Keener J P
Department of Mathematics, University of Utah, Salt Lake City 84112.
J Math Biol. 1991;29(7):629-51. doi: 10.1007/BF00163916.
We derive an "eikonal-curvature" equation to describe the propagation of action potential wavefronts in myocardium. This equation is used to study the effects of fiber orientation on propagation in the myocardial wall. There are significant computational advantages to the use of an eikonal-curvature equation over a full ionic model of action potential spread. With this model, it is shown that the experimentally observed misalignment of spreading action potential "ellipses" from fiber orientation in level myocardial surfaces is adequately explained by the rotation of fiber orientation through the myocardial wall. Additionally, it is shown that apparently high propagation velocities on the epicardial and endocardial surfaces are the result of propagation into the midwall region and acceleration along midwall fibers before reemergence at an outer surface at a time preceding what could be accomplished with propagation along the surface alone.
我们推导了一个“程函-曲率”方程来描述心肌中动作电位波前的传播。该方程用于研究纤维方向对心肌壁中传播的影响。与完整的动作电位传播离子模型相比，使用程函-曲率方程具有显著的计算优势。通过该模型表明，实验观察到的水平心肌表面上传播的动作电位“椭圆”与纤维方向的错位可以通过纤维方向在心肌壁中的旋转得到充分解释。此外，还表明心外膜和心内膜表面上明显较高的传播速度是由于传播到中层壁区域并沿中层壁纤维加速，然后在外表面重新出现，且出现时间早于仅沿表面传播所能达到的时间。
