Journal
INVERSE PROBLEMS AND IMAGING
Volume 9, Issue 3, Pages 645-659Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/ipi.2015.9.645
Keywords
Cable equation; boundary control; inverse problem; metric graph; tree graph; parameter recovery
Categories
Funding
- NSF [DMS 1411564]
- Ministry of Education and Science of Republic of Kazakhstan [4290/GF4]
- Simons Foundation Collaboration Grant [283689]
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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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