Spiral-Wave Turbulence and Its Control in the Presence of Inhomogeneities in Four Mathematical Models of Cardiac Tissue

Abstract

Regular electrical activation waves in cardiac tissue lead to the rhythmic contraction and expansion of the heart that ensures blood supply to the whole body. Irregularities in the propagation of these activation waves can result in cardiac arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), which are major causes of death in the industrialised world. Indeed there is growing consensus that spiral or scroll waves of electrical activation in cardiac tissue are associated with VT, whereas, when these waves break to yield spiral- or scroll-wave turbulence, VT develops into life-threatening VF: in the absence of medical intervention, this makes the heart incapable of pumping blood and a patient dies in roughly two-and-a-half minutes after the initiation of VF. Thus studies of spiral- and scroll-wave dynamics in cardiac tissue pose important challenges for in vivo and in vitro experimental studies and for in silico numerical studies of mathematical models for cardiac tissue. A major goal here is to develop low-amplitude defibrillation schemes for the elimination of VT and VF, especially in the presence of inhomogeneities that occur commonly in cardiac tissue. We present a detailed and systematic study of spiral- and scroll-wave turbulence and spatiotemporal chaos in four mathematical models for cardiac tissue, namely, the Panfilov, Luo-Rudy phase 1 (LRI), reduced Priebe-Beuckelmann (RPB) models, and the model of ten Tusscher, Noble, Noble, and Panfilov (TNNP). In particular, we use extensive numerical simulations to elucidate the interaction of spiral and scroll waves in these models with conduction and ionic inhomogeneities; we also examine the suppression of spiral- and scroll-wave turbulence by low-amplitude control pulses. Our central qualitative result is that, in all these models, the dynamics of such spiral waves depends very sensitively on such inhomogeneities. We also study two types of control schemes that have been suggested for the control of spiral turbulence, via low amplitude current pulses, in such mathematical models for cardiac tissue; our investigations here are designed to examine the efficacy of such control schemes in the presence of inhomogeneities. We find that a local pulsing scheme does not suppress spiral turbulence in the presence of inhomogeneities; but a scheme that uses control pulses on a spatially extended mesh is more successful in the elimination of spiral turbulence. We discuss the theoretical and experimental implications of our study that have a direct bearing on defibrillation, the control of life-threatening cardiac arrhythmias such as ventricular fibrillation.

Spiral Waves, Obstacles and Cardiac Arrhythmias

“…Partially excitable obstacles are inhomogeneities in the tissue that originate from changes in single-cell properties such as the conductance of ion channels (Shajahan et al, 2009). Such inhomogeneities can arise from damaged or scar tissue (Starobin et al, 1996), when a lesion is created via ablation (Azene et al, 2001) or by regional hyperkalemia (Xie et al, 2001).…”

“…Such inhomogeneities can arise from damaged or scar tissue (Starobin et al, 1996), when a lesion is created via ablation (Azene et al, 2001) or by regional hyperkalemia (Xie et al, 2001). These changes affect the propagation speed of the pulse (Kléber & Rudy, 2004), the action potential duration (Beeler & Reuter, 1977;Efimov et al, 1995;Shajahan et al, 2009) and prolongs recovery of excitability after the occurrence of an action potential (Xie et al, 2001). The stability of spiral waves depending on inhomogeneities in the medium has been studied by Shajahan (Shajahan et al, 2009) and Xie (Xie et al, 2001).…”

“…These changes affect the propagation speed of the pulse (Kléber & Rudy, 2004), the action potential duration (Beeler & Reuter, 1977;Efimov et al, 1995;Shajahan et al, 2009) and prolongs recovery of excitability after the occurrence of an action potential (Xie et al, 2001). The stability of spiral waves depending on inhomogeneities in the medium has been studied by Shajahan (Shajahan et al, 2009) and Xie (Xie et al, 2001). In this work, we focus on partially excitable obstacles of circular shape.…”

“…Obstacles in cardiac tissue have been modeled with regions where the zero flux condition is imposed (Azene et al, 2001;Isomura et al, 2008;Panfilov & Kenner, 1993;Shajahan et al, 2009;Starobin et al, 1996;Valderrábano et al, 2000). Arteries (Valderrábano et al, 2000) and the natural orifices in the atria, (Azene et al, 2001) are examples of this type of obstacles.…”

“…This 17 www.intechopen.com transition is clinically important because as it has been shown, fibrillation like activity changes to a tachycardia regime (Kim et al, 1999). The interaction of spiral waves with obstacles and its relationship with the transition between different arrhythmic regimes has been experimentally and computationally studied by different researchers (Azene et al, 2001;Comtois & Vinet, 2005;Ikeda et al, 1997;Shajahan et al, 2007;2009;Valderrábano et al, 2000). Valderrabano et al (Valderrábano et al, 2000) studied in a cardiac tissue preparation the transition between ventricular fibrillation and ventricular tachycardia due to the presence of obstacles; Ikeda et al (Ikeda et al, 1997), also considered the transition of different arrhythmic regimes due to the attachment of a spiral wave to an obstacle of minimum size.…”