The impact of input node placement in controllability of brain networks

Network control theory can be used to model how one should steer the brain between different states by driving a specific region with an input. The needed energy to control a network is often used to quantify its controllability, and controlling brain networks requires diverse energy depending on the selected input region. We use the theory of how input node placement affects the longest control chain (LCC) in the controllability of brain networks to study the role of the architecture of white matter fibers in the required control energy. We show that the energy needed to control human brain networks is related to the LCC, i.e., the longest distance between the input region and other regions in the network. We indicate that regions that control brain networks with lower energy have small LCCs. These regions align with areas that can steer the brain around the state space smoothly. By contrast, regions that need higher energy to move the brain toward different target states have larger LCCs. We also investigate the role of the number of paths between regions in the control energy. Our results show that the more paths between regions, the lower cost needed to control brain networks. We evaluate the number of paths by counting specific motifs in brain networks since determining all paths in graphs is a difficult problem.