Generalized eigensystem techniques for the inverse problem of electrocardiography applied to a realistic heart-torso geometry

Estimation of Heart-Surface Potentials Using Regularized Multipole Sources

Direct inference of heart-surface potentials from body-surface potentials has been the goal of most recent work on electrocardiographic inverse solutions. We developed and tested indirect methods for inferring heart-surface potentials based on estimation of regularized multipole sources. Regularization was done using Tikhonov, constrained-least-squares, and multipole-truncation techniques. These multipole-equivalent methods (MEMs) were compared to the conventional mixed boundary-value method (BVM) in a realistic torso model with up to 20% noise added to body-surface potentials and +/-1 cm error in heart position and size. Optimal regularization was used for all inverse solutions. The relative error of inferred heart-surface potentials of the MEM was significantly less (p < 0.05) than that of the BVM using zeroth-order Tikhonov regularization in 10 of the 12 cases tested. These improvements occurred with a fourth-degree (24 coefficients) or smaller multipole moment. From these multipole coefficients, heart-surface potentials can be found at an unlimited number of heart-surface locations. Our indirect methods for estimating heart-surface potentials based on multipole inference appear to offer significant improvement over the conventional direct approach.

Detection of the fingerprint of the electrophysiological abnormalities that increase vulnerability to life-threatening ventricular arrhythmias

Reduction of sudden death requires accurate identification of patients at risk for ventricular tachycardia (VT) and effective therapies. The Multicenter Unsustained Tachycardia Trial and Multicenter Automatic Defibrillator Implantation Trials demonstrate that the implantable cardioverter defibrillator impacts favorably on the incidence of VT in patients with myocardial infarction, underscoring the need to detect the electrophysiologic abnormalities required for the development of VT. Methods used for this purpose include: Holter monitoring, ejection fraction, signal-averaged ECG, heart rate variability, T-wave alternans, baroreflex sensitivity, and programmed stimulation. Performance of each method alone has demonstrated high-negative but low-positive predictive values. Recent studies confirm that their use in combination augments performance.A second approach for improving performance has been to reexamine how well each method detects the electrophysiological derangements that lead to VT. Our recent work has focused on the signal-averaged ECG. Judging from transmural maps of ventricular activation during VT and sinus rhythm obtained from patients, late potentials fail to detect completely signals from myocardium responsible for VT. To obviate this limitation we developed an approach based on inferred epicardial potentials in the frequency domain from 190-surface ECGs using individualized heart-torso models. Torso geometry and electrode positions are measured with a 3-armed digitizer. The location of cardiac structures is determined using echocardiography. The pericardial surface is approximated by a sphere that encloses the heart. Epicardial potentials are inferred using the boundary element method with zero-order Tikhonov regularization and the Composite Residual Smoothing Operator over the QRS complex. Studies are underway to determine if analysis of bioelectrical signals enveloping arrhythmogenic tissue improves identification of patients vulnerable to VT.

Noninvasive localization of the site of origin of paced cardiac activation in human by means of a 3-D heart model

A recently developed heart-model-based localization approach is experimentally evaluated in noninvasively localizing the site of origin of cardiac activation in a patient with a pacemaker. The heart-torso model of the patient was constructed from the contrast ultrafast computed tomography images. The site of initial paced activation in the patient was quantitatively localized and compared with the tip position of the pacemaker lead. The localization error of the inverse estimation was found to be 5.2 mm with respect to the true lead tip position. The promising result of this pilot experimental study suggests the feasibility of localizing the site of origin of cardiac activation in an experimental setting. The heart-model-based localization approach may become an alternative tool in localizing the site of origin of cardiac activation.

Body surface Laplacian electrocardiogram of ventricular depolarization in normal human subjects

INTRODUCTION

The body surface Laplacian electrocardiogram (ECG) mapping provides a noninvasive means for spatiotemporal mapping of cardiac electrical events. The aim of the present study was to explore the relationship between the Laplacian ECG and the underlying cardiac activities during ventricular depolarization in healthy human subjects.

