Dynamics of Pivoting Electrical Waves in a Cardiac Tissue Model

Through a detailed mathematical analysis we seek to advance our understanding of how cardiac tissue conductances govern pivoting (spiral, scroll, rotor, functional reentry) wave dynamics. This is an important problem in cardiology since pivoting waves likely underlie most reentrant tachycardias. The problem is complex, and to advance our methods of analysis we introduce two new tools: a ray tracing method and a moving-interface model. When used in combination with an ionic model, they permit us to elucidate the role played by tissue conductances on pivoting wave dynamics. Specifically we simulate traveling electrical waves with an ionic model that can reproduce the characteristics of plane and pivoting waves in small patches of cardiac tissue. Then ray tracing is applied to the simulated pivoting waves in a manner to expose their real displacement. In this exercise we find loci with special characteristics, as well as zones where a part of a pivoting wave quickly transitions from a regenerative to a non-regenerative propagation mode. The loci themselves and the monitoring of the ionic model state variables in this zone permit to elucidate several aspects of pivoting wave dynamics. We then formulate the moving-interface model based on the information gathered with the above-mentioned analysis. Equipped with a velocity profile v(s), s: distance along of the pivoting wave contour and the steady- state action potential duration (APD) of a plane wave during entrainment, APDss(T), at period T, this simple model can predict: shape, orbit of revolution, rotation period, whether a pivoting wave will break up or not, and whether the tissue will admit pivoting waves or not. Because v(s) and APDss(T) are linked to the ionic model, dynamical analysis with the moving-interface model conveys information on the role played by tissue conductances on pivoting wave dynamics. The analysis conducted here enables us to better understand previous results on the termination of pivoting waves. We surmise the method put forth here could become a means to discover how to alter tissue conductances in a manner to terminate pivoting waves at the origin of reentrant tachycardias.