Parameter estimation of the FitzHugh-Nagumo model using noisy measurements for membrane potential

Abstract

This paper proposes an identification method to estimate the parameters of the FitzHugh-Nagumo (FHN) model for a neuron using noisy measurements available from a voltage-clamp experiment. By eliminating an unmeasurable recovery variable from the FHN model, a parametric second order ordinary differential equation for the only measurable membrane potential variable can be obtained. In the presence of the measurement noise, a simple least squares method is employed to estimate the associated parameters involved in the FHN model. Although the available measurements for the membrane potential are contaminated with noises, the proposed identification method aided by wavelet denoising can also give the FHN model parameters with satisfactory accuracy. Finally, two simulation examples demonstrate the effectiveness of the proposed method.

Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control

“…This could be done by estimating the parameters of FHN neurons to replicate the experimental data. For instance, Che et al 77 developed an identification method to estimate the parameters of FHN models to replicate the experimental data recorded from real neurons. Furthermore, in the present study, only synchronization within a network of neurons is considered and how two or more networks with different dynamics and configurations (non-identical neurons, unknown parameters, external disturbances, and different direction-dependent coupling) communicate and synchronize their activities is yet to be explored in future work.…”

Parameter Estimation of a Class of Neural Systems with Limit Cycles

“…In spite of these advances, little attention on parameter estimation of the FitzHugh-Nagumo (FHN) model has been received, including Bayesian statistical approaches [17,18], and least-squares algorithms [19,20]. In [17], a Bayesian framework was proposed for drift parameter estimation of the stochastic FHN model.…”

“…The two methods were only suitable for the case with noncontinuous input current stimulus, at the cost of a linear integral filter. Che et al [20] employed the recursive least-squares algorithm for parameter estimation of the FHN model, which requires the first and second time derivatives of the membrane potential and the input current stimulus being continuously differentiable. It is well known that the stochastic gradient algorithm is a class of important stochastic approximation methods, which have received much attention and have been widely used in different systems, such as Hammerstein systems [21], Wiener systems [22] and sampled systems [23].…”

“…In this paper, to improve the convergence rate of the stochastic gradient algorithm, we extend the innovation concept in [24] and explore the multiinnovation stochastic gradient algorithm for parameter estimation of the FHN neuron system. The parameterized FHN model in [20] can also be performed by using the proposed multiinnovation recursive least-squares algorithm in this paper and a better accuracy of the parameter estimation will be obtained due to the use of past innovations and repeated available data. However, from the aspect of the computing style, identification algorithms with qualified identification accuracy and convergence are desired for parameter estimation of the neural models.…”

On the convergence rate of Fletcher‐Reeves nonlinear conjugate gradient methods satisfying strong Wolfe conditions: Application to parameter identification in problems governed by general dynamics

“…These mathematical models often need to be tailored to experimental data through the identification of parameters. Parameter identification techniques have been successfully used in a large spectrum of dynamical models ranging from macro‐scale modelings such as fluid‐mechanics, 1–3 aerospace, and kinematics to micro‐scale modelings such as neuron science, 4 biological, 5 semiconductors, 6,7 and chemical applications. Many numerical methods have been developed recently to enhance the commonly existing techniques and also to identify complex dynamical systems.…”