title: Forward problem of electrocardiography: is it solved?
abstract: BACKGROUND
  The relationship between epicardial and body surface potentials defines the forward problem of electrocardiography. A robust formulation of the forward problem is instrumental to solving the inverse problem, in which epicardial potentials are computed from known body surface potentials. Here, the accuracy of different forward models has been evaluated experimentally.
  
  
  RESULTS
  Body surface and epicardial potentials were recorded simultaneously in anesthetized closed-chest pigs (n=5) during sinus rhythm, and epicardial and endocardial ventricular pacing (65 records in total). Body surface potentials were simulated from epicardial recordings using experiment-specific volume conductor models constructed from magnetic resonance imaging. Results for homogeneous (isotropic electric properties) and inhomogeneous (incorporating lungs, anisotropic skeletal muscle, and subcutaneous fat) forward models were compared with measured body surface potentials. Correlation coefficients were 0.85±0.08 across all animals and activation sequences with no significant difference between homogeneous and inhomogeneous solutions (P=0.85). Despite this, there was considerable variance between simulated and measured body surface potential distributions. Differences between the body surface potential extrema predicted with homogeneous forward models were 55% to 78% greater than observed (P<0.05) and attenuation of potentials adjacent to extrema were 10% to 171% greater (P<0.03). The length and orientation of the vector between potential extrema were also significantly different. Inclusion of inhomogeneous electric properties in the forward model reduced, but did not eliminate these differences.
  
  
  CONCLUSIONS
  These results demonstrate that homogeneous volume conductor models introduce substantial spatial inaccuracies in forward problem solutions. This probably affects the precision of inverse reconstructions of cardiac potentials, in which this assumption is made.
authors.affiliation: From the Auckland Bioengineering Institute (L.R.B., L.K.C., I.J.L., G.B.S., N.A.L., D.J.P., B.H.S.), Department of Physiology (I.J.L., D.J.P., B.H.S.), and Department of Medicine (N.A.L.), University of Auckland, Auckland, New Zealand; L'Institut de Rythmologie et Modélisation Cardiaque IHU-LIRYC, Université de Bordeaux, CRCTB U1045; Université de Bordeaux, Centre de Recherche Cardio-Thoracique de Bordeaux U1045; and Inserm U1045, Centre de Recherche Cardio-Thoracique de Bordeaux, Bordeaux, France (L.R.B.); Green Lane Cardiovascular Service, Auckland City Hospital, Auckland, New Zealand (N.A.L.); and Department of Physiology, Anatomy, and Genetics, University of Oxford, Oxford, United Kingdom (D.J.P.).
authors.forename: Laura R
authors.initials: LR
authors.lastname: Bear
authors.affiliation: From the Auckland Bioengineering Institute (L.R.B., L.K.C., I.J.L., G.B.S., N.A.L., D.J.P., B.H.S.), Department of Physiology (I.J.L., D.J.P., B.H.S.), and Department of Medicine (N.A.L.), University of Auckland, Auckland, New Zealand; L'Institut de Rythmologie et Modélisation Cardiaque IHU-LIRYC, Université de Bordeaux, CRCTB U1045; Université de Bordeaux, Centre de Recherche Cardio-Thoracique de Bordeaux U1045; and Inserm U1045, Centre de Recherche Cardio-Thoracique de Bordeaux, Bordeaux, France (L.R.B.); Green Lane Cardiovascular Service, Auckland City Hospital, Auckland, New Zealand (N.A.L.); and Department of Physiology, Anatomy, and Genetics, University of Oxford, Oxford, United Kingdom (D.J.P.).
authors.forename: Leo K
authors.initials: LK
authors.lastname: Cheng
authors.affiliation: From the Auckland Bioengineering Institute (L.R.B., L.K.C., I.J.L., G.B.S., N.A.L., D.J.P., B.H.S.), Department of Physiology (I.J.L., D.J.P., B.H.S.), and Department of Medicine (N.A.L.), University of Auckland, Auckland, New Zealand; L'Institut de Rythmologie et Modélisation Cardiaque IHU-LIRYC, Université de Bordeaux, CRCTB U1045; Université de Bordeaux, Centre de Recherche Cardio-Thoracique de Bordeaux U1045; and Inserm U1045, Centre de Recherche Cardio-Thoracique de Bordeaux, Bordeaux, France (L.R.B.); Green Lane Cardiovascular Service, Auckland City Hospital, Auckland, New Zealand (N.A.L.); and Department of Physiology, Anatomy, and Genetics, University of Oxford, Oxford, United Kingdom (D.J.P.).
