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.
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
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U2 - 10.3390/math2030119
DO - 10.3390/math2030119
M3 - Article
AN - SCOPUS:84945305830
SN - 2227-7390
VL - 2
SP - 119
EP - 135
JO - Mathematics
JF - Mathematics
IS - 3
ER -