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Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable complex functions. Yet, understanding, and ultimately harnessing, the structure-function relationship in oscillator networks remains an outstanding challenge of modern science. Here, we address this challenge by presenting a principled method to prescribe exact and robust functional configurations from local network interactions through optimal tuning of the oscillators' parameters. To quantify the behavioral synchrony between coupled oscillators, we introduce the notion of functional pattern, which encodes the pairwise relationships between the oscillators' phases. Our procedure is computationally efficient and provably correct, accounts for constrained interaction types, and allows to concurrently assign multiple desired functional patterns. Further, we derive algebraic and graph-theoretic conditions to guarantee the feasibility and stability of target functional patterns. These conditions provide an interpretable mapping between the structural constraints and their functional implications in oscillator networks. As a proof of concept, we apply the proposed method to replicate empirically recorded functional relationships from cortical oscillations in a human brain, and to redistribute the active power flow in different models of electrical grids., (© 2022. The Author(s).) more...

Dynamical brain state transitions are critical for flexible working memory but the network mechanisms are incompletely understood. Here, we show that working memory performance entails brain-wide switching between activity states using a combination of functional magnetic resonance imaging in healthy controls and individuals with schizophrenia, pharmacological fMRI, genetic analyses and network control theory. The stability of states relates to dopamine D1 receptor gene expression while state transitions are influenced by D2 receptor expression and pharmacological modulation. Individuals with schizophrenia show altered network control properties, including a more diverse energy landscape and decreased stability of working memory representations. Our results demonstrate the relevance of dopamine signaling for the steering of whole-brain network dynamics during working memory and link these processes to schizophrenia pathophysiology. more...

Our ability to manipulate the behavior of complex networks depends on the design of efficient control algorithms and, critically, on the availability of an accurate and tractable model of the network dynamics. While the design of control algorithms for network systems has seen notable advances in the past few years, knowledge of the network dynamics is a ubiquitous assumption that is difficult to satisfy in practice. In this paper we overcome this limitation, and develop a data-driven framework to control a complex network optimally and without any knowledge of the network dynamics. Our optimal controls are constructed using a finite set of data, where the unknown network is stimulated with arbitrary and possibly random inputs. Although our controls are provably correct for networks with linear dynamics, we also characterize their performance against noisy data and in the presence of nonlinear dynamics, as they arise in power grid and brain networks. more...

Opioid addiction is a chronic, relapsing disorder associated with persistent changes in brain plasticity. Reconfiguration of neuronal connectivity may explain heightened abuse liability in individuals with a history of chronic drug exposure. To characterize network-level changes in neuronal activity induced by chronic opiate exposure, we compared FOS expression in mice that are morphine-naïve, morphine-dependent, or have undergone 4 wk of withdrawal from chronic morphine exposure, relative to saline-exposed controls. Pairwise interregional correlations in FOS expression data were used to construct network models that reveal a persistent reduction in connectivity strength following opiate dependence. Further, we demonstrate that basal gene expression patterns are predictive of changes in FOS correlation networks in the morphine-dependent state. Finally, we determine that regions of the hippocampus, striatum, and midbrain are most influential in driving transitions between opiate-naïve and opiate-dependent brain states using a control theoretic approach. This study provides a framework for predicting the influence of specific therapeutic interventions on the state of the opiate-dependent brain., Competing Interests: The authors declare no competing interest., (Copyright © 2020 the Author(s). Published by PNAS.) more...

The human brain is composed of distinct regions that are each associated with particular functions and distinct propensities for the control of neural dynamics. However, the relation between these functions and control profiles is poorly understood, as is the variation in this relation across diverse scales of space and time. Here we probe the relation between control and dynamics in brain networks constructed from diffusion tensor imaging data in a large community sample of young adults. Specifically, we probe the control properties of each brain region and investigate their relationship with dynamics across various spatial scales using the Laplacian eigenspectrum. In addition, through analysis of regional modal controllability and partitioning of modes, we determine whether the associated dynamics are fast or slow, as well as whether they are alternating or monotone. We find that brain regions that facilitate the control of energetically easy transitions are associated with activity on short length scales and slow timescales. Conversely, brain regions that facilitate control of difficult transitions are associated with activity on long length scales and fast timescales. Built on linear dynamical models, our results offer parsimonious explanations for the activity propagation and network control profiles supported by regions of differing neuroanatomical structure. more...

