The impact of input node placement in the controllability of structural brain networks

Network controllability refers to the ability to steer the state of a network towards a target state by driving certain nodes, known as input nodes. This concept can be applied to brain networks for studying brain function and its relation to the structure, which has numerous practical applications. Brain network controllability involves using external signals such as electrical stimulation to drive specific brain regions and navigate the neurophysiological activity level of the brain around the state space. Although controllability is mainly theoretical, the energy required for control is critical in real-world implementations. With a focus on the structural brain networks, this study explores the impact of white matter fiber architecture on the control energy in brain networks using the theory of how input node placement affects the LCC (the longest distance between inputs and other network nodes). Initially, we use a single input node as it is theoretically possible to control brain networks with just one input. We show that highly connected brain regions that lead to lower LCCs are more energy-efficient as a single input node. However, there may still be a need for a significant amount of control energy with one input, and achieving controllability with less energy could be of interest. We identify the minimum number of input nodes required to control brain networks with smaller LCCs, demonstrating that reducing the LCC can significantly decrease the control energy in brain networks. Our results show that relying solely on highly connected nodes is not effective in controlling brain networks with lower energy by using multiple inputs because of densely interconnected brain network hubs. Instead, a combination of low and high-degree nodes is necessary.