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Comprehensive Electrocardiology pp 247–298Cite as

The Forward Problem of Electrocardiography

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1 8.1 Introduction

In this chapter we describe a class of problems known collectively as the “forward problem of electrocardiography,” which all share the goal of describing cardiac and torso electrical potentials starting from some description of electrical sources within the heart. To solve this forward problem, these electrical sources must be known beforehand, which may suggest a certain degree of artificiality, or at least impracticality, when viewed from the clinical context. The goal of clinical electrocardiography is to use the body-surface potentials from a patient to extract relevant parameters of the cardiac sources, which is the essence of the inverse problem of electrocardiography discussed in the following chapter. The forward problem, in contrast, has a more fundamental role in that it must capture the entire relationships between some description of the sources and the remote manifestations of cardiac bioelectricity.

In its full scope, the forward problem begins with...

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References

  1. Gulrajani R.M., Models of the electrical activity of the heart and the computer simulation of the electrocardiogram. Crit. Rev. Biomed. Eng., 1988;16: 1–66.

    CAS  PubMed  Google Scholar 

  2. Hunter P., P. Robbins, and D. Noble, The iups human physiome project. Pflugers Arch., 2002;445(1): 1–9.

    Article  CAS  PubMed  Google Scholar 

  3. Beatty G.E., S.C. Remole, M.K. Johnston, J.E. Holte, and D.G. Benditt, Non-contact electrical extrapolation technique to reconstruct endocardial potentials. PACE, 1994;17(4): 765.

    Article  Google Scholar 

  4. Gulrajani R.M., F.A. Roberge, and G.E. Mailloux, The forward problem of electrocardiography, in Comprehensive Electrocardiology, P.W. Macfarlane and T.D. Veitch Lawrie, Editors. Pergamon Press, Oxford, England, 1989, pp. 197–236.

    Google Scholar 

  5. Waller A.D., A demonstration on man of electromotive changes accompanying the heart’s beat. J. Physiol., 1887;8: 229–234.

    CAS  PubMed  Google Scholar 

  6. Einthoven W., G. Fahr, and A. de Waart, Über die Richting und manifest Grösse der Potentialschwankungen im menschlichen Herzen und über den Einfluss der Herzlage auf die Form des Elektrokardiograms. Pflügers Arch. ges. Physiol., 1913;150:275–315.

    Article  Google Scholar 

  7. Hodgkin A.L. and A.F. Huxley, Resting and action potentials in single nerve fibres. J. Physiol., 1945;10: 176–195.

    Google Scholar 

  8. Neher E., B. Sakmann, and J.H. Steinbach, The extracellular patch clamp: A method for resolving currents through individual open channels in biological membranes. Pflügers Arch. ges. Physiol., 1978;37: 219–228.

    Google Scholar 

  9. Ling G. and R.W. Gerard, The normal membrane potential of frog sartorius fibers. J. Cell Physiol., 1949;34: 383–396.

    Article  CAS  PubMed  Google Scholar 

  10. Smith T.G., J.L. Barker, B.M. Smith, and T.R. Colburn, Voltage clamping with microelectrodes. J. Neurosci. Methods, 1980;3: 105–128.

    Article  PubMed  Google Scholar 

  11. Hodgkin A.L. and A.F. Huxley, A quantatative decription of membrane current and its application to conduction and excitation in nerve. J. Physiol., 1952;11: 500–544.

    Google Scholar 

  12. Hodgkin A.L. and A.F. Huxley, The components of membrane conductance in the giant axon of loligo. J. Physiol., 1952;11: 473–496.

    Google Scholar 

  13. Li R.A., M. Leppo, T. Miki, S. Seino, and E. Marban, Molecular basis of electrocardiographic ST-segment elevation. Circ. Res., 2000;87(10): 837–909.

