Symmetry Breaking in Space-Time Hierarchies Shapes Brain Dynamics and Behavior

Metastability demystified - the foundational past, the pragmatic present and the promising future

Healthy brain function depends on balancing stable integration between brain areas for effective coordinated functioning, with coexisting segregation that allows subsystems to express their functional specialization. Metastability, a concept from the dynamical systems literature, has been proposed as a key signature that characterizes this balance. Building on this principle, the neuroscience literature has leveraged the phenomenon of metastability to investigate various aspects of brain function in health and disease. However, this body of work often uses the notion of metastability heuristically, and sometimes inaccurately, making it difficult to navigate the vast literature, interpret findings and foster further development of theoretical and experimental methodologies. Here, we provide a comprehensive review of metastability and its applications in neuroscience, covering its scientific and historical foundations and the practical measures used to assess it in empirical data. We also provide a critical analysis of recent theoretical developments, clarifying common misconceptions and paving the road for future developments.

Symmetry breaking organizes the brain's resting state manifold

Spontaneously fluctuating brain activity patterns that emerge at rest have been linked to the brain's health and cognition. Despite detailed descriptions of the spatio-temporal brain patterns, our understanding of their generative mechanism is still incomplete. Using a combination of computational modeling and dynamical systems analysis we provide a mechanistic description of the formation of a resting state manifold via the network connectivity. We demonstrate that the symmetry breaking by the connectivity creates a characteristic flow on the manifold, which produces the major data features across scales and imaging modalities. These include spontaneous high-amplitude co-activations, neuronal cascades, spectral cortical gradients, multistability, and characteristic functional connectivity dynamics. When aggregated across cortical hierarchies, these match the profiles from empirical data. The understanding of the brain's resting state manifold is fundamental for the construction of task-specific flows and manifolds used in theories of brain function. In addition, it shifts the focus from the single recordings towards the brain's capacity to generate certain dynamics characteristic of health and pathology.

The motifs of radical embodied neuroscience

In this paper, I analyse how the emerging scientific framework of radical embodied neuroscience is different from contemporary mainstream cognitive neuroscience. To do so, I propose the notion of motif to enrich the philosophical toolkit of cognitive neuroscience. This notion can be used to characterize the guiding ideas of any given scientific framework in psychology and neuroscience. Motifs are highly unconstrained, open-ended concepts that support equally open-ended families of explanations. Different scientific frameworks-e.g., psychophysics or cognitive neuroscience-provide these motifs to answer the overarching themes of these disciplines, such as the relationship between stimuli and sensations or the proper methods of the sciences of the mind. Some motifs of mainstream cognitive neuroscience are the motif of encoding, the motif of input-output systems, and the motif of algorithms. The two first ones answer the question about the relationship between stimuli, sensations and experience (e.g., stimuli are input and are encoded by brain structures). The latter one answers the question regarding the mechanism of cognition and experience. The three of them are equally unconstrained and open-ended, and they serve as an umbrella for different kinds of explanation-i.e., different positions regarding what counts as a code or as an input. Along with the articulation of the notion of motif, the main aim of this article is to present three motifs for radical embodied neuroscience: the motif of complex stimulation, the motif of organic behaviour and the motif of resonance.

Linking fast and slow: The case for generative models

A pervasive challenge in neuroscience is testing whether neuronal connectivity changes over time due to specific causes, such as stimuli, events, or clinical interventions. Recent hardware innovations and falling data storage costs enable longer, more naturalistic neuronal recordings. The implicit opportunity for understanding the self-organised brain calls for new analysis methods that link temporal scales: from the order of milliseconds over which neuronal dynamics evolve, to the order of minutes, days, or even years over which experimental observations unfold. This review article demonstrates how hierarchical generative models and Bayesian inference help to characterise neuronal activity across different time scales. Crucially, these methods go beyond describing statistical associations among observations and enable inference about underlying mechanisms. We offer an overview of fundamental concepts in state-space modeling and suggest a taxonomy for these methods. Additionally, we introduce key mathematical principles that underscore a separation of temporal scales, such as the slaving principle, and review Bayesian methods that are being used to test hypotheses about the brain with multiscale data. We hope that this review will serve as a useful primer for experimental and computational neuroscientists on the state of the art and current directions of travel in the complex systems modelling literature.

Does the brain behave like a (complex) network? I. Dynamics

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

Multiscale co-simulation design pattern for neuroscience applications

Integration of information across heterogeneous sources creates added scientific value. Interoperability of data, tools and models is, however, difficult to accomplish across spatial and temporal scales. Here we introduce the toolbox Parallel Co-Simulation, which enables the interoperation of simulators operating at different scales. We provide a software science co-design pattern and illustrate its functioning along a neuroscience example, in which individual regions of interest are simulated on the cellular level allowing us to study detailed mechanisms, while the remaining network is efficiently simulated on the population level. A workflow is illustrated for the use case of The Virtual Brain and NEST, in which the CA1 region of the cellular-level hippocampus of the mouse is embedded into a full brain network involving micro and macro electrode recordings. This new tool allows integrating knowledge across scales in the same simulation framework and validating them against multiscale experiments, thereby largely widening the explanatory power of computational models.

Neural manifolds carry reactivation of phonetic representations during semantic processing

Traditional models of speech perception posit that neural activity encodes speech through a hierarchy of cognitive processes, from low-level representations of acoustic and phonetic features to high-level semantic encoding. Yet it remains unknown how neural representations are transformed across levels of the speech hierarchy. Here, we analyzed unique microelectrode array recordings of neuronal spiking activity from the human left anterior superior temporal gyrus, a brain region at the interface between phonetic and semantic speech processing, during a semantic categorization task and natural speech perception. We identified distinct neural manifolds for semantic and phonetic features, with a functional separation of the corresponding low-dimensional trajectories. Moreover, phonetic and semantic representations were encoded concurrently and reflected in power increases in the beta and low-gamma local field potentials, suggesting top-down predictive and bottom-up cumulative processes. Our results are the first to demonstrate mechanisms for hierarchical speech transformations that are specific to neuronal population dynamics.

