Electrical wave propagation in the heart
The contraction of the heart is coordinated by electrical signals. The propagation of these signals is facilitated by the electrical excitability of the cardiomyocytes (cardiac muscle cells): The increase of the transmembrane potential of a cell beyond threshold triggers an action potential which in turn leads to an increase of the transmembrane potentials of adjacent cells. In consequence, a nonlinear electrical wave propagates though the cardiac tissue. The disturbance of the coordination of this wave can be fatal. Ventricular fibrillation, the uncoordinated contraction of the ventricular myocytes, is one of the most common cause of death. The only effective therapy is electrical defibrillation, i.e., the delivery of a strong electrical current to the heart. Naturally, this involve severe side effects. A better understanding of the underlying physical and physiological processes can be expected to contribute to optimized defibrillation.
The complex electrophysiology of the heart
The cardiac conduction system is obviously a complex system. While the function of most cardiomyocytes involves coordinated contraction and propagation of action potentials, particular cardiomyocytes are specialized in initiation (in the sinoatrial node) and rapid propagation (in the His and Purkinje system) of action potentials. Numerous voltage- and ligand-gated ion channels trigger the action potential and the contraction of cardiomyocytes in a coordinated fashion. Gap junctions facilitate ion diffusion in adjacent cells and thus electrical wave propagation. In consequence, cardiac tissue can be considered as an excitable medium. Due to the mentioned diversity of cardiomyocytes, the medium is very heterogenous. Other major sources of electrophysiological heterogeneity are blood vessels, cardiac fibrosis, and irregular invaginations on the interior of ventricles. Moreover, the medium is highly anisotropic due to the elongated shape of cardiomyocytes and the biased distribution of gap junctions. However, typical excitation patterns (plane waves, spirals, chaotic patterns) arise also in the strongly simplified model of a homogenous, isotropic medium. Thus, the complex anatomical structure does not seem to be necessary for the complex spatiotemporal excitation dynamics. On the other hand, it appears that anatomical details are crucial in particular situations and have to be included in the modeling effort. For instance, re-entries, i.e., circulating excitation waves, develop preferentially in the vicinity of fibrotic regions of cardiac tissue where the electrical wave propagation is degraded. Numerical simulations of a discrete tissue model reveal that regular excitation waves break apart in such regions if the fraction of nonconducting links is close to the percolation threshold [Alonso, Bär, PRL 2013]. The heterogeneity of tissue is also crucial for the medical control of electrical wave propagation, particularly during defibrillation.
Low-Energy Anti-fibrillation Pacing (LEAP)
Although defibrillation is established for decades, the underlying physiological principles are, for the most part, not understood well. Of central interest is the exact location of excitation waves within the heart: Where do the potential drops during defibrillation suffice to trigger an action potential? Traditionally, it has been hypothesized that cardiac tissue is activated simultaneously, as potential drops have been assumed to be evenly distributed at the scale of individual cells. Nowadays, the importance of heterogeneities is establihed, resulting in hot spots, i.e., localized activation sites. However, the locations of these hot spots is controversial: Coronary arteries, invaginations on the interior of ventricles, and particular sites within the cardiac tissue have been suggested. A few years ago, defibrillation by a sequence of five weak pulses has been demonstrated. By this method, the delivered defibrillation energy was reduced by more than 80%. Due to the smaller electrical field, hot spots only emerge at large blood vessels. Only the delivery of several pulses excites large parts of tissue, thereby suppresses the chaotic dynamics, and results in successful defibrillation. Because of obvious experimental difficulties, numerical simulations of electrophysiological heart models are very valuable. In particular, we hope to gain insight into the mechanism of LEAP. This would possibly allow us to suggest further improvements of the method. In this respect, the interaction of individual pulses is crucial, see Fig. 1.