    Article  CAS  PubMed  Google Scholar 

  14. Lux R.L., M. Akhtar, and R.S. MacLeod, Mapping and invasive analysis, in Foundations of Cardiac Arrhythmias: Basic Concepts and Clinical Approaches, chapter 15, P.M. Spooner and M.R. Rosen, Editors. Marcel Dekker, New York, 2001, pp. 393–424.

    Google Scholar 

  15. Lux P.R. and P.R. Ershler, Reducing uncertainty in the measures of cardiac activation and recovery. in Proceedings of the IEEE Engineering in Medicine and Biology Society 9th Annual International Conference. IEEE Press, New York, 1987, pp. 1871–1872.

    Google Scholar 

  16. Ndrepepa G., E.B. Caref, H Yin, N. El-Sherif, and M. Restivo, Activation time determination by high-resolution unipolar and bipolar extracellulcar electrograms. J. Cardiovasc. Electrophysiol., 1995;6(3): 174–188.

    Article  CAS  PubMed  Google Scholar 

  17. Macleod R.S., R.O. Kuenzler, B. Taccardi, and R.L. Lux, Estimation of epicardial activation maps from multielectrode venous catheter measurements. PACE, 1998;21(4): 595.

    Google Scholar 

  18. Ni Q., R.S. MacLeod, and R.L. Lux, Three-dimensional activation mapping in canine ventricles: Interpolation and approximation of activation times. Ann. Biomed. Eng., 1999;27(5): 617–626.

    Article  CAS  PubMed  Google Scholar 

  19. Punske B.P., Q. Ni, R.L. Lux, R.S. MacLeod, P.R. Ershler, T.J. Dustman, Y. Vyhmeister, and B. Taccardi, Alternative methods of excitation time determination on the epicardial surface. In Proceedings of the IEEE Engineering in Medicine and Biology Society 22nd Annual International Conference, 2000.

    Google Scholar 

  20. Pieper C.F. and A. Pacifico, The epicardial field potential in dog: Implications for recording site density during epicardial mapping. PACE, 1993;16: 1263–1274.

    Article  CAS  PubMed  Google Scholar 

  21. Ni Q., R.S. MacLeod, R.L. Lux, and B. Taccardi, Interpolation of cardiac electric potentials. Ann. Biomed. Eng., 1997, 25(Suppl): 61. Biomed. Eng. Soc. Annual Fall Meeting.

    Google Scholar 

  22. Ni Q., R.S. MacLeod, R.L. Lux, and B. Taccardi, A novel interpolation method for electric potential fields in the heart during excitation. Ann. Biomed. Eng., 1998;26(4): 597–607.

    Article  CAS  PubMed  Google Scholar 

  23. Yılmaz B., R.S. MacLeod, B.B. Punske, B. Taccardi, and D.H. Brooks, Training set selection for statistical estimation of epicardial activation mapping from intravenous multielectrode catheters. IEEE Trans. Biomed. Eng., 2005;52(11): 1823–1831.

    Article  PubMed  Google Scholar 

  24. Yılmaz B., R.S. MacLeod, B.B. Punske, B. Taccardi, and D.H. Brooks, Venous catheter mapping of epicardial ectopic activation: Leadset analysis for statistical estimation. Comp. in Biol. & Med., (in press), 2006.

    Google Scholar 

  25. Pullan A.J. and M.P. Nash, Challenges facing validation of noninvasive electrical imaging of the heart. Ann. Noninvasive Electrocardiol., 2005;10(1): 73–82.

    Article  PubMed  Google Scholar 

  26. MacLeod R.S. and D.H. Brooks, Validation approaches for electrocardiographic inverse problems, in Computational Inverse Problems in Electrocardiography Peter Johnston, Editor. WIT Press, Ashurst, UK, 2001, pp. 229–268.

    Google Scholar 

  27. Burger H.C. and J.B. van Milaan, Heart-vector and leads. Part II. Br. Heart J., 1947;9: 154–160.

    Article  CAS  PubMed  Google Scholar 

  28. Burger H.C. and J.B. van Milaan, Heart-vector and leads. Part III: Geometrical representation. Br. Heart J., 1948;10: 229–333.

