Determining distributed parameters in a neuronal cable model on a tree graph. (16th January 2017)

• Record Type: Journal Article
• Authors: Avdonin, Sergei; Bell, Jonathan; Nurtazina, Karlygash
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 11(2017)
• Page Start: 3973
• Page End: 3981
• Publication Date: 2017-01-16
• Subjects: cable equation -- inverse problems -- parameter identification -- boundary control method -- metric tree graph; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4277
• Languages: English
• ISSNs: 0170-4214

Abstract

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.