Cardiac dynamics: a simplified model for action potential propagation.

Angelina Peñaranda,Jean Bragard,Blas Echebarria,Inma R Cantalapiedra

doi:10.1186/1742-4682-9-50

Angelina Peñaranda, Jean Bragard + Show 2 more

Open Access

https://doi.org/10.1186/1742-4682-9-50

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Abstract

This paper analyzes a new semiphysiological ionic model, used recently to study reexitations and reentry in cardiac tissue [I.R. Cantalapiedra et al, PRE 82 011907 (2010)]. The aim of the model is to reproduce action potencial morphologies and restitution curves obtained, either from experimental data, or from more complex electrophysiological models. The model divides all ion currents into four groups according to their function, thus resulting into fast-slow and inward-outward currents. We show that this simplified model is flexible enough as to accurately capture the electrical properties of cardiac myocytes, having the advantage of being less computational demanding than detailed electrophysiological models. Under some conditions, it has been shown to be amenable to mathematical analysis. The model reproduces the action potential (AP) change with stimulation rate observed both experimentally and in realistic models of healthy human and guinea pig myocytes (TNNP and LRd models, respectively). When simulated in a cable it also gives the right dependence of the conduction velocity (CV) with stimulation rate. Besides reproducing correctly these restitution properties, it also gives a good fit for the morphology of the AP, including the notch typical of phase 1. Finally, we perform simulations in a realistic geometric model of the rabbit’s ventricles, finding a good qualitative agreement in AP propagation and the ECG. Thus, this simplified model represents an alternative to more complex models when studying instabilities in wave propagation.

Highlights

Cardiac action potentials (APs) are electrical signals that trigger the synchronous contraction of the heart
The model divides all ion currents into four groups according to their function, resulting into fast-slow and inward-outward currents. We show that this simplified model is flexible enough as to accurately capture the electrical properties of cardiac myocytes, having the advantage of being less computational demanding than detailed electrophysiological models
In order to tackle the problem of modeling AP propagation in the computer, simplified models have been proposed, from the very simple but unphysiological [12,13,14], to the so-called semiphysiological models [15,16,17,18,19], somewhere in between the former and the extremely detailed physiological models mentioned earlier. These semi-physiological models preserve particular sets of properties of the action potential, as for instance, the dependence of the AP duration (APD, time during which the voltage is above a certain threshold, characterizing the duration of the excited state) or the conduction velocity (CV, propagation speed of the AP pulse) on the stimulation period, known as restitution curves

Summary

Introduction

Cardiac action potentials (APs) are electrical signals that trigger the synchronous contraction of the heart. These semi-physiological models preserve particular sets of properties of the action potential, as for instance, the dependence of the AP duration (APD, time during which the voltage is above a certain threshold, characterizing the duration of the excited state) or the conduction velocity (CV, propagation speed of the AP pulse) on the stimulation period, known as restitution curves In this respect, these can be viewed as mesoscopic models, that bridge the gap between dynamics at the molecular level (ion channel gating) and whole heart description, being still manageable for both computation and theoretical analysis. With the aim of providing models that fit better the AP morphology, a modification of the three-variable Fenton-Karma model has been proposed in [19] This new model includes an additional gate that modulates the slow inward current, in a fashion that resembles the effect of the fast outward potassium current (Ito) in physiological models. The determination of the numerical values of the parameters will be explained

Results

Conclusions and further works

12. FitzHugh R

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