    Article  CAS  PubMed  Google Scholar 

  29. Grayzel J. and F. Lizzi, The combined influence of inhomogeneities and dipole location. Am. Heart J., 1967;74: 503–512.

    Article  CAS  PubMed  Google Scholar 

  30. Grayzel J. and F. Lizzi, The performance of VCG leads in homogenous and heterogenous torsos. J. Electrocardiol., 1969;2(1): 17–26.

    Article  CAS  PubMed  Google Scholar 

  31. Nagata Y., The electrocardiographic leads for telemetering as evaluated from the view point of the transfer impedance vector. Jap. Heart J., 1970;11(2): 183–194.

    Article  CAS  PubMed  Google Scholar 

  32. Nagata Y., The influence of the inhomogeneities of electrical conductance within the torso on the electrocardiogram as evaluated from the view point of the transfer impedance vector. Jap. Heart J., 1970;11(5): 489–505.

    Article  CAS  PubMed  Google Scholar 

  33. De Ambroggi L. and B. Taccardi, Current and potential fields generated by two dipoles. Circ. Res., 1970;27: 910–911.

    Article  Google Scholar 

  34. Mirvis D.M., F.W. Keller, R.E. Ideker, J.W. Cox, R.F. Dowdie, and D.G. Zettergren, Detection and localization of a multple epicardial electrical generator by a two dipole ranging technique. Circ. Res., 1977;41: 551.

    Article  CAS  PubMed  Google Scholar 

  35. Mirvis D.M., F.W. Keller, R.E. Ideker, D.G. Zettergren, and R.F. Dowdie, Equivalent generator properties of acute ischemic lesions in the isolated rabbit heart. Circ. Res., 1978;42: 676–685.

    Article  CAS  PubMed  Google Scholar 

  36. Mirvis D.M., Electrocardiographic QRS changes induced by acute coronary ligation in the isolated rabbit heart. J. Electrocardiol., 1979;12: 141–150.

    Article  CAS  PubMed  Google Scholar 

  37. Barr R.C. and M.S. Spach, Inverse solutions directly in terms of potentials, in The Theoretical Basis of Electrocardiography, C.V. Nelson and D.B. Geselowitz, Editors.. Clarendon Press, Oxford, 1976, pp. 294–304.

    Google Scholar 

  38. Barr R.C., M. Ramsey, and M.S. Spach, Relating epicardial to body surface potential distributions by means of transfer coefficients based on geometry measurements. IEEE Trans. Biomed. Eng., 1977;24: 1–11.

    Google Scholar 

  39. Barr R.C. and M.S. Spach, A comparison of measured epicardial potentials with epicardial potentials computed from body surface measurements in the intact dog. Adv. Cardiol., 1978;21: 19–22.

    CAS  PubMed  Google Scholar 

  40. Pilkington T.C., M.N. Morrow, and P.C. Stanley, A comparison of finite element and integral equation formulations for the calculation of electrocardiographic potentials. IEEE Trans. Biomed. Eng., 1985;32: 166–173.

    Article  CAS  PubMed  Google Scholar 

  41. Pilkington T.C., M.N. Morrow, and P.C. Stanley, A comparison of finite element and integral equation formulations for the calculation of electrocardiographic potentials – II. IEEE Trans. Biomed. Eng., 1987;34: 258–260.

    Article  CAS  PubMed  Google Scholar 

  42. Bradley C.P., M.P. Nash and D.J. Paterson, Imaging electrocardiographic dispersion of depolarization and repolarization during ischemia: simultaneous body surface and epicardial mapping. Circ., 2003.

    Google Scholar 

  43. Oster H.S., B. Taccardi, R.L. Lux, P.R. Ershler, and Y. Rudy, Noninvasive electrocardiographic imaging: Reconstruction of epicardial potentials, electrograms, and isochrones and localization of single and multiple electrocardiac events. Circ., 1997;96(3): 1012–1024.

