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.
Dahlem
M A
MA
Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany. dahlem@physik.tu-berlin.de
Schneider
F M
FM
Schöll
E
E
D000200:Action Potentials / Q000187:drug effects; D000927:Anticonvulsants / Q000627:therapeutic use*; D002493:Central Nervous System Diseases / Q000188:drug therapy* / Q000503:physiopathology; D003198:Computer Simulation; D004305:Dose-Response Relationship, Drug; D006801:Humans; D008959:Models, Neurological; D017711:Nonlinear Dynamics
D000927:Anticonvulsants