Complex spatiotemporal dynamics underlie many arrhythmic disorders of the heart. Despite decades of biomedical research and the development of increasingly detailed computational models, the mechanisms that induce and sustain these arrhythmias remain elusive. We seek to improve our fundamental understanding of these mechanisms by developing a radical and urgently needed paradigm shift from computationally intensive direct numerical simulations to a description of cardiac dynamics in terms of a finite repertoire of spatiotemporal patterns. Using cutting-edge numerical algorithms, we will compute a hierarchy of exact steady and time-periodic solutions of detailed ionic models of cardiac dynamics. These unstable solutions describe cardiac dynamics in terms of a finite repertoire of spatiotemporal patterns that are currently hidden from view. Their determination for fully resolved cardiac tissue models is computationally intensive, but once these solutions are obtained, they yield a radically new understanding of the spatiotemporally chaotic dynamics as a walk through a repertoire of corresponding recurrent patterns. This representation also allows development of nonlinear control of cardiac dynamics using electrical stimulation that may require lower voltages than current defibrillation approaches. Numerical computations will be tightly integrated with experiments involving both cardiac tissue and cell cultures. The experiments will be used both to validate the proposed computational analysis and to test the control approach.
Cardiac arrhythmias are a major cause of mortality in the industrialized world, and any reduction in their incidence derived from a deeper understanding of their behavior could have a significant societal impact. By combining state-of-the-art numerical, analytical, and experimental approaches to the study of cardiac tissue, this project aims to initiate a radical paradigm shift: we propose to use direct numerical simulation as a tool to develop a new kind of quantitative template description of the dynamics of cardiac tissue. In this approach, the dynamics of arrhythmias is understood as a set of possible transitions between different cardiac rhythms, leading not only to a deeper dynamical understanding of the initiation and evolution of cardiac arrhythmias, but also to improved strategies for their prevention or termination. Although the focus is on cardiac dynamics, the methods developed will impact other fields dealing with high-dimensional complex systems that exhibit unstable recurrent patterns, such as neural disorders, dynamics of fluids and plasmas, and climate studies.