The first description of epileptic seizures due to brain tumours occurred in 19th century. Nevertheless, after over one hundred years, scientific literature is still lacking on how epilepsy and its treatment can affect tumour burden, progression and clinical outcomes. In patients with brain tumours, epilepsy dramatically impacts their quality of life (QoL). Even antiepileptic therapy seems to affect tumor lesion development. Numerous studies suggest that certain actors involved in epileptogenesis (inflammatory changes, glutamate and its ionotropic and metabotropic receptors, GABA-A and its GABA-AR receptor, as well as certain ligand- and voltage-gated ion channel) may also contribute to tumorigenesis. Although some antiepileptic drugs (AEDs) are known operating on such mechanisms underlying epilepsy and tumor development, few preclinical and clinical studies have tried to investigate them as targets of pharmacological tools acting to control both phenomena. The primary aim of this review is to summarize known determinants and pathophysiological mechanisms of seizures, as well as of cell growth and spread, in patients with brain tumors. Therefore, a special focus will be provided on the anticancer effects of commonly prescribed AEDs (including levetiracetam, valproic acid, oxcarbazepine and others), with an overview of both preclinical and clinical data. Potential clinical applications of this finding are discussed., Competing Interests: Declaration of Competing Interest None., (Copyright © 2020 Elsevier Ltd. All rights reserved.) more...

Objective: Predicting how the brain can be driven to specific states by means of internal or external control requires a fundamental understanding of the relationship between neural connectivity and activity. Network control theory is a powerful tool from the physical and engineering sciences that can provide insights regarding that relationship; it formalizes the study of how the dynamics of a complex system can arise from its underlying structure of interconnected units., Approach: Given the recent use of network control theory in neuroscience, it is now timely to offer a practical guide to methodological considerations in the controllability of structural brain networks. Here we provide a systematic overview of the framework, examine the impact of modeling choices on frequently studied control metrics, and suggest potentially useful theoretical extensions. We ground our discussions, numerical demonstrations, and theoretical advances in a dataset of high-resolution diffusion imaging with 730 diffusion directions acquired over approximately 1 h of scanning from ten healthy young adults., Main Results: Following a didactic introduction of the theory, we probe how a selection of modeling choices affects four common statistics: average controllability, modal controllability, minimum control energy, and optimal control energy. Next, we extend the current state-of-the-art in two ways: first, by developing an alternative measure of structural connectivity that accounts for radial propagation of activity through abutting tissue, and second, by defining a complementary metric quantifying the complexity of the energy landscape of a system. We close with specific modeling recommendations and a discussion of methodological constraints., Significance: Our hope is that this accessible account will inspire the neuroimaging community to more fully exploit the potential of network control theory in tackling pressing questions in cognitive, developmental, and clinical neuroscience. more...

Executive function develops during adolescence, yet it remains unknown how structural brain networks mature to facilitate activation of the fronto-parietal system, which is critical for executive function. In a sample of 946 human youths (ages 8-23y) who completed diffusion imaging, we capitalized upon recent advances in linear dynamical network control theory to calculate the energetic cost necessary to activate the fronto-parietal system through the control of multiple brain regions given existing structural network topology. We found that the energy required to activate the fronto-parietal system declined with development, and the pattern of regional energetic cost predicts unseen individuals' brain maturity. Finally, energetic requirements of the cingulate cortex were negatively correlated with executive performance, and partially mediated the development of executive performance with age. Our results reveal a mechanism by which structural networks develop during adolescence to reduce the theoretical energetic costs of transitions to activation states necessary for executive function., Competing Interests: ZC, JS, GB, JK, DR, RB, SG, ZL, CX, XH, RC, DO, TM, KR, CD, FP, RG, RG, DB, TS No competing interests declared, RS has received legal consulting and advisory board income from Genentech/Roche., (© 2020, Cui et al.) more...

The use of network control theory to analyze the organization of white matter fibers in the human brain has the potential to enable mechanistic theories of cognition, and to inform the development of novel diagnostics and treatments for neurological disease and psychiatric disorders (Gu et al., 2015). The recent article (Tu et al., 2018) aims to challenge several of the contributions of (Gu et al., 2015), and particularly the conclusions that brain networks are theoretically controllable from single regions, and that brain networks feature no specific controllability profiles when compared to random network models. Here we provide additional theoretical arguments in support of (Gu et al., 2015) and against the results and methodologies used in (Tu et al., 2018), thus settling that (i) brain networks are controllable from a single region, (ii) brain networks require large control energy, and (iii) brain networks feature distinctive controllability properties with respect to a class of random network models., (Copyright © 2019 Elsevier Inc. All rights reserved.) more...