Event-related variability is modulated by task and development

In carefully designed experimental paradigms, cognitive scientists interpret the mean event-related potentials (ERP) in terms of cognitive operations. However, the huge signal variability from one trial to the next, questions the representability of such mean events. We explored here whether this variability is an unwanted noise, or an informative part of the neural response. We took advantage of the rapid changes in the visual system during human infancy and analyzed the variability of visual responses to central and lateralized faces in 2-to 6-month-old infants compared to adults using high-density electroencephalography (EEG). We observed that neural trajectories of individual trials always remain very far from ERP components, only moderately bending their direction with a substantial temporal jitter across trials. However, single trial trajectories displayed characteristic patterns of acceleration and deceleration when approaching ERP components, as if they were under the active influence of steering forces causing transient attraction and stabilization. These dynamic events could only partly be accounted for by induced microstate transitions or phase reset phenomena. Importantly, these structured modulations of response variability, both between and within trials, had a rich sequential organization, which in infants, was modulated by the task difficulty and age. Our approaches to characterize Event Related Variability (ERV) expand on classic ERP analyses and provide the first evidence for the functional role of ongoing neural variability in human infants.

One ring to rule them all: The unifying role of prefrontal cortex in steering task-related brain dynamics

Surviving and thriving in a complex world require intricate balancing of higher order brain functions with essential survival-related behaviours. Exactly how this is achieved is not fully understood but a large body of work has shown that different regions in the prefrontal cortex (PFC) play key roles for diverse cognitive and emotional tasks including emotion, control, response inhibition, mental set shifting and working memory. We hypothesised that the key regions are hierarchically organised and we developed a framework for discovering the driving brain regions at the top of the hierarchy, responsible for steering the brain dynamics of higher brain function. We fitted a time-dependent whole-brain model to the neuroimaging data from large-scale Human Connectome Project with over 1,000 participants and computed the entropy production for rest and seven tasks (covering the main domains of cognition). This thermodynamics framework allowed us to identify the main common, unifying drivers steering the orchestration of brain dynamics during difficult tasks; located in key regions of the PFC (inferior frontal gyrus, lateral orbitofrontal cortex, rostral and caudal frontal cortex and rostral anterior cingulate cortex). Selectively lesioning these regions in the whole-brain model demonstrated their causal mechanistic importance. Overall, this shows the existence of a 'ring' of specific PFC regions ruling over the orchestration of higher brain function.

Repairing Artifacts in Neural Activity Recordings Using Low-Rank Matrix Estimation

Electrophysiology recordings are frequently affected by artifacts (e.g., subject motion or eye movements), which reduces the number of available trials and affects the statistical power. When artifacts are unavoidable and data are scarce, signal reconstruction algorithms that allow for the retention of sufficient trials become crucial. Here, we present one such algorithm that makes use of large spatiotemporal correlations in neural signals and solves the low-rank matrix completion problem, to fix artifactual entries. The method uses a gradient descent algorithm in lower dimensions to learn the missing entries and provide faithful reconstruction of signals. We carried out numerical simulations to benchmark the method and estimate optimal hyperparameters for actual EEG data. The fidelity of reconstruction was assessed by detecting event-related potentials (ERP) from a highly artifacted EEG time series from human infants. The proposed method significantly improved the standardized error of the mean in ERP group analysis and a between-trial variability analysis compared to a state-of-the-art interpolation technique. This improvement increased the statistical power and revealed significant effects that would have been deemed insignificant without reconstruction. The method can be applied to any time-continuous neural signal where artifacts are sparse and spread out across epochs and channels, increasing data retention and statistical power.

Information transmission velocity-based dynamic hierarchical brain networks

The brain functions as an accurate circuit that regulates information to be sequentially propagated and processed in a hierarchical manner. However, it is still unknown how the brain is hierarchically organized and how information is dynamically propagated during high-level cognition. In this study, we developed a new scheme for quantifying the information transmission velocity (ITV) by combining electroencephalogram (EEG) and diffusion tensor imaging (DTI), and then mapped the cortical ITV network (ITVN) to explore the information transmission mechanism of the human brain. The application in MRI-EEG data of P300 revealed bottom-up and top-down ITVN interactions subserving P300 generation, which was comprised of four hierarchical modules. Among these four modules, information exchange between visual- and attention-activated regions occurred at a high velocity, related cognitive processes could thus be efficiently accomplished due to the heavy myelination of these regions. Moreover, inter-individual variability in P300 was probed to be attributed to the difference in information transmission efficiency of the brain, which may provide new insight into the cognitive degenerations in clinical neurodegenerative disorders, such as Alzheimer's disease, from the transmission velocity perspective. Together, these findings confirm the capacity of ITV to effectively determine the efficiency of information propagation in the brain.

Stability of sensorimotor network sculpts the dynamic repertoire of resting state over lifespan

Temporally stable patterns of neural coordination among distributed brain regions are crucial for survival. Recently, many studies highlight association between healthy aging and modifications in organization of functional brain networks, across various time-scales. Nonetheless, quantitative characterization of temporal stability of functional brain networks across healthy aging remains unexplored. This study introduces a data-driven unsupervised approach to capture high-dimensional dynamic functional connectivity (dFC) via low-dimensional patterns and subsequent estimation of temporal stability using quantitative metrics. Healthy aging related changes in temporal stability of dFC were characterized across resting-state, movie-viewing, and sensorimotor tasks (SMT) on a large (n = 645) healthy aging dataset (18-88 years). Prominent results reveal that (1) whole-brain temporal dynamics of dFC movie-watching task is closer to resting-state than to SMT with an overall trend of highest temporal stability observed during SMT followed by movie-watching and resting-state, invariant across lifespan aging, (2) in both tasks conditions stability of neurocognitive networks in young adults is higher than older adults, and (3) temporal stability of whole brain resting-state follows a U-shaped curve along lifespan-a pattern shared by sensorimotor network stability indicating their deeper relationship. Overall, the results can be applied generally for studying cohorts of neurological disorders using neuroimaging tools.

