Journal
JOURNAL OF MATHEMATICAL BIOLOGY
Volume 67, Issue 1, Pages 123-141Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-012-0537-6
Keywords
Cable equation; Boundary control; Inverse problem; Metric graph; Parameter recovery
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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.
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