2007/05/23 by Markus A. Dahlem, Dahlem, Markus A., Felix Schneider +3
Computer Science · Neuroscience · #FOS: Physical sciences #Neuroscience and Neuropharmacology Research #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #Photoreceptor and optogenetics research
paper · pdf · doi:10.48550/arxiv.0705.3398
openalex publication_date 2007/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.