Iterations of Diagrammatic Solutions of the Cable Equation Using Arbitrary Dendritic Geometry
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Literature Review from the year 2015 in the subject Biology - Neurobiology, West Virginia University, language: English, abstract: Cable theory, an intricate neuronal postulate, elucidates neuritic characteristics, that of which, membrane voltage along a dendrite is most salient. This subjective review focuses on the progression of diagrammatic, i.e., analytical and graphical, solutions of the linear cable equation. Geometrical calculus, the mathematical underpinnings of neural cable theory, provided the proper tools to advance dendritic computational paradigms. The first implemented computati...
Literature Review from the year 2015 in the subject Biology - Neurobiology, West Virginia University, language: English, abstract: Cable theory, an intricate neuronal postulate, elucidates neuritic characteristics, that of which, membrane voltage along a dendrite is most salient. This subjective review focuses on the progression of diagrammatic, i.e., analytical and graphical, solutions of the linear cable equation. Geometrical calculus, the mathematical underpinnings of neural cable theory, provided the proper tools to advance dendritic computational paradigms. The first implemented computational model was rudimentary, which obtained respective variables in the Laplace, or frequency, domain. The following work, somewhat heuristic, reformulated the linear cable equation in attempt to increase computational efficacy and produce results in the temporal domain. The derivation of such a complex dendritic neuronal model has ranging implications. However, in many respects, such a computational model is a methodological asset, which can be used implicitly in other models providing a stringently detailed paradigm, both biophysically and phenomenologically. In effect, neural system dynamics can be simulated and once adequately described, can be used to discern neuronal perturbations that, potentially, yield ill results psychologically, psychiatrically, and neurologically.
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