The Numerical Solution of the Modified Hodgkin-Huxley Model
Yajni Warnapala *
Mathematics, Roger Williams University, Bristol, RI, United States of America.
Danielle Vogt
Mathematics, Roger Williams University, Bristol, RI, United States of America.
*Author to whom correspondence should be addressed.
Abstract
The primary signal in the model represents the membrane potential of a neuron. Some have modified this model to methods that validate broad simulations of the experiment of Hodgkin-Huxley signals using real data from squid giant axons. This research builds a modified nonlinear ordinary differential equation model derived from the Hodgkin-Huxley Model (HH Model). This model was previously used for the axon of a squid. The theoretical concept of the Hodgkin-Huxley model was extended to human axons. The nonlinear system was not analytically solvable. Therefore, we solved the model numerically to obtain good convergence results. The modified Hodgkin-Huxley system adds two additional voltage-gating variables, namely low- and high-voltage calcium (Purves et al., 2001).
Keywords: Nonlinear differential equations, exponential Euler method, modified Hodgkin-Huxley model, human axon