Dynamical interactions reconfigure the gradient of cortical timescales

The functional organization of the brain is usually presented with a back-to-front gradient of timescales, reflecting regional specialization with sensory areas (back) processing information faster than associative areas (front), which perform information integration. However, cognitive processes require not only local information processing but also coordinated activity across regions. Using magnetoencephalography recordings, we find that the functional connectivity at the edge level (between two regions) is also characterized by a back-to-front gradient of timescales following that of the regional gradient. Unexpectedly, we demonstrate a reverse front-to-back gradient when nonlocal interactions are prominent. Thus, the timescales are dynamic and can switch between back-to-front and front-to-back patterns.

Fundamental Cause of Bio-Chirality: Space-Time Symmetry—Concept Review

The search for fundamental determinants of bio-molecular chirality is a hot topic in biology, clarifying the meaning of evolution and the enigma of life’s origin. The question of origin may be resolved assuming that non-biological and biological entities obey nature’s universal laws grounded on space-time symmetry (STS) and space-time relativity (SPR). The fabric of STS is our review’s primary subject. This symmetry, encompassing the behavior of elementary particles and galaxy structure, imposes its fundamental laws on all hierarchical levels of the biological world. From the perspective of STS, objects across spatial scales may be classified as chiral or achiral concerning a specific space-related symmetry transformation: mirror reflection. The chiral object is not identical (i.e., not superimposable) to its mirror image. In geometry, distinguish two kinds of chiral objects. The first one does not have any reflective symmetry elements (a point or plane of symmetry) but may have rotational symmetry axes (dissymmetry). The second one does not have any symmetry elements (asymmetry). As the form symmetry deficiency, Chirality is the critical structural feature of natural systems, including sub-atomic particles and living matter. According to the Standard Model (SM) theory and String Theory (StrT), elementary particles associated with the four fundamental forces of nature determine the existence of micro- and galaxy scales of nature. Therefore, the inheritance of molecular symmetry from the symmetry of elementary particles indicates a bi-directional (internal [(micro-scale) and external (galaxy sale)] causal pathway of prevalent bio-chirality. We assume that the laws of the physical world impact the biological matter’s appearance through both extremities of spatial dimensions. The extended network of multi-disciplinary experimental evidence supports this hypothesis. However, many experimental results are derived and interpreted based on the narrow-view prerogative and highly specific terminology. The current review promotes a holistic approach to experimental results in two fast-developing, seemingly unrelated, divergent branches of STS and biological chirality. The generalized view on the origin of prevalent bio-molecular chirality is necessary for understanding the link between a diverse range of biological events. The chain of chirality transfer links ribosomal protein synthesis, cell morphology, and neuronal signaling with the laterality of cognitive functions.

It's about time: Linking dynamical systems with human neuroimaging to understand the brain

Most human neuroscience research to date has focused on statistical approaches that describe stationary patterns of localized neural activity or blood flow. While these patterns are often interpreted in light of dynamic, information-processing concepts, the static, local, and inferential nature of the statistical approach makes it challenging to directly link neuroimaging results to plausible underlying neural mechanisms. Here, we argue that dynamical systems theory provides the crucial mechanistic framework for characterizing both the brain's time-varying quality and its partial stability in the face of perturbations, and hence, that this perspective can have a profound impact on the interpretation of human neuroimaging results and their relationship with behavior. After briefly reviewing some key terminology, we identify three key ways in which neuroimaging analyses can embrace a dynamical systems perspective: by shifting from a local to a more global perspective, by focusing on dynamics instead of static snapshots of neural activity, and by embracing modeling approaches that map neural dynamics using "forward" models. Through this approach, we envisage ample opportunities for neuroimaging researchers to enrich their understanding of the dynamic neural mechanisms that support a wide array of brain functions, both in health and in the setting of psychopathology.

Cross-attractor repertoire provides new perspective on structure-function relationship in the brain

The brain exhibits complex intrinsic dynamics, i.e., spontaneously arising activity patterns without any external inputs or tasks. Such intrinsic dynamics and their alteration are thought to play crucial roles in typical as well as atypical cognitive functioning. Linking the ever-changing intrinsic dynamics to the rather static anatomy is a challenging endeavor. Dynamical systems models are important tools for understanding how structure and function are linked in the brain. Here, we provide a novel modeling framework to examine how functional connectivity depends on structural connectivity in the brain. Existing modeling frameworks typically focus on noise-driven (or stochastic) dynamics near a single attractor. Complementing existing approaches, we examine deterministic features of the distribution of attractors, in particular, how regional states are correlated across all attractors - cross-attractor coordination. We found that cross-attractor coordination between brain regions better predicts human functional connectivity than noise-driven single-attractor dynamics. Importantly, cross-attractor coordination better accounts for the nonlinear dependency of functional connectivity on structural connectivity. Our findings suggest that functional connectivity patterns in the brain may reflect transitions between attractors, which impose an energy cost. The framework may be used to predict transitions and energy costs associated with experimental or clinical interventions.

Attaining the recesses of the cognitive space

Existing neuropsychological tests of executive function often manifest a difficulty pinpointing cognitive deficits when these are intermittent and come in the form of omissions. We discuss the hypothesis that two partially interrelated reasons for this failure stem from relative inability of neuropsychological tests to explore the cognitive space and to explicitly take into account strategic and opportunistic resource allocation decisions, and to address the temporal aspects of both behaviour and task-related brain function in data analysis. Criteria for tasks suitable for neuropsychological assessment of executive function, as well as appropriate ways to analyse and interpret observed behavioural data are suggested. It is proposed that experimental tasks should be devised which emphasize typical rather than optimal performance, and that analyses should quantify path-dependent fluctuations in performance levels rather than averaged behaviour. Some implications for experimental neuropsychology are illustrated for the case of planning and problem-solving abilities and with particular reference to cognitive impairment in closed-head injury.

The path of voices in our brain

Categorising voices is crucial for auditory-based social interactions. This Primer explores a PLOS Biiology study that capitalises on human intracranial recordings to describe the spatiotemporal pattern of neural activity leading to voice-selective responses in associative auditory cortex.

