Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie-Paris 6, UMR 7598, 75005, and Département de Rythmologie-Stimulation, Hôpital Saint-Joseph, 185, rue Raymond Losserand, 75014 Paris, France.
Ann Biomed Eng. 2010 Mar;38(3):1071-97. doi: 10.1007/s10439-009-9873-0. Epub 2009 Dec 24.
This paper deals with the numerical simulation of electrocardiograms (ECG). Our aim is to devise a mathematical model, based on partial differential equations, which is able to provide realistic 12-lead ECGs. The main ingredients of this model are classical: the bidomain equations coupled to a phenomenological ionic model in the heart, and a generalized Laplace equation in the torso. The obtention of realistic ECGs relies on other important features--including heart-torso transmission conditions, anisotropy, cell heterogeneity and His bundle modeling--that are discussed in detail. The numerical implementation is based on state-of-the-art numerical methods: domain decomposition techniques and second order semi-implicit time marching schemes, offering a good compromise between accuracy, stability and efficiency. The numerical ECGs obtained with this approach show correct amplitudes, shapes and polarities, in all the 12 standard leads. The relevance of every modeling choice is carefully discussed and the numerical ECG sensitivity to the model parameters investigated.
本文讨论了心电图（ECG）的数值模拟。我们的目标是设计一个基于偏微分方程的数学模型，该模型能够提供真实的 12 导联心电图。该模型的主要成分是经典的：在心脏中与现象离子模型耦合的双域方程，以及在躯干中的广义拉普拉斯方程。获得真实的心电图依赖于其他重要特征——包括心脏-躯干传输条件、各向异性、细胞异质性和希氏束建模——这些特征在文中都有详细讨论。数值实现基于最先进的数值方法：域分解技术和二阶半隐式时间推进方案，在准确性、稳定性和效率之间提供了良好的折衷。通过这种方法得到的数值心电图在所有 12 个标准导联中都显示出正确的幅度、形状和极性。对每个建模选择的相关性进行了仔细的讨论，并研究了数值心电图对模型参数的敏感性。
