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 exc...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
23.05.2007
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Subjects | |
Online Access | Get full text |
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Summary: | 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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DOI: | 10.48550/arxiv.0705.3398 |