(226c) A Closed Loop Control Perspective on the Reconfiguration of Brain Networks

It is well established that the human brain exhibits certain topological features, such as small world and sparsity, that favor stability and efficiency of communication [1, 2]. However, the effect of these features on the control of the brain is not completely understood. Concepts from control theory have been applied to structural brain networks, focusing on controllability and minimum energy control [3, 4]. Although these approaches provide insights on the selection of driver nodes and the transition between different states, they treat the brain as an open loop system.

In this work, we will consider the brain as a closed loop system where the cognitive functions of the brain are the results of feedback control action. In recent research we have developed a novel feedback control formulation which incorporates H infinity sparse controller synthesis and a constraint on the placement of the eigenvalues of the closed loop system (D stability constraints) [5]. We use this problem formulation as a generic framework for characterizing and evaluating efficiency of the cognitive behavior of the brain in terms of both performance in rejecting external disturbances (bound on the H infinity norm) and cost/sparsity of the control architecture.

We apply this framework to the Macaque visual cortex and a human brain network. We show that the structure of the optimal control architecture exhibits a transition which depends on the topological properties on the brain when sparsity is promoted. For slow response, the structure of the feedback gain matrix is similar to the structure of the graph and the control action is concentrated inside the communities. An increase in the speed of response leads to a less sparse feedback gain matrix and higher inter-community interactions. This transition is analogous to the observation that functional brain networks in humans during high cognitive demand seek a trade-off between wiring cost and information carried between nodes [6,7]. These analogies suggest a possible connection between functional brain networks and the closed loop behavior of brain networks under sparse feedback control.

References:

[1 Bullmore, E. and Sporns, O., 2009. Complex brain networks: graph theoretical analysis of structural and functional systems. Nature reviews neuroscience, 10(3), pp.186-198.

[2]. Van den Heuvel, M.P. and Sporns, O., 2013. Network hubs in the human brain. Trends in cognitive sciences, 17(12), pp.683-696.

[3] Gu, S., Pasqualetti, F., Cieslak, M., Telesford, Q.K., Alfred, B.Y., Kahn, A.E., Medaglia, J.D., Vettel, J.M., Miller, M.B., Grafton, S.T. and Bassett, D.S., 2015. Controllability of structural brain networks. Nature communications, 6(1), pp.1-10.

[4]. Betzel, R.F., Gu, S., Medaglia, J.D., Pasqualetti, F. and Bassett, D.S., 2016. Optimally controlling the human connectome: the role of network topology. Scientific reports, 6(1), pp.1-14.

[5]. I. Mitrai, C. Stamoulis, and P. Daoutidis, “A sparse H∞ controller design perspective on the reconfiguration of functional brain networks,” in 2021 Annual American Control Conference (ACC)

[6]. Bullmore, E. and Sporns, O., 2012. The economy of brain network organization. Nature Reviews Neuroscience, 13(5), pp.336-349.

[7]. Kitzbichler, M.G., Henson, R.N., Smith, M.L., Nathan, P.J. and Bullmore, E.T., 2011. Cognitive effort drives workspace configuration of human brain functional networks. Journal of Neuroscience, 31(22), pp.8259-8270.