Role of Graph Architecture in Controlling Dynamical Networks with Applications to Neural Systems

A topology-dynamics-based control strategy for multi-dimensional complex networked dynamical systems

Complex systems are omnipresent and play a vital role in in our every-day lives. Adverse behavior of such systems has generated considerable interest in being able to control complex systems modeled as networks. Here, we propose a topology-dynamics-based approach for controlling complex systems modeled as networks of coupled multi-dimensional dynamical entities. For given dynamics and topology, we introduce an efficient scheme to identify in polynomial time a finite set of driver nodes, which – when endowed with the control function – steer the network to the desired behavior. We demonstrate the high suitability of our approach by controlling various networked multi-dimensional dynamics, coupled onto different topologies.

White Matter Network Architecture Guides Direct Electrical Stimulation through Optimal State Transitions

Optimizing direct electrical stimulation for the treatment of neurological disease remains difficult due to an incomplete understanding of its physical propagation through brain tissue. Here, we use network control theory to predict how stimulation spreads through white matter to influence spatially distributed dynamics. We test the theory's predictions using a unique dataset comprising diffusion weighted imaging and electrocorticography in epilepsy patients undergoing grid stimulation. We find statistically significant shared variance between the predicted activity state transitions and the observed activity state transitions. We then use an optimal control framework to posit testable hypotheses regarding which brain states and structural properties will efficiently improve memory encoding when stimulated. Our work quantifies the role that white matter architecture plays in guiding the dynamics of direct electrical stimulation and offers empirical support for the utility of network control theory in explaining the brain's response to stimulation.

Functional control of electrophysiological network architecture using direct neurostimulation in humans

Chronically implantable neurostimulation devices are becoming a clinically viable option for treating patients with neurological disease and psychiatric disorders. Neurostimulation offers the ability to probe and manipulate distributed networks of interacting brain areas in dysfunctional circuits. Here, we use tools from network control theory to examine the dynamic reconfiguration of functionally interacting neuronal ensembles during targeted neurostimulation of cortical and subcortical brain structures. By integrating multimodal intracranial recordings and diffusion-weighted imaging from patients with drug-resistant epilepsy, we test hypothesized structural and functional rules that predict altered patterns of synchronized local field potentials. We demonstrate the ability to predictably reconfigure functional interactions depending on stimulation strength and location. Stimulation of areas with structurally weak connections largely modulates the functional hubness of downstream areas and concurrently propels the brain towards more difficult-to-reach dynamical states. By using focal perturbations to bridge large-scale structure, function, and markers of behavior, our findings suggest that stimulation may be tuned to influence different scales of network interactions driving cognition.

Brain stimulation devices capable of perturbing the physiological state of neural systems are rapidly gaining popularity for their potential to treat neurological and psychiatric disease. A root problem is that underlying dysfunction spans a large-scale network of brain regions, requiring the ability to control the complex interactions between multiple brain areas. Here, we use tools from network control theory to examine the dynamic reconfiguration of functionally interacting neuronal ensembles during targeted neurostimulation of cortical and subcortical brain structures. We demonstrate the ability to predictably reconfigure patterns of interactions between functional brain areas by modulating the strength and location of stimulation. Our findings have high significance for designing stimulation protocols capable of modulating distributed neural circuits in the human brain.

Topology Effects on Sparse Control of Complex Networks with Laplacian Dynamics

Ease of control of complex networks has been assessed extensively in terms of structural controllability and observability, and minimum control energy criteria. Here we adopt a sparsity-promoting feedback control framework for undirected networks with Laplacian dynamics and distinct topological features. The control objective considered is to minimize the effect of disturbance signals, magnitude of control signals and cost of feedback channels. We show that depending on the cost of feedback channels, different complex network structures become the least expensive option to control. Specifically, increased cost of feedback channels favors organized topological complexity such as modularity and centralization. Thus, although sparse and heterogeneous undirected networks may require larger numbers of actuators and sensors for structural controllability, networks with Laplacian dynamics are shown to be easier to control when accounting for the cost of feedback channels.

RE: Warnings and caveats in brain controllability

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.

Sex differences in network controllability as a predictor of executive function in youth

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.