Modes of cognition: Evidence from metastable brain dynamics

Managing cognitive load depends on adequate resource allocation by the human brain through the engagement of metastable substates, which are large-scale functional networks that change over time. We employed a novel analysis method, deep autoencoder dynamical analysis (DADA), with 100 healthy adults selected from the Human Connectome Project (HCP) data set in rest and six cognitive tasks. The deep autoencoder of DADA described seven recurrent stochastic metastable substates from the functional connectome of BOLD phase coherence matrices. These substates were significantly differentiated in terms of their probability of appearance, time duration, and spatial attributes. We found that during different cognitive tasks, there was a higher probability of having more connected substates dominated by a high degree of connectivity in the thalamus. In addition, compared with those during tasks, resting brain dynamics have a lower level of predictability, indicating a more uniform distribution of metastability between substates, quantified by higher entropy. These novel findings provide empirical evidence for the philosophically motivated cognitive theory, suggesting on-line and off-line as two fundamentally distinct modes of cognition. On-line cognition refers to task-dependent engagement with the sensory input, while off-line cognition is a slower, environmentally detached mode engaged with decision and planning. Overall, the DADA framework provides a bridge between neuroscience and cognitive theory that can be further explored in the future.

Linking Brain Structure, Activity, and Cognitive Function through Computation

Understanding the human brain is a "Grand Challenge" for 21st century research. Computational approaches enable large and complex datasets to be addressed efficiently, supported by artificial neural networks, modeling and simulation. Dynamic generative multiscale models, which enable the investigation of causation across scales and are guided by principles and theories of brain function, are instrumental for linking brain structure and function. An example of a resource enabling such an integrated approach to neuroscientific discovery is the BigBrain, which spatially anchors tissue models and data across different scales and ensures that multiscale models are supported by the data, making the bridge to both basic neuroscience and medicine. Research at the intersection of neuroscience, computing and robotics has the potential to advance neuro-inspired technologies by taking advantage of a growing body of insights into perception, plasticity and learning. To render data, tools and methods, theories, basic principles and concepts interoperable, the Human Brain Project (HBP) has launched EBRAINS, a digital neuroscience research infrastructure, which brings together a transdisciplinary community of researchers united by the quest to understand the brain, with fascinating insights and perspectives for societal benefits.

Focal neural perturbations reshape low-dimensional trajectories of brain activity supporting cognitive performance

The emergence of distributed patterns of neural activity supporting brain functions and behavior can be understood by study of the brain's low-dimensional topology. Functional neuroimaging demonstrates that brain activity linked to adaptive behavior is constrained to low-dimensional manifolds. In human participants, we tested whether these low-dimensional constraints preserve working memory performance following local neuronal perturbations. We combined multi-session functional magnetic resonance imaging, non-invasive transcranial magnetic stimulation (TMS), and methods translated from the fields of complex systems and computational biology to assess the functional link between changes in local neural activity and the reshaping of task-related low dimensional trajectories of brain activity. We show that specific reconfigurations of low-dimensional trajectories of brain activity sustain effective working memory performance following TMS manipulation of local activity on, but not off, the space traversed by these trajectories. We highlight an association between the multi-scale changes in brain activity underpinning cognitive function.

The role of PFC networks in cognitive control and executive function

Systems neuroscience approaches with a focus on large-scale brain organization and network analysis are advancing foundational knowledge of how cognitive control processes are implemented in the brain. Over the past decade, technological and computational innovations in the study of brain connectivity have led to advances in our understanding of how brain networks function, inspiring new conceptualizations of the role of prefrontal cortex (PFC) networks in the coordination of cognitive control. In this review, we describe six key PFC networks involved in cognitive control and elucidate key principles relevant for understanding how these networks implement cognitive control. Implementation of cognitive control in a constantly changing environment depends on the dynamic and flexible organization of PFC networks. In this context, we describe major empirical and theoretical models that have emerged in recent years and describe how their functional architecture and dynamic organization supports flexible cognitive control. We take an overarching view of advances made in the past few decades and consider fundamental issues regarding PFC network function, global brain dynamics, and cognition that still need to be resolved. We conclude by clarifying important future directions for research on cognitive control and their implications for advancing our understanding of PFC networks in brain disorders.

Pathologically reduced neural flexibility recovers during psychotherapy of OCD patients

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Psychiatric impairment is associated with decreased neural flexibility.

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Psychotherapy was able to increase the neural flexibility of the patients.

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Psychotherapy should increase adaptivity of cognitive-emotional-behavioral patterns.

Flexibility is a key feature of psychological health, allowing the individual to dynamically adapt to changing environmental demands, which is impaired in many psychiatric disorders like obsessive–compulsive disorder (OCD). Adequately responding to varying demands requires the brain to switch between different patterns of neural activity, which are represented by different brain network configurations (functional connectivity patterns). Here, we operationalize neural flexibility as the dissimilarity between consecutive connectivity matrices of brain regions (jump length). In total, 132 fMRI scans were obtained from 17 patients that were scanned four to five times during inpatient psychotherapy, and from 17 controls that were scanned at comparable time intervals. Significant negative correlations were found between the jump lengths and the symptom severity scores of OCD, depression, anxiety, and stress, suggesting that high symptom severity corresponds to inflexible brain functioning. Further analyses revealed that impaired reconfiguration (pattern stability) of the brain seems to be more related to general psychiatric impairment rather than to specific symptoms, e.g., of OCD or depression. Importantly, the group × time interaction of a repeated measures ANOVA was significant, as well as the post-hoc paired t-tests of the patients (first vs. last scan). The results suggest that psychotherapy is able to significantly increase the neural flexibility of patients. We conclude that psychiatric symptoms like anxiety, stress, depression, and OCD are associated with an impaired adaptivity of the brain. In general, our results add to the growing evidence that dynamic functional connectivity captures meaningful properties of brain functioning.

