title: Determining a distributed parameter in a neural cable model via a boundary control method.
abstract: Dendrites of nerve cells have membranes with spatially distributed densities of ionic channels and hence non-uniform conductances. These conductances are usually represented as constant parameters in neural models because of the difficulty in experimentally estimating them locally. In this paper we investigate the inverse problem of recovering a single spatially distributed conductance parameter in a one-dimensional diffusion (cable) equation through a new use of a boundary control method. We also outline how our methodology can be extended to cable theory on finite tree graphs. The reconstruction is unique.
authors.affiliation: Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775, USA. s.avdonin@alaska.edu
authors.forename: Sergei
authors.initials: S
authors.lastname: Avdonin
authors.forename: Jonathan
authors.initials: J
authors.lastname: Bell
mesh_terms: D000465:Algorithms; D000818:Animals; D003712:Dendrites / Q000502:physiology; D055724:Electrophysiological Phenomena; D007473:Ion Channels / Q000378:metabolism; D055641:Mathematical Concepts; D008959:Models, Neurological; D009431:Neural Conduction / Q000502:physiology
chemical_list: D007473:Ion Channels