Rudy Y, Messinger-Rapport B J
Department of Biomedical Engineering, Case Western Reserve University, Cleveland, Ohio.
Crit Rev Biomed Eng. 1988;16(3):215-68.
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
心电图逆问题的目标是从体表的电测量中无创地恢复有关心内电活动的区域信息。选择心外膜电位作为逆问题的解决方案，其动机在于每个体表电位分布都有唯一的心外膜电位解，能够通过实验验证逆恢复的心外膜电位，心外膜电位与心内区域事件细节之间已证实的关系，以及在手术干预前将逆解用作临床心外膜电位标测的补充或可能替代方法的可能性。尽管原则上可以从体表电位分布恢复心外膜电位分布，但电位方面的逆问题是不适定的，直接尝试重建心外膜电位会导致高度振荡的错误解。数据测量的不准确、对整个躯干电位数据的不完全了解以及对非均匀躯干容积导体的不准确描述，都可能导致与实际解有很大偏差。本综述首先从心外膜电位的角度对逆问题进行数学和定性描述。使用理论边值问题证明了该问题的不适定性。介绍了体表电位数据不准确（稳定性估计）的影响，并使用解析偏心球模型对几何和不均匀性参数进行了敏感性分析。描述并比较了用于关联心外膜电位与体表电位的各种计算方法，即正向传递矩阵的计算。证明了由于需要对病态传递矩阵求逆，对心外膜电位逆恢复进行正则化的必要性。比较了几种正则化技术在数据噪声、几何和不均匀性不准确方面的性能。最后，介绍并比较了几种现有的、从测量的体表电位数据计算心外膜电位的正则化逆程序。综述最后一部分指出了提高逆重建心外膜电位质量的未来方向。利用逆问题在实验动物和临床患者中无创获取心外膜电位分布的未来方向。
