THE METHOD OF HYBRID FUNCTIONS FOR THE NUMERICAL SOLUTION OF THE HODGKIN-HUXLEY MODEL

Abstract

Background and objective: The Hodgkin-Huxley framework of equations represent the generation of the nerve action potential. It is a fairly complex biophysical model that is non-linear in nature. It has four sets of coupled differential equations representing the membrane voltage and the gate variables. The conventional way of solving such systems is usually the forward Euler method. Some other computational methods are the Rush-Larsen (RL) method and, Runge-Kutta (RK) methods. In MATLAB, a popular method used is the ODE45 solver, which is actually 4 th order Runge Kutta method. Method: In this paper, a new and simplified computational method is proposed which is called the Hybrid Functions (HF) method. To solve these differential equations representing a complex biological model, we present a detailed derivation of the proposed algorithm. Results: A detailed comparative study based on computational speed, absolute error and Integral Timed Squared Error (ITSE) was then conducted on the aforementioned algorithms. Conclusion: The results show that, due to the simplification of steps because of approximations considered in solving the system of equations, the HF method is quite effective for computing solutions of complex biophysical models with ease.