How structure sculpts function: Unveiling the contribution of anatomical connectivity to the brain's spontaneous correlation structure

A general framework for characterizing optimal communication in brain networks

Efficient communication in brain networks is foundational for cognitive function and behavior. However, how communication efficiency is defined depends on the assumed model of signaling dynamics, e.g., shortest path signaling, random walker navigation, broadcasting, and diffusive processes. Thus, a general and model-agnostic framework for characterizing optimal neural communication is needed. We address this challenge by assigning communication efficiency through a virtual multi-site lesioning regime combined with game theory, applied to large-scale models of human brain dynamics. Our framework quantifies the exact influence each node exerts over every other, generating optimal influence maps given the underlying model of neural dynamics. These descriptions reveal how communication patterns unfold if regions are set to maximize their influence over one another. Comparing these maps with a variety of brain communication models showed that optimal communication closely resembles a broadcasting regime in which regions leverage multiple parallel channels for information dissemination. Moreover, we found that the brain's most influential regions are its rich-club, exploiting their topological vantage point by broadcasting across numerous pathways that enhance their reach even if the underlying connections are weak. Altogether, our work provides a rigorous and versatile framework for characterizing optimal brain communication, and uncovers the most influential brain regions, and the topological features underlying their influence.

Structural connectome construction using constrained spherical deconvolution in multi-shell diffusion-weighted magnetic resonance imaging

Connectional neuroanatomical maps can be generated in vivo by using diffusion-weighted magnetic resonance imaging (dMRI) data, and their representation as structural connectome (SC) atlases adopts network-based brain analysis methods. We explain the generation of high-quality SCs of brain connectivity by using recent advances for reconstructing long-range white matter connections such as local fiber orientation estimation on multi-shell dMRI data with constrained spherical deconvolution, which yields both increased sensitivity to detecting crossing fibers compared with competing methods and the ability to separate signal contributions from different macroscopic tissues, and improvements to streamline tractography such as anatomically constrained tractography and spherical-deconvolution informed filtering of tractograms, which have increased the biological accuracy of SC creation. Here, we provide step-by-step instructions to creating SCs by using these methods. In addition, intermediate steps of our procedure can be adapted for related analyses, including region of interest-based tractography and quantification of local white matter properties. The associated software MRtrix3 implements the relevant tools for easy application of the protocol, with specific processing tasks deferred to components of the FSL software. The protocol is suitable for users with expertise in dMRI and neuroscience and requires between 2 h and 13 h to complete, depending on the available computational system.

Structure-function coupling in macroscale human brain networks

Precisely how the anatomical structure of the brain gives rise to a repertoire of complex functions remains incompletely understood. A promising manifestation of this mapping from structure to function is the dependency of the functional activity of a brain region on the underlying white matter architecture. Here, we review the literature examining the macroscale coupling between structural and functional connectivity, and we establish how this structure-function coupling (SFC) can provide more information about the underlying workings of the brain than either feature alone. We begin by defining SFC and describing the computational methods used to quantify it. We then review empirical studies that examine the heterogeneous expression of SFC across different brain regions, among individuals, in the context of the cognitive task being performed, and over time, as well as its role in fostering flexible cognition. Last, we investigate how the coupling between structure and function is affected in neurological and psychiatric conditions, and we report how aberrant SFC is associated with disease duration and disease-specific cognitive impairment. By elucidating how the dynamic relationship between the structure and function of the brain is altered in the presence of neurological and psychiatric conditions, we aim to not only further our understanding of their aetiology but also establish SFC as a new and sensitive marker of disease symptomatology and cognitive performance. Overall, this Review collates the current knowledge regarding the regional interdependency between the macroscale structure and function of the human brain in both neurotypical and neuroatypical individuals.

Effects of packetization on communication dynamics in brain networks

Computational studies in network neuroscience build models of communication dynamics in the connectome that help us understand the structure-function relationships of the brain. In these models, the dynamics of cortical signal transmission in brain networks are approximated with simple propagation strategies such as random walks and shortest path routing. Furthermore, the signal transmission dynamics in brain networks can be associated with the switching architectures of engineered communication systems (e.g., message switching and packet switching). However, it has been unclear how propagation strategies and switching architectures are related in models of brain network communication. Here, we investigate the effects of the difference between packet switching and message switching (i.e., whether signals are packetized or not) on the transmission completion time of propagation strategies when simulating signal propagation in mammalian brain networks. The results show that packetization in the connectome with hubs increases the time of the random walk strategy and does not change that of the shortest path strategy, but decreases that of more plausible strategies for brain networks that balance between communication speed and information requirements. This finding suggests an advantage of packet-switched communication in the connectome and provides new insights into modeling the communication dynamics in brain networks.

