This article summarizes the theoretical underpinnings of both the forward and inverse problems of electrocardiography. Space limitations prohibit describing all of the research work done in these areas, and the author apologizes in advance for any omissions on this account or due to oversight. The article should enable one to gain a better qualitative and quantitative understanding of the heart's electrical activity.

The forward and inverse problems of electrocardiography

The sequences of activation and recovery of the heart have physiological and clinical relevance. We report on progress made over the last years in the method that images these timings based on an equivalent double layer on the myocardial surface serving as the equivalent source of cardiac activity, with local transmembrane potentials (TMP) acting as their strength. The TMP wave forms were described analytically by timing parameters, found by minimizing the difference between observed body surface potentials and those based on the source description. The parameter estimation procedure involved is non-linear, and consequently requires the specification of initial estimates of its solution. Those of the timing of depolarization were based on the fastest route algorithm, taking into account properties of anisotropic propagation inside the myocardium. Those of recovery were based on electrotonic effects. Body surface potentials and individual geometry were recorded on: a healthy subject, a WPW patient and a Brugada patient during an Ajmaline provocation test. In all three cases, the inversely estimated timing agreed entirely with available physiological knowledge. The improvements to the inverse procedure made are attributed to our use of initial estimates based on the general electrophysiology of propagation. The quality of the results and the required computation time permit the application of this inverse procedure in a clinical setting.

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Non-Invasive Imaging of Cardiac Activation and Recovery

Background:Cardiac arrhythmias continue to be a leading cause of death and disability. Despite this alarming fact, a noninvasive imaging modality for cardiac electrophysiology (EP) has not been developed. Standard electrocardiographic techniques attempt to infer electrophysiological processes in the heart from a limited number of recordings on the body surface. This traditional approach is limited in its ability to provide information on regional electrocardiac activity and to localize electrophysiological events in the heart (e.g., arrhythmogenic foci; regions of elevated dispersion of myocardial repolarization). This article reviews the development of a novel imaging modality (electrocardiographic imaging [ECGI]) for the reconstruction of cardiac electrical activity from potentials measured away from the heart (i.e., on the torso surface). The results presented demonstrate that ECGI can noninvasively reconstruct epicardial potentials, electrograms, and isochrones with good accuracy and resolution.



Results:The locations of ectopic pacing sites are reconstructed within 10 mm of their actual positions. Dual epicardial pacing sites separated by 52 mm, 35 mm, and 17 mm can be resolved. The depth of intramural ectopic activity can be estimated and the direction of intramural activation spread can be determined from the reconstructed epicardial potential pattern and its evolution in time. Results from infarcted hearts demonstrate that ECGI can detect and reconstruct the abnormal electrophysiological substrate associated with the infarct. The figure-of-eight pattern of reentrant activation in the epicardial border zone during ventricular tachycardia is also reconstructed by ECGI noninvasively.



Conclusions:These results demonstrate the potential of ECGI as a clinical noninvasive imaging modality for identifying patients at risk of cardiac arrhythmias and for guiding and evaluating antiarrhythmic interventions in such patients. A.N.E. 1999;4(3):340–359

Noninvasive Electrocardiographic Imaging

We have developed a new approach for imaging cardiac transmembrane potentials (TMPs) within the three-dimensional (3-D) myocardium by means of an anisotropic heart model. The cardiac TMP distribution is estimated from body surface electrocardiograms by minimizing 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 present 3-D TMP imaging approach using pacing protocols. Simulations of single-site pacing at 24 sites throughout the ventricles, as well as dual-site pacing at 12 pairs of sites in the vicinity of atrio-ventricular ring were performed. The present simulation results show that the correlation coefficient (CC) and relative error (RE) between the "true" and inversely estimated TMP distributions were 0.9915/spl plusmn/0.0041 and 0.1266/spl plusmn/0.0326, for single-site pacing, and 0.9889/spl plusmn/0.0034 and 0.1473/spl plusmn/0.0237 for dual-site pacing, respectively, when 10 /spl mu/V Gaussian white noise (GWN) was added to the BSPMs. The effects of heart and torso geometry uncertainty were also evaluated by shifting the heart position by 10 mm and altering the torso size by 10%. The CC between the "true" and inversely estimated TMP distributions was above 0.97 when these geometry uncertainties were considered. The present simulation results demonstrate the feasibility of noninvasive estimation of TMP distribution throughout the ventricles from body surface electrocardiographic measurements, and suggest that the present method may become a useful alternative in noninvasive imaging of distributed cardiac electrophysiological processes within the 3-D myocardium.

Noninvasive imaging of cardiac transmembrane potentials within three-dimensional myocardium by means of a realistic geometry anisotropic heart model

Single-Beat Noninvasive Imaging of Cardiac Electrophysiology of Ventricular Pre-Excitation

Noninvasive images of the myocardial activation sequence are acquired, based on a new formulation of the inverse problem of electrocardiography in terms of the critical points of the ventricular surface activation map. It is shown that the method is stable with respect to substantial amounts of correlated noise common in the measurements and modeling of electrocardiography and that problems associated with conventional regularization techniques can be circumvented. Examples of application of the method to measured human data are presented. This first invasive validation of results compares well to previously published results obtained by using a standard approach. The method can provide additional constraints on, and thus improve, traditional methods aimed at solving the inverse problem of electrocardiography.

G. Huiskamp

Papers

A new method for myocardial activation imaging