Energy Cost Analysis for Optimally Controlling Structural Brain Networks

In this paper, we investigate the problem of energy cost in controlling brain networks, in which the difficulty of achieving brain state transitions is quantified from the perspective of energy cost. Among them, we utilize the controllability Gramian matrix, an energy related controllability metric. We estimate a new upper bound on the minimum eigenvalue of the controllability Gramian matrix to obtain the relationship between the control energy and the number of control nodes. Simulation examples of brain networks verify the validity of the results. The results can provide a useful tool to characterize the energy cost of controlling brain networks and make predictions about the energy required to complete different control tasks of brain networks, thus providing potential theoretical support for regulatory interventions in many brain diseases, such as Schizophrenia, Parkinsons Disease, Alzheimer's Disease (AD), and so on.