Controlling the human connectome with spatially diffuse input signals

The human brain is never at rest: its activity continuously fluctuates, transitioning between whole-brain patterns, or brain states. Network control theory provides a framework for quantifying the energy required to drive these transitions. A particularly relevant approach is optimal control, in which inputs steer the brain toward a target state. Traditionally, inputs are modeled as acting independently on individual network nodes. While convenient, this assumption neglects the spatial continuity of cerebral cortex: neighboring regions are anatomically/functionally coupled, allowing signals to spread. Moreover, brain stimulation techniques have limited spatial specificity, with effects extending beyond the stimulation site. Here, we adapt network control models to incorporate spatially extended inputs whose influence decays exponentially with distance from the input site. We show that this more realistic strategy exploits spatial dependencies in structural connectivity and activity, substantially reducing the energy required for brain state transitions. We identify near-optimal control strategies that reduce the number of inputs, in some cases by two orders of magnitude. This approximation yields network-wide maps of input site density that closely correspond to independent functional, metabolic, genetic, and neurochemical maps. Together, these findings provide an efficient and neurobiologically grounded framework for understanding optimal control of brain dynamics.