Analysis of Excitation Conduction in the Heart and the Reconstruction of Electrocardiogram Using Ionic -channel Models

心脏中的正常兴奋和传导是通过每个细胞的离子电导的动力学和细胞之间的电耦合之间的协调来维持的。(1)使用空间离散模型的传导兴奋，我们研究了这两个因素的功能作用。该模型是一维的，由五种心肌细胞组成。我们首先从视空间常数定量地确定了耦合系数，然后找到了SA结起搏活动的细胞数条件和耦合系数。我们还研究了房室结中非常慢的传导，发现房室结中细胞之间的弱耦合系数具有最强的影响。(2)建立了心室激动和复极过程中心电图的数字计算机模型。用730个单元的二维阵列表示心脏的室间隔和左心室游离壁。离子电流模型被用来确定这些单位的电活动的空间分布在每个时刻的模拟心动周期。为了重建心电图，首先将模型沿第三轴沿着等电位假设，然后用立体角法计算表面电位。正常人心电图重建良好。还通过修改相关离子电流动力学来重建高钾血症和低钾血症的ECG。在本计画中，我们使用欧拉法进行数值积分。但是，为了适应离子电流模型的改进，我们采用了GEAR方法，该方法具有求解所谓的“刚性”微分方程的能力。

The normal excitation and conduction in the heart are maintained by the coordination between the dynamics of ionic conductance of each cell and the electrical coupling between cells.(1) Using a spatially-discrete model of conduction of excitation, we examined functional roles of these two factors. The model is one-dimensional and is composed of five kinds of myocardial cells. We first determined quantitatively the coupling coefficients from the apparent space constants, then found the conditions of cell number and the couping coefficients for the pacemaker activities of SA-node. We also investigated the very slow conduction in AV-node and revealed that the weak coupling coefficients between cells in AV-node has the strongest effect.(2) A digital computer model was constructed for the simulation of the electrocardiogram during ventricular activation and repolarization. The part of the ventricular septum and the left ventricula free wall of the heart were represented by a two dimensional array of 730 units. Ionic current models were used to determine the spatial distribution of the electric activities of these units at each instant of time during simulated cardiac cycle. In order to reconstruct the electrocardiogram, the model was expanded three dimensionally with equipotential assumption along the third axis and then the surface potentials were calculated using solid angle method. ECG for normal subject was well reconstructed. ECGs for hyper-and hypokalemia were also reconstructed by modifying the related ionic current dynamics. We used Euler-method for numerical integration through this project. However, in order to accomodate the improvement of ionic current model, we adopted GEAR method which has a power to solve so-called "stiff" differential equation.