Spiral Waves, Obstacles and Cardiac Arrhythmias

Abstract

The propagation of electrical waves through cardiac tissue is a very important phenomenon to study since those waves activate the mechanisms for cardiac contraction, responsible to pump blood to the body. An electrical wave of excitation, called also an action potential wave, is initiated periodically at a place called the sinoatrial node, the natural pacemaker of the heart. This wave, propagates throughout the atria where it arrives at the atrioventricular node, where after some time delay, it propagates to the ventricles via the Purkinje fibers (Zaret et al., 1992). In normal conditions, this process is repeated approximately 70 to 100 times each minute and is commonly referred to as a heartbeat. The condition at which abnormal generation or propagation of excitation waves during the process described above, is termed as arrhythmia. One of the proposedmechanisms involved in the development of certain type of arrhythmias, are spiral waves, a particular form of functional reentry (Fenton et al., 2002; Veenhuyzen et al., 2004). Spiral waves, are self sustained waves of excitation that rotate freely or around an obstacle, reactivating the same area of tissue at a higher frequency than the normal SA node would do, increasing the normal heartbeat rate. In the worst scenario, a spiral wave might break up into smaller spiral waves giving uncoordinated contractions of the heart in a phenomenon known as fibrillation. When this phenomenon occurs in the ventricles, the heart quivers and looses its strength to pump blood to the body leading to immediate cardiac arrest (Fenton et al., 2002; Zaret et al., 1992). Fibrillation, is the main cause of death in industrialized countries (Fenton et al., 2002; Priori et al., 2002; Tang et al., 2005; Zipes, 2005). An important research area is the study of the interaction of spiral waves in cardiac tissuewith obstacles. Obstacles in cardiac tissue can be partially excitable or non excitable. Examples of partially excitable obstacles are scar tissue (Starobin et al., 1996) or ionic heterogeneities (Starobin et al., 1996; Tusscher & Panfilov, 2002; Valderrabano et al., 2000), whereas examples of non excitable obstacles are arteries (Valderrabano et al., 2000) or the natural orifices in the atria (Azene et al., 2001). It has been observed that an obstacle in cardiac tissue might act as a stabilizer of spiral wave dynamics (Davidenko et al., 1992; Ikeda et al., 1997; Kim et al., 1999; Lim et al., 2006; Pertsov et al., 1993; Valderrabano et al., 2000), as it provides a transition between meandering spiral waves (Ikeda et al., 1997) or multiple spiral waves (Shajahan et al., 2007; Valderrabano et al., 2000) into a simple rotation spiral, which is attached to the obstacle. This 17