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Determining a distributed parameter in a neural cable model via a boundary control method. (English) Zbl 1264.92011

Summary: 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. 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.

MSC:

92C20 Neural biology
35R02 PDEs on graphs and networks (ramified or polygonal spaces)
35Q93 PDEs in connection with control and optimization
05C90 Applications of graph theory
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35R30 Inverse problems for PDEs
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