene expression signatures, including proteolytic and post translational modifications, play a role in vulnerability to disease. Non-autonomous mechanisms, likely involving the brain's anatomic or functional connectivity patterns, might also be responsible for selective vulnerability in HD. Leveraging a large dataset of 635 subjects from a multinational study, this paper tests various cell-autonomous and non-autonomous models that can explain HD topography. We test whether the expression patterns of implicated genes is sufficient to explain regional HD atrophy, or whether the network transmission of protein products is required to explain them. We find that network models are capable of predicting, to a high degree, observed atrophy in human subjects. Lastly, we propose a model of anterograde network transmission, and show that it is the most parsimonious yet most likely to explain observed atrophy patterns in HD. Collectively, these data indicate that pathology spread in HD may be mediated by the brain's intrinsic structural network organization. This is the first study to systematically and quantitatively test multiple hypotheses of pathology spread in living human subjects with HD.

Robustness of connectome harmonics to local gray matter and long-range white matter connectivity changes

Recently, it has been proposed that the harmonic patterns emerging from the brain's structural connectivity underlie the resting state networks of the human brain. These harmonic patterns, termed connectome harmonics, are estimated as the Laplace eigenfunctions of the combined gray and white matters connectivity matrices and yield a connectome-specific extension of the well-known Fourier basis. However, it remains unclear how topological properties of the combined connectomes constrain the precise shape of the connectome harmonics and their relationships to the resting state networks. Here, we systematically study how alterations of the local and long-range connectivity matrices affect the spatial patterns of connectome harmonics. Specifically, the proportion of local gray matter homogeneous connectivity versus long-range white-matter heterogeneous connectivity is varied by means of weight-based matrix thresholding, distance-based matrix trimming, and several types of matrix randomizations. We demonstrate that the proportion of local gray matter connections plays a crucial role for the emergence of wide-spread, functionally meaningful, and originally published connectome harmonic patterns. This finding is robust for several different cortical surface templates, mesh resolutions, or widths of the local diffusion kernel. Finally, using the connectome harmonic framework, we also provide a proof-of-concept for how targeted structural changes such as the atrophy of inter-hemispheric callosal fibers and gray matter alterations may predict functional deficits associated with neurodegenerative conditions.

Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome

Tools from the field of graph signal processing, in particular the graph Laplacian operator, have recently been successfully applied to the investigation of structure-function relationships in the human brain. The eigenvectors of the human connectome graph Laplacian, dubbed "connectome harmonics", have been shown to relate to the functionally relevant resting-state networks. Whole-brain modelling of brain activity combines structural connectivity with local dynamical models to provide insight into the large-scale functional organization of the human brain. In this study, we employ the graph Laplacian and its properties to define and implement a large class of neural activity models directly on the human connectome. These models, consisting of systems of stochastic integrodifferential equations on graphs, are dubbed graph neural fields, in analogy with the well-established continuous neural fields. We obtain analytic predictions for harmonic and temporal power spectra, as well as functional connectivity and coherence matrices, of graph neural fields, with a technique dubbed CHAOSS (shorthand for Connectome-Harmonic Analysis Of Spatiotemporal Spectra). Combining graph neural fields with appropriate observation models allows for estimating model parameters from experimental data as obtained from electroencephalography (EEG), magnetoencephalography (MEG), or functional magnetic resonance imaging (fMRI). As an example application, we study a stochastic Wilson-Cowan graph neural field model on a high-resolution connectome graph constructed from diffusion tensor imaging (DTI) and structural MRI data. We show that the model equilibrium fluctuations can reproduce the empirically observed harmonic power spectrum of resting-state fMRI data, and predict its functional connectivity, with a high level of detail. Graph neural fields natively allow the inclusion of important features of cortical anatomy and fast computations of observable quantities for comparison with multimodal empirical data. They thus appear particularly suitable for modelling whole-brain activity at mesoscopic scales, and opening new potential avenues for connectome-graph-based investigations of structure-function relationships.

Algebraic relationship between the structural network's Laplacian and functional network's adjacency matrix is preserved in temporal lobe epilepsy subjects

The relationship between anatomic and resting state functional connectivity of large-scale brain networks is a major focus of current research. In previous work, we introduced a model based on eigen decomposition of the Laplacian which predicts the functional network from the structural network in healthy brains. In this work, we apply the eigen decomposition model to two types of epilepsy; temporal lobe epilepsy associated with mesial temporal sclerosis, and MRI-normal temporal lobe epilepsy. Our findings show that the eigen relationship between function and structure holds for patients with temporal lobe epilepsy as well as normal individuals. These results suggest that the brain under TLE conditions reconfigures and rewires the fine-scale connectivity (a process which the model parameters are putatively sensitive to), in order to achieve the necessary structure-function relationship.