Connectome-based reservoir computing with the conn2res toolbox

The connection patterns of neural circuits form a complex network. How signaling in these circuits manifests as complex cognition and adaptive behaviour remains the central question in neuroscience. Concomitant advances in connectomics and artificial intelligence open fundamentally new opportunities to understand how connection patterns shape computational capacity in biological brain networks. Reservoir computing is a versatile paradigm that uses high-dimensional, nonlinear dynamical systems to perform computations and approximate cognitive functions. Here we present conn2res: an open-source Python toolbox for implementing biological neural networks as artificial neural networks. conn2res is modular, allowing arbitrary network architecture and dynamics to be imposed. The toolbox allows researchers to input connectomes reconstructed using multiple techniques, from tract tracing to noninvasive diffusion imaging, and to impose multiple dynamical systems, from spiking neurons to memristive dynamics. The versatility of the conn2res toolbox allows us to ask new questions at the confluence of neuroscience and artificial intelligence. By reconceptualizing function as computation, conn2res sets the stage for a more mechanistic understanding of structure-function relationships in brain networks.

Evidence for increased parallel information transmission in human brain networks compared to macaques and male mice

Brain communication, defined as information transmission through white-matter connections, is at the foundation of the brain's computational capacities that subtend almost all aspects of behavior: from sensory perception shared across mammalian species, to complex cognitive functions in humans. How did communication strategies in macroscale brain networks adapt across evolution to accomplish increasingly complex functions? By applying a graph- and information-theory approach to assess information-related pathways in male mouse, macaque and human brains, we show a brain communication gap between selective information transmission in non-human mammals, where brain regions share information through single polysynaptic pathways, and parallel information transmission in humans, where regions share information through multiple parallel pathways. In humans, parallel transmission acts as a major connector between unimodal and transmodal systems. The layout of information-related pathways is unique to individuals across different mammalian species, pointing at the individual-level specificity of information routing architecture. Our work provides evidence that different communication patterns are tied to the evolution of mammalian brain networks.

Forecasting brain activity based on models of spatiotemporal brain dynamics: A comparison of graph neural network architectures

Comprehending the interplay between spatial and temporal characteristics of neural dynamics can contribute to our understanding of information processing in the human brain. Graph neural networks (GNNs) provide a new possibility to interpret graph-structured signals like those observed in complex brain networks. In our study we compare different spatiotemporal GNN architectures and study their ability to model neural activity distributions obtained in functional MRI (fMRI) studies. We evaluate the performance of the GNN models on a variety of scenarios in MRI studies and also compare it to a VAR model, which is currently often used for directed functional connectivity analysis. We show that by learning localized functional interactions on the anatomical substrate, GNN-based approaches are able to robustly scale to large network studies, even when available data are scarce. By including anatomical connectivity as the physical substrate for information propagation, such GNNs also provide a multimodal perspective on directed connectivity analysis, offering a novel possibility to investigate the spatiotemporal dynamics in brain networks.

Neural substrates of psychosis revealed by altered dependencies between brain activity and white-matter architecture in individuals with 22q11 deletion syndrome

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Function-structural dependency is altered in patients with 22q11 deletion syndrome.

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Stronger dependency in subcortical regions correlates with psychotic symptoms.

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Weaker dependency in cingulate cortex correlates with psychotic symptoms.

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Multimodal and not unimodal indexes were correlated with psychosis emergence.

Background

Dysconnectivity has been consistently proposed as a major key mechanism in psychosis. Indeed, disruptions in large-scale structural and functional brain networks have been associated with psychotic symptoms. However, brain activity is largely constrained by underlying white matter pathways and the study of function-structure dependency, compared to conventional unimodal analysis, allows a biologically relevant assessment of neural mechanisms. The 22q11.2 deletion syndrome (22q11DS) constitutes a remarkable opportunity to study the pathophysiological processes of psychosis.

Methods

58 healthy controls and 57 deletion carriers, aged from 16 to 32 years old, underwent resting-state functional and diffusion-weighted magnetic resonance imaging. Deletion carriers were additionally fully assessed for psychotic symptoms. Firstly, we used a graph signal processing method to combine brain activity and structural connectivity measures to obtain regional structural decoupling indexes (SDIs). We use SDI to assess the differences of functional structural dependency (FSD) across the groups. Subsequently we investigated how alterations in FSDs are associated with the severity of positive psychotic symptoms in participants with 22q11DS.

