A Comparative Analysis of Numerical Methods for Solving the Leaky Fire and Integrate Model

Abstract

The human nervous system is one of the most complex systems of the human body. Understanding its behavior is crucial in drug discovery and developing medical devices. One approach to understanding such a system is to model its most basic unit, neurons. The leaky integrate and fire (LIF) method models the neurons’ response to a stimulus. Given the fact that the model’s equation is a linear ordinary differential equation, the purpose of this research is to compare which numerical analysis method gives the best results for the simplified version of this model. Adams predictor and corrector (AB4-AM4) and Heun’s methods were then used to solve the equation. In addition, this study further researches the effects of different current input models on the LIF’s voltage output. In terms of the computational time, Heun’s method was 0.01191 s on average which is much less than that of the AB-AM4 method (0.057138) for a constant DC input. As for the root mean square error, the AB-AM4 method had a much lower value (0.0061) compared to that of Heun’s method (0.3272) for the same constant input. Therefore, our results show that Heun’s method is best suited for the simplified LIF model since it had the lowest computation time of 36 ms, was stable over a larger range, and had an accuracy of 72% for the varying sinusoidal current input model.