The physics of brain network structure, function and control

Abstract

The brain is a complex organ characterized by heterogeneous patterns of structural connections supporting unparalleled feats of cognition and a wide range of behaviors. New noninvasive imaging techniques now allow these patterns to be carefully and comprehensively mapped in individual humans and animals. Yet, it remains a fundamental challenge to understand how the brain's structural wiring supports cognitive processes, with major implications for the personalized treatment of mental health disorders. Here, we review recent efforts to meet this challenge that draw on intuitions, models, and theories from physics, spanning the domains of statistical mechanics, information theory, and dynamical systems and control. We begin by considering the organizing principles of brain network architecture instantiated in structural wiring under constraints of symmetry, spatial embedding, and energy minimization. We next consider models of brain network function that stipulate how neural activity propagates along these structural connections, producing the long-range interactions and collective dynamics that support a rich repertoire of system functions. Finally, we consider perturbative experiments and models for brain network control, which leverage the physics of signal transmission along structural wires to infer intrinsic control processes that support goal-directed behavior and to inform stimulation-based therapies for neurological disease and psychiatric disorders. Throughout, we highlight several open questions in the physics of brain network structure, function, and control that will require creative efforts from physicists willing to brave the complexities of living matter. resents 36 , whether it be a brain, a granular material 306 , or a quantum lattice 307 . By far the simplest network model is represented by a binary undirected graph in which identical nodes represent system components and identical edges indicate relations or connections between pairs of nodes (see the figure). Such a network can be encoded in an adjacency matrix A, where each element A ij indicates the strength of connectivity between nodes i and j. When all edge strengths are unity, the network is said to be binary. When edges have a range of weights, the network represented by the adjacency matrix is said to be weighted. When A = A , the network is undirected; otherwise, the network is directed.One can extend this simple encoding to study multilayer, multislice, and multiplex networks 308 ; dynamic or temporal networks 127, 309 ; annotated networks 310 ; hypergraphs 311 ; and simplicial complexes 230 . One can also calculate various statistics to quantify the architecture of a network and to infer the function thereof (see figure). Intuitively, these statistics range from measures of the local structure in the network, which depend solely on the links directly emanating from a given node (e.g., degree and clustering), to measures of the network's global structure, which depend on the complex pattern of interconnections between all nodes (e.g.,...

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