Results

In line with previous findings, participants in both groups showed a spatial gradient of FSD ranging from sensory-motor regions (stronger FSD) to regions involved in higher-order function (weaker FSD). Compared to controls, in participants with 22q11DS, and further in deletion carriers with more severe positive psychotic symptoms, the functional activity was more strongly dependent on the structure in parahippocampal gyrus and subcortical dopaminergic regions, while it was less dependent within the cingulate cortex. This analysis revealed group differences not otherwise detected when assessing the structural and functional nodal measures separately.

Conclusions

Our findings point toward a disrupted modulation of functional activity on the underlying structure, which was further associated to psychopathology for candidate critical regions in 22q11DS. This study provides the first evidence for the clinical relevance of function-structure dependency and its contribution to the emergence of psychosis.

Inferring excitation-inhibition dynamics using a maximum entropy model unifying brain structure and function

Neural activity coordinated across different scales from neuronal circuits to large-scale brain networks gives rise to complex cognitive functions. Bridging the gap between micro- and macroscale processes, we present a novel framework based on the maximum entropy model to infer a hybrid resting-state structural connectome, representing functional interactions constrained by structural connectivity. We demonstrate that the structurally informed network outperforms the unconstrained model in simulating brain dynamics, wherein by constraining the inference model with the network structure we may improve the estimation of pairwise BOLD signal interactions. Further, we simulate brain network dynamics using Monte Carlo simulations with the new hybrid connectome to probe connectome-level differences in excitation-inhibition balance between apolipoprotein E (APOE)-ε4 carriers and noncarriers. Our results reveal sex differences among APOE-ε4 carriers in functional dynamics at criticality; specifically, female carriers appear to exhibit a lower tolerance to network disruptions resulting from increased excitatory interactions. In sum, the new multimodal network explored here enables analysis of brain dynamics through the integration of structure and function, providing insight into the complex interactions underlying neural activity such as the balance of excitation and inhibition.

Multiscale communication in cortico-cortical networks

Signaling in brain networks unfolds over multiple topological scales. Areas may exchange information over local circuits, encompassing direct neighbours and areas with similar functions, or over global circuits, encompassing distant neighbours with dissimilar functions. Here we study how the organization of cortico-cortical networks mediate localized and global communication by parametrically tuning the range at which signals are transmitted on the white matter connectome. We show that brain regions vary in their preferred communication scale. By investigating the propensity for brain areas to communicate with their neighbors across multiple scales, we naturally reveal their functional diversity: unimodal regions show preference for local communication and multimodal regions show preferences for global communication. We show that these preferences manifest as region- and scale-specific structure-function coupling. Namely, the functional connectivity of unimodal regions emerges from monosynaptic communication in small-scale circuits, while the functional connectivity of transmodal regions emerges from polysynaptic communication in large-scale circuits. Altogether, the present findings reveal that communication preferences are highly heterogeneous across the cortex, shaping regional differences in structure-function coupling.

Recurrent dynamics in the cerebral cortex: Integration of sensory evidence with stored knowledge

Current concepts of sensory processing in the cerebral cortex emphasize serial extraction and recombination of features in hierarchically structured feed-forward networks in order to capture the relations among the components of perceptual objects. These concepts are implemented in convolutional deep learning networks and have been validated by the astounding similarities between the functional properties of artificial systems and their natural counterparts. However, cortical architectures also display an abundance of recurrent coupling within and between the layers of the processing hierarchy. This massive recurrence gives rise to highly complex dynamics whose putative function is poorly understood. Here a concept is proposed that assigns specific functions to the dynamics of cortical networks and combines, in a unifying approach, the respective advantages of recurrent and feed-forward processing. It is proposed that the priors about regularities of the world are stored in the weight distributions of feed-forward and recurrent connections and that the high-dimensional, dynamic space provided by recurrent interactions is exploited for computations. These comprise the ultrafast matching of sensory evidence with the priors covertly represented in the correlation structure of spontaneous activity and the context-dependent grouping of feature constellations characterizing natural objects. The concept posits that information is encoded not only in the discharge frequency of neurons but also in the precise timing relations among the discharges. Results of experiments designed to test the predictions derived from this concept support the hypothesis that cerebral cortex exploits the high-dimensional recurrent dynamics for computations serving predictive coding.

