TY - JOUR

T1 - A graphical approach to a model of a neuronal tree with a variable diameter

AU - Herrera-Valdez, Marco A.

AU - Suslov, Sergei

AU - Vega-Guzmán, José M.

N1 - Publisher Copyright:
© 2014 by the authors. licensee MDPI, Basel, Switzerland.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2014/9/1

Y1 - 2014/9/1

N2 - 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.

AB - 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.

KW - Bessel functions

KW - Cable equation

KW - Hyperbolic functions

KW - Ince's equation

UR - http://www.scopus.com/inward/record.url?scp=84945305830&partnerID=8YFLogxK

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U2 - 10.3390/math2030119

DO - 10.3390/math2030119

M3 - Article

AN - SCOPUS:84945305830

VL - 2

SP - 119

EP - 135

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 3

ER -