METHODS AND RESULTS

A 95-channel body surface potential ECG was recorded over the anterolateral chest from 11 healthy male subjects. The surface Laplacian (SL) ECG was estimated from the recorded potentials during QRS complex by means of a novel spline SL estimator, as well as by the conventional 5-point SL estimator for comparison purpose. A simulation study was also conducted using a realistic geometry heart-torso model in an attempt to qualitatively interpret the experimental results. For all subjects, more spatial details were observed in the SL ECG maps compared with the potential ECG maps, with spline SL more robust against noise than the 5-point SL. In total, three positive activities (denoted as P1, P2, P3) and four negative activities (denoted as N1, N2, N3, N4) in the spline SL ECG maps were observed during ventricular depolarization. Initial localized P1 and N1 activities were observed in 11 and 8 subjects, respectively. Then, the initial P1 was divided into three positive activities (P1, P2, P3) in 9 subjects. After the appearance of multiple positive activities, three negative activities (N2, N3, N4) appeared in 11, 8, and 9 subjects, respectively. Similar findings were obtained in the computer simulation study.

CONCLUSION

The present study demonstrates that the SL ECG provides more spatial details than the potential ECG, and multiple simultaneously active ventricular activities could be revealed in the SL ECG maps. The results suggest that the SL ECG may provide an alternative for noninvasive mapping of cardiac electrical activity.

Noninvasive three-dimensional activation time imaging of ventricular excitation by means of a heart-excitation model

We propose a new method for imaging activation time within three-dimensional (3D) myocardium by means of a heart-excitation model. The activation time is estimated from body surface electrocardiograms by minimizing multiple objective functions of the measured body surface potential maps (BSPMs) and the heart-model-generated BSPMs. Computer simulation studies have been conducted to evaluate the proposed 3D myocardial activation time imaging approach. Single-site pacing at 24 sites throughout the ventricles, as well as dual-site pacing at 12 pairs of sites in the vicinity of atrioventricular ring, was performed. The present simulation results show that the average correlation coefficient (CC) and relative error (RE) for single-site pacing were 0.9992+/-0.0008/0.9989+/-0.0008 and 0.05+/-0.02/0.07+/-0.03, respectively, when 5 microV/10 microV Gaussian white noise (GWN) was added to the body surface potentials. The average CC and RE for dual-site pacing were 0.9975+/-0.0037 and 0.08+/-0.04, respectively, when 10 microV GWN was added to the body surface potentials. The present simulation results suggest the feasibility of noninvasive estimation of activation time throughout the ventricles from body surface potential measurement, and suggest that the proposed method may become an important alternative in imaging cardiac electrical activity noninvasively.

A new method for incorporating weighted temporal and spatial smoothing in the inverse problem of electrocardiography

In this paper, we present a method for incorporating temporal smoothing (TS) into the estimate of epicardial potentials from body surface potential data. Our algorithm employs a different spatial smoothing parameter, chosen by the composite residual error and smoothing operator criteria, at each time step in the sequence. The total spatial smoothing term is then simply partitioned between temporal and spatial smoothing. The algorithm appears to be quite robust with regard to this partitioning. The new method was evaluated in the setting of additive Gaussian noise, but otherwise realistic conditions of body geometry and reference epicardial potentials. In examining the match between estimated and measured electrograms, or the match between estimated isopotential maps and measured isopotential maps, the estimates constructed using the new TS algorithm produced consistently smaller relative errors than those constructed using a quasi-static (QS) algorithm or those constructed by postprocessing the QS estimate with a moving average filter.

Localization of the site of origin of cardiac activation by means of a heart-model-based electrocardiographic imaging approach

We have developed a new approach to solve the inverse problem of electrocardiography in terms of heart model parameters. The inverse solution of the electrocardiogram (ECG) inverse problem is defined, in the present study, as the parameters of the heart model, which are closely related to the physiological and pathophysiological status of the heart, and is estimated by using an optimization system of heart model parameters, instead of solving the matrix equation relating the body surface ECGs and equivalent cardiac sources. An artificial neural network based preliminary diagnosis system has been developed to limit the searching space of the optimization algorithm and to initialize the model parameters in the computer heart model. The optimal heart model parameters were obtained by minimizing the objective functions, as functions of the observed and model-generated body surface ECGs. We have tested the feasibility of the newly developed technique in localizing the site of origin of cardiac activation using a pace mapping protocol. The present computer simulation results show that, the present approach for localization of the site of origin of ventricular activation achieved an averaged localization error of about 3 mm [for 5-muV Gaussian white noise (GWN)] and 4 mm (for 10-muV GWN), with standard deviation of the localization errors of being about 1.5 mm. The present simulation study suggests that this newly developed approach provides a robust inverse solution, circumventing the difficulties of the ECG inverse problem, and may become an important alternative to other ECG inverse solutions.