    Article  CAS  Google Scholar 

  44. Messinger-Rapport B.J. and Y. Rudy, Noninvasive recovery of epicardial potentials in a realistic heart-torso geometry. Circ. Res., 1990;66(4): 1023–1039.

    Article  CAS  PubMed  Google Scholar 

  45. Ahmad G.F., D. H Brooks, and R.S. MacLeod, An admissible solution approach to inverse electrocardiography. Ann. Biomed. Eng., 1998;26: 278–292.

    Article  CAS  PubMed  Google Scholar 

  46. Brooks D.H., G.F. Ahmad, R.S. MacLeod, and G.M. Maratos,. Inverse electrocardiography by simultaneous imposition of multiple constraints. IEEE Trans. Biomed. Eng., 1999;46(1):3–18.

    Article  CAS  PubMed  Google Scholar 

  47. Burns J.E., B. Taccardi, R.S. MacLeod, and Y. Rudy, Noninvasive electrocardiographic imaging of electrophysiologically abnormal substrates in infarcted hearts: A model study. Circ., 2000;101: 533–540.

    Article  Google Scholar 

  48. Colli Franzone P., L. Guerri, B. Taccardi, and C. Viganotti, The direct and inverse problems in electrocardiology. Numerical aspects of some regularization methods and applications to data collected in isolated dog heart experiments. Lab. Anal. Numerica C.N.R., Pub. N:222, 1979.

    Google Scholar 

  49. Colli Franzone P., G. Gassaniga, L. Guerri, B. Taccardi, and C. Viganotti, Accuracy evaluation in direct and inverse electrocardiology, In Progress in Electrocardiography, P.W. Macfarlane, Editor. Pitman Medical, 1979, pp. 83–87.

    Google Scholar 

  50. Colli Franzone P., L. Guerri, B. Taccardi, and C. Viganotti, Finite element approximation of regularized solution of the inverse potential problem of electrocardiography and application to experimental data. Calcolo, 1985;22: 91.

    Article  Google Scholar 

  51. Colli Franzone P., L. Guerri, S. Tentonia, C. Viganotti, S. Spaggiari, and B. Taccardi, A numerical procedure for solving the inverse problem of electrocardiography. Analysis of the time-space accuracy from in vitro experimental data. Math. Biosci., 1985;77: 353–396.

    Article  Google Scholar 

  52. Soucy B., R.M. Gulrajani, and R. Cardinal, Inverse epicardial potential solutions with an isolated heart preparation, in Proceedings of the IEEE Engineering in Medicine and Biology Society 11th Annual International Conference. IEEE Press, New York, 1989, pp. 193–194.

    Google Scholar 

  53. Oster H. and Y. Rudy, The use of temporal information in the regularization of the inverse problem of electrocardiography, in Proceedings of the IEEE Engineering in Medicine and Biology Society 12th Annual International Conference. IEEE Press, New York, 1990, pp. 599–600.

    Google Scholar 

  54. Rudy Y. and Oster H. The electrocardiographic inverse problem. Crit. Rev. Biomed. Eng., 1992;20: 22–45.

    Google Scholar 

  55. MacLeod R.S., B. Taccardi, and R.L. Lux, The influence of torso inhomogeneities on epicardial potentials, in IEEE Comput. Cardiol.. IEEE Computer Society, 1994, pp. 793–796.

    Google Scholar 

  56. Brooks D.H. and R.S. MacLeod, Imaging the electrical activity of the heart: Direct and inverse approaches, in IEEE International Conference on Image Processing. IEEE Computer Society, 1994, pp. 548–552.

    Google Scholar 

  57. Brooks D.H., H. On, and R.S. MacLeod, Multidimensional multiresolution analysis of array ECG signals during PTCA procedures, in IEEE Symposium on Time-Frequency and Time-Scale. IEEE Computer Society, 1994, pp. 552–555.

