The inverse problem in electrocardiography: solutions in terms of epicardial potentials.
The inverse problem in electrocardiography: solutions in terms of epicardial potentials.
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发表时间：
1988
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通讯作者：
Y. Rudy;B. Messinger-Rapport
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作者：
Y. Rudy;B. Messinger-Rapport
心电图逆问题的目标是从体表的电测量中无创地恢复关于心内电事件的区域信息。选择心外膜电位作为逆问题的解决方案的动机是针对每个体表电位分布的唯一心外膜电位解决方案的可用性，通过实验验证逆恢复的心外膜电位的能力，通过心外膜电位与心内区域事件的细节之间的已证明的关系，以及通过在外科手术之前使用逆解作为临床心外膜电位标测的补充或可能的替代的可能性。虽然，在原则上，心外膜电位分布可以恢复从身体表面电位分布，在电位方面的逆问题是不适定的，和天真的尝试，以重建心外膜电位的结果在不正确的解决方案是高度振荡。与实际解的较大偏差可能是由于数据测量不准确、整个躯干上的电位数据知识不完整以及不均匀躯干体积导体的描述不准确。这篇综述首先从心外膜电位逆问题的数学和定性描述开始。的不适定性质的问题证明了使用理论边值问题。介绍了体表电位数据（稳定性估计）不准确的影响，并使用分析偏心球模型对几何和不均匀性参数进行了敏感性分析。用于将心外膜电位与体表电位相关联的各种计算方法，前向传输矩阵的计算，并进行了比较。证明了需要正则化的逆恢复的心外膜电位，从需要反转病态的传递矩阵。几种正则化技术进行了比较，在其性能方面的噪声的数据和不准确的几何形状和不均匀性。最后，几个现有的，正则化的逆程序，计算心外膜电位测量体表电位数据进行了介绍和比较。综述最后一节指出了未来提高逆重建心外膜电位质量的方向。未来的方向，使用反问题，以获得心外膜电位分布在实验动物和病人在临床上无创性
The objective of the inverse problem in electrocardiography is to recover noninvasively regional information about intracardiac electrical events from electrical measurements on the body surface. The choice of epicardial potentials as the solution to the inverse problem is motivated by the availability of a unique epicardial potential solution for each body surface potential distribution, by the ability to verify experimentally the inverse-recovered epicardial potentials, by the proven relationship between epicardial potentials and the details of intracardiac regional events, and by the possibility of using the inverse solution as a supplement or possible replacement to clinical epicardial potential mapping prior to surgical intervention. Although, in principle, the epicardial potential distribution can be recovered from the body surface potential distribution, the inverse problem in terms of potentials is ill-posed, and naive attempts to reconstruct the epicardial potentials result in incorrect solutions which are highly oscillatory. Large deviations from the actual solution may result from inaccuracy of the data measurement, incomplete knowledge of the potential data over the entire torso, and inaccurate description of the inhomogeneous torso volume conductor. This review begins with a mathematical and qualitative description of the inverse problem in terms of epicardial potentials. The ill-posed nature of the problem is demonstrated using a theoretical boundary value problem. Effects of inaccuracies in the body surface potential data (stability estimates) are introduced, and a sensitivity analysis of geometrical and inhomogeneity parameters is presented using an analytical eccentric spheres model. Various computational methods for relating epicardial to body surface potentials, i.e., the computation of the forward transfer matrix, are described and compared. The need for regularization of the inverse recovery of epicardial potentials, resulting from the need to invert the ill-conditioned transfer matrix, is demonstrated. Several regularization techniques are compared in terms of their performance regarding noise in the data and inaccuracies in geometry and inhomogeneities. Finally, several existing, regularized inverse procedures that compute epicardial potentials from measured body surface potential data are introduced and compared. The review concludes with a section that points toward future directions for improving the quality of the inverse-reconstructed epicardial potentials. Future directions for the use of the inverse problem to obtain epicardial potential distributions noninvasively in both experimental animals and patients in a clinical se