Asymmetric high-order anatomical brain connectivity sculpts effective connectivity

Bridging the gap between symmetric, direct white matter brain connectivity and neural dynamics that are often asymmetric and polysynaptic may offer insights into brain architecture, but this remains an unresolved challenge in neuroscience. Here, we used the graph Laplacian matrix to simulate symmetric and asymmetric high-order diffusion processes akin to particles spreading through white matter pathways. The simulated indirect structural connectivity outperformed direct as well as absent anatomical information in sculpting effective connectivity, a measure of causal and directed brain dynamics. Crucially, an asymmetric diffusion process determined by the sensitivity of the network nodes to their afferents best predicted effective connectivity. The outcome is consistent with brain regions adapting to maintain their sensitivity to inputs within a dynamic range. Asymmetric network communication models offer a promising perspective for understanding the relationship between structural and functional brain connectomes, both in normalcy and neuropsychiatric conditions.

The evolution of white matter microstructural changes after mild traumatic brain injury: A longitudinal DTI and NODDI study

Neuroimaging biomarkers that can detect white matter (WM) pathology after mild traumatic brain injury (mTBI) and predict long-term outcome are needed to improve care and develop therapies. We used diffusion tensor imaging (DTI) and neurite orientation dispersion and density imaging (NODDI) to investigate WM microstructure cross-sectionally and longitudinally after mTBI and correlate these with neuropsychological performance. Cross-sectionally, early decreases of fractional anisotropy and increases of mean diffusivity corresponded to WM regions with elevated free water fraction on NODDI. This elevated free water was more extensive in the patient subgroup reporting more early postconcussive symptoms. The longer-term longitudinal WM changes consisted of declining neurite density on NODDI, suggesting axonal degeneration from diffuse axonal injury for which NODDI is more sensitive than DTI. Therefore, NODDI is a more sensitive and specific biomarker than DTI for WM microstructural changes due to mTBI that merits further study for mTBI diagnosis, prognosis, and treatment monitoring.

Spectral graph theory of brain oscillations

The relationship between the brain's structural wiring and the functional patterns of neural activity is of fundamental interest in computational neuroscience. We examine a hierarchical, linear graph spectral model of brain activity at mesoscopic and macroscopic scales. The model formulation yields an elegant closed-form solution for the structure-function problem, specified by the graph spectrum of the structural connectome's Laplacian, with simple, universal rules of dynamics specified by a minimal set of global parameters. The resulting parsimonious and analytical solution stands in contrast to complex numerical simulations of high dimensional coupled nonlinear neural field models. This spectral graph model accurately predicts spatial and spectral features of neural oscillatory activity across the brain and was successful in simultaneously reproducing empirically observed spatial and spectral patterns of alpha-band (8-12 Hz) and beta-band (15-30 Hz) activity estimated from source localized magnetoencephalography (MEG). This spectral graph model demonstrates that certain brain oscillations are emergent properties of the graph structure of the structural connectome and provides important insights towards understanding the fundamental relationship between network topology and macroscopic whole-brain dynamics. .

Mapping functional brain networks from the structural connectome: Relating the series expansion and eigenmode approaches

Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. ​Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks.

Structural mediation of human brain activity revealed by white-matter interpolation of fMRI

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.

Hierarchical Connectome Modes and Critical State Jointly Maximize Human Brain Functional Diversity

The brain requires diverse segregated and integrated processing to perform normal functions in terms of anatomical structure and self-organized dynamics with critical features, but the fundamental relationships between the complex structural connectome, critical state, and functional diversity remain unknown. Herein, we extend the eigenmode analysis to investigate the joint contribution of hierarchical modular structural organization and critical state to brain functional diversity. We show that the structural modes inherent to the hierarchical modular structural connectome allow a nested functional segregation and integration across multiple spatiotemporal scales. The real brain hierarchical modular organization provides large structural capacity for diverse functional interactions, which are generated by sequentially activating and recruiting the hierarchical connectome modes, and the critical state can best explore the capacity to maximize the functional diversity. Our results reveal structural and dynamical mechanisms that jointly support a balanced segregated and integrated brain processing with diverse functional interactions, and they also shed light on dysfunctional segregation and integration in neurodegenerative diseases and neuropsychiatric disorders.

