Nonlinear Dynamics and Bifurcations in Cardiac Tissue

心脏利用通常以协调方式传播的电波来启动机械收缩，但在病理状态下，电波的传播可能被预先存在的异质区域或由于快速起搏和系统的非线性动力学而产生的动态异质破坏。后者的一个重要例子是电交替，这通常是危及生命的心律失常的前兆，其中两个连续的有节奏的节拍引起不同幅度和持续时间的电反应（因此是机械反应）。尽管受到了广泛的关注，但对互感器的基本特征仍未充分研究，并且在全球范围内，使用电干预来控制互感器的尝试尚未取得成功。我们的研究目的是在最基本的层面上推进对心脏交替的理解，并利用这些知识来实现使用基本非线性动力学原理的电气控制改进方案。特别是，我们将描述电交替下的倍周期分岔类型，开发数学模型来研究交替下的动态和生物物理机制，并实现和测试新的控制算法。单处理器和多处理器环境中的数学建模和计算机模拟将与实验技术结合使用，包括微电极、激光扫描共聚焦显微镜和利用心脏组织中电压敏感染料获得的荧光信号进行光学测绘。本研究将阐明双周期分岔到电交替的本质，量化细胞内钙动力学和跨膜电压在交替起源中的作用，并提高对组织中全局控制算法的理解。在这个项目的过程中，研究生和本科生将参与这项研究，并将受益于跨学科的环境。该项目的一个关键组成部分是促进广泛传播信息。在此建议中开发的数学模型和算法将通过网站以独立代码和交互式Java小程序的形式免费提供。结果也将呈现，特别强调为科学家和公众提供互动节目和动画。最终，这项研究可能会改善危及生命的心律失常的治疗方法：通过预防交替，交替可能引发的致命心律失常也可以避免。此外，对电异常的更好理解和控制复杂动力学的新方法可能会转化为其他相关系统，包括大脑、周围神经系统和其他类型的肌肉。

The heart utilizes electrical waves that normally spread in a coordinated manner to initiate a mechanical contraction, but in pathologic states, electrical wave propagation can be disrupted by pre-existing heterogeneous regions or by dynamic heterogeneities that develop as a consequence of rapid pacing and the nonlinear dynamics of the system. An important example of the latter that is often a precursor to life-threatening arrhythmias is electrical alternans, in which two successive paced beats elicit electrical responses (and thus mechanical responses) of different amplitudes and durations. Despite much attention, fundamental characteristics about alternans remain under-studied, and attempts to use electrical interventions to control alternans have not been successful on a global level. Our research aims to advance the understanding of cardiac alternans at the most basic level and to use this knowledge to implement improved schemes of electrical control using fundamental nonlinear dynamics principles. In particular, we will characterize the type of period-doubling bifurcation underlying electrical alternans, develop mathematical models to investigate the dynamical and biophysical mechanisms underlying alternans, and to implement and test novel control algorithms. Mathematical modeling and computer simulations in single-and multi-processor environments will be used in conjunction with experimental techniques, including microelectrodes, laser-scanning confocal microscopy, and optical mapping using fluorescence signals obtained with voltage-sensitive dyes in cardiac tissue. The proposed research will elucidate the nature of the period-doubling bifurcation to electrical alternans, quantify the roles of intracellular calcium dynamics and transmembrane voltage in the origin of alternans, and improve the understanding of global control algorithms in tissue. In the course of this project, graduate and undergraduate students will participate in this research and will benefit from an interdisciplinary environment. A key component of the project is to promote broad dissemination of information. The mathematical models and algorithms developed in this proposal will be made available free as stand alone codes and interactive Java applets via web sites. Results will be presented as well, with a special emphasis on interactive programs and animations for both scientists and the general public. Ultimately, this research may lead to improved treatments for life-threatening cardiac arrhythmias: by preventing alternans, the lethal cardiac arrhythmias that alternans can trigger also can be avoided. Furthermore, the improved understanding of electrical abnormalities and novel methods for controlling complex dynamics may translate to other related systems, including the brain and peripheral nervous system and other types of muscle.