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arXiv · 0705.3398

Efficient control of transient wave forms to prevent spreading depolarizations

Markus A. Dahlem·Felix M. Schneider·Eckehard Schoell
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Abstract

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 differential manifold endowed with a metric. We suggest to equip M with a metric given by pharmacokinetic-pharmacodynamic models of drug receptor interaction.

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Markus A. Dahlem, Felix M. Schneider, Eckehard Schoell. 2007-09-27. Efficient control of transient wave forms to prevent spreading depolarizations. https://arxiv.org/abs/0705.3398

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