title: Application of L1-norm regularization to epicardial potential solution of the inverse electrocardiography problem.
abstract: The electrocardiographic inverse problem of computing epicardial potentials from multi-electrode body-surface ECG measurements, is an ill-posed problem. Tikhonov regularization is commonly employed, which imposes penalty on the L2-norm of the potentials (zero-order) or their derivatives. Previous work has indicated superior results using L2-norm of the normal derivative of the solution (a first order regularization). However, L2-norm penalty function can cause considerable smoothing of the solution. Here, we use the L1-norm of the normal derivative of the potential as a penalty function. L1-norm solutions were compared to zero-order and first-order L2-norm Tikhonov solutions and to measured 'gold standards' in previous experiments with isolated canine hearts. Solutions with L1-norm penalty function (average relative error [RE] = 0.36) were more accurate than L2-norm (average RE = 0.62). In addition, the L1-norm method localized epicardial pacing sites with better accuracy (3.8 +/- 1.5 mm) compared to L2-norm (9.2 +/- 2.6 mm) during pacing in five pediatric patients with congenital heart disease. In a pediatric patient with Wolff-Parkinson-White syndrome, the L1-norm method also detected and localized two distinct areas of early activation around the mitral valve annulus, indicating the presence of two left-sided pathways which were not distinguished using L2 regularization.
authors.affiliation: Department of Biomedical Engineering, Cardiac Bioelectricity and Arrhythmia Center, Washington University in St Louis, 290 Whitaker Hall, Campus Box 1097, One Brookings Dr., Saint Louis, MO 63130-4899, USA. sg7@cec.wustl.edu
authors.forename: Subham
authors.initials: S
authors.lastname: Ghosh
authors.forename: Yoram
authors.initials: Y
authors.lastname: Rudy
mesh_terms: D000293:Adolescent; D000328:Adult; D000818:Animals; D002304:Cardiac Pacing, Artificial; D002648:Child; D002675:Child, Preschool; D004285:Dogs; D004562:Electrocardiography; D006330:Heart Defects, Congenital / Q000175:diagnosis / Q000628:therapy; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods; D008297:Male; D008955:Models, Cardiovascular; D009203:Myocardial Infarction / Q000175:diagnosis; D010496:Pericardium / Q000502:physiology* / Q000503:physiopathology; D014927:Wolff-Parkinson-White Syndrome / Q000175:diagnosis