Mood disorders disrupt the functional dynamics, not spatial organization of brain resting state networks

Spontaneous fluctuations in the blood oxygenation level dependent signal measured through resting-state functional magnetic resonance imaging have been corroborated to aggregate into multiple functional networks. Abnormal resting brain activity is observed in mood disorder patients, however with inconsistent results. How do such alterations relate to clinical symptoms; e.g., level of depression and rumination tendencies? Here we recovered spatially and temporally overlapping functional networks from 31 mood disorder patients and healthy controls during rest, by applying novel methods that identify transient changes in spontaneous brain activity. Our unique approach disentangles the dynamic engagement of resting-state networks unconstrained by the slow hemodynamic response. This time-varying characterization provides moment-to-moment information about functional networks in terms of their durations and dynamic coupling, and offers novel evidence for selective contributionsto particular clinical symptoms. Patients showed increased duration of default-mode network (DMN), increased duration and occurrence of posterior DMN as well as insula- and amygdala-centered networks, but decreased occurrence of visual and anterior salience networks. Coupling between limbic (insula and amygdala) networks was also reduced. Depression level modulated DMN duration, whereas intrusive thoughts correlated with occurrence of insula and posterior DMN. Anatomical network organization was similar to controls. In sum, altered brain dynamics in mood disorder patients appear to mediate distinct clinical dimensions including increased self-processing, and decreased attention to external world.

Continuous attractors for dynamic memories

Episodic memory has a dynamic nature: when we recall past episodes, we retrieve not only their content, but also their temporal structure. The phenomenon of replay, in the hippocampus of mammals, offers a remarkable example of this temporal dynamics. However, most quantitative models of memory treat memories as static configurations, neglecting the temporal unfolding of the retrieval process. Here, we introduce a continuous attractor network model with a memory-dependent asymmetric component in the synaptic connectivity, which spontaneously breaks the equilibrium of the memory configurations and produces dynamic retrieval. The detailed analysis of the model with analytical calculations and numerical simulations shows that it can robustly retrieve multiple dynamical memories, and that this feature is largely independent of the details of its implementation. By calculating the storage capacity, we show that the dynamic component does not impair memory capacity, and can even enhance it in certain regimes.

When we recall a past experience, accessing what is known as an ‘episodic memory’, it usually does not appear as a still image or a snapshot of what occurred. Instead, our memories tend to be dynamic: we remember how a sequence of events unfolded, and when we do this, we often re-experience at least part of that same sequence. If the memory includes physical movement, the sequence combines space and time to remember a trajectory. For example, a mouse might remember how it went down a hole and found cheese there.

However, mathematical models of how past experiences are stored in our brains and retrieved when we remember them have so far focused on snapshot memories. ‘Attractor network models’ are one type of mathematical model that neuroscientists use to represent how neurons communicate with each other to store memories. These models can provide insights into how circuits of neurons, for example those in the hippocampus (a part of the brain crucial for memory), may have evolved to remember the past, but so far they have only focused on how single moments, rather than sequences of events, are represented by populations of neurons.

Spalla et al. found a way to extend these models, so they could analyse how networks of neurons can store and retrieve dynamic memories. These memories are represented in the brain as ‘continuous attractors’, which can be thought of as arrows that attract mental trajectories first to the arrow itself, and once on the arrow, to the arrowhead. Each recalled event elicits the next one on the arrow, as the mental trajectory advances towards the arrowhead. Spalla et al. determined that memory networks in the hippocampus of mammals can store large numbers of these ‘arrows’, up to the same amount of ‘snapshot’ memories predicted to be stored with similar models.

Spalla et al.’s results may allow researchers to better understand memory storage and recall, since they allow for the modelling of complex and realistic aspects of episodic memories. This could provide insights into processes such as why our minds wander, as well as having implications for the study of how neurons physically interact with each other to transmit information.

Principles and open questions in functional brain network reconstruction

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network representation involves often covert theoretical assumptions and methodological choices which affect the way networks are reconstructed from experimental data, and ultimately the resulting network properties and their interpretation. Here, we review some fundamental conceptual underpinnings and technical issues associated with brain network reconstruction, and discuss how their mutual influence concurs in clarifying the organization of brain function.

The Haken-Kelso-Bunz (HKB) model: from matter to movement to mind

This article presents a brief retrospective on the Haken-Kelso-Bunz (HKB) model of certain dynamical properties of human movement. Though unanticipated, HKB introduced, and demonstrated the power of, a new vocabulary for understanding behavior, cognition and the brain, revealed through a visually compelling mathematical picture that accommodated highly reproducible experimental facts and predicted new ones. HKB stands as a harbinger of paradigm change in several scientific fields, the effects of which are still being felt. In particular, HKB constitutes the foundation of a mechanistic science of coordination called Coordination Dynamics that extends from matter to movement to mind, and beyond.

Virtual Connectomic Datasets in Alzheimer's Disease and Aging Using Whole-Brain Network Dynamics Modelling

Large neuroimaging datasets, including information about structural connectivity (SC) and functional connectivity (FC), play an increasingly important role in clinical research, where they guide the design of algorithms for automated stratification, diagnosis or prediction. A major obstacle is, however, the problem of missing features [e.g., lack of concurrent DTI SC and resting-state functional magnetic resonance imaging (rsfMRI) FC measurements for many of the subjects]. We propose here to address the missing connectivity features problem by introducing strategies based on computational whole-brain network modeling. Using two datasets, the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset and a healthy aging dataset, for proof-of-concept, we demonstrate the feasibility of virtual data completion (i.e., inferring “virtual FC” from empirical SC or “virtual SC” from empirical FC), by using self-consistent simulations of linear and nonlinear brain network models. Furthermore, by performing machine learning classification (to separate age classes or control from patient subjects), we show that algorithms trained on virtual connectomes achieve discrimination performance comparable to when trained on actual empirical data; similarly, algorithms trained on virtual connectomes can be used to successfully classify novel empirical connectomes. Completion algorithms can be combined and reiterated to generate realistic surrogate connectivity matrices in arbitrarily large number, opening the way to the generation of virtual connectomic datasets with network connectivity information comparable to the one of the original data.

Blankets at birth: Transitional objects: Commentary on "The growth of cognition: Free energy minimization and the embryogenesis of cortical computation" by Wright and Bourke

Birth is accompanied by a complete reset of metabolic flows in the neonate, challenging the brain to fulfill the basic needs of life through action - breathing, feeding, crying. The perinatal period is fundamentally a transitional one, such that the basic conditions for thermodynamic self-regulation are re-established ex utero. Wright and Bourke lay out the core tenants of these conditions [1]; the emergence of regularities in cortical geometry and activity that allow "crisp" states. Before this can occur - in the immediate perinatal phase - electrical recordings of neonatal cortex suggest it passes through a highly critical regime - a phase transition - with disordered statistical fingerprints. The resolution of this state is a necessary condition for the more stable metabolic conditions that support the conjectures of Wright and Bourke.