authors.forename: Ian J
authors.initials: IJ
authors.lastname: LeGrice
authors.affiliation: From the Auckland Bioengineering Institute (L.R.B., L.K.C., I.J.L., G.B.S., N.A.L., D.J.P., B.H.S.), Department of Physiology (I.J.L., D.J.P., B.H.S.), and Department of Medicine (N.A.L.), University of Auckland, Auckland, New Zealand; L'Institut de Rythmologie et Modélisation Cardiaque IHU-LIRYC, Université de Bordeaux, CRCTB U1045; Université de Bordeaux, Centre de Recherche Cardio-Thoracique de Bordeaux U1045; and Inserm U1045, Centre de Recherche Cardio-Thoracique de Bordeaux, Bordeaux, France (L.R.B.); Green Lane Cardiovascular Service, Auckland City Hospital, Auckland, New Zealand (N.A.L.); and Department of Physiology, Anatomy, and Genetics, University of Oxford, Oxford, United Kingdom (D.J.P.).
authors.forename: Gregory B
authors.initials: GB
authors.lastname: Sands
authors.affiliation: From the Auckland Bioengineering Institute (L.R.B., L.K.C., I.J.L., G.B.S., N.A.L., D.J.P., B.H.S.), Department of Physiology (I.J.L., D.J.P., B.H.S.), and Department of Medicine (N.A.L.), University of Auckland, Auckland, New Zealand; L'Institut de Rythmologie et Modélisation Cardiaque IHU-LIRYC, Université de Bordeaux, CRCTB U1045; Université de Bordeaux, Centre de Recherche Cardio-Thoracique de Bordeaux U1045; and Inserm U1045, Centre de Recherche Cardio-Thoracique de Bordeaux, Bordeaux, France (L.R.B.); Green Lane Cardiovascular Service, Auckland City Hospital, Auckland, New Zealand (N.A.L.); and Department of Physiology, Anatomy, and Genetics, University of Oxford, Oxford, United Kingdom (D.J.P.).
authors.forename: Nigel A
authors.initials: NA
authors.lastname: Lever
authors.affiliation: From the Auckland Bioengineering Institute (L.R.B., L.K.C., I.J.L., G.B.S., N.A.L., D.J.P., B.H.S.), Department of Physiology (I.J.L., D.J.P., B.H.S.), and Department of Medicine (N.A.L.), University of Auckland, Auckland, New Zealand; L'Institut de Rythmologie et Modélisation Cardiaque IHU-LIRYC, Université de Bordeaux, CRCTB U1045; Université de Bordeaux, Centre de Recherche Cardio-Thoracique de Bordeaux U1045; and Inserm U1045, Centre de Recherche Cardio-Thoracique de Bordeaux, Bordeaux, France (L.R.B.); Green Lane Cardiovascular Service, Auckland City Hospital, Auckland, New Zealand (N.A.L.); and Department of Physiology, Anatomy, and Genetics, University of Oxford, Oxford, United Kingdom (D.J.P.).
authors.forename: David J
authors.initials: DJ
authors.lastname: Paterson
authors.affiliation: From the Auckland Bioengineering Institute (L.R.B., L.K.C., I.J.L., G.B.S., N.A.L., D.J.P., B.H.S.), Department of Physiology (I.J.L., D.J.P., B.H.S.), and Department of Medicine (N.A.L.), University of Auckland, Auckland, New Zealand; L'Institut de Rythmologie et Modélisation Cardiaque IHU-LIRYC, Université de Bordeaux, CRCTB U1045; Université de Bordeaux, Centre de Recherche Cardio-Thoracique de Bordeaux U1045; and Inserm U1045, Centre de Recherche Cardio-Thoracique de Bordeaux, Bordeaux, France (L.R.B.); Green Lane Cardiovascular Service, Auckland City Hospital, Auckland, New Zealand (N.A.L.); and Department of Physiology, Anatomy, and Genetics, University of Oxford, Oxford, United Kingdom (D.J.P.). b.smaill@auckland.ac.nz.
authors.forename: Bruce H
authors.initials: BH
authors.lastname: Smaill
mesh_terms: D000200:Action Potentials; D000818:Animals; D018780:Body Surface Potential Mapping / Q000379:methods*; D004562:Electrocardiography / Q000379:methods*; D056149:Epicardial Mapping / Q000379:methods*; D006329:Heart Conduction System / Q000502:physiology*; D023421:Models, Animal; D008955:Models, Cardiovascular; D010496:Pericardium / Q000502:physiology*; D011237:Predictive Value of Tests; D015203:Reproducibility of Results; D012815:Signal Processing, Computer-Assisted; D013552:Swine
keywords: body surface potential mapping; electrocardiography; epicardial mapping