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，电波的传播可能会被预先存在的异质性区域或由于快速起搏和系统的非线性动力学而发展的动态异质性所干扰。后者的一个重要例子往往是危及生命的心律失常的先兆，即电交替，在这种情况下，两个连续的起搏引起不同幅度和持续时间的电反应(从而引起机械反应)。尽管受到了很多关注，但关于交替者的基本特征仍然没有得到充分的研究，而且使用电子干预来控制交替者的尝试在全球范围内都没有成功。我们的研究目的是在最基本的水平上促进对心脏交替的理解，并利用这些知识来实施使用基本非线性动力学原理的改进的电子控制方案。具体地说，我们将描述电气交错的倍周期分叉的类型，开发数学模型来研究交错的动力学和生物物理机制，并实施和测试新的控制算法。将在单处理器和多处理器环境中使用数学建模和计算机模拟，并结合实验技术，包括微电极、激光扫描共聚焦显微镜，以及使用心脏组织中的电压敏感染料获得的荧光信号进行光学测绘。这项拟议的研究将阐明电交替的倍周期分叉的本质，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，并将从一个跨学科的环境中受益。该项目的一个重要组成部分是促进信息的广泛传播。本提案中开发的数学模型和算法将作为独立代码和交互式Java小程序通过网站免费提供。也将展示结果，特别强调为科学家和普通公众提供的互动节目和动画。最终，这项研究可能会改进危及生命的心律失常的治疗方法：通过预防交替，也可以避免交替可能引发的致命心律失常。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，包括大脑和周围神经系统以及其他类型的肌肉。

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.