Brain functional network modeling and analysis based on fMRI: a systematic review

In recent years, the number of patients with neurodegenerative diseases (i.e., Alzheimer's disease, Parkinson's disease, mild cognitive impairment) and mental disorders (i.e., depression, anxiety and schizophrenia) have increased dramatically. Researchers have found that complex network analysis can reveal the topology of brain functional networks, such as small-world, scale-free, etc. In the study of brain diseases, it has been found that these topologies have undergoed abnormal changes in different degrees. Therefore, the research of brain functional networks can not only provide a new perspective for understanding the pathological mechanism of neurological and psychiatric diseases, but also provide assistance for the early diagnosis. Focusing on the study of human brain functional networks, this paper reviews the research results in recent years. First, this paper introduces the background of the study of brain functional networks under complex network theory and the important role of topological properties in the study of brain diseases. Second, the paper describes how to construct a brain functional network using neural image data. Third, the common methods of functional network analysis, including network structure analysis and disease classification, are introduced. Fourth, the role of brain functional networks in pathological study, analysis and diagnosis of brain functional diseases is studied. Finally, the paper summarizes the existing studies of brain functional networks and points out the problems and future research directions.

Atypical core-periphery brain dynamics in autism

The intrinsic function of the human brain is dynamic, giving rise to numerous behavioral subtypes that fluctuate distinctively at multiple timescales. One of the key dynamical processes that takes place in the brain is the interaction between core-periphery brain regions, which undergoes constant fluctuations associated with developmental time frames. Core-periphery dynamical changes associated with macroscale brain network dynamics span multiple timescales and may lead to atypical behavior and clinical symptoms. For example, recent evidence suggests that brain regions with shorter intrinsic timescales are located at the periphery of brain networks (e.g., sensorimotor hand, face areas) and are implicated in perception and movement. On the contrary, brain regions with longer timescales are core hub regions. These hubs are important for regulating interactions between the brain and the body during self-related cognition and emotion. In this review, we summarize a large body of converging evidence derived from time-resolved fMRI studies in autism to characterize atypical core-periphery brain dynamics and how they relate to core and contextual sensory and cognitive profiles.

In silico exploration of mouse brain dynamics by focal stimulation reflects the organization of functional networks and sensory processing

Resting-state functional networks such as the default mode network (DMN) dominate spontaneous brain dynamics. To date, the mechanisms linking brain structure and brain dynamics and functions in cognition, perception, and action remain unknown, mainly due to the uncontrolled and erratic nature of the resting state. Here we used a stimulation paradigm to probe the brain’s resting behavior, providing insights on state-space stability and multiplicity of network trajectories after stimulation. We performed explorations on a mouse model to map spatiotemporal brain dynamics as a function of the stimulation site. We demonstrated the emergence of known functional networks in brain responses. Several responses heavily relied on the DMN and were suggestive of the DMN playing a mechanistic role between functional networks. We probed the simulated brain responses to the stimulation of regions along the information processing chains of sensory systems from periphery up to primary sensory cortices. Moreover, we compared simulated dynamics against in vivo brain responses to optogenetic stimulation. Our results underwrite the importance of anatomical connectivity in the functional organization of brain networks and demonstrate how functionally differentiated information processing chains arise from the same system.

We demonstrate how functionally differentiated information processing chains arise from the same anatomical network. The main result of the in-silico mouse brain simulations is the emergence of specific functional networks based on structural data from the mouse brain. When the brain is stimulated, for example, by sensory inputs or direct electrical stimulation, the brain initially responds with activities in specific regions. The brain’s anatomical connectivity constrains the subsequent pattern formation. We built a high-resolution mouse brain network model. The model structure originated from experimental data. We systematically explored the mouse model and investigated the simulated brain dynamics after stimulation. Known functional networks emerged in the simulated brain responses. The default mode network occurred in almost all characteristic response patterns. Simulated brain response dynamics and in-vivo response dynamics of the mouse brain to optogenetic stimulation showed similarities even without parameter tuning. Anatomical connectivity and dynamics shape the functional organization of brain networks.

Degeneracy and Complexity in Neuro-Behavioral Correlates of Team Coordination

Team coordination-members of a group acting together rather than performing specific actions individually-is essential for success in many real-world tasks such as military missions, sports, workplace, or school interactions. However, team coordination is highly variable, which is one reason why its underlying neural processes are largely unknown. Here we used dual electroencephalography (EEG) in dyads to study the neurobehavioral dynamics of team coordination in an ecologically valid task that places intensive demands on joint performance. We present a novel conceptual framework to interpret neurobehavioral variability in terms of degeneracy, a fundamental property of complex biological systems said to enhance flexibility and robustness. We characterize degeneracy conceptually in terms of a manifold representing the geometric locus of the dynamics in the high dimensional state-space of neurobehavioral signals. The geometry and dimensionality of the manifold are determined by task constraints and team coordination requirements which restrict the manifold to trajectories that are conducive to successful task performance. Our results indicate that team coordination is associated with dimensionality reduction of the manifold as evident in increased inter-brain phase coherence of beta and gamma rhythms during critical phases of task performance where subjects exchange information. Team coordination was also found to affect the shape of the manifold manifested as a symmetry breaking of centro-parietal wavelet power patterns across subjects in trials with high team coordination. These results open a conceptual and empirical path to identifying the mechanisms underlying team performance in complex tasks.

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.

