Parameter Identification Problem in the Hodgkin and Huxley Model
This work addresses the tedious parameter estimation problem in the Hodgkin-Huxley model for computational neuroscience researchers, but the method is incremental as it applies an existing iterative technique to a known bottleneck.
The authors propose an iterative method (Landweber iteration) to estimate parameters in the Hodgkin-Huxley model from membrane potential data, demonstrating accurate parameter recovery even with noisy measurements.
The Hodgkin and Huxley (H-H) model is a nonlinear system of four equations that describes how action potentials in neurons are initiated and propagated, and represents a major advance in the understanding of nerve cells. However, some of the parameters are obtained through a tedious combination of experiments and data tuning. In this paper, we propose the use of an iterative method (Landweber iteration) to estimate some of the parameters in the H-H model, given the membrane electric potential. We provide numerical results showing that the method is able to capture the correct parameters using the measured voltage as data, even in the presence of noise.