When functional blurring becomes deleterious: Reduced system segregation is associated with less white matter integrity and cognitive decline in aging

Healthy aging is accompanied by progressive decline in cognitive performance and concomitant changes in brain structure and functional architecture. Age-accompanied alterations in brain function have been characterized on a network level as weaker functional connections within brain networks along with stronger interactions between networks. This phenomenon has been described as age-related differences in functional network segregation. It has been suggested that functional networks related to associative processes are particularly sensitive to age-related deterioration in segregation, possibly related to cognitive decline in aging. However, there have been only a few longitudinal studies with inconclusive results. Here, we used a large longitudinal sample of 284 participants between 25 to 80 years of age at baseline, with cognitive and neuroimaging data collected at up to three time points over a 10-year period. We investigated age-related changes in functional segregation among two large-scale systems comprising associative and sensorimotor-related resting-state networks. We found that functional segregation of associative systems declines in aging with exacerbated deterioration from the late fifties. Changes in associative segregation were positively associated with changes in global cognitive ability, suggesting that decreased segregation has negative consequences for domain-general cognitive functions. Age-related changes in system segregation were partly accounted for by changes in white matter integrity, but white matter integrity only weakly influenced the association between segregation and cognition. Together, these novel findings suggest a cascade where reduced white-matter integrity leads to less distinctive functional systems which in turn contributes to cognitive decline in aging.

Brain Connectivity Studies on Structure-Function Relationships: A Short Survey with an Emphasis on Machine Learning

This short survey reviews the recent literature on the relationship between the brain structure and its functional dynamics. Imaging techniques such as diffusion tensor imaging (DTI) make it possible to reconstruct axonal fiber tracks and describe the structural connectivity (SC) between brain regions. By measuring fluctuations in neuronal activity, functional magnetic resonance imaging (fMRI) provides insights into the dynamics within this structural network. One key for a better understanding of brain mechanisms is to investigate how these fast dynamics emerge on a relatively stable structural backbone. So far, computational simulations and methods from graph theory have been mainly used for modeling this relationship. Machine learning techniques have already been established in neuroimaging for identifying functionally independent brain networks and classifying pathological brain states. This survey focuses on methods from machine learning, which contribute to our understanding of functional interactions between brain regions and their relation to the underlying anatomical substrate.

Inferring network properties from time series using transfer entropy and mutual information: Validation of multivariate versus bivariate approaches

Functional and effective networks inferred from time series are at the core of network neuroscience. Interpreting properties of these networks requires inferred network models to reflect key underlying structural features. However, even a few spurious links can severely distort network measures, posing a challenge for functional connectomes. We study the extent to which micro- and macroscopic properties of underlying networks can be inferred by algorithms based on mutual information and bivariate/multivariate transfer entropy. The validation is performed on two macaque connectomes and on synthetic networks with various topologies (regular lattice, small-world, random, scale-free, modular). Simulations are based on a neural mass model and on autoregressive dynamics (employing Gaussian estimators for direct comparison to functional connectivity and Granger causality). We find that multivariate transfer entropy captures key properties of all network structures for longer time series. Bivariate methods can achieve higher recall (sensitivity) for shorter time series but are unable to control false positives (lower specificity) as available data increases. This leads to overestimated clustering, small-world, and rich-club coefficients, underestimated shortest path lengths and hub centrality, and fattened degree distribution tails. Caution should therefore be used when interpreting network properties of functional connectomes obtained via correlation or pairwise statistical dependence measures, rather than more holistic (yet data-hungry) multivariate models.

We compare bivariate and multivariate methods for inferring networks from time series, which are generated using a neural mass model and autoregressive dynamics. We assess their ability to reproduce key properties of the underlying structural network. Validation is performed on two macaque connectomes and on synthetic networks with various topologies (regular lattice, small-world, random, scale-free, modular). Even a few spurious links can severely bias key network properties. Multivariate transfer entropy performs best on all topologies for longer time series.

Preserved fractal character of structural brain networks is associated with covert consciousness after severe brain injury

Self-similarity is ubiquitous throughout natural phenomena, including the human brain. Recent evidence indicates that fractal dimension of functional brain networks, a measure of self-similarity, is diminished in patients diagnosed with disorders of consciousness arising from severe brain injury. Here, we set out to investigate whether loss of self-similarity is observed in the structural connectome of patients with disorders of consciousness. Using diffusion MRI tractography from N = 11 patients in a minimally conscious state (MCS), N = 10 patients diagnosed with unresponsive wakefulness syndrome (UWS), and N = 20 healthy controls, we show that fractal dimension of structural brain networks is diminished in DOC patients. Remarkably, we also show that fractal dimension of structural brain networks is preserved in patients who exhibit evidence of covert consciousness by performing mental imagery tasks during functional MRI scanning. These results demonstrate that differences in fractal dimension of structural brain networks are quantitatively associated with chronic loss of consciousness induced by severe brain injury, highlighting the close connection between structural organisation of the human brain and its ability to support cognitive function.

