Mathematical and electronic model resistance/capacitor circuit of the action potential in an excitable cell

Abstract

Excitable cells are those that, when stimulated, generate an ion-dependent action potential; between them are neurons. The action potential has been a relevant target of study concerning cellular communication and behavior. This work aims to implement and validate the action potential of an excitable cell through resistance/capacitor (RC) circuits based on a mathematical/electrical model. This perspective can help researchers understand an excitable cell’s action potential from a mathematical and electrical approximation using a simple model. The experiment was designed based on RC circuits associated with the ionic channels of sodium (Na+) and potassium (K+). The proposed model also incorporates the ‘dendrite’ action not employed in the Hodgkin and Huxley model. Thus, a linear function by parts was used in mathematical modeling, recreating the excitable cell’s behavior through numerical and electronic simulation. The proposed mathematical/electrical model includes dendrites and capacitors not considered in previous models. In this scheme, the dendrite joined to the RC circuit describes the behavior as physiological, concerning the action potentials and the ions responsible.