The potential for Laplacian maps to solve the inverse problem of electrocardiography

Presents a method to solve the inverse problem of electrocardiography using the Laplacian of the body surface potentials. The method presented is studied first using trade-off curves from a concentric spheres model representing a heart-torso system. Then a more conventional study is undertaken where a limited number of current dipoles are placed within the inner sphere and noise is added to the resulting potentials and Laplacians on the surface of the outer sphere. The results indicate that measurements of the outer surface Laplacian can more accurately reconstruct epicardial potentials than measurements of the outer surface potentials. The reconstructions are more accurate in that extrema are placed very close to their correct positions and multiple extrema and high potential gradients are recovered. Identical conclusions are observed in the presence of noise and even when the Laplacians are subject to greater noise than the potentials.

[1]  R. Cohen,et al.  Body surface Laplacian ECG mapping , 1992, IEEE Transactions on Biomedical Engineering.

[2]  D Kilpatrick,et al.  The inverse problem of electrocardiology: the performance of inversion techniques as a function of patient anatomy. , 1995, Mathematical biosciences.

[3]  R J Cohen,et al.  Body Surface Laplacian Mapping of Cardiac Excitation in Intact Pigs , 1993, Pacing and clinical electrophysiology : PACE.

[4]  S J Walker,et al.  Derived epicardial potentials differentiate ischemic ST depression from ST depression secondary to ST elevation in acute inferior myocardial infarction in humans. , 1989, Journal of the American College of Cardiology.

[5]  R. Gulrajani,et al.  Improving Tikhonov regularization with linearly constrained optimization: application to the inverse epicardial potential solution. , 1992, Mathematical biosciences.

[6]  S J Walker,et al.  Inverse electrocardiographic transformations: dependence on the number of epicardial regions and body surface data points. , 1994, Mathematical biosciences.

[7]  B. Hjorth.  An on-line transformation of EEG scalp potentials into orthogonal source derivations. , 1975, Electroencephalography and clinical neurophysiology.

[8]  R. M. Arthur,et al.  Effect of inhomogeneities on the apparent location and magnitude of a cardiac current dipole source. , 1970, IEEE transactions on bio-medical engineering.

[9]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[10]  P. Nunez,et al.  High-resolution EEG using spline generated surface Laplacians on spherical and ellipsoidal surfaces , 1993, IEEE Transactions on Biomedical Engineering.

[11]  S J Walker,et al.  Inverse electrocardiographic transformations: dependence on the number of epicardial regions and body surface data points. , 1994, Mathematical biosciences.

[12]  D Durrer,et al.  Mechanism and Time Course of S‐T and T‐Q Segment Changes during Acute Regional Myocardial Ischemia in the Pig Heart Determined by Extracellular and Intracellular Recordings , 1978, Circulation research.