Int J Neural Syst - Principal dynamic mode analysis of the Hodgkin-Huxley equations.

Tópicos

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Resumo

We develop an autoregressive model framework based on the concept of Principal Dynamic Modes (PDMs) for the process of action potential (AP) generation in the excitable neuronal membrane described by the Hodgkin-Huxley (H-H) equations. The model's exogenous input is injected current, and whenever the membrane potential output exceeds a specified threshold, it is fed back as a second input. The PDMs are estimated from the previously developed Nonlinear Autoregressive Volterra (NARV) model, and represent an efficient functional basis for Volterra kernel expansion. The PDM-based model admits a modular representation, consisting of the forward and feedback PDM bases as linear filterbanks for the exogenous and autoregressive inputs, respectively, whose outputs are then fed to a static nonlinearity composed of polynomials operating on the PDM outputs and cross-terms of pair-products of PDM outputs. A two-step procedure for model reduction is performed: first, influential subsets of the forward and feedback PDM bases are identified and selected as the reduced PDM bases. Second, the terms of the static nonlinearity are pruned. The first step reduces model complexity from a total of 65 coefficients to 27, while the second further reduces the model coefficients to only eight. It is demonstrated that the performance cost of model reduction in terms of out-of-sample prediction accuracy is minimal. Unlike the full model, the eight coefficient pruned model can be easily visualized to reveal the essential system components, and thus the data-derived PDM model can yield insight into the underlying system structure and function.

Resumo Limpo

develop autoregress model framework base concept princip dynam mode pdms process action potenti ap generat excit neuron membran describ hodgkinhuxley hh equat model exogen input inject current whenev membran potenti output exceed specifi threshold fed back second input pdms estim previous develop nonlinear autoregress volterra narv model repres effici function basi volterra kernel expans pdmbase model admit modular represent consist forward feedback pdm base linear filterbank exogen autoregress input respect whose output fed static nonlinear compos polynomi oper pdm output crossterm pairproduct pdm output twostep procedur model reduct perform first influenti subset forward feedback pdm base identifi select reduc pdm base second term static nonlinear prune first step reduc model complex total coeffici second reduc model coeffici eight demonstr perform cost model reduct term outofsampl predict accuraci minim unlik full model eight coeffici prune model can easili visual reveal essenti system compon thus dataderiv pdm model can yield insight under system structur function

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