Modular slowing of resting-state dynamic functional connectivity as a marker of cognitive dysfunction induced by sleep deprivation

Dynamic Functional Connectivity (dFC) in the resting state (rs) is considered as a correlate of cognitive processing. Describing dFC as a flow across morphing connectivity configurations, our notion of dFC speed quantifies the rate at which FC networks evolve in time. Here we probe the hypothesis that variations of rs dFC speed and cognitive performance are selectively interrelated within specific functional subnetworks. In particular, we focus on Sleep Deprivation (SD) as a reversible model of cognitive dysfunction. We found that whole-brain level (global) dFC speed significantly slows down after 24h of SD. However, the reduction in global dFC speed does not correlate with variations of cognitive performance in individual tasks, which are subtle and highly heterogeneous. On the contrary, we found strong correlations between performance variations in individual tasks -including Rapid Visual Processing (RVP, assessing sustained visual attention)- and dFC speed quantified at the level of functional sub-networks of interest. Providing a compromise between classic static FC (no time) and global dFC (no space), modular dFC speed analyses allow quantifying a different speed of dFC reconfiguration independently for sub-networks overseeing different tasks. Importantly, we found that RVP performance robustly correlates with the modular dFC speed of a characteristic frontoparietal module.

Dynamic Functional Connectivity between order and randomness and its evolution across the human adult lifespan

Functional Connectivity (FC) during resting-state or task conditions is not static but inherently dynamic. Yet, there is no consensus on whether fluctuations in FC may resemble isolated transitions between discrete FC states rather than continuous changes. This quarrel hampers advancing the study of dynamic FC. This is unfortunate as the structure of fluctuations in FC can certainly provide more information about developmental changes, aging, and progression of pathologies. We merge the two perspectives and consider dynamic FC as an ongoing network reconfiguration, including a stochastic exploration of the space of possible steady FC states. The statistical properties of this random walk deviate both from a purely "order-driven" dynamics, in which the mean FC is preserved, and from a purely "randomness-driven" scenario, in which fluctuations of FC remain uncorrelated over time. Instead, dynamic FC has a complex structure endowed with long-range sequential correlations that give rise to transient slowing and acceleration epochs in the continuous flow of reconfiguration. Our analysis for fMRI data in healthy elderly revealed that dynamic FC tends to slow down and becomes less complex as well as more random with increasing age. These effects appear to be strongly associated with age-related changes in behavioural and cognitive performance.

Dimensional reduction of emergent spatiotemporal cortical dynamics via a maximum entropy moment closure

Modern electrophysiological recordings and optical imaging techniques have revealed a diverse spectrum of spatiotemporal neural activities underlying fundamental cognitive processing. Oscillations, traveling waves and other complex population dynamical patterns are often concomitant with sensory processing, information transfer, decision making and memory consolidation. While neural population models such as neural mass, population density and kinetic theoretical models have been used to capture a wide range of the experimentally observed dynamics, a full account of how the multi-scale dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Here we apply a recently developed coarse-graining framework for reduced-dimensional descriptions of neuronal networks to model visual cortical dynamics. We show that, without introducing any new parameters, how a sequence of models culminating in an augmented system of spatially-coupled ODEs can effectively model a wide range of the observed cortical dynamics, ranging from visual stimulus orientation dynamics to traveling waves induced by visual illusory stimuli. In addition to an efficient simulation method, this framework also offers an analytic approach to studying large-scale network dynamics. As such, the dimensional reduction naturally leads to mesoscopic variables that capture the interplay between neuronal population stochasticity and network architecture that we believe to underlie many emergent cortical phenomena.

Making Sense of Computational Psychiatry

In psychiatry we often speak of constructing "models." Here we try to make sense of what such a claim might mean, starting with the most fundamental question: "What is (and isn't) a model?" We then discuss, in a concrete measurable sense, what it means for a model to be useful. In so doing, we first identify the added value that a computational model can provide in the context of accuracy and power. We then present limitations of standard statistical methods and provide suggestions for how we can expand the explanatory power of our analyses by reconceptualizing statistical models as dynamical systems. Finally, we address the problem of model building-suggesting ways in which computational psychiatry can escape the potential for cognitive biases imposed by classical hypothesis-driven research, exploiting deep systems-level information contained within neuroimaging data to advance our understanding of psychiatric neuroscience.

Graph-theoretical analysis for energy landscape reveals the organization of state transitions in the resting-state human cerebral cortex

The resting-state brain is often considered a nonlinear dynamic system transitioning among multiple coexisting stable states. Despite the increasing number of studies on the multistability of the brain system, the processes of state transitions have rarely been systematically explored. Thus, we investigated the state transition processes of the human cerebral cortex system at rest by introducing a graph-theoretical analysis of the state transition network. The energy landscape analysis of brain state occurrences, estimated using the pairwise maximum entropy model for resting-state fMRI data, identified multiple local minima, some of which mediate multi-step transitions toward the global minimum. The state transition among local minima is clustered into two groups according to state transition rates and most inter-group state transitions were mediated by a hub transition state. The distance to the hub transition state determined the path length of the inter-group transition. The cortical system appeared to have redundancy in inter-group transitions when the hub transition state was removed. Such a hub-like organization of transition processes disappeared when the connectivity of the cortical system was altered from the resting-state configuration. In the state transition, the default mode network acts as a transition hub, while coactivation of the prefrontal cortex and default mode network is captured as the global minimum. In summary, the resting-state cerebral cortex has a well-organized architecture of state transitions among stable states, when evaluated by a graph-theoretical analysis of the nonlinear state transition network of the brain.

The hidden repertoire of brain dynamics and dysfunction

The purpose of this paper is to describe a framework for the understanding of rules that govern how neural system dynamics are coordinated to produce behavior. The framework, structured flows on manifolds (SFM), posits that neural processes are flows depicting system interactions that occur on relatively low-dimension manifolds, which constrain possible functional configurations. Although this is a general framework, we focus on the application to brain disorders. We first explain the Epileptor, a phenomenological computational model showing fast and slow dynamics, but also a hidden repertoire whose expression is similar to refractory status epilepticus. We suggest that epilepsy represents an innate brain state whose potential may be realized only under certain circumstances. Conversely, deficits from damage or disease processes, such as stroke or dementia, may reflect both the disease process per se and the adaptation of the brain. SFM uniquely captures both scenarios. Finally, we link neuromodulation effects and switches in functional network configurations to fast and slow dynamics that coordinate the expression of SFM in the context of cognition. The tools to measure and model SFM already exist, giving researchers access to the dynamics of neural processes that support the concomitant dynamics of the cognitive and behavioral processes.

