Identification of Two FitzHugh-Nagumo Neuron Models Based on the Speed-Gradient and Filtering

Abstract

The paper is devoted to the problem of parameter identification of two FitzHugh-Nagumo neuron models. The FitzHugh-Nagumo model is a simplification of the Hodgkin-Huxley model and it is very valuable for using on practice thanks to its simplicity. However, within an experiment only one variable of the FitzHugh-Nagumo model, the membrane potential, is measured, while another variable of cumulative effects of all slow ion currents responsible for restoring the resting potential of the membranes and both variables’ derivatives cannot be measured. This circumstance brings additional difficulties to the parameters estimation problem and, therefore, this case needs special attention. Firstly, the model was transformed to more simple form without unmeasured variables. Variables obtained from applying second-order real filter-differentiator were used instead of unmeasured derivatives in model’s equations. As a result, a linear equation was gotten and for this equation the identification goal, which guarantees correct parameters’ adjustment, was formulated and an adaptive system, parameters of which are estimations of original system’s parameters and an output of which estimates the output of the linear equation, was constructed. Then, the integral objective function was defined and the algorithm for the original model parameters identification was designed with the speed-gradient method. The results of computer simulation in the Simulink environment are presented. These results demonstrate that estimates of the model’s state and parameters converge to their true values rather fast. Unlike existing solutions of the FitzHugh-Nagumo identification problem, we propose a much easier deterministic algorithm. Moreover, the parameters are estimated for a system collected from two FitzHugh-Nagumo models, which opens perspectives for using the proposed method in modeling neuron population activity.