Various approaches to the solution to the inverse problem of electrocardiography have been proposed over the years. Recently, the use of inverse algorithms using measured body surface Laplacians has been proposed, and in various studies this technique has been shown to outperform the traditional use of body surface potentials in certain model problems. In this paper, the authors compare the use of body surface potentials and body surface Laplacians on two model problems with different assumed cardiac sources. For the spherical cap model problems with an anterior source, the epicardial estimates using body surface potentials had smaller average relative errors than when body surface Laplacians were used. For the spherical cap model problems with a posterior source, the epicardial estimates using body surface potential or body surface Laplacian sensors generally produced similar relative errors. For the radial dipole model, the epicardial estimates using body surface Laplacians had smaller errors than when body surface potentials were used. The authors introduce a fusion algorithm that combines the different types of signals and generally produces a good estimate for both model problems.
Recent studies have reported a significant false positive rate in delivery of therapy by implantable antitachycardia devices utilizing detection algorithms based on sustained high rate. More selective decision schemes for the recognition of life‐threatening arrhythmias have been recently proposed that use analysis of the intrinsic electrogram rather than rate alone. Morphological discrimination of abnormal electrograms using correlation waveform analysis (CWA) has been proposed as an effective method of intracardiac electrogram analysis, but its computational demands limit its use in implantable devices. A new method for intracardiac electrogram analysis, the bin area method (BAM), was created to detect abnormal cardiac conduction with computational requirements of one‐half to one‐tenth those of CWA. Like CWA, BAM is a template matching method that is sensitive to conduction changes revealed in the electrogram morphology and is independent of amplitude and baseline fluctuations. Performance of BAM and CWA were compared using bipolar right ventricular and right atrial electrode recordings from 47 patients undergoing clinical cardiac electrophysiology studies. Nineteen patients had 31 distinct monomorphic ventricular tachycardias (VTs) induced (group I), thirteen patients had paroxysmal bundle branch block of supraventricular origin (BBB) induced (group II), and 19 patients had retrograde atrial activation during right ventricular overdrive pacing (group III). (One patient was common to all three groups, and two patients were common to groups II and III.) Using the ventricular electrogram, both BAM and CWA distinguished VT from sinus rhythm in 28/31 (90%) cases, and BBB from Normal Sinus Rhythm (NSR) in 13/13 (100%) patients. Using the atrial electrogram, both BAM and CWA distinguished anterograde from retrograde atrial activation in 19/19 (100%) patients. BAM achieves similar performance to CWA with significantly reduced computational demands, and may make real‐time analysis of intracardiac electrograms feasible for implantable pacemakers and antitachycardia devices.
We compare various eigenvector expansion techniques for a realistic heart-torso geometry using experimental data studied by other researchers in inverse electrocardiography. With this model, the recently proposed generalized eigensystem (GES) approach and the modified GES (tGES) technique perform better than singular value decomposition (SVD) and a modified SVD (tSVD) technique. The tGES and tSVD techniques are combination methods which constrain, the solutions like zero-order Tikhonov regularization but allow the truncation of modes like GES and SVD.
Abstract In a recent series of papers we proposed a new class of methods, the generalized eigensystem (GES) methods, for solving the inverse problem of electrocardiography. In this paper, we compare zero, first, and second order regularized GES methods to zero, first, and second order Tikhonov methods. Both optimal results and results from parameter estimation techniques are compared in terms of relative error and accuracy of epicardial potential maps. Results from higher order regularization depend heavily on the exact form of the regularization operator, and operators generated by finite element techniques give the most accurate and consistent results. In the optimal parameter case, the GES techniques produce smaller average relative errors than the Tikhonov techniques. However, as the regularization order increases, the difference in average relative errors between the two techniques becomes less pronounced. We introduce the minimum distance to the origin (MDO) technique to choose the number of expansion modes for the GES techniques. This produces average relative errors similar to those obtained using the composite residual and smoothing operator (CRESO) with Tikhonov regularization. Second order regularization gives the smallest average relative errors but over-smoothes important epicardial features. In general, GES with MDO resolves the epicardial features better than Tikhonov with CRESO for the data set studied. Keywords: Electrocardiographynumerical methodsregularization methodsinverse problems *This work was supported in part by NSF grant numbers BES-9410385 and BES-9622158, and the National Center for Supercomputing Applications under grant BCS930005N. It utilized the Power Challenge Array at NCSA, University of Illinois at Urbana-Champaign. †Corresponding author.rthrone@unlinfo.unl.edu *This work was supported in part by NSF grant numbers BES-9410385 and BES-9622158, and the National Center for Supercomputing Applications under grant BCS930005N. It utilized the Power Challenge Array at NCSA, University of Illinois at Urbana-Champaign. †Corresponding author.rthrone@unlinfo.unl.edu Notes *This work was supported in part by NSF grant numbers BES-9410385 and BES-9622158, and the National Center for Supercomputing Applications under grant BCS930005N. It utilized the Power Challenge Array at NCSA, University of Illinois at Urbana-Champaign. †Corresponding author.rthrone@unlinfo.unl.edu
The identification of tool/chip interface temperatures from remote sensor measurements is a steady inverse heat transfer problem that arises in online machine tool monitoring. In a previous paper we developed a set of inverse approaches, vector projection inverse methods, specifically for this problem. These methods rely on two types of sensor measurements: temperatures and heat fluxes. However, because of the extreme ill-conditioning of the tool configuration we studied previously, only a very limited amount of information could be obtained using any of the inverse approaches examined. In an effort to understand the impact of physical parameters on the conditioning of the problem we examined two modifications to the simulated cutting tool: we increased the thermal conductivity of the tool insert, and we reduced the thickness of the tool insert. Inverse solutions were computed on both configurations with all methods for two temperature profiles and various noise levels. The estimated tool/chip interface temperature for the high conductivity tool showed no improvement compared to the original configuration, since the temperature profiles on the sensor surface were unchanged. However, for the thinner tool, the estimated temperatures were substantially more accurate than with the original configuration. With this thinner tool configuration, an optimal set of four sensors could be used to estimate these temperatures at the tool/chip interface to within a few degrees, even with noisy sensor data.
Abstract Singular Value Decomposition (SVD) and Generalized Eigensystem (GES) inverse techniques are compared for their ability to solve the inverse problem of electrocardiography. In the inverse problem of electrocardiography, electrical potential data for numerous locations on the body (torso) surface is used to infer the electrical potentials on the heart surface, while the governing equation and material properties are assumed known. This paper addresses two areas. First, the previously observed improved performance of GES compared to SVD is explained in terms of the unique nature of the GES vectors. Second, epicardial data from six in-vitro rabbit heart experiments are used to project body surface data for six different geometries, and inverse solutions are computed both with and without added noise. For concentric geometries, GES outperformed SVD in all instances. For eccentric heart/body geometries, GES outperformed SVD when the inverse errors themselves were small. In all cases, GES was less sensitive to added noise than SVD. Keywords: Inverse ProblemsSingular Value DecompositionGeneralized Eigensystem methods