White Matter Connectome Correlates of Auditory Over-Responsivity: Edge Density Imaging and Machine-Learning Classifiers

Sensory over-responsivity (SOR) commonly involves auditory and/or tactile domains, and can affect children with or without additional neurodevelopmental challenges. In this study, we examined white matter microstructural and connectome correlates of auditory over-responsivity (AOR), analyzing prospectively collected data from 39 boys, aged 8–12 years. In addition to conventional diffusion tensor imaging (DTI) maps – including fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD), and axial diffusivity (AD); we used DTI and high-resolution T1 scans to develop connectome Edge Density (ED) maps. The tract-based spatial statistics was used for voxel-wise comparison of diffusion and ED maps. Then, stepwise penalized logistic regression was applied to identify independent variable (s) predicting AOR, as potential imaging biomarker (s) for AOR. Finally, we compared different combinations of machine learning algorithms (i.e., naïve Bayes, random forest, and support vector machine (SVM) and tract-based DTI/connectome metrics for classification of children with AOR. In direct sensory phenotype assessment, 15 (out of 39) boys exhibited AOR (with or without neurodevelopmental concerns). Voxel-wise analysis demonstrates extensive impairment of white matter microstructural integrity in children with AOR on DTI maps – evidenced by lower FA and higher MD and RD; moreover, there was lower connectome ED in anterior-superior corona radiata, genu and body of corpus callosum. In stepwise logistic regression, the average FA of left superior longitudinal fasciculus (SLF) was the single independent variable distinguishing children with AOR (p = 0.007). Subsequently, the left SLF average FA yielded an area under the curve of 0.756 in receiver operating characteristic analysis for prediction of AOR (p = 0.008) as a region-of-interest (ROI)-based imaging biomarker. In comparative study of different combinations of machine-learning models and DTI/ED metrics, random forest algorithms using ED had higher accuracy for AOR classification. Our results demonstrate extensive white matter microstructural impairment in children with AOR, with specifically lower connectomic ED in anterior-superior tracts and associated commissural pathways. Also, average FA of left SLF can be applied as ROI-based imaging biomarker for prediction of SOR. Finally, machine-learning models can provide accurate and objective image-based classifiers for identification of children with AOR based on white matter tracts connectome ED.

White Matter Connectome Edge Density in Children with Autism Spectrum Disorders: Potential Imaging Biomarkers Using Machine-Learning Models

Prior neuroimaging studies have reported white matter network underconnectivity as a potential mechanism for autism spectrum disorder (ASD). In this study, we examined the structural connectome of children with ASD using edge density imaging (EDI), and then applied machine-learning algorithms to identify children with ASD based on tract-based connectivity metrics. Boys aged 8-12 years were included: 14 with ASD and 33 typically developing children. The edge density (ED) maps were computed from probabilistic streamline tractography applied to high angular resolution diffusion imaging. Tract-based spatial statistics was used for voxel-wise comparison and coregistration of ED maps in addition to conventional diffusion tensor imaging (DTI) metrics of fractional anisotropy (FA), mean diffusivity (MD), and radial diffusivity (RD). Tract-based average DTI/connectome metrics were calculated and used as input for different machine-learning models: naïve Bayes, random forest, support vector machines (SVMs), and neural networks. For these models, cross-validation was performed with stratified random sampling ( × 1,000 permutations). The average accuracy among validation samples was calculated. In voxel-wise analysis, the body and splenium of corpus callosum, bilateral superior and posterior corona radiata, and left superior longitudinal fasciculus showed significantly lower ED in children with ASD; whereas, we could not find significant difference in FA, MD, and RD maps between the two study groups. Overall, machine-learning models using tract-based ED metrics had better performance in identification of children with ASD compared with those using FA, MD, and RD. The EDI-based random forest models had greater average accuracy (75.3%), specificity (97.0%), and positive predictive value (81.5%), whereas EDI-based polynomial SVM had greater sensitivity (51.4%) and negative predictive values (77.7%). In conclusion, we found reduced density of connectome edges in the posterior white matter tracts of children with ASD, and demonstrated the feasibility of connectome-based machine-learning algorithms in identification of children with ASD.

