A Graphical Approach to a Model of a Neuronal Tree With a Variable Diameter
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.
- Author (aut): Herrera-Valdez, Marco A.
- Author (aut): Suslov, Sergei
- Author (aut): Vega-Guzman, Jose M.
- Contributor (ctb): Simon M. Levin Mathematical, Computational and Modeling Sciences Center
- Contributor (ctb): College of Liberal Arts and Sciences