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

Avdonin Sergei | Zendy; Bell Jonathan | Zendy; Nurtazina Karlygash | Zendy

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

Author(s) -

Avdonin Sergei,

Bell Jonathan,

Nurtazina Karlygash

Publication year - 2017

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4277

Subject(s) - mathematics , graph , cable theory , tree (set theory) , inverse , boundary value problem , topology (electrical circuits) , mathematical analysis , combinatorics , discrete mathematics , geometry , computer science , telecommunications , cable gland , cable harness

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.

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