Global alternans instability and its effect on non-linear wave propagation: dynamical Wenckebach block and self terminating spiral waves

Nele Vandersickel,Alexander V Panfilov,Arne Defauw,Peter Dawyndt

doi:10.1038/srep29397

Nele Vandersickel, Alexander V Panfilov + Show 2 more

Open Access

https://doi.org/10.1038/srep29397

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Abstract

The main mechanism of formation of reentrant cardiac arrhythmias is via formation of waveblocks at heterogeneities of cardiac tissue. We report that heterogeneity and the area of waveblock can extend itself in space and can result formation of new additional sources, or termination of existing sources of arrhythmias. This effect is based on a new form of instability, which we coin as global alternans instability (GAI). GAI is closely related to the so-called (discordant) alternans instability, however its onset is determined by the global properties of the APD-restitution curve and not by its slope. The APD-restitution curve relates the duration of the cardiac pulse (APD) to the time interval between the pulses, and can easily be measured in an experimental or even clinical setting. We formulate the conditions for the onset of GAI, study its manifestation in various 1D and 2D situations and discuss its importance for the onset of cardiac arrhythmias.

Highlights

The pumping function of the heart is controlled by electrical waves of excitation, which propagate through the heart and initiate cardiac contraction
We considered a homogeneous cable of cardiac cells, which we paced at the left border with a period T = 220 ms, corresponding to action potential duration (APD) = 187 ms
Wave N + 3 will be able to excite the complete cable, and the process is repeated as APDN+3 will be longer again

Summary

Introduction

The pumping function of the heart is controlled by electrical waves of excitation, which propagate through the heart and initiate cardiac contraction Abnormal propagation of these electrical waves can result in the formation of vortices which excite the heart with a high frequency and cause a cardiac arrhythmia, called a tachycardia. In many cases, such vortices break down into complex turbulent patterns and the excitation of the heart becomes spatially asynchronous. It was shown that it occurs if the slope of the APD restitution curve is more than one

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