A Framework to Control Functional Connectivity in the Human Brain

In this paper, we propose a framework to control brain-wide functional connectivity by selectively acting on the brain's structure and parameters. Functional connectivity, which measures the degree of correlation between neural activities in different brain regions, can be used to distinguish between healthy and certain diseased brain dynamics and, possibly, as a control parameter to restore healthy functions. In this work, we use a collection of interconnected Kuramoto oscillators to model oscillatory neural activity, and show that functional connectivity is essentially regulated by the degree of synchronization between different clusters of oscillators. Then, we propose a minimally invasive method to correct the oscillators' interconnections and frequencies to enforce arbitrary and stable synchronization patterns among the oscillators and, consequently, a desired pattern of functional connectivity. Additionally, we show that our synchronization-based framework is robust to parameter mismatches and numerical inaccuracies, and validate it using a realistic neurovascular model to simulate neural activity and functional connectivity in the human brain.Comment: To appear in the proceedings of the 58th IEEE Conference on Decision and Contro

SENSORI DI VISIONE LINEARI E RELATIVO UTILIZZO NEL CONTROLLO DI UNA SMART CAR

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Stability Conditions for Cluster Synchronization in Networks of Heterogeneous Kuramoto Oscillators

In this paper we study cluster synchronization in networks of oscillators with heterogenous Kuramoto dynamics, where multiple groups of oscillators with identical phases coexist in a connected network. Cluster synchronization is at the basis of several biological and technological processes; yet the underlying mechanisms to enable cluster synchronization of Kuramoto oscillators have remained elusive. In this paper we derive quantitative conditions on the network weights, cluster configuration, and oscillators' natural frequency that ensure asymptotic stability of the cluster synchronization manifold; that is, the ability to recover the desired cluster synchronization configuration following a perturbation of the oscillators' states. Qualitatively, our results show that cluster synchronization is stable when the intra-cluster coupling is sufficiently stronger than the inter-cluster coupling, the natural frequencies of the oscillators in distinct clusters are sufficiently different, or, in the case of two clusters, when the intra-cluster dynamics is homogeneous. We illustrate and validate the effectiveness of our theoretical results via numerical studies.Comment: To apper in IEEE Transactions on Control of Network System

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

Electrical brain stimulation is currently being investigated as a therapy for neurological disease. However, opportunities to optimize such therapies are challenged by the fact that the beneficial impact of focal stimulation on both neighboring and distant regions is not well understood. Here, we use network control theory to build a model of brain network function that makes predictions about how stimulation spreads through the brain's white matter network and influences large-scale dynamics. We test these predictions using combined electrocorticography (ECoG) and diffusion weighted imaging (DWI) data who volunteered to participate in an extensive stimulation regimen. We posit a specific model-based manner in which white matter tracts constrain stimulation, defining its capacity to drive the brain to new states, including states associated with successful memory encoding. In a first validation of our model, we find that the true pattern of white matter tracts can be used to more accurately predict the state transitions induced by direct electrical stimulation than the artificial patterns of null models. We then use a targeted optimal control framework to solve for the optimal energy required to drive the brain to a given state. We show that, intuitively, our model predicts larger energy requirements when starting from states that are farther away from a target memory state. We then suggest testable hypotheses about which structural properties will lead to efficient stimulation for improving memory based on energy requirements. Our work demonstrates that individual white matter architecture plays a vital role in guiding the dynamics of direct electrical stimulation, more generally offering empirical support for the utility of network control theoretic models of brain response to stimulation

Uncovering the Biological Basis of Control Energy: Structural and Metabolic Correlates of Energy Inefficiency in Temporal Lobe Epilepsy

