Stephen J. Walker

Forward and inverse electrocardiographic calculations using resistor network models of the human torso.

An automated method of modelling the electrical properties of the human thorax from horizontal section data such as computerized tomographic scans has been used to develop both forward and inverse transformations between epicardial and body surface potential distributions. Eleven torso models with varying geometry and organ configurations have been studied. For the forward calculations, a standard dipole-like source is placed along the axis of the heart. Inverse calculations are performed using a measured body surface potential distribution and are based on a division of the surface of the heart into 25 source regions, producing epicardial potentials on these regions. A regularization method is used to stabilize the inverse solutions. Both forward and inverse solutions show substantial differences between models. These findings imply that matching models with patient geometry may be necessary in order to use such solutions in a clinical setting.

Inverse electrocardiographic transformations: dependence on the number of epicardial regions and body surface data points

Abstract The inverse problem of electrocardiography, the computation of epicardial potentials from body surface potentials, is influenced by the desired resolution on the epicardium, the number of recording points on the body surface, and the method of limiting the inversion process. To examine the role of these variables in the computation of the inverse transform, Tikhonovs zero-order regularization and singular value decomposition (SVD) have been used to invert the forward transfer matrix. The inverses have been compared in a data-independent manner using the resolution and the noise amplification as endpoints. Sets of 32, 50, 192, and 384 leads were chosen as sets of body surface data, and 26, 50, 74, and 98 regions were chosen to represent the epicardium. The resolution and noise were both improved by using a greater number of electrodes on the body surface. When 60% of the singular values are retained, the results show a trade-off between noise and resolution, with typical maximal epicardial noise levels of less than 0.5% of maximum epicardial potentials for 26 epicardial regions, 2.5% for 50 epicardial regions, 7.5% for 74 epicardial regions, and 50% for 98 epicardial regions. As the number of epicardial regions is increased, the regularization technique effectively fixes the noise amplification but markedly decreases the resolution, whereas SVD results in an increase in noise and a moderate decrease in resolution. Overall the regularization technique performs slightly better than SVD in the noise-resolution relationship. There is a region at the posterior of the heart that was poorly resolved regardless of the number of regions chosen. The variance of the resolution was such as to suggest the use of variable-size epicardial regions based on the resolution.

Derived epicardial potentials differentiate ischemic ST depression from ST depression secondary to ST elevation in acute inferior myocardial infarction in humans

It was hypothesized that in acute inferior wall myocardial infarction, an additional ischemic area in the subendocardium of the noninfarcting territory would produce a selective current dipole between the infarcting and ischemic regions. A resistance network model to calculate epicardial potentials from body surface electrocardiographic potentials was developed and used to examine the hypothesis in 219 patients with acute inferior myocardial infarction. In the learning set of 110 patients, two characteristic dipole patterns were observed, each associated with a high mortality rate in the ensuing 15 months when compared with that in the remaining patients. In the test set of 109 patients, a double-blind analysis of the patterns showed that the 34 patients with a dipole pattern had a collective mortality rate of 35% at 15 months compared with a 15 month rate of 5% in the remaining patients. In the total group of 219 patients, the magnitude of ST segment elevation and both the magnitude and integral of the area voltage of ST depression on the epicardium were significantly correlated with the mortality rate (p less than 0.0002 for all variables against death at 15 months). This study strongly suggests that ST depression due to ischemia can be differentiated from ST depression secondary to the ST elevation in acute inferior infarction by the examination of epicardial potential distributions.

Electrical current paths in acute pericarditis

The electrocardiographic changes accompanying pericarditis consist of ST elevation in most of the leads of the 12-lead electrocardiogram. The source of this ST elevation is thought to be local inflammatory changes in the epicardium underlying the inflamed pericardium. The current from this area of ST elevation must return to some unaffected region of the heart and this should be associated with a region of ST depression. This current path from the external epicardial surface has been postulated to flow back into the endocardium through the great vessels and atria. To test this hypothesis, 18 patients with pericarditis were studied by body surface potential mapping and inverse epicardial potential distributions were computed. The resultant maps were compared to those of normal people and patients with acute anterior infraction. Epicardial maps from patients with pericarditis showed a region of current flow into the heart over the great vessels and atria in all 18 patients. This pattern was not seen in normal patients or infarction patients and was consistent with the mechanism resulting in ST elevation in pericarditis being one of current flowing from the epicardium out into the thorax and back into the heart through the great vessels and atria.

Prognostic significance of ST potentials determined by body surface mapping in inferior wall acute myocardial infarction

Electrocardiographic body surface mapping on admission to coronary care has been shown to predict prognosis in a previous study of 100 patients with inferior wall acute myocardial infarction (AMI). A further 98 patients with first inferior wall AMI were now studied by body surface mapping on admission to coronary care to confirm that both the spatial distribution or map pattern of ST-segment potentials and the precise measurement of the maxima and minima are of prognostic significance. Each ST-segment map was compared by correlation coefficient to the average map pattern of the 4 groups derived in a previous study and placed in the group with the highest correlation coefficient. Analysis of these groups against outcome confirmed that the group dominated by a large area of marked anterior ST depression was associated with a high rate of complications and a significantly lower survival free of coronary artery bypass grafting (p less than 0.01). Patients in this group had more extensive and severe coronary artery disease than patients in the other groups. Increasing values of maximal ST depression correlated with mortality and complication rates. The extent by which the magnitude of ST-segment depression exceeded the magnitude of ST-segment elevation correlated with mortality and incidence of left ventricular failure. The results confirm the findings of the original study. Body surface mapping is of prognostic significance in inferior wall AMI.