How do spatially distinct frequency specific MEG networks emerge from one underlying structural connectome? The role of the structural eigenmodes

Functional networks obtained from magnetoencephalography (MEG) from different frequency bands show distinct spatial patterns. It remains to be elucidated how distinct spatial patterns in MEG networks emerge given a single underlying structural network. Recent work has suggested that the eigenmodes of the structural network might serve as a basis set for functional network patterns in the case of functional MRI. Here, we take this notion further in the context of frequency band specific MEG networks. We show that a selected set of eigenmodes of the structural network can predict different frequency band specific networks in the resting state, ranging from delta (1-4 Hz) to the high gamma band (40-70 Hz). These predictions outperform predictions based from surrogate data, suggesting a genuine relationship between eigenmodes of the structural network and frequency specific MEG networks. We then show that the relevant set of eigenmodes can be excited in a network of neural mass models using linear stability analysis only by including delays. Excitation of an eigenmode in this context refers to a dynamic instability of a network steady state to a spatial pattern with a corresponding coherent temporal oscillation. Simulations verify the results from linear stability analysis and suggest that theta, alpha and beta band networks emerge very near to the bifurcation. The delta and gamma bands in the resting state emerges further away from the bifurcation. These results show for the first time how delayed interactions can excite the relevant set of eigenmodes that give rise to frequency specific functional connectivity patterns.

Functional brain connectivity is predictable from anatomic network's Laplacian eigen-structure

How structural connectivity (SC) gives rise to functional connectivity (FC) is not fully understood. Here we mathematically derive a simple relationship between SC measured from diffusion tensor imaging, and FC from resting state fMRI. We establish that SC and FC are related via (structural) Laplacian spectra, whereby FC and SC share eigenvectors and their eigenvalues are exponentially related. This gives, for the first time, a simple and analytical relationship between the graph spectra of structural and functional networks. Laplacian eigenvectors are shown to be good predictors of functional eigenvectors and networks based on independent component analysis of functional time series. A small number of Laplacian eigenmodes are shown to be sufficient to reconstruct FC matrices, serving as basis functions. This approach is fast, and requires no time-consuming simulations. It was tested on two empirical SC/FC datasets, and was found to significantly outperform generative model simulations of coupled neural masses.

Delineation of early brain development from fetuses to infants with diffusion MRI and beyond

Dynamic macrostructural and microstructural changes take place from the mid-fetal stage to 2 years after birth. Delineating structural changes of the brain during early development provides new insights into the complicated processes of both typical development and the pathological mechanisms underlying various psychiatric and neurological disorders including autism, attention deficit hyperactivity disorder and schizophrenia. Decades of histological studies have identified strong spatial and functional maturation gradients in human brain gray and white matter. The recent improvements in magnetic resonance imaging (MRI) techniques, especially diffusion MRI (dMRI), relaxometry imaging, and magnetization transfer imaging (MTI) have provided unprecedented opportunities to non-invasively quantify and map the early developmental changes at whole brain and regional levels. Here, we review the recent advances in understanding early brain structural development during the second half of gestation and the first two postnatal years using modern MR techniques. Specifically, we review studies that delineate the emergence and microstructural maturation of white matter tracts, as well as dynamic mapping of inhomogeneous cortical microstructural organization unique to fetuses and infants. These imaging studies converge into maturational curves of MRI measurements that are distinctive across different white matter tracts and cortical regions. Furthermore, contemporary models offering biophysical interpretations of the dMRI-derived measurements are illustrated to infer the underlying microstructural changes. Collectively, this review summarizes findings that contribute to charting spatiotemporally heterogeneous gray and white matter structural development, offering MRI-based biomarkers of typical brain development and setting the stage for understanding aberrant brain development in neurodevelopmental disorders.

Preserved Structural Network Organization Mediates Pathology Spread in Alzheimer's Disease Spectrum Despite Loss of White Matter Tract Integrity

Models of Alzheimer's disease (AD) hypothesize stereotyped progression via white matter (WM) fiber connections, most likely via trans-synaptic transmission of toxic proteins along neuronal pathways. An important question in the field is whether and how organization of fiber pathways is affected by disease. It remains unknown whether fibers act as conduits of degenerative pathologies, or if they also degenerate with the gray matter network. This work uses graph theoretic modeling in a longitudinal design to investigate the impact of WM network organization on AD pathology spread. We hypothesize if altered WM network organization mediates disease progression, then a previously published network diffusion model will yield higher prediction accuracy using subject-specific connectomes in place of a healthy template connectome. Neuroimaging data in 124 subjects from ADNI were assessed. Graph topology metrics show preserved network organization in patients compared to controls. Using a published diffusion model, we further probe the effect of network alterations on degeneration spread in AD. We show that choice of connectome does not significantly impact the model's predictive ability. These results suggest that, despite measurable changes in integrity of specific fiber tracts, WM network organization in AD is preserved. Further, there is no difference in the mediation of putative pathology spread between healthy and AD-impaired networks. This conclusion is somewhat at variance with previous results, which report global topological disturbances in AD. Our data indicates the combined effect of edge thresholding, binarization, and inclusion of subcortical regions to network graphs may be responsible for previously reported effects.