STUDIES ON MECHANISM OF ABNORMAL CARDIAC RHYTHMS

这项提案涉及将开展的研究的五个主要方面 旨在阐明正常/异常心律的机制。 第一部分是全面调查 与单粒子重置和湮灭相关的现象 心脏节律对外界刺激的反应。为了研究这样一个 将进行现象、计算机模拟和分叉分析 在(之前发表的)心脏电学模型上。第二 部分是为了(I)最小化这些方程中的微分方程式的数目 模型和(Ii)统一它们，以便一组方程可以描述 任何心脏起搏细胞的电活动。为了获得一个更简单的 数学模型我们将尝试找出浇口之间的关系 动态变量；为了制定统一的模型，我们将考虑角色 细胞内Ca~(2+)、Na~+离子浓度和细胞内钙缓冲能力 细胞内储存，以及细胞外K+区隔。 第三部分是(I)在计算机上模拟 脉冲沿一串起搏的心脏细胞，以及(Ii)将其扩展到2- 以及可兴奋细胞的三维网络。模拟脉冲 在字符串上的传播，我们将使用在 第二部分；为了在2维和3维网络上进行模拟，我们将 使用两个变量的Fitzhugh-Nagumo类型模型。这部分研究是 意在进一步查明心律失常的原因。在 第四部分，我们将研究周期倍增和混沌 从实验和理论上都观察到，在电学活动中 心脏。为了做到这一点，我们打算建造波辛凯尔第一返回号 地图，并使用 心脏数学模型。从我们的结果中，我们将努力确定一个 心脏分叉现象与心律失常的可能关系 心脏。在第五部分中，我们将对两种模式进行详细的比较 计算机预测和实验来源提供的预测。这 将验证我们的模拟是真实的，并与心脏生理学相关。

This proposal addresses five major aspects of research that will be carried out to elucidate the mechanism underlying normal/abnormal cardiac rhythms. The first part is to perform a comprehensive investigation of the phenomenon associated with phase-resetting and annihilation of single cardiac rhythm in response to external stimuli. In order to study such a phenomenon, computer simulations and bifurcation analysis will be carried out on the (previously published) cardiac electrical models. The second part is to (i) minimize the number of differential equations in these models and (ii) unified them so that one set of equations can describe electrical activity of any cardiac pacemaker cell. To obtain a simpler mathematical model we will try to find a relationship among the gating dynamic variables; to formulate a unified model we will consider the role of intracellular Ca2+ and Na+ ions and the Ca+ -buffering power of the intracellular stores, in addition to extracellular K+ compartmentation. The third part is to (i) stimulate on a computer the propagation of an impulse along a string of pacemake cardiac cells and (ii) extend it to a 2- and 3-dimensional network of excitable cells. To simulate impulse propagation on a string, we will use the mathematical model obtained in the second part; to simulate that on a 2- and 3-dimensional network, we will use a 2- variable FitzHugh-Nagumo type model. This part of research is intended to further identify the cause of cardiac arrhythmias. In the fourth part, we will examine periodic doubling and chaos that have been observed, both experimentally and theoretically, in electrical activity of the heart. To do this, we intend to construct the Poincaire first return maps and to carry out a bifurcation and power spectrum analysis using the mathematical cardiac models. From our results, we will try to identify a possible relationship between the bifurcation phenomenon and arrhythmias in the heart. In the fifth part, we will make a detailed comparison between the computer predictions and those provided by experimental sources. This will verify our simulation to be realistic and relevant to cardiophysiology.