A Graphical Approach to a Model of a Neuronal Tree with a Variable Diameter
AbstractTree-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. View Full-Text
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Herrera-Valdez, M.A.; Suslov, S.K.; Vega-Guzmán, J.M. A Graphical Approach to a Model of a Neuronal Tree with a Variable Diameter. Mathematics 2014, 2, 119-135.
Herrera-Valdez MA, Suslov SK, Vega-Guzmán JM. A Graphical Approach to a Model of a Neuronal Tree with a Variable Diameter. Mathematics. 2014; 2(3):119-135.Chicago/Turabian Style
Herrera-Valdez, Marco A.; Suslov, Sergei K.; Vega-Guzmán, José M. 2014. "A Graphical Approach to a Model of a Neuronal Tree with a Variable Diameter." Mathematics 2, no. 3: 119-135.