A graph neural network framework for causal inference in brain networks

A central question in neuroscience is how self-organizing dynamic interactions in the brain emerge on their relatively static structural backbone. Due to the complexity of spatial and temporal dependencies between different brain areas, fully comprehending the interplay between structure and function is still challenging and an area of intense research. In this paper we present a graph neural network (GNN) framework, to describe functional interactions based on the structural anatomical layout. A GNN allows us to process graph-structured spatio-temporal signals, providing a possibility to combine structural information derived from diffusion tensor imaging (DTI) with temporal neural activity profiles, like that observed in functional magnetic resonance imaging (fMRI). Moreover, dynamic interactions between different brain regions discovered by this data-driven approach can provide a multi-modal measure of causal connectivity strength. We assess the proposed model's accuracy by evaluating its capabilities to replicate empirically observed neural activation profiles, and compare the performance to those of a vector auto regression (VAR), like that typically used in Granger causality. We show that GNNs are able to capture long-term dependencies in data and also computationally scale up to the analysis of large-scale networks. Finally we confirm that features learned by a GNN can generalize across MRI scanner types and acquisition protocols, by demonstrating that the performance on small datasets can be improved by pre-training the GNN on data from an earlier study. We conclude that the proposed multi-modal GNN framework can provide a novel perspective on the structure-function relationship in the brain. Accordingly this approach appears to be promising for the characterization of the information flow in brain networks.

Signature of consciousness in brain-wide synchronization patterns of monkey and human fMRI signals

During the sleep-wake cycle, the brain undergoes profound dynamical changes, which manifest subjectively as transitions between conscious experience and unconsciousness. Yet, neurophysiological signatures that can objectively distinguish different consciousness states based are scarce. Here, we show that differences in the level of brain-wide signals can reliably distinguish different stages of sleep and anesthesia from the awake state in human and monkey fMRI resting state data. Moreover, a whole-brain computational model can faithfully reproduce changes in global synchronization and other metrics such as functional connectivity, structure-function relationship, integration and segregation across vigilance states. We demonstrate that the awake brain is close to a Hopf bifurcation, which naturally coincides with the emergence of globally correlated fMRI signals. Furthermore, simulating lesions of individual brain areas highlights the importance of connectivity hubs in the posterior brain and subcortical nuclei for maintaining the model in the awake state, as predicted by graph-theoretical analyses of structural data.

Creative destruction: Sparse activity emerges on the mammal connectome under a simulated communication strategy with collisions and redundancy

Signal interactions in brain network communication have been little studied. We describe how nonlinear collision rules on simulated mammal brain networks can result in sparse activity dynamics characteristic of mammalian neural systems. We tested the effects of collisions in "information spreading" (IS) routing models and in standard random walk (RW) routing models. Simulations employed synchronous agents on tracer-based mesoscale mammal connectomes at a range of signal loads. We find that RW models have high average activity that increases with load. Activity in RW models is also densely distributed over nodes: a substantial fraction is highly active in a given time window, and this fraction increases with load. Surprisingly, while IS models make many more attempts to pass signals, they show lower net activity due to collisions compared to RW, and activity in IS increases little as function of load. Activity in IS also shows greater sparseness than RW, and sparseness decreases slowly with load. Results hold on two networks of the monkey cortex and one of the mouse whole-brain. We also find evidence that activity is lower and more sparse for empirical networks compared to degree-matched randomized networks under IS, suggesting that brain network topology supports IS-like routing strategies.

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.

Dynamic representations in networked neural systems

A group of neurons can generate patterns of activity that represent information about stimuli; subsequently, the group can transform and transmit activity patterns across synapses to spatially distributed areas. Recent studies in neuroscience have begun to independently address the two components of information processing: the representation of stimuli in neural activity and the transmission of information in networks that model neural interactions. Yet only recently are studies seeking to link these two types of approaches. Here we briefly review the two separate bodies of literature; we then review the recent strides made to address this gap. We continue with a discussion of how patterns of activity evolve from one representation to another, forming dynamic representations that unfold on the underlying network. Our goal is to offer a holistic framework for understanding and describing neural information representation and transmission while revealing exciting frontiers for future research.

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.

Deriving pairwise transfer entropy from network structure and motifs

Transfer entropy (TE) is an established method for quantifying directed statistical dependencies in neuroimaging and complex systems datasets. The pairwise (or bivariate) TE from a source to a target node in a network does not depend solely on the local source-target link weight, but on the wider network structure that the link is embedded in. This relationship is studied using a discrete-time linearly coupled Gaussian model, which allows us to derive the TE for each link from the network topology. It is shown analytically that the dependence on the directed link weight is only a first approximation, valid for weak coupling. More generally, the TE increases with the in-degree of the source and decreases with the in-degree of the target, indicating an asymmetry of information transfer between hubs and low-degree nodes. In addition, the TE is directly proportional to weighted motif counts involving common parents or multiple walks from the source to the target, which are more abundant in networks with a high clustering coefficient than in random networks. Our findings also apply to Granger causality, which is equivalent to TE for Gaussian variables. Moreover, similar empirical results on random Boolean networks suggest that the dependence of the TE on the in-degree extends to nonlinear dynamics.

