Causally Regularized Graph State-Space Modeling and Risk-Sensitive Control for Closed-Loop Neurostimulation in Drug-Resistant Focal Epilepsy

Abstract

Epilepsy is a network disorder in which pathological dynamics emerge from distributed brain circuits and can evolve rapidly across space and time. In drug-resistant focal epilepsy, minimally invasive neurostimulation is increasingly used when resection is infeasible or when seizure onset involves multiple interacting regions, yet current targeting and programming workflows remain limited by sparse sampling, nonstationary propagation, and uncertainty in how stimulation perturbs seizure circuitry. This paper proposes a unified computational framework that connects time-varying directed connectivity inferred from stereo-electroencephalography to a principled control objective for closed-loop stimulation. The core contribution is a causally regularized graph state-space model that jointly estimates latent ictal state, dynamic directed edges, and stimulation response parameters while explicitly accounting for partial observability and electrode-dependent measurement distortion. On top of this model, we derive an interventional controllability functional that ranks candidate stimulation sites by expected seizure-suppressive impact under uncertainty, and we embed the resulting reduced actuator set into a risk-sensitive model predictive controller that optimizes stimulation amplitude and timing subject to safety constraints and probabilistic state forecasts. The framework is designed to support both unilateral and bilateral onset patterns, incorporates robust uncertainty quantification via variational inference, and enables retrospective evaluation using counterfactual rollouts conditioned on observed seizures. The result is a technical pathway from SEEG-derived network structure to closed-loop stimulation policies that can be stress-tested under identifiable assumptions rather than tuned purely by heuristic response.