Executive function is a quintessential human capacity that emerges late in development and displays different developmental trends in males and females. Sex differences in executive function in youth have been linked to vulnerability to psychopathology as well as to behaviors that impinge on health, wellbeing, and longevity. Yet, the neurobiological basis of these differences is not well understood, in part due to the spatiotemporal complexity inherent in patterns of brain network maturation supporting executive function. Here we test the hypothesis that sex differences in impulsivity in youth stem from sex differences in the controllability of structural brain networks as they rewire over development. Combining methods from network neuroscience and network control theory, we characterize the network control properties of structural brain networks estimated from diffusion imaging data acquired in males and females in a sample of 879 youth aged 8-22 years. We summarize the control properties of these networks by estimating average and modal controllability, two statistics that probe the ease with which brain areas can drive the network towards easy versus difficult-to-reach states. We find that females have higher modal controllability in frontal, parietal, and subcortical regions while males have higher average controllability in frontal and subcortical regions. Furthermore, controllability profiles in males are negatively related to the false positive rate on a continuous performance task, a common measure of impulsivity. Finally, we find associations between average controllability and individual differences in activation during an n-back working memory task. Taken together, our findings support the notion that sex differences in the controllability of structural brain networks can partially explain sex differences in executive function. Controllability of structural brain networks also predicts features of task-relevant activation, suggesting the potential for controllability to represent context-specific constraints on network state more generally., (Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.) more...

A critical mystery in neuroscience lies in determining how anatomical structure impacts the complex functional dynamics of the brain. How does large-scale brain circuitry constrain states of neuronal activity and transitions between those states? We address these questions using a maximum entropy model of brain dynamics informed by white matter tractography. We demonstrate that the most probable brain states - characterized by minimal energy - display common activation profiles across brain areas: local spatially-contiguous sets of brain regions reminiscent of cognitive systems are co-activated frequently. The predicted activation rate of these systems is highly correlated with the observed activation rate measured in a separate resting state fMRI data set, validating the utility of the maximum entropy model in describing neurophysiological dynamics. This approach also offers a formal notion of the energy of activity within a system, and the energy of activity shared between systems. We observe that within- and between-system energies cleanly separate cognitive systems into distinct categories, optimized for differential contributions to integrated versus segregated function. These results support the notion that energetic and structural constraints circumscribe brain dynamics, offering insights into the roles that cognitive systems play in driving whole-brain activation patterns. more...

Traditional approaches to understanding the brain's resilience to neuropathology have identified neurophysiological variables, often described as brain or cognitive "reserve," associated with better outcomes. However, mechanisms of function and resilience in large-scale brain networks remain poorly understood. Dynamic network theory may provide a basis for substantive advances in understanding functional resilience in the human brain. In this perspective, we describe recent theoretical approaches from network control theory as a framework for investigating network level mechanisms underlying cognitive function and the dynamics of neuroplasticity in the human brain. We describe the theoretical opportunities offered by the application of network control theory at the level of the human connectome to understand cognitive resilience and inform translational intervention., (Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.) more...

The complexity of neural dynamics stems in part from the complexity of the underlying anatomy. Yet how white matter structure constrains how the brain transitions from one cognitive state to another remains unknown. Here we address this question by drawing on recent advances in network control theory to model the underlying mechanisms of brain state transitions as elicited by the collective control of region sets. We find that previously identified attention and executive control systems are poised to affect a broad array of state transitions that cannot easily be classified by traditional engineering-based notions of control. This theoretical versatility comes with a vulnerability to injury. In patients with mild traumatic brain injury, we observe a loss of specificity in putative control processes, suggesting greater susceptibility to neurophysiological noise. These results offer fundamental insights into the mechanisms driving brain state transitions in healthy cognition and their alteration following injury., (Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.) more...

The ability to modulate brain states using targeted stimulation is increasingly being employed to treat neurological disorders and to enhance human performance. Despite the growing interest in brain stimulation as a form of neuromodulation, much remains unknown about the network-level impact of these focal perturbations. To study the system wide impact of regional stimulation, we employ a data-driven computational model of nonlinear brain dynamics to systematically explore the effects of targeted stimulation. Validating predictions from network control theory, we uncover the relationship between regional controllability and the focal versus global impact of stimulation, and we relate these findings to differences in the underlying network architecture. Finally, by mapping brain regions to cognitive systems, we observe that the default mode system imparts large global change despite being highly constrained by structural connectivity. This work forms an important step towards the development of personalized stimulation protocols for medical treatment or performance enhancement., Competing Interests: The authors have declared that no competing interests exist. more...

Cognitive function is driven by dynamic interactions between large-scale neural circuits or networks, enabling behaviour. However, fundamental principles constraining these dynamic network processes have remained elusive. Here we use tools from control and network theories to offer a mechanistic explanation for how the brain moves between cognitive states drawn from the network organization of white matter microstructure. Our results suggest that densely connected areas, particularly in the default mode system, facilitate the movement of the brain to many easily reachable states. Weakly connected areas, particularly in cognitive control systems, facilitate the movement of the brain to difficult-to-reach states. Areas located on the boundary between network communities, particularly in attentional control systems, facilitate the integration or segregation of diverse cognitive systems. Our results suggest that structural network differences between cognitive circuits dictate their distinct roles in controlling trajectories of brain network function. more...