Efficient control of transient wave forms to prevent spreading depolarizations

In various neurological disorders spatio-temporal excitation patterns constitute examples of excitable behavior emerging from pathological pathways. During migraine, seizure, and stroke an initially localized pathological state can temporarily spread indicating a transition from non-excitable to excitable behavior. We investigate these transient wave forms in the generic FitzHugh–Nagumo (FHN) system of excitable media. Our goal is to define an efficient control minimizing the volume of invaded tissue. The general point of such a therapeutic optimization is how to apply control theory in the framework of structures in differential geometry by regarding parameter plane M of the FHN system as a differentiable manifold endowed with a metric. We suggest to equip M with a metric given by pharmacokinetic–pharmacodynamic models of drug receptor interaction.