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

Sergei Avdonin; Jonathan  Bell

doi:10.3934/ipi.2015.9.645

Article Contents

2015, Volume 9, Issue 3: 645-659. Doi: 10.3934/ipi.2015.9.645

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

Sergei Avdonin^1, and
Jonathan Bell^2,

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

Received: March 31, 2014

Revised: October 31, 2014

Published: July 2015

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Abstract

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.

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Mathematics Subject Classification: 92, 93, 35.

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References

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