Determining distributed parameters in a neuronal cable model on a tree graph

Sergei Anatol'evich Avdonin, Jonathan Bell, Karlygash Nurtazina

2017

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DOI 10.1002/mma.4277
Data confidence 70 medium
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Abstract

For graph domains without cycles, we show how unknown coefficients and source terms for a parabolic equation can be recovered from the dynamical Neumann‐to‐Dirichlet map associated with the boundary vertices. Through use of a companion wave equation problem, the topology of the tree graph, degree of the vertices, and edge lengths can also be recovered. The motivation for this work comes from a neuronal cable equation defined on the neuron's dendritic tree, and the inverse problem concerns parameter identification of k unknown distributed conductance parameters. Copyright © 2017 John Wiley & Sons, Ltd.