Model-based whole-brain effective connectivity to study distributed cognition in health and disease

Neuroimaging techniques are now widely used to study human cognition. The functional associations between brain areas have become a standard proxy to describe how cognitive processes are distributed across the brain network. Among the many analysis tools available, dynamic models of brain activity have been developed to overcome the limitations of original connectivity measures such as functional connectivity. This goes in line with the many efforts devoted to the assessment of directional interactions between brain areas from the observed neuroimaging activity. This opinion article provides an overview of our model-based whole-brain effective connectivity to analyze fMRI data, while discussing the pros and cons of our approach with respect to other established approaches. Our framework relies on the multivariate Ornstein-Uhlenbeck (MOU) process and is thus referred to as MOU-EC. Once tuned, the model provides a directed connectivity estimate that reflects the dynamical state of BOLD activity, which can be used to explore cognition. We illustrate this approach using two applications on task-evoked fMRI data. First, as a connectivity measure, MOU-EC can be used to extract biomarkers for task-specific brain coordination, understood as the patterns of areas exchanging information. The multivariate nature of connectivity measures raises several challenges for whole-brain analysis, for which machine-learning tools present some advantages over statistical testing. Second, we show how to interpret changes in MOU-EC connections in a collective and model-based manner, bridging with network analysis. Our framework provides a comprehensive set of tools that open exciting perspectives to study distributed cognition, as well as neuropathologies.

Linking Structure and Function in Macroscale Brain Networks

Structure-function relationships are a fundamental principle of many naturally occurring systems. However, network neuroscience research suggests that there is an imperfect link between structural connectivity and functional connectivity in the brain. Here, we synthesize the current state of knowledge linking structure and function in macroscale brain networks and discuss the different types of models used to assess this relationship. We argue that current models do not include the requisite biological detail to completely predict function. Structural network reconstructions enriched with local molecular and cellular metadata, in concert with more nuanced representations of functions and properties, hold great potential for a truly multiscale understanding of the structure-function relationship.

The road ahead in clinical network neuroscience

Clinical network neuroscience, the study of brain network topology in neurological and psychiatric diseases, has become a mainstay field within clinical neuroscience. Being a multidisciplinary group of clinical network neuroscience experts based in The Netherlands, we often discuss the current state of the art and possible avenues for future investigations. These discussions revolve around questions like "How do dynamic processes alter the underlying structural network?" and "Can we use network neuroscience for disease classification?" This opinion paper is an incomplete overview of these discussions and expands on ten questions that may potentially advance the field. By no means intended as a review of the current state of the field, it is instead meant as a conversation starter and source of inspiration to others.

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.

Network analysis of whole-brain fMRI dynamics: A new framework based on dynamic communicability

Neuroimaging techniques such as MRI have been widely used to explore the associations between brain areas. Structural connectivity (SC) captures the anatomical pathways across the brain and functional connectivity (FC) measures the correlation between the activity of brain regions. These connectivity measures have been much studied using network theory in order to uncover the distributed organization of brain structures, in particular FC for task-specific brain communication. However, the application of network theory to study FC matrices is often "static" despite the dynamic nature of time series obtained from fMRI. The present study aims to overcome this limitation by introducing a network-oriented analysis applied to whole-brain effective connectivity (EC) useful to interpret the brain dynamics. Technically, we tune a multivariate Ornstein-Uhlenbeck (MOU) process to reproduce the statistics of the whole-brain resting-state fMRI signals, which provides estimates for MOU-EC as well as input properties (similar to local excitabilities). The network analysis is then based on the Green function (or network impulse response) that describes the interactions between nodes across time for the estimated dynamics. This model-based approach provides time-dependent graph-like descriptor, named communicability, that characterize the roles that either nodes or connections play in the propagation of activity within the network. They can be used at both global and local levels, and also enables the comparison of estimates from real data with surrogates (e.g. random network or ring lattice). In contrast to classical graph approaches to study SC or FC, our framework stresses the importance of taking the temporal aspect of fMRI signals into account. Our results show a merging of functional communities over time, moving from segregated to global integration of the network activity. Our formalism sets a solid ground for the analysis and interpretation of fMRI data, including task-evoked activity.

What Can Computational Models Contribute to Neuroimaging Data Analytics?

