A graphical approach to a model of a neuronal tree with a variable diameter

Marco A. Herrera-Valdez, Sergei Suslov, José M. Vega-Guzmán

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Tree-like structures are ubiquitous in nature. In particular, neuronal axons and dendrites have tree-like geometries that mediate electrical signaling within and between cells. Electrical activity in neuronal trees is typically modeled using coupled cable equations on multi-compartment representations, where each compartment represents a small segment of the neuronal membrane. The geometry of each compartment is usually defined as a cylinder or, at best, a surface of revolution based on a linear approximation of the radial change in the neurite. The resulting geometry of the model neuron is coarse, with non-smooth or even discontinuous jumps at the boundaries between compartments. We propose a hyperbolic approximation to model the geometry of neurite compartments, a branched, multi-compartment extension, and a simple graphical approach to calculate steady-state solutions of an associated system of coupled cable equations. A simple case of transient solutions is also briefly discussed.

Original languageEnglish (US)
Pages (from-to)119-135
Number of pages17
JournalMathematics
Volume2
Issue number3
DOIs
StatePublished - Sep 1 2014

Keywords

  • Bessel functions
  • Cable equation
  • Hyperbolic functions
  • Ince's equation

ASJC Scopus subject areas

  • Mathematics(all)

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