Coding brain neurons via electrical network models for neuro-signal synthesis in computational neuroscience

Abstract

This paper develops a methodology for modeling and analysis of neural excitability that forms one of the most extensively studied mathematical frameworks in computational neuroscience. This framework is described by a set of differential equations known as Hodgkin-Huxley model and it synthesizes the influence of ionic currents on the cell voltage. The electrical equivalent circuit and the derivation of the conductance-based model of a neuron is based on a mathematical model that utilizes Hodgkin-Huxley equations which are considered as the single most influential finding in the biophysical description of excitable membranes to implement the current research in neurosciences. The neuron response with varying currents is demonstrated through analytical results and numerical simulations. The investigations in this paper lay the foundation for further deeper study and higher-order network models that can help eventually, through simulation and prediction, in the therapeutic treatment of brain diseases such as Alzheimer and Parkinson.