Collaborative Research: CDI Type II: Dynamics and Control of Cardiac Tissue

复杂的时空动力学是许多心脏心律失常的基础。尽管经过了几十年的生物医学研究和越来越详细的计算模型的开发，但诱发和维持这些心律失常的机制仍然难以捉摸。我们试图通过发展一种根本性的和迫切需要的范式转变来提高我们对这些机制的基本理解，从计算密集型的直接数值模拟到根据有限的时空模式来描述心脏动力学。使用尖端的数值算法，我们将计算心脏动力学的详细离子模型的一系列精确的稳态和时间周期解。这些不稳定的解决方案以目前隐藏在视野中的时空模式的有限曲目来描述心脏动力学。他们对完全分解的心脏组织模型的确定是计算密集型的，但一旦获得这些解，他们就产生了对时空混沌动力学的全新理解，因为他们经历了一系列相应的重复模式。这种表示还允许使用可能需要比当前除颤方法更低的电压的电刺激来开发心脏动力学的非线性控制。数值计算将与涉及心脏组织和细胞培养的实验紧密结合。这些实验将被用来验证所提出的计算分析和测试控制方法。心律失常是工业化世界中死亡的主要原因，通过对其行为的深入了解来降低其发病率可能会产生重大的社会影响。通过将最先进的数值、分析和实验方法结合到心脏组织的研究中，该项目旨在启动一种激进的范式转变：我们建议使用直接数值模拟作为工具来开发一种新的心脏组织动力学的定量模板描述。在这种方法中，心律失常的动力学被理解为不同心律之间的一组可能的过渡，不仅导致对心律失常的开始和演变的更深层次的动力学理解，而且还改进了预防或终止心律失常的策略。虽然重点放在心脏动力学上，但所开发的方法将影响其他处理高维复杂系统的领域，这些系统表现出不稳定的反复模式，如神经障碍、流体和血浆动力学以及气候研究。

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.