Over the past years, nonlinear dynamical models have significantly contributed to the general understanding of brain activity as well as brain disorders. Appropriately validated and optimized mathematical models can be used to mechanistically explain properties of brain structure and neuronal dynamics observed from neuroimaging data. A thorough exploration of the model parameter space and hypothesis testing with the methods of nonlinear dynamical systems and statistical physics can assist in classification and prediction of brain states. On the one hand, such a detailed investigation and systematic parameter variation are hardly feasible in experiments and data analysis. On the other hand, the model-based approach can establish a link between empirically discovered phenomena and more abstract concepts of attractors, multistability, bifurcations, synchronization, noise-induced dynamics, etc. Such a mathematical description allows to compare and differentiate brain structure and dynamics in health and disease, such that model parameters and dynamical regimes may serve as additional biomarkers of brain states and behavioral modes. In this perspective paper we first provide very brief overview of the recent progress and some open problems in neuroimaging data analytics with emphasis on the resting state brain activity. We then focus on a few recent contributions of mathematical modeling to our understanding of the brain dynamics and model-based approaches in medicine. Finally, we discuss the question stated in the title. We conclude that incorporating computational models in neuroimaging data analytics as well as in translational medicine could significantly contribute to the progress in these fields.

Microstructure-Informed Connectomics: Enriching Large-Scale Descriptions of Healthy and Diseased Brains

Rapid advances in neuroimaging and network science have produced powerful tools and measures to appreciate human brain organization at multiple spatial and temporal scales. It is now possible to obtain increasingly meaningful representations of whole-brain structural and functional brain networks and to formally assess macroscale principles of network topology. In addition to its utility in characterizing healthy brain organization, individual variability, and life span-related changes, there is high promise of network neuroscience for the conceptualization and, ultimately, management of brain disorders. In the current review, we argue for a science of the human brain that, while strongly embracing macroscale connectomics, also recommends awareness of brain properties derived from meso- and microscale resolutions. Such features include MRI markers of tissue microstructure, local functional properties, as well as information from nonimaging domains, including cellular, genetic, or chemical data. Integrating these measures with connectome models promises to better define the individual elements that constitute large-scale networks, and clarify the notion of connection strength among them. By enriching the description of large-scale networks, this approach may improve our understanding of fundamental principles of healthy brain organization. Notably, it may also better define the substrate of prevalent brain disorders, including stroke, autism, as well as drug-resistant epilepsies that are each characterized by intriguing interactions between local anomalies and network-level perturbations.

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.

A computational network control theory analysis of depression symptoms

Rumination and impaired inhibition are considered core characteristics of depression. However, the neurocognitive mechanisms that contribute to these atypical cognitive processes remain unclear. To address this question, we apply a computational network control theory approach to structural brain imaging data acquired via diffusion tensor imaging in a large sample of participants, to examine how network control theory relates to individual differences in subclinical depression. Recent application of this theory at the neural level is built on a model of brain dynamics, which mathematically models patterns of inter-region activity propagated along the structure of an underlying network. The strength of this approach is its ability to characterize the potential role of each brain region in regulating whole-brain network function based on its anatomical fingerprint and a simplified model of node dynamics. We find that subclinical depression is negatively related to higher integration abilities in the right anterior insula, replicating and extending previous studies implicating atypical switching between the default mode and Executive Control Networks in depression. We also find that subclinical depression is related to the ability to “drive” the brain system into easy to reach neural states in several brain regions, including the bilateral lingual gyrus and lateral occipital gyrus. These findings highlight brain regions less known in their role in depression, and clarify their roles in driving the brain into different neural states related to depression symptoms.

Driving the brain towards creativity and intelligence: A network control theory analysis

High-level cognitive constructs, such as creativity and intelligence, entail complex and multiple processes, including cognitive control processes. Recent neurocognitive research on these constructs highlight the importance of dynamic interaction across neural network systems and the role of cognitive control processes in guiding such a dynamic interaction. How can we quantitatively examine the extent and ways in which cognitive control contributes to creativity and intelligence? To address this question, we apply a computational network control theory (NCT) approach to structural brain imaging data acquired via diffusion tensor imaging in a large sample of participants, to examine how NCT relates to individual differences in distinct measures of creative ability and intelligence. Recent application of this theory at the neural level is built on a model of brain dynamics, which mathematically models patterns of inter-region activity propagated along the structure of an underlying network. The strength of this approach is its ability to characterize the potential role of each brain region in regulating whole-brain network function based on its anatomical fingerprint and a simplified model of node dynamics. We find that intelligence is related to the ability to "drive" the brain system into easy to reach neural states by the right inferior parietal lobe and lower integration abilities in the left retrosplenial cortex. We also find that creativity is related to the ability to "drive" the brain system into difficult to reach states by the right dorsolateral prefrontal cortex (inferior frontal junction) and higher integration abilities in sensorimotor areas. Furthermore, we found that different facets of creativity-fluency, flexibility, and originality-relate to generally similar but not identical network controllability processes. We relate our findings to general theories on intelligence and creativity.

