Next Article in Journal
DGS-HSA: A Dummy Generation Scheme Adopting Hierarchical Structure of the Address
Next Article in Special Issue
Computational Simulation of Cardiac Function and Blood Flow in the Circulatory System under Continuous Flow Left Ventricular Assist Device Support during Atrial Fibrillation
Previous Article in Journal
Study on the Common Rail Type Injector Nozzle Design Based on the Nozzle Flow Model
Previous Article in Special Issue
Emotion, Respiration, and Heart Rate Variability: A Mathematical Model and Simulation Analyses
Open AccessArticle

Estimating Time-Varying Applied Current in the Hodgkin-Huxley Model

Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, USA
*
Author to whom correspondence should be addressed.
Appl. Sci. 2020, 10(2), 550; https://doi.org/10.3390/app10020550
Received: 21 November 2019 / Revised: 29 December 2019 / Accepted: 8 January 2020 / Published: 11 January 2020
(This article belongs to the Special Issue Dynamic Models of Biology and Medicine, Volume II)
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. View Full-Text
Keywords: inverse problems; time-varying parameter estimation; ensemble Kalman filter; Hodgkin-Huxley; neuron dynamics inverse problems; time-varying parameter estimation; ensemble Kalman filter; Hodgkin-Huxley; neuron dynamics
Show Figures

Figure 1

MDPI and ACS Style

Campbell, K.; Staugler, L.; Arnold, A. Estimating Time-Varying Applied Current in the Hodgkin-Huxley Model. Appl. Sci. 2020, 10, 550.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop