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 throughout the brain. 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. The structural network of the brain is modeled using the HCP-1065 connectome, which divides the brain into 360 regions according to the Glasser atlas. While the connectome was built using the full 360-region atlas of the brain, a densely connected sub-network of 60 brain regions was used to develop and test the proposed control system. Each region of the brain is modeled as a nonlinear supercritical Hopf oscillator. A detector continuously monitors certain features of the dynamics of each region of the brain, such as variance and lag-1 autocorrelation, to identify the onset of 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) applied directly to the Pontryagin Hamiltonian to provide pre-emptive control should the system enter a region of unsafe operation. The predictive detector displays high accuracy in detecting seizure transitions, achieving an AUC of 0.889 (95% CI [0.820, 0.950]) on an independent test fold containing 50 trajectories per class, and demonstrating a mean lead time to the onset of the seizure of 56.9 seconds. Within the modeled regime of neuronal excitability, the model is able to prevent the development of seizure-like bifurcations in 100% of 100 Monte Carlo simulations (95% CI: 96.3–100%).