Boundary element method in spatial characterization of the electrocardiogram

Abstract

The electrochemical activity of the heart gives rise to an electric field. In electrocardiography, cardiac electrical activity is assessed by analyzing the potential distribution of this field on the body surface. The potential distribution, or the set of measured surface-voltage signals, is called the electrocardiogram (ECG). Spatial properties of the ECG can be captured with body surface potential mapping (BSPM), in which the electrocardiogram is measured using dozens of electrodes. In this Thesis, methods for solving the forward and inverse problems of electrocardiography are developed and applied to characterization of acute myocardial ischemia. The methodology is based on numerical computation of quasi-static electric fields in a volume conductor model. An open-source Matlab toolbox for solving volume conductor problems with the boundary element method (BEM) is presented. The Galerkin BEM and analytical operator-integrals are, for the first time, applied to the epicardial potential problem; the formulation for a piece-wise homogeneous volume conductor is presented in detail, enabling straightforward inclusion of the lungs or other inhomogeneities in the thorax model. The results show that errors due to discretization and forward-computation are smaller with the linear Galerkin (LG) method than with the conventional methods. These benefits do, however, not reflect to the Tikhonov-regularized inverse solution. If the lungs are omitted, as commonly is done, the choice of the computational method is not significant. In a set of 22 patients measured with BSPM during coronary angioplasty (PTCA), the application of a BEM thorax model with dipolar equivalent sources enabled accurate discrimination between occluded coronary arteries: the correct classification was obtained in 21 patients using the BSPM and in 20 patients using a 5-electrode set suggested elsewhere. The ischemic regions could also be localized anatomically correctly with simplified epicardial potential imaging, even though patient-specific thorax models were not used. In another set, comprising 79 acute ischemic patients and 84 controls, dipole-markers performed well in detection and quantification of acute ischemia. These results show that the modeling-approach can provide valuable information also without patient-specific models and complicated protocols.