A network-control approach to seizure intervention via adjoint optimal control: a computational study on a connectome-coupled Hopf oscillator model

Most existing open-loop Deep Brain Stimulation (DBS) systems for drug-resistant epilepsy do not take into account the temporal dynamics of seizures or the spread of seizure activity. In this paper, we propose a closed-loop control system that models seizure prevention as a constraint on the nonlinear dynamics of the brain's structural network, and we evaluate it entirely in simulation. The structural network of the brain is modeled using the HCP-1065 (Human Connectome Project) connectome, which divides the brain into 360 regions. A densely connected sub-network of 60 brain regions was used to develop and test the proposed control system. Each region is modeled as a nonlinear supercritical Hopf oscillator, and the seizures modeled are focal-onset events that spread from a hippocampal onset zone through the connectome. A detector continuously monitors critical-slowing-down features of the dynamics, such as variance and lag-1 autocorrelation, to identify the approach to seizure activity. Two levels of control are applied: a linear-quadratic regulator (Level 1) that maintains the Hopf oscillators' basal state, and a dormant network-wide optimal controller (Level 2) that employs an adjoint-based optimal-control method (Adjoint Optimal Control; AOC) to provide pre-emptive control. Within the model, the predictive detector identifies the approach to the seizure transition with an area under the receiver operating characteristic curve (AUC) of 0.889 (95% confidence interval (CI) [0.820, 0.950]) on an independent test fold containing 50 trajectories per class, with a mean lead time of 56.9 model-time seconds; at the recall-maximizing operating point its false-positive rate is high (0.90 per 120-s seizure-free record), which we identify as the principal limitation of the present design. The controller prevented the seizure-like transition in 93% of 100 Monte Carlo simulations (95% CI: 86.2--96.6%) on the 60-node sub-network, against 21% for a connectome-naive targeting baseline; in the same continuously seizure-prone benchmark, a continuous open-loop push at matched amplitude and a PI controller suppressed every trial at lower energy, so the closed loop's advantages lie in pre-emptive lead time, network-wide homeostasis and delivering no stimulation when no risk is detected, not in energy per event. All validation uses synthetic trajectories generated by the same model; no patient or EEG data are used, and the results constitute a methodological proof-of-concept rather than evidence of clinical efficacy.