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Mathematical Medicine and Biology Advance Access published online on June 7, 2007
Mathematical Medicine and Biology, doi:10.1093/imammb/dqm001
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© The author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Modelling the geometric features and investigating electrical properties of dendrites in a fish thalamic neuron

Wojciech Krzyzanski{dagger}

Department of Pharamaceutical Sciences, University of Buffalo, State University of New York, Buffalo, NY 14260, USA

Jonathan Bell

Department of Mathematics & Statistics, University of Maryland, Baltimore, County, Baltimore, MD 21250, USA

{dagger} Email: wk{at}buffalo.edu

Received on 23 November 2005. Revised on 16 January 2007.
  Abstract

A certain pacific fish has a thalamic nerve cell with a unique dendritic geometry. Instead of the cell having a branching dendritic structure, the large cell of the corpus glomerulosum has, generally, a single dendritic stalk with a large bulbous tip. We formulate a cable-theory model that incorporates the geometry, and then, we solve the problem for a single, localized synaptic current source at the bulb. From the solution representation, we numerically examine the characteristics of the postsynaptic potential due to the presence of the bulbous tip.

Keywords: dendritic bulb; corpus glomerulosum; cable theory; eigenvalue problem; Legendre equation; Legendre functions; Green's function; postsynaptic potential; Galerkin approximation


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