A pilot study of ion current estimation by ANN from action potential waveforms

Abstract

Experiments using conventional experimental approaches to capture the dynamics of ion channels are not always feasible, and even when possible and feasible, some can be time-consuming. In this work, the ionic current-time dynamics during cardiac action potentials (APs) are predicted from a single AP waveform by means of artificial neural networks (ANNs). The data collection is accomplished by the use of a single-cell model to run electrophysiological simulations in order to identify ionic currents based on fluctuations in ion channel conductance. The relevant ionic currents, as well as the corresponding cardiac AP, are then calculated and fed into the ANN algorithm, which predicts the desired currents solely based on the AP curve. The validity of the proposed methodology for the Bayesian approach is demonstrated by the R (validation) scores obtained from training data, test data, and the entire data set. The Bayesian regularization's (BR) strength and dependability are further supported by error values and the regression presentations, all of which are positive indicators. As a result of the high convergence between the simulated currents and the currents generated by including the efficacy of a developed Bayesian solver, it is possible to generate behavior of ionic currents during time for the desired AP waveform for any electrical excitable cell.

Keywords: Artificial neural networks; Bayesian regularization; Cardiac action potential; Current–time dynamics; Numerical modeling.

Fig. 1

A description of the ANN design for the BR algorithm

Fig. 2

AP waveforms that were generated through simulation after conductances were altered. The model receives these curves as inputs and processes them accordingly

Fig. 3

A through O illustrate the outcomes of the simulation following the application of the perturbations to channel conductances. The control currents are shown by the red lines in the illustration. Here, A I_Na is Na⁺ current, B I_CaL is L-Type (long-opening) Ca²⁺ current, C I_CaT is T-Type (transient) Ca²⁺ current, D I_Ks is slowly activated outward rectifier K⁺ current, E I_Kr is rapidly activated outward rectifier K⁺ current, F I_t is transient outward K⁺ current, G I_K1 is inward rectifier K⁺ current, H I_NaKp is Na⁺-K⁺ pump current, I I_NaCap is Na⁺-K⁺ exchanger (NCX) current, J I_Cap is sarcolemmal Ca²⁺ pump current, K I_Nab is Na⁺, L I_Cab is Ca²⁺, M I_Kb is K⁺, N I_Clb is Cl⁻ background currents, and O I_hf is hyperpolarization-activated current

Fig. 4

Predictions for one cell (2000 rows) resulting from one set of AP. A The AP. B–I show the currents. Red dots and blue dots represent the real values and the predictions, respectively

Fig. 5

A False perfect fit for I_K1 regression. B The predictions for one cell, which has 2000 rows, based on one particular set of AP. The measured (numerical) values are represented by the red dots, and the predictions are shown by the blue dots (although it may be difficult to see them without zooming in C). Zoomed in on the time area that occurs between 78 and 78.6 ms during an I_K1 simulation and the ANN’s prediction for it