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Objective. Developing a new neuromodulation method for epilepsy treatment requires a large amount of time and resources to find effective stimulation parameters and often fails due to inter-subject variability in stimulation effect. As an alternative, we present a novel data-driven surrogate approach which can optimize the neuromodulation efficiently by investigating the stimulation effect on surrogate neural states. Approach. Medial septum (MS) optogenetic stimulation was applied for modulating electrophysiological activities of the hippocampus in a rat temporal lobe epilepsy model. For the new approach, we implemented machine learning techniques to describe the pathological neural states and to optimize the stimulation parameters. Specifically, first, we found neural state surrogates to estimate a seizure susceptibility based on hippocampal local field potentials. Second, we modulated the neural state surrogates in a desired way with the subject-specific optimal stimulation parameters found by in vivo Bayesian optimization. Finally, we tested whether modulating the neural state surrogates affected seizure frequency. Main results. We found two neural state surrogates: The first was hippocampal theta power by considering its well-known relationship with epilepsy, and the second was the output of pre-ictal state model (PriSM) which was built by characterizing the hippocampal activity during pre-ictal period. The optimal stimulation parameters found by Bayesian optimization outperformed the other parameters in terms of modulating the surrogates toward anti-seizure neural state. When treatment efficacy was tested, the subject-specific optimal parameters for increasing theta power were more effective to suppress seizures than fixed stimulation parameter (7Hz). However, modulation of the other neural state surrogate, PriSM, did not suppress seizures. Significance. The surrogate approach can save enormous time and resources to find subject-specific optimal stimulation parameters which can effectively modulate neural states and further improve therapeutic effectiveness. This approach also can be used for improving neuromodulation treatment of other neurological or psychiatric diseases.

The aim of this work is to present a sampling-based algorithm designed to solve a certain class of stochastic optimal control problems, utilizing forward and backward stochastic differential equations (FBSDEs). Specifically, we address the class of problems in which the running cost of the performance index involves an L 1 -type minimization problem in terms of the control effort. Such problems are typically called minimum fuel problems in optimal control literature. By means of a nonlinear version of the Feynman–Kac lemma, we obtain a probabilistic representation of the solution to the nonlinear Hamilton–Jacobi–Bellman equation, expressed in the form of a system of decoupled FBSDEs. This system of FBSDEs can be solved by employing linear regression techniques.