Equivalent Dispersion Dependence: A Concept to Characterize the Cardiac Myocardium in the Normal State and Before Fibrillation

Abstract

We use the formalism of wave-packet propagation in passive media to characterize the spread of the electrical excitation in excitable media, namely the cardiac myocardium. We introduce equivalent concepts of group and phase velocities, attenuation coefficient and refraction index to describe the myocardial excitation wave and apply the wavelet approach to construct an analogue of the classical dispersion dependence for active media — the "equivalent dispersion dependence". Using the wavelet decomposition we develop a method for the reconstruction of the equivalent dispersion dependence for the myocardium on the basis of electrical intracardiac signals that are measured in two spatially separated points. The novel method is applied to two different sets of experimental data and to data obtained from a numerical simulation of the atrial myocardium. We show that the introduced equivalent dispersion dependence under physiological conditions is similar to the one that is obtained for resonant wave-medium interaction. The analysis of both experimental data sets clearly shows that the number of cardiac cycles with a resonant form of the equivalent dispersion dependence predominates in the normal state of the myocardium while it decreases early before the onset of atrial fibrillation. We set up the hypothesis that an increasing number of non-resonant cardiac cycles is a precursor of atrial fibrillation and thus can serve to predict fibrillation already at an early stage before its onset. The proposed conception can be applied to investigate the properties of the atrial as well as the ventricular myocardium.