Network control theory is increasingly used to profile the brain\u27s energy landscape via simulations of neural dynamics. This approach estimates the control energy required to simulate the activation of brain circuits based on structural connectome measured using diffusion magnetic resonance imaging, thereby quantifying those circuits\u27 energetic efficiency. The biological basis of control energy, however, remains unknown, hampering its further application. To fill this gap, investigating temporal lobe epilepsy as a lesion model, we show that patients require higher control energy to activate the limbic network than healthy volunteers, especially ipsilateral to the seizure focus. The energetic imbalance between ipsilateral and contralateral temporolimbic regions is tracked by asymmetric patterns of glucose metabolism measured using positron emission tomography, which, in turn, may be selectively explained by asymmetric gray matter loss as evidenced in the hippocampus. Our investigation provides the first theoretical framework unifying gray matter integrity, metabolism, and energetic generation of neural dynamics

A Novel Characterization of Strong Structural Controllability: Sparsity Conditions and Control Paths

La controllabilità di una rete è una proprietà strutturale. Questo vuol dire che tramite semplici e note condizioni sulle interconnessioni della rete è pos- sibile assicurarne la controllabilità da un determinato set di nodi di controllo e per un buon numero di scelte dei pesi degli archi. Nel caso in cui si voglia però garantire la controllabilità della rete per ogni scelta di pesi delle interconnessioni è necessario soddisfare delle condizioni meno note e più stringenti; si parla quindi di strong structural controllability. In questo lavoro vengono fornite condizioni intuitive relative proprio a questo tipo di controllabilità in reti con auto-archi. Oltre ad una bassa complessità di calcolo paragonabile a quella dei risultati esistenti, le condizioni fornite rivelano che sistemi strongly structurally controllable contengono una struttura grafica costituita da percorsi di controllo separati che partono dai nodi controllori e permettono la controllabilità della rete. Infine, note le cardinalitá dei nodi della rete e dei nodi controllori, con questa caratterizzazione è possibile sia enumerare tutte le reti strongly structurally controllable, sia generare reti con le caratteristiche di controllabilità desiderate

Reverse Engineering Synchronization of Brain Network Dynamics: Controllability Properties and Functional Patterns

Reverse engineering the brain holds the promise to overhaul the quality of life of human beings and vastly benefit mankind. Further advances towards this goal will lead to the reversal of cognitive decline, the creation of pioneering neural prostheses, the establishments of novel treatments for neurological disorders, and the development of human augmentation methods. This dissertation presents a cross-disciplinary approach to the study of the structure-function relationship in neural systems. Specifically, we study the brain as a dynamical system that obeys network-wide principles, and address three foundational challenges by using mathematically grounded methods that lie at the intersection of control theory, network science, and neuroscience.First, through the application of control and graph-theoretic paradigms, we investigate how the spatial organization of anatomical brain network components governs and constrains its complex dynamical behaviors. The first chapters are dedicated to the study of structural brain networks – that is, empirically reconstructed large-scale networks that describe the interconnection scheme between different brain regions. We rigorously reveal that brain state transitions can be controlled by a single region, and that structural brain networks possess distinct controllability profiles with respect to random networks of the same size.Second, we address the modeling and analysis of neural activity synchronization across different brain areas – which can be described by functional brain networks. To do so, we juxtapose a bottom-up approach and a top-down approach. In the former, we utilize data-driven dynamical models to reveal that the synchronization of brain network dynamics is resilient to data heterogeneity, thus supporting the utilization of large heterogeneous repositories of brain recordings. In the latter, we abstract rhythmic activity of a neural system as the output of a network of diffusively coupled oscillators, and derive prescriptive conditions for the emergence of cluster synchronization. Such a phenomenon emerges when different groups of synchronized components coexist in a network, and regulates the functional interactions among network components.Third and final, we build upon our previous findings and take aim at the tantalizing idea of controlling the synchronization of brain dynamics through minimally invasive local interventions. We derive a method to optimally intervene on the structural network parameters to achieve desired cluster-synchronized trajectories and, thus, prescribed functional interactions. Additionally, we show that our synchronization-based framework is robust to mismatches in network parameters, and validate it using a realistic neurovascular model to simulate neural activity and functional connectivity in the human brain