Towards Model-Based Observation and Control of Seizures
In the past decade, we have seen the concurrent development of sophisticated control theoretic techniques suitable for nonlinear networked systems, as well as computational models of neuronal systems that have improving fidelity to the behavior of neuronal ensembles in health and disease. Using nonlinear ensemble Kalman filters, we have in recent years demonstrated that we can fuse computational neuroscience models with data from single cells, small network motifs, and larger scale neuronal network dynamics. Simultaneously, the ability to quantify both analytically and numerically the formal observability of nonlinear dynamical systems has been developed using several approaches. Such metrics of observability define how much of the experimentally inaccessible variables of a complex system can be reconstructed from measurements of only a subset of the state variables, and whether different system trajectories are discriminable from measurement observations. I will show how model-based control principles can be applied to reconstruct seizure dynamics at the cellular and network level. I will also discuss some of the open questions in structural observability and controllability, and symmetry, where mathematical developments are needed.