MATHEMATICAL MODELS OF PROPAGATION IN CARDIAC CELLS

数学建模、超级计算机和大规模并行计算机 这项技术将用于研究基本的电生理过程 与哺乳动物心脏的启动和繁殖有关 冲动，无论是在正常情况下还是在疾病状态下。模型 单房室结、浦肯野和心室细胞 用于进行复杂非线性研究的数值模拟 动力学和混沌行为。在单细胞模型中，我们将测试 假设周期速率依赖的激活模式在单个 心肌细胞是兴奋性非线性恢复的结果 在舒张期，并将开发一个基于兴奋性的分析模型 关于适当的恢复动力学和电压依赖关系 跨膜电流，试图预测精确的动力学 单个心肌细胞的速率依赖性激活。我们还将 在一和二中研究传播的非线性动力学 维度连接的房室结细胞束，线形浦肯野纤维 和分支的浦肯野网络。我们将研究变化的影响 单个元素的再生属性，或程度 它们之间的电相互作用。局部传导抑制区 正常活动的分离区域也将由高 电阻耦合和/或低兴奋性，以检验假设 率相关传导阻滞是细胞内不连续的结果 兴奋性、细胞间连接的几何布置和/或 电气耦合。我们还将分析这些模型对 基于动力系统理论的重复刺激 (混沌理论)，特别注意放大或 减少激活参数的局部节拍到节拍的变化(例如， 潜伏期、动作电位持续时间等)通过传播。的性质 将研究各向同性和各向异性心肌的传播。 在一维和二维的心室细胞阵列耦合的模型中 通过缝隙连接。细胞间耦合的相互作用 膜发生器的电阻特性及其对性能的影响 我们将研究传导速度和传播模式。 系统地。此外，我们将确定功能块和 在这些二维模型中，迂回路径可以作为 轴向各向异性分布不均匀的后果 电阻率，以及再入是否需要在 块体区域的相对大小和方向以及 到达那个区域的波前。来自模拟的预测将 与其他工程和模型的实验结果进行比较 这些预测将被用来设计进一步的生物实验。 总体而言，这些模拟将用于探测潜在的细胞 心率和节律正常和异常的机制。

Mathematical modelling, a supercomputer and massively parallel computer technology will be used to investigate basic electrophysiological processes involved in the initiation and propagation of the mammalian cardiac impulse, both under normal conditions and during disease states. Models of single atrioventricular (AV) nodal, Purkinje and ventricular cells will be used to perform numerical simulations for the study of complex non-linear dynamics and chaotic behavior. In single cell models, we will test the hypothesis that periodic rate-dependent activations patterns in single cardiac cells are a consequence of a non-linear recovery of excitability during diastole, and will develop an analytical model of excitability based on the recovery kinetics and voltage-dependence of the appropriate transmembrane currents, in an attempt to predict the precise dynamics of rate-dependent activation of single cardiac cells. We will also investigate the non-linear dynamics of propagation in one and two- dimensionally connected bundles of AV nodal cells, linear Purkinje fibers and branching Purkinje networks. We will study the influence of varying the regenerative properties of the individual elements, or the degree of electrical interaction among them. Localized zones of depressed conduction separating regions of normal activity will also be created by high resistance coupling and/or by low excitability, to test the hypothesis that rate-dependent conduction block is a result of the discontinuities in cell excitability, geometrical arrangements of cell-to-cell connections and/or electrical coupling. We will also analyze the response of these models to repetitive stimulation on the basis of the theory of dynamical systems (chaos theory), with particular attention paid to amplification or reduction of local beat-to-beat changes in activation parameters (e.g., latency, action potential duration, etc.) by propagation. The nature of propagation in isotropic and anisotropic ventricular muscle will be studied in models of one-and two-dimensional arrays of ventricular cells coupled through gap junctions. The interplay between intercellular coupling resistance an membrane generator properties, and their effects on conduction velocity and patterns of propagation will be investigated systematically. Further, we will determine whether functional block and circuitous pathways can be generated in these two-dimensional models as a consequence of the nonuniform anisotropic distribution of axial resistivity, and whether reentry requires a critical relationship between relative size and orientation of the region of block and the curvature of the wavefront reaching that region. Predictions from the simulations will be compared with experimental results obtained in other projects and model predictions will be used to design further biological experiments. Overall, the simulations will be used to probes the underlying cellular mechanisms of normal and abnormal heart rate and rhythm.