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.

Network neuroscience for optimizing brain-computer interfaces

Human-machine interactions are being increasingly explored to create alternative ways of communication and to improve our daily life. Based on a classification of the user's intention from the user's underlying neural activity, brain-computer interfaces (BCIs) allow direct interactions with the external environment while bypassing the traditional effector of the musculoskeletal system. Despite the enormous potential of BCIs, there are still a number of challenges that limit their societal impact, ranging from the correct decoding of a human's thoughts, to the application of effective learning strategies. Despite several important engineering advances, the basic neuroscience behind these challenges remains poorly explored. Indeed, BCIs involve complex dynamic changes related to neural plasticity at a diverse range of spatiotemporal scales. One promising antidote to this complexity lies in network science, which provides a natural language in which to model the organizational principles of brain architecture and function as manifest in its interconnectivity. Here, we briefly review the main limitations currently affecting BCIs, and we offer our perspective on how they can be addressed by means of network theoretic approaches. We posit that the emerging field of network neuroscience will prove to be an effective tool to unlock human-machine interactions.

Clarifying cognitive control and the controllable connectome

Cognitive control researchers aim to describe the processes that support adaptive cognition to achieve specific goals. Control theorists consider how to influence the state of systems to reach certain user-defined goals. In brain networks, some conceptual and lexical similarities between cognitive control and control theory offer appealing avenues for scientific discovery. However, these opportunities also come with the risk of conceptual confusion. Here, I suggest that each field of inquiry continues to produce novel and distinct insights. Then, I describe opportunities for synergistic research at the intersection of these subdisciplines with a critical stance that reduces the risk of conceptual confusion. Through this exercise, we can observe that both cognitive neuroscience and systems engineering have much to contribute to cognitive control research in human brain networks. This article is categorized under: Neuroscience > Cognition Computer Science > Neural Networks Neuroscience > Clinical Neuroscience.

On the nature and use of models in network neuroscience

Network theory provides an intuitively appealing framework for studying relationships among interconnected brain mechanisms and their relevance to behaviour. As the space of its applications grows, so does the diversity of meanings of the term network model. This diversity can cause confusion, complicate efforts to assess model validity and efficacy, and hamper interdisciplinary collaboration. In this Review, we examine the field of network neuroscience, focusing on organizing principles that can help overcome these challenges. First, we describe the fundamental goals in constructing network models. Second, we review the most common forms of network models, which can be described parsimoniously along the following three primary dimensions: from data representations to first-principles theory; from biophysical realism to functional phenomenology; and from elementary descriptions to coarse-grained approximations. Third, we draw on biology, philosophy and other disciplines to establish validation principles for these models. We close with a discussion of opportunities to bridge model types and point to exciting frontiers for future pursuits.

Understanding the Emergence of Neuropsychiatric Disorders With Network Neuroscience

Major neuropsychiatric disorders such as psychosis are increasingly acknowledged to be disorders of brain connectivity. Yet tools to map, model, predict, and change connectivity are difficult to develop, largely because of the complex, dynamic, and multivariate nature of interactions between brain regions. Network neuroscience (NN) provides a theoretical framework and mathematical toolset to address these difficulties. Building on areas of mathematics such as graph theory, NN in its simplest form summarizes neuroimaging data by treating brain regions as nodes in a graph and by treating interactions or connections between nodes as edges in the graph. Network metrics can then be used to quantitatively describe the architecture of the graph, which in turn reflects the network's function. We review evidence supporting the utility of NN in understanding psychiatric disorders, with a focus on normative brain network development and abnormalities associated with psychosis. We also emphasize relevant methodological challenges, such as motion artifact correction, which are particularly important to consider when applying network tools to developmental neuroimaging data. We close with a discussion of several emerging frontiers of NN in psychiatry, including generative network modeling and network control theory. We aim to offer an accessible introduction to this emerging field and motivate further work that uses NN to better understand the normative development of brain networks and alterations in that development that accompany or foreshadow psychiatric disease.

