  Electrical neuromodulation as a palliative treatment has been increasingly
applied to epilepsy. However, most of the current neuromodulation implement
pre-determined actuation strategies rather than closed-loop neurofeedback. In
this paper, rooted in optimal control theory, we propose a novel framework for
real-time closed-loop electrical neuromodulation in epilepsy. Our framework
combines a deep Koopman-operator based model for seizure prediction in an
approximated finite dimensional linear dynamics and the model predictive
control (MPC) for designing optimal seizure suppression strategies. We validate
our model with synthetic seizure data from Jansen-Rit Model which generates
neural dynamics in a single cortical column and two distant cortical columns.
The results demonstrate that the deep Koopman-operator based model has great
capabilities to map the nonlinear neural dynamics into finite dimensional
linear dynamics, which is suitable for real-time seizure prediction and
naturally compatible with the optimal-based linear MPC design for seizure
suppression. Our framework opens a new window for the development and
implementation of robust real-time closed-loop electrical neuromodulation in
epileptic seizure suppression and sheds light on understanding the
neurodynamics and feedback control policies.
