Finite volume modeling of neural communication: Exploring electrical signaling in biological systems

Abstract

This article investigates neuronal dynamics in neuroscience, employing mathematical frameworks such as the Hodgkin Huxley model to describe them. Action potentials electrical signals generated by neurons are crucial for communication within the nervous system. The Hodgkin–Huxley model offers an analytically representation of how neurons produce and propagate these action potentials by accounting for key factors, including membrane potential variations influenced by ion channel conductances. These ion channels regulate ion movement across cell membranes, which is essential for neuronal activity. The model has been widely applied to study phenomena such as neural network behavior and the impact of drugs on neuronal function. The proposed numerical approach, based on a hyperbolic tangent (tanh) function, is shown to be second-order accurate and unconditionally stable. Validation through comparison with existing literature and computational simulations demonstrates strong agreement between predicted outcomes and those generated by the model. The numerical method proves to be a reliable and precise tool for modeling the dynamics of physical systems, with potential applications in fields such as electromagnetism, acoustics, and fluid mechanics.