Network Analysis in Disorders of Consciousness: Four Problems and One Proposed Solution (Exponential Random Graph Models)

In recent years, the study of the neural basis of consciousness, particularly in the context of patients recovering from severe brain injury, has greatly benefited from the application of sophisticated network analysis techniques to functional brain data. Yet, current graph theoretic approaches, as employed in the neuroimaging literature, suffer from four important shortcomings. First, they require arbitrary fixing of the number of connections (i.e., density) across networks which are likely to have different "natural" (i.e., stable) density (e.g., patients vs. controls, vegetative state vs. minimally conscious state patients). Second, when describing networks, they do not control for the fact that many characteristics are interrelated, particularly some of the most popular metrics employed (e.g., nodal degree, clustering coefficient)-which can lead to spurious results. Third, in the clinical domain of disorders of consciousness, there currently are no methods for incorporating structural connectivity in the characterization of functional networks which clouds the interpretation of functional differences across groups with different underlying pathology as well as in longitudinal approaches where structural reorganization processes might be operating. Finally, current methods do not allow assessing the dynamics of network change over time. We present a different framework for network analysis, based on Exponential Random Graph Models, which overcomes the above limitations and is thus particularly well suited for clinical populations with disorders of consciousness. We demonstrate this approach in the context of the longitudinal study of recovery from coma. First, our data show that throughout recovery from coma, brain graphs vary in their natural level of connectivity (from 10.4 to 14.5%), which conflicts with the standard approach of imposing arbitrary and equal density thresholds across networks (e.g., time-points, subjects, groups). Second, we show that failure to consider the interrelation between network measures does lead to spurious characterization of both inter- and intra-regional brain connectivity. Finally, we show that Separable Temporal ERGM can be employed to describe network dynamics over time revealing the specific pattern of formation and dissolution of connectivity that accompany recovery from coma.

Framework based on communicability and flow to analyze complex network dynamics

Graph theory constitutes a widely used and established field providing powerful tools for the characterization of complex networks. The intricate topology of networks can also be investigated by means of the collective dynamics observed in the interactions of self-sustained oscillations (synchronization patterns) or propagationlike processes such as random walks. However, networks are often inferred from real-data-forming dynamic systems, which are different from those employed to reveal their topological characteristics. This stresses the necessity for a theoretical framework dedicated to the mutual relationship between the structure and dynamics in complex networks, as the two sides of the same coin. Here we propose a rigorous framework based on the network response over time (i.e., Green function) to study interactions between nodes across time. For this purpose we define the flow that describes the interplay between the network connectivity and external inputs. This multivariate measure relates to the concepts of graph communicability and the map equation. We illustrate our theory using the multivariate Ornstein-Uhlenbeck process, which describes stable and non-conservative dynamics, but the formalism can be adapted to other local dynamics for which the Green function is known. We provide applications to classical network examples, such as small-world ring and hierarchical networks. Our theory defines a comprehensive framework that is canonically related to directed and weighted networks, thus paving a way to revise the standards for network analysis, from the pairwise interactions between nodes to the global properties of networks including community detection.

Multiple Kernel Learning Model for Relating Structural and Functional Connectivity in the Brain

A challenging problem in cognitive neuroscience is to relate the structural connectivity (SC) to the functional connectivity (FC) to better understand how large-scale network dynamics underlying human cognition emerges from the relatively fixed SC architecture. Recent modeling attempts point to the possibility of a single diffusion kernel giving a good estimate of the FC. We highlight the shortcomings of the single-diffusion-kernel model (SDK) and propose a multi-scale diffusion scheme. Our multi-scale model is formulated as a reaction-diffusion system giving rise to spatio-temporal patterns on a fixed topology. We hypothesize the presence of inter-regional co-activations (latent parameters) that combine diffusion kernels at multiple scales to characterize how FC could arise from SC. We formulated a multiple kernel learning (MKL) scheme to estimate the latent parameters from training data. Our model is analytically tractable and complex enough to capture the details of the underlying biological phenomena. The parameters learned by the MKL model lead to highly accurate predictions of subject-specific FCs from test datasets at a rate of 71%, surpassing the performance of the existing linear and non-linear models. We provide an example of how these latent parameters could be used to characterize age-specific reorganization in the brain structure and function.