Numerical study of defibrillation mechanisms using a one-dimensional model of cardiac tissue

In the study presented in this thesis we have used one-dimensional model to study mechanisms associated with the application of the external stimulus to the cardiac tissue. Arrhythmic dynamics is approximated with the reentrant wave on a ring of cardiac tissue. Successful defibrillation is modeled with the complete removal of the reentrant dynamics. The propagation of the electrical signal is modeled with the bidomain model, while cellular membrane current is modeled with the modified Beeler-Reuter model. Three well known and clinically used defibrillation protocols have been compared for different parameters of the system: monophasic, symmetric biphasic and asymmetric biphasic. Extensive numerical simulations performed for the shock duration of 8ms confirmed common medical wisdom that biphasic shocks are superior to monophasic shocks. More precisely, to yield a 90% success rate, a asymmetric biphasic protocol will require 26% less energy than the monophasic protocol. The order of efficiency of the three protocols is maintained for shock duration greater or equal than 4ms, while for smaller durations of the shock, monophasic protocols results to be the most successful of the three. Energy required to produce 50% and 90% success rate will also depend on the dynamics of the reentrant wave present on the ring prior to the shock. We have compared defibrillation protocols applied to reentrant quasiperiodic and chaotic dynamics. The results reveal that it is easier to defibrillate quasiperiodic that the chaotic dynamics. Careful examination of the defibrillation trials revealed, that for the shock duration of 8ms, all successful defibrillation trials can be classified into one of the four defibrillation protocols. These are: direct block, annihilation, delayed block and direct activation. Which defibrillation mechanism prevails depends on the energy level, the current dynamic state of the system and the shock protocol. Having tested and analyzed the validity of the one-dimensional model with the well known defibrillation protocols, the model was also used to examine the efficiency of a non-standard approach to defibrillation: application of the shock with the four electrode system instead of the common approach with two electrodes. Results revealed that a drastic reduction in defibrillation threshold is achieved with the four electrode technique with respect to the standard two electrode technique. The highest saving in required energy is achieved with the asymmetric biphasic protocol. When compared to the two-electrode monophasic protocol, it was found that the required energy reduced approximately 88%. Mechanism of successful defibrillation are analyzed and revealed that the advantage of biphasic shocks for the case of four electrodes protocol lies behind the interplay of the duration of the cathodal and anodal phase. While this study rely heavily on numerical results in a very simplified geometry, one would be tempted to hypothesize that some of the important findings will continue to hold in a more detailed and realistic study of defibrillation. The realization of the implantable four-electrode or similar multi-electrode setup has already been patented (European Patent No EP 0095726(A1) (1983), United States Patent No US 4641656 (1987)). Both patents are relatively old and date to the same decade of the first implanted defibrillator (1980). Given the advancement of the technological aspect of the implanted defibrillators over the past 30 years and the optimistic results obtained with four electrode setup, one simple message of this study is that the idea of the four-electrode setup is worth pursuing with a more detailed three dimensional study and possibly with animal experiments.