# American Institute of Mathematical Sciences

August  2015, 9(3): 645-659. doi: 10.3934/ipi.2015.9.645

## Determining a distributed conductance parameter for a neuronal cable model defined on a tree graph

 1 Department of Mathematics and Statistics, University of Alaska, Fairbanks, AK 99775-6660 2 Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250, United States

Received  April 2014 Revised  November 2014 Published  July 2015

In this paper we solve the inverse problem of recovering a single spatially distributed conductance parameter in a cable equation model (one-dimensional diffusion) defined on a metric tree graph that represents a dendritic tree of a neuron. Dendrites of nerve cells have membranes with spatially distributed densities of ionic channels and hence non-uniform conductances. We employ the boundary control method that gives a unique reconstruction and an algorithmic approach.
Citation: Sergei Avdonin, Jonathan Bell. Determining a distributed conductance parameter for a neuronal cable model defined on a tree graph. Inverse Problems & Imaging, 2015, 9 (3) : 645-659. doi: 10.3934/ipi.2015.9.645
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