    Google Scholar 

  58. Brooks D.H., G. Ahmad, and R.S. MacLeod, Multiply constrained inverse electrocardiology: Combining temporal, multiple spatial, and iterative regularization, in Proceedings of the IEEE Engineering in Medicine and Biology Society 16th Annual International Conference. IEEE Computer Society, 1994, pp. 137–138.

    Google Scholar 

  59. MacLeod R.S., B. Taccardi, and R.L. Lux, Electrocardiographic mapping in a realistic torso tank preparation, in Proceedings of the IEEE Engineering in Medicine and Biology Society 17th Annual International Conference. IEEE Press, New York, 1995, pp. 245–246.

    Google Scholar 

  60. Oster H.S., B. Taccardi, R.L. Lux, P.R. Ershler, and Y. Rudy, Electrocardiographic imaging: Noninvasive characterization of intramural myocardial activation from inverse-reconstructed epicardial potentials and electrograms. Circ., 1997;96:1496–1507.

    Article  Google Scholar 

  61. MacLeod R.S., Q. Ni, B. Punske, P.R. Ershler, B. Yilmaz, and B. Taccardi, Effects of heart position on the body-surface ECG. J. Electrocardiol., 2000, 33(Suppl): 229–238.

    Article  Google Scholar 

  62. MacLeod R.S., B. Punske, S. Shome, B. Yilmaz, and B. Taccardi, The role of heart rate and coronary flow during myocardial ischemia. J. Electrocardiol., 2001: 43–51.

    Google Scholar 

  63. MacLeod R.S., S. Shome, J.G. Stinstra, B.B. Punske, and B. Hopenfeld, Mechanisms of ischemia-induced ST-segment changes. J. Electrocardiol., 2005;38(Suppl): 8–13.

    Article  PubMed  Google Scholar 

  64. Khoury D.S. and Y. Rudy, A model study of volume conductor effects on endocardial and intracavitary potentials. Circ. Res., 1992;71(3): 511–525.

    Article  CAS  PubMed  Google Scholar 

  65. Khoury D.S. and Y. Rudy, Reconstruction of endocardial potentials from intracavitary probe potentials: a model study. IEEE Comput. Cardiol., 1992: 9–12.

    Google Scholar 

  66. Lui Z.W., P.R. Ershler, B. Taccardi, R.L. Lux, D.S. Khoury, and Y. Rudy, Noncontact endocardial mapping: Reconstruction of electrocardiograms and isochrones from intracavitary probe potentials. J. Cardiovasc. Electrophysiol., 1997;8:415–431.

    Article  Google Scholar 

  67. MacLeod R.S., B. Taccardi, and R.L. Lux, Mapping of cardiac ischemia in a realistic torso tank preparation. In Building Bridges: International Congress on Electrocardiology International Meeting, 1995, pp. 76–77.

    Google Scholar 

  68. MacLeod R.S., R.L. Lux, M.S. Fuller, and B. Taccardi, Evaluation of novel measurement methods for detecting heterogeneous repolarization. J. Electrocardiol., 1996;29(Suppl): 145–153.

    Article  PubMed  Google Scholar 

  69. MacLeod R.S., R.L. Lux, and B. Taccardi, A possible mechanism for electrocardiographically silent changes in cardiac repolarization. J. Electrocardiol., 1997;30(Suppl): 114–121.

    Article  Google Scholar 

  70. Hodgkin A.L. and A.F. Huxley, The dual effect of membrane potential on sodium conductance in the giant axon of loligo. J. Physiol., 1952;11: 497–506.

    Google Scholar 

  71. Plonsey R. and R.C. Barr, Bioelectricity: A Quantitative Approach. Plenum Publishing, New York, London, 1988.

    Google Scholar 

  72. Keener J. and J. Sneyd, Mathematical Physiology. Spinger, Berlin, 1998.

    Google Scholar 

  73. Sachse F.B., Computational Cardiology: Modeling of anatomy, electrophysiology, and mechanics. Springer, Berlin, 2004.