Warnings and caveats in brain controllability

A recent article by Gu et al. (Nat. Commun. 6, 2015) proposed to characterize brain networks, quantified using anatomical diffusion imaging, in terms of their "controllability", drawing on concepts and methods of control theory. They reported that brain activity is controllable from a single node, and that the topology of brain networks provides an explanation for the types of control roles that different regions play in the brain. In this work, we first briefly review the framework of control theory applied to complex networks. We then show contrasting results on brain controllability through the analysis of five different datasets and numerical simulations. We find that brain networks are not controllable (in a statistical significant way) by one single region. Additionally, we show that random null models, with no biological resemblance to brain network architecture, produce the same type of relationship observed by Gu et al. between the average/modal controllability and weighted degree. Finally, we find that resting state networks defined with fMRI cannot be attributed specific control roles. In summary, our study highlights some warning and caveats in the brain controllability framework.

Network Approaches to Understand Individual Differences in Brain Connectivity: Opportunities for Personality Neuroscience

Over the past decade, advances in the interdisciplinary field of network science have provided a framework for understanding the intrinsic structure and function of human brain networks. A particularly fruitful area of this work has focused on patterns of functional connectivity derived from non-invasive neuroimaging techniques such as functional magnetic resonance imaging (fMRI). An important subset of these efforts has bridged the computational approaches of network science with the rich empirical data and biological hypotheses of neuroscience, and this research has begun to identify features of brain networks that explain individual differences in social, emotional, and cognitive functioning. The most common approach estimates connections assuming a single configuration of edges that is stable across the experimental session. In the literature, this is referred to as a static network approach, and researchers measure static brain networks while a subject is either at rest or performing a cognitively demanding task. Research on social and emotional functioning has primarily focused on linking static brain networks with individual differences, but recent advances have extended this work to examine temporal fluctuations in dynamic brain networks. Mounting evidence suggests that both the strength and flexibility of time-evolving brain networks influence individual differences in executive function, attention, working memory, and learning. In this review, we first examine the current evidence for brain networks involved in cognitive functioning. Then we review some preliminary evidence linking static network properties to individual differences in social and emotional functioning. We then discuss the applicability of emerging dynamic network methods for examining individual differences in social and emotional functioning. We close with an outline of important frontiers at the intersection between network science and neuroscience that will enhance our understanding of the neurobiological underpinnings of social behavior.

Fronto-limbic dysconnectivity leads to impaired brain network controllability in young people with bipolar disorder and those at high genetic risk

Recent investigations have used diffusion-weighted imaging to reveal disturbances in the neurocircuitry that underlie cognitive-emotional control in bipolar disorder (BD) and in unaffected siblings or children at high genetic risk (HR). It has been difficult to quantify the mechanism by which structural changes disrupt the superimposed brain dynamics, leading to the emotional lability that is characteristic of BD. Average controllability is a concept from network control theory that extends structural connectivity data to estimate the manner in which local neuronal fluctuations spread from a node or subnetwork to alter the state of the rest of the brain. We used this theory to ask whether structural connectivity deficits previously observed in HR individuals (n = 84, mean age 22.4), patients with BD (n = 38, mean age 23.9), and age- and gender-matched controls (n = 96, mean age 22.6) translate to differences in the ability of brain systems to be manipulated between states. Localized impairments in network controllability were seen in the left parahippocampal, left middle occipital, left superior frontal, right inferior frontal, and right precentral gyri in BD and HR groups. Subjects with BD had distributed deficits in a subnetwork containing the left superior and inferior frontal gyri, postcentral gyrus, and insula (p = 0.004). HR participants had controllability deficits in a right-lateralized subnetwork involving connections between the dorsomedial and ventrolateral prefrontal cortex, the superior temporal pole, putamen, and caudate nucleus (p = 0.008). Between-group controllability differences were attenuated after removal of topological factors by network randomization. Some previously reported differences in network connectivity were not associated with controllability-differences, likely reflecting the contribution of more complex brain network properties. These analyses highlight the potential functional consequences of altered brain networks in BD, and may guide future clinical interventions.

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Control theory estimates how neuronal fluctuations spread from local networks.

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We compare brain controllability in bipolar disorder and their high-risk relatives.

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These groups have impaired controllability in networks supporting cognitive and emotional control.

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Weaker connectivity as well as topological alterations contribute to these changes.