Abstract
The classic Hodgkin-Huxley model is widely used for understanding the electrophysiological dynamics of a single neuron. While applying a low-amplitude constant current to the system results in a single voltage spike, it is possible to produce multiple voltage spikes by applying time-varying currents, which may not be experimentally measurable. The aim of this work is to estimate time-varying applied currents of different deterministic forms given noisy voltage data. In particular, we utilize an augmented ensemble Kalman filter with parameter tracking to estimate four different time-varying applied current parameters and associated Hodgkin-Huxley model states, along with uncertainty bounds in each case. We test the efficiency of the parameter tracking algorithm in this setting by analyzing the effects of changing the standard deviation of the parameter drift and the frequency of data available on the resulting time-varying applied current estimates and related uncertainty.
Highlights
The Hodgkin-Huxley model is a classical system of differential equations that is widely used for understanding the electrophysiological dynamics of a single neuron [1]
We further explore the efficiency of the algorithm by analyzing the effects of changing the standard deviation of the parameter drift in (32) as well as the amount of time series voltage data available
Further numerical experiments were conducted to analyze how the parameter tracking estimates of the applied current parameter are affected under different implementation conditions, namely, when changing the standard deviation of the parameter drift term in (32) and when the algorithm is provided increasingly less voltage data
Summary
The Hodgkin-Huxley model is a classical system of differential equations that is widely used for understanding the electrophysiological dynamics of a single neuron [1]. While the Hodgkin-Huxley equations can be used to model the total current resulting from an applied voltage, the model can be used to predict voltage given an externally applied current The latter is useful in experimental settings where voltage measurements are obtainable, making it possible to estimate the applied current based on observed voltage data [4,5]. In this setting, the applied current can be thought of as a synaptic input stimulus received by a single neuron. It remains an important challenge to estimate the underlying input current given experimentally obtainable measurements of voltage
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