    Book  Google Scholar 

  74. Luo C.H. and Y. Rudy, A model of the ventricular cardiac action potential. Circ. Res., 1991;68(6): 1501–1526.

    Article  CAS  PubMed  Google Scholar 

  75. Luo C.H. and Y. Rudy, A dynamic model of the cardiac ventricular action potential: I. Simulations of ionic currents and concentration changes. Circ. Res., 1994;74(6): 1071–1096.

    Article  CAS  PubMed  Google Scholar 

  76. Einthoven W., Le telecardiogramme. Arch. Int. de Physiol., 1906;4: 132–164.

    Google Scholar 

  77. Goldberger A.L. and E. Goldberger, Clinical Electrocardiography. C.V. Mosby, 1986.

    Google Scholar 

  78. Taccardi B., Distribution of heart potentials on the thoracic surface of normal human subjects. Circ. Res., 1963;1: 341–351.

    Article  Google Scholar 

  79. Macchi E., G. Arisi, and B. Taccardi, Identification of ectopic ventricular foci by means of intracavity potential mapping: A proposed method. Acta Cardiol., 1992;XLVII(5): 421–433.

    Google Scholar 

  80. Cobb F.R., S.D. Blumenschein, and W.C. Sealy, Successful surgical interruption of the bundle of Kent in a patient with Wolff–Parkinson–White syndrome. Circ., 1968;38: 1016.

    Article  Google Scholar 

  81. De Ambroggi L., B. Taccardi, and E. Macchi, Body surface maps of heart potential: Tentative localization of preexcited area of forty-two Wolff–Parkinson–White patients. Circ., 1976;54: 251.

    Article  CAS  Google Scholar 

  82. Lux R.L., P.R. Ershler, K.P. Anderson, and J.W. Mason, Rapid localization of accessory pathways in WPW syndrome using unipolar potential mapping, in Proceedings of the IEEE Engineering in Medicine and Biology Society 11th Annual International Conference. IEEE Press, New York, 1989, pp. 195–196.

    Google Scholar 

  83. Shenasa M., R. Cardinal, P. Savard, M. Dubac, P. Page, and R. Nadeau, Cardiac mapping. part I: Wolff-Parkison-White syndrome. PACE, 1990;13: 223–230.

    Article  CAS  PubMed  Google Scholar 

  84. Shahidi A.V., P. Savard, and R. Nadeau, Forward and inverse problems of electrocardiography: Modeling and recovery of epicardial potentials in humans. IEEE Trans. Biomed. Eng., 1994;41(3): 249–256.

    Article  CAS  PubMed  Google Scholar 

  85. Penney C.J., J.C. Clements, M.J. Gardner, L. Sterns, and B.M. Horáček, The inverse problem of electrocardiography: Application to localization of Wolff-Parkinson-White pre-excitation sites, in Proceedings of the IEEE Engineering in Medicine and Biology Society 17th Annual International Conference. IEEE Press, New York, 1995, pp. 215–216.

    Google Scholar 

  86. Yee R., G.J. Klein, and G.M. Guiraudon, The Wolff–Parkinson–White syndrome, in Cardiac Electrophysiology, From Cell to Bedside, D.P. Zipes and J. Jalife, Editors. W.B. Saunders Co., London, 1995, pp. 1199–1214.

    Google Scholar 

  87. Gallagher J.J., M. Gilbert, R.H. Svenson, W.C. Sealy, J. Kasell, and A.G. Wallace, Wolff–Parkinson–White syndrome: The problem, evaluation, and surgical correction. Circ., 1975;5: 767–785.

    Article  Google Scholar 

  88. Barr R.C. and T.C. Pilkington, Computing inverse solutions for an on-off heart model. IEEE Trans. Biomed. Eng., 1969;16: 205–214.

    CAS  PubMed  Google Scholar 

  89. Schmitt O.H., Biological information processing using the concept of interpenetrating domains, in Information Processing in the Nervous System, K.N. Leibovