Roth B J
Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA.
Ann Biomed Eng. 1996 Nov-Dec;24(6):639-46. doi: 10.1007/BF02684177.
Experiments show that the rate of rise of the action potential depends on the direction of propagation in cardiac tissue. Two interpretations of these experiments have been presented: (i) the data are evidence of discrete propagation in cardiac tissue, and (ii) the data are an effect of the perfusing bath. In this paper we present a mathematical model that supports the second interpretation. We use the bidomain model to simulate action potential propagation through a slab of cardiac tissue perfused by a bath. We assume an intracellular potential distribution and solve the bidomain equations analytically for the transmembrane and extracellular potentials. The key assumption in our model is that the intracellular potential is independent of depth within the tissue. This assumption ensures that all three boundary conditions at the surface of a bidomain are satisfied simultaneously. One advantage of this model over previous numerical calculations is that we obtain an analytical solution for the transmembrane potential. The model predicts that the bath reduces the rate of rise of the transmembrane action potential at the tissue surface, and that this reduction depends on the direction of propagation. The model is consistent with the hypothesis that the perfusing bath causes the observed dependence of the action-potential rate of rise on the direction of propagation, and that this dependence has nothing to do with discrete properties of cardiac tissue.
实验表明，动作电位的上升速率取决于心脏组织中的传播方向。针对这些实验，已提出两种解释：（i）数据是心脏组织中离散传播的证据，以及（ii）数据是灌注浴的一种效应。在本文中，我们提出了一个支持第二种解释的数学模型。我们使用双域模型来模拟动作电位通过由浴灌注的一块心脏组织的传播。我们假设一个细胞内电位分布，并解析求解双域方程以得到跨膜电位和细胞外电位。我们模型中的关键假设是细胞内电位与组织内的深度无关。这一假设确保了双域表面的所有三个边界条件能同时得到满足。该模型相对于先前数值计算的一个优势在于，我们得到了跨膜电位的解析解。该模型预测，浴会降低组织表面跨膜动作电位的上升速率，并且这种降低取决于传播方向。该模型与以下假设一致：灌注浴导致了观察到的动作电位上升速率对传播方向的依赖性，并且这种依赖性与心脏组织的离散特性无关。