A new computational approach for cortical imaging

Estimation of current or potential distribution on the cortex is used to obtain information about neural sources from the scalp recorded electroencephalogram. If the active sources in the brain are superficial, the estimated field distribution on the cortex also yields information about the active source configuration. In these cases, these methods can be used as source localization methods. In this study, we concentrate on finite-element-based cortex potential estimation. Usually these methods require surface interpolation of the recorded voltages at the electrodes onto the entire scalp surface. We propose a new computational approach which does not require the use of surface interpolation but does it implicitly and uses only the recorded data at the electrodes. We refer to this method as the systematic approach (SA). We compare the SA with the surface interpolation approach (IA) and show that the SA is able to produce somewhat better accuracy than the IA. However, the main asset is that the sensitivity of the cortical potential maps to the regularization parameter is significantly lower than with the IA.

Fusion of body surface potential and body surface Laplacian signals for electrocardiographic imaging

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, we 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. We introduce a fusion algorithm that combines the different types of signals and generally produces a good estimate for both model problems.

The use of the spatial covariance in computing pericardial potentials

This paper investigates the incorporation of the spatial covariance of the pericardial potentials, assumed known a priori as a regularization function, when computing the pericardial potential distribution from observed body surface potentials. The resulting inverse solutions are compared with those using as a regularization function: 1) the norm of the solution, 2) the norm of the surface Laplacian of the solution, as well as with those based on using the truncated singular value decomposition. The study uses a realistic source model to simulate potentials throughout the QRS-interval. This source is placed in an anatomically accurate inhomogeneous volume conductor model of the torso. The use of a single value of the regularization parameter is shown to be feasible: for data incorporating 2% noise, the use of the spatial covariance is demonstrated to result in a relative error over the entire QRS interval as low as 10%. Major errors are demonstrated to result if the effect of the inhomogeneity of the lungs is ignored. The spatial covariance based inverse is shown to be more robust with respect to the perturbations (noise; inhomogeneity) than the other estimators included in this study.

Adaptive local regularization methods for the inverse ECG problem

One of the fundamental problems in theoretical electrocardiography can be characterized by an inverse problem. We present new methods for achieving better estimates of heart surface potential distributions in terms of torso potentials through an inverse procedure. First, we outline an automatic adaptive refinement algorithm that minimizes the spatial discretization error in the transfer matrix, increasing the accuracy of the inverse solution. Second, we introduce a new local regularization procedure, which works by partitioning the global transfer matrix into sub-matrices, allowing for varying amounts of smoothing. Each submatrix represents a region within the underlying geometric model in which regularization can be specifically 'tuned' using an a priori scheme based on the L-curve method. This local regularization method can provide a substantial increase in accuracy compared to global regularization schemes. Within this context of local regularization, we show that a generalized version of the singular value decomposition (GSVD) can further improve the accuracy of ECG inverse solutions compared to standard SVD and Tikhonov approaches. We conclude with specific examples of these techniques using geometric models of the human thorax derived from MRI data.

Useful lessons from body surface mapping

Useful Lessons from Body Surface Mapping. Body surface potential maps (BSMs) depict the time varying distribution of cardiac potentials on the entire surface of the torso. Hundreds of studies have shown that BSMs contain more diagnostic and prognostic information than can be elicited from the 12-lead ECG. Despite these advantages, body surface mapping has not become a routinely used clinical method. One reason is that visual examination and sophisticated analysis of BSMs do not permit inferring the sequence of excitation and repolarization in the heart with a sufficient degree of certainty and detail. These limitations can be partially overcome by implementing inverse procedures that reconstruct epicardial potentials, isochrones, and ECGs from body surface measurements. Furthermore, ongoing experimental work and simulation studies show that a great deal of information about intramural events can be elicited from measured or reconstructed epicardial potential distributions. Interpreting epicardial data in terms of deep activity requires extensive knowledge of the architecture of myocardial fibers, their anisotropic properties, and the role of rotational anisotropy in affecting propagation and the associated potential fields.