Parameter Identification Problem in the Hodgkin-Huxley Model

Abstract

The Hodgkin-Huxley (H-H) landmark model is described by a system of four nonlinear differential equations that describes how action potentials in neurons are initiated and propagated. However, obtaining some of the parameters of the model requires a tedious combination of experiments and data tuning. In this letter, we propose the use of a minimal error iteration method to estimate some of the parameters in the H-H model, given the measurements of membrane potential. We provide numerical results showing that the approach approximates well some of the model's parameters, using the measured voltage as data, even in the presence of noise.

ElectroPhysiomeGAN: Generation of Biophysical Neuron Model Parameters from Recorded Electrophysiological Responses

“…As discussed in Methods section, it’s worth noting that EP-GAN does not necessarily recover the ground truth parameters that are associated with the input membrane potential responses and steady-state current profiles. This is mainly due to the fact that there may exist multiple parameter regimes for the HH-model which support the given inputs [5, 10, 11, 12, 13, 18, 44, 45]. The parameters generated by a single forward pass of EP-GAN (i.e., a single flow of information from the input to the output) could thus be interpreted as a one time sampling from such a regime and a small perturbation to inputs may result in a different set of parameters.…”

“…Such generative nature of GAN is advantageous for addressing the multi-modal nature of our problem, where the parameter solution is not guaranteed to be unique for a given neuron recording. Indeed, several computational works attempting to solve inverse HH-model have pointed out the ill-posed nature of the parameter solutions [5, 10, 11, 12, 13, 18, 44, 45]. Our approach is therefore leveraging GAN to learn a domain of parameter sets compatible with a neuron recordings instead of mapping onto a single solution.…”

“…From statistical standpoint, Wang et al 2022 used the Markov-Chain-Monte-Carlo method to obtain the posterior distribution of channel parameters for HH-models featuring 3 and 8 ion channels (2 and 9 parameters respectively) given the simulated membrane potential responses data [17]. From an analytic standpoint, Valle et al 2022 suggested an iterative gradient descent based method that directly manipulates HH-model to infer 3 conductance parameters and 3 exponents of activation functions given the measurements of membrane potential responses [18]. Recent advances in machine learning gave rise to deep learning based methods which infer steady-state activation functions and posterior distributions of 3-channel HH-model parameters inferred by an artificial neural network model given the membrane potential responses data [19, 20].…”