Efficient neuromodulation of excitability to prevent the spread of
Spatio-temporal excitation patterns in various neurological disorders
constitute examples of excitable behaviour emerging from pathological
pathways. During migraine, seizure, and stroke, an initially localized
pathological state can start to spread indicating a transition from
unexcitable to excitable medium. We investigate this transition in
the generic FitzHugh-Nagumo (FHN) system of excitable media. Our goal
is to define an efficient neuromodulation minimizing the volume of
invaded tissue. The question of such a therapeutic optimization is
whether structures in control theory can be treated as a structure in
differential geometry by regarding parameter plane S of the FHN
system as a differential manifold endowed with a Riemannian metric.
We suggest to equip S with a metric given by
pharmacokinetic-pharmacodynamic models of drug receptor interaction.