Next Generation Networks: Featuring the Potential Role of Emerging Applications in Translational Oncology

Nowadays, networks are pervasively used as examples of models suitable to mathematically represent and visualize the complexity of systems associated with many diseases, including cancer. In the cancer context, the concept of network entropy has guided many studies focused on comparing equilibrium to disequilibrium (i.e., perturbed) conditions. Since these conditions reflect both structural and dynamic properties of network interaction maps, the derived topological characterizations offer precious support to conduct cancer inference. Recent innovative directions have emerged in network medicine addressing especially experimental omics approaches integrated with a variety of other data, from molecular to clinical and also electronic records, bioimaging etc. This work considers a few theoretically relevant concepts likely to impact the future of applications in personalized/precision/translational oncology. The focus goes to specific properties of networks that are still not commonly utilized or studied in the oncological domain, and they are: controllability, synchronization and symmetry. The examples here provided take inspiration from the consideration of metastatic processes, especially their progression through stages and their hallmark characteristics. Casting these processes into computational frameworks and identifying network states with specific modular configurations may be extremely useful to interpret or even understand dysregulation patterns underlying cancer, and associated events (onset, progression) and disease phenotypes.

Neurofeedback: Principles, appraisal, and outstanding issues

Neurofeedback is a form of brain training in which subjects are fed back information about some measure of their brain activity which they are instructed to modify in a way thought to be functionally advantageous. Over the last 20 years, neurofeedback has been used to treat various neurological and psychiatric conditions, and to improve cognitive function in various contexts. However, in spite of a growing popularity, neurofeedback protocols typically make (often covert) assumptions on what aspects of brain activity to target, where in the brain to act and how, which have far-reaching implications for the assessment of its potential and efficacy. Here we critically examine some conceptual and methodological issues associated with the way neurofeedback's general objectives and neural targets are defined. The neural mechanisms through which neurofeedback may act at various spatial and temporal scales, and the way its efficacy is appraised are reviewed, and the extent to which neurofeedback may be used to control functional brain activity discussed. Finally, it is proposed that gauging neurofeedback's potential, as well as assessing and improving its efficacy will require better understanding of various fundamental aspects of brain dynamics and a more precise definition of functional brain activity and brain-behaviour relationships.

Human cognition involves the dynamic integration of neural activity and neuromodulatory systems

The human brain integrates diverse cognitive processes into a coherent whole, shifting fluidly as a function of changing environmental demands. Despite recent progress, the neurobiological mechanisms responsible for this dynamic system-level integration remain poorly understood. Here we investigated the spatial, dynamic, and molecular signatures of system-wide neural activity across a range of cognitive tasks. We found that neuronal activity converged onto a low-dimensional manifold that facilitates the execution of diverse task states. Flow within this attractor space was associated with dissociable cognitive functions, unique patterns of network-level topology, and individual differences in fluid intelligence. The axes of the low-dimensional neurocognitive architecture aligned with regional differences in the density of neuromodulatory receptors, which in turn relate to distinct signatures of network controllability estimated from the structural connectome. These results advance our understanding of functional brain organization by emphasizing the interface between neural activity, neuromodulatory systems, and cognitive function.

The multidimensional brain

Brain activity takes place in three spatial-plus time dimensions. This rather obvious claim has been recently questioned by papers that, taking into account the big data outburst and novel available computational tools, are starting to unveil a more intricate state of affairs. Indeed, various brain activities and their correlated mental functions can be assessed in terms of trajectories embedded in phase spaces of dimensions higher than the canonical ones. In this review, I show how further dimensions may not just represent a convenient methodological tool that allows a better mathematical treatment of otherwise elusive cortical activities, but may also reflect genuine functional or anatomical relationships among real nervous functions. I then describe how to extract hidden multidimensional information from real or artificial neurodata series, and make clear how our mind dilutes, rather than concentrates as currently believed, inputs coming from the environment. Finally, I argue that the principle "the higher the dimension, the greater the information" may explain the occurrence of mental activities and elucidate the mechanisms of human diseases associated with dimensionality reduction.

Resting state dynamics meets anatomical structure: Temporal multiple kernel learning (tMKL) model

Over the last decade there has been growing interest in understanding the brain activity, in the absence of any task or stimulus, captured by the resting-state functional magnetic resonance imaging (rsfMRI). The resting state patterns have been observed to be exhibiting complex spatio-temporal dynamics and substantial effort has been made to characterize the dynamic functional connectivity (dFC) configurations. However, the dynamics governing the state transitions that the brain undergoes and their relationship to stationary functional connectivity still remains an open problem. One class of approaches attempts to characterize the dynamics in terms of finite number of latent brain states, however, such attempts are yet to amalgamate the underlying anatomical structural connectivity (SC) with the dynamics. Another class of methods links individual dynamic FCs with the underlying SC but does not characterize the temporal evolution of FC. Further, the latent states discovered by previous approaches could not be directly linked to the SC, thereby motivating us to discover the underlying lower-dimensional manifold that represents the temporal structure. In the proposed approach, the discovered manifold is further parameterized as a set of local density distributions, or latent transient states. We propose an innovative method that learns parameters specific to the latent states using a graph-theoretic model (temporal Multiple Kernel Learning, tMKL) that inherently links dynamics to the structure and finally predicts the grand average FC of the test subjects by leveraging a state transition Markov model. The proposed solution does not make strong assumptions about the underlying data and is generally applicable to resting or task data for learning subject-specific state transitions and for successfully characterizing SC-dFC-FC relationship through a unifying framework. Training and testing were done using the rs-fMRI data of 46 healthy participants. tMKL model performs significantly better than the existing models for predicting resting state functional connectivity based on whole-brain dynamic mean-field model (DMF), single diffusion kernel (SDK) model and multiple kernel learning (MKL) model. Further, the learned model was tested on an independent cohort of 100 young, healthy participants from the Human Connectome Project (HCP) and the results establish the generalizability of the proposed solution. More importantly, the model retains sensitivity toward subject-specific anatomy, a unique contribution towards a holistic approach for SC-FC characterization.