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The brain is a non-linear dynamical system with a self-restoration process, which protects itself from external damage but is often a bottleneck for clinical treatment. To treat the brain to induce the desired functionality, formulation of a self-restoration process is necessary for optimal brain control. This study proposes a computational model for the brain's self-restoration process following the free-energy and degeneracy principles. Based on this model, a computational framework for brain control is established. We posited that the pre-treatment brain circuit has long been configured in response to the environmental (the other neural populations') demands on the circuit. Since the demands persist even after treatment, the treated circuit's response to the demand may gradually approximate the pre-treatment functionality. In this framework, an energy landscape of regional activities, estimated from resting-state endogenous activities by a pairwise maximum entropy model, is used to represent the pre-treatment functionality. The approximation of the pre-treatment functionality occurs via reconfiguration of interactions among neural populations within the treated circuit. To establish the current framework's construct validity, we conducted various simulations. The simulations suggested that brain control should include the self-restoration process, without which the treatment was not optimal. We also presented simulations for optimizing repetitive treatments and optimal timing of the treatment. These results suggest a plausibility of the current framework in controlling the non-linear dynamical brain with a self-restoration process.

A Computational Framework for Controlling the Self-Restorative Brain Based on the Free Energy and Degeneracy Principles