Importance of the great vessels in the genesis of the electrocardiogram.

The electrocardiogram is the graphic representation against time of the difference in potential between points of the body caused by the current field of the heart. To examine the origin of this current field, a method of transforming body surface electrocardiographic data to the epicardial surface has been developed. The computed epicardial current density distributions in 219 patients with acute inferior myocardial infarction showed that, in 89% of patients, the current flow out of the heart during the ST segment came from two regions, not only from the infarction region but also from a region over the great vessels. This findings suggests that current flows from the ischemic region, through the low-resistance pathway provided by the intracavity blood, out the great vessels, and back to the epicardium. A similar pathway has been hypothesized when ischemia caused endocardial ST elevation, such as during a stress test or with unstable angina. To test this hypothesis, a group of patients with ST depression on the 12-lead electrocardiogram, not associated with ST elevation, was examined with body surface mapping. Ninety-four percent of patients had epicardial current density distributions that showed a region of current flow out of the heart and over the great vessels that was consistent with this hypothesis. This could explain the poor localization of coronary artery disease by electrocardiographic techniques when there is ST depression on the body surface.

Natural history of ST-segment potential distribution determined by body surface mapping in patients with acute inferior infarction

The authors studied the natural history of the electrocardiographic ST-segment using body surface mapping in 123 patients with acute inferior infarction who were not treated with thrombolytic agents. In 91 patients they compared body surface ST-segment maps recorded at 7.9 +/- 5.4 hours after the onset of acute myocardial infarction with maps recorded at 32.6 +/- 21.6 hours after infarction. In 46% of the patients the ST-segment distribution map pattern was unchanged. Twenty-eight percent of the patients moved to a ST-segment distribution associated with low mortality, and 7% correlated with a normal ST-segment distribution. Patients who started in a group dominated by marked anterior ST-segment depression or who developed this pattern at the time of the late map had a 45% morbidity, compared to 13% for patients who never developed this pattern (p less than 0.005). In a second group of 61 patients they compared maps recorded at 15.0 +/- 15.8 hours after infarction and repeat maps 19.6 +/- 13.0 recorded months later. At follow-up mapping, 44% of the patients correlated with a normal ST-segment distribution, 38% of patients had a low-risk pattern map and in 7% the map pattern was dominated by anterior ST-segment potential depression. The latter patients had a higher morbidity than patients in the other groups, but this did not reach statistical significance. Four of seven patients in this last group had significant angina at the time of follow-up mapping, compared to 2 of 54 patients in the other two groups (p less than 0.001).

Derived Epicardial ST Segment Potential Distribution Compared to the Resting Distribution of Thallium Scintigraphic Defect in Acute Myocardial Infarction

To test the validity of an inverse transformation of body surface electrocardiographic maps, we compared the calculated epicardial potential distribution with thallium scintigraphic scans. Seventeen patients with first acute myocardial infarction had body surface electrocardiographic maps a mean of 12.1±13.8 ,h after the onset of symptoms. Thallium scanning was performed a mean of 3.6±2.5 months after the myocardial infarction and before further clinical cardiac events

Inverse electrocardiographic transformations: Dependence on the number of epicardial regions and body surface data points

The inverse problem of electrocardiography, the computation of epicardial potentials from body surface potentials, is influenced by the desired resolution on the epicardium, the number of recording points on the body surface, and the method of limiting the inversion process. To examine the role of these variables in the computation of the inverse transform, Tikhonovs zero-order regularization and singular value decomposition (SVD) have been used to invert the forward transfer matrix. The inverses have been compared in a data-independent manner using the resolution and the noise amplification as endpoints. Sets of 32, 50, 192, and 384 leads were chosen as sets of body surface data, and 26, 50, 74, and 98 regions were chosen to represent the epicardium. The resolution and noise were both improved by using a greater number of electrodes on the body surface. When 60% of the singular values are retained, the results show a trade-off between noise and resolution, with typical maximal epicardial noise levels of less than 0.5% of maximum epicardial potentials for 26 epicardial regions, 2.5% for 50 epicardial regions, 7.5% for 74 epicardial regions, and 50% for 98 epicardial regions. As the number of epicardial regions is increased, the regularization technique effectively fixes the noise amplification but markedly decreases the resolution, whereas SVD results in an increase in noise and a moderate decrease in resolution. Overall the regularization technique performs slightly better than SVD in the noise-resolution relationship. There is a region at the posterior of the heart that was poorly resolved regardless of the number of regions chosen. The variance of the resolution was such as to suggest the use of variable-size epicardial regions based on the resolution.