New quantitative and qualitative approaches to the inverse problem of electrocardiology: Their theoretical relationship and experimental consistency

Abstract

In addition to formidable theoretical obstacles that a proposed solution to the inverse electrocardiology problem must overcome, there are great practical difficulties in establishing its accuracy in actual clinical application. However, the recent appearance of two fundamentally independent treatments of the inverse problem raises the possibility that they may be used in tandem to help establish their individual accuracy. Thus, if the two methods give incompatible results in application then one of the methods must be inaccurate. Conversely, if the two methods give compatible results then the accuracy of both methods is supported (for the particular quantities measured) subject only to the validity of the assumptions common to both methods. We have compared results from the application of a quantitative "integral equations based" method with that of a qualitative "differential topology inspired" approach in three healthy volunteers. The output examined consists of measurements of the times of appearance of epicardial sources (depolarization wavefront breakthroughs) and sinks of the ventricular surface activation map. The extent of agreement on source/sink times between the methods was consistent with the resolution limits imposed by noise and discrete sampling on derivatives of the electrocardiogram. When events defined by the integral method occurring within 2 ms of each other are grouped together (and their times averaged), the two methods agreed on source/sink times to within 3 ms except in two instances where they differed by 5 ms. The measurements made by the two methods were found to be highly correlated (R = 0.95). While the quantitative method alone rests on a variety of modeling and procedural assumptions, the only assumption common to both methods is the uniform dipole layer hypothesis. Thus, subject to this single assumption, one may infer the accuracy of the quantitative method in healthy individuals for epicardial source/sink times. On the other hand, coupling with the far more detailed quantitative method allows further useful characterization of the output of the qualitative method. In particular, this study provides convincing evidence that the major deflections of the spatial velocity electrocardiogram are coupled to particular epicardial sources and sinks, as has been previously conjectured on theoretical grounds. This raises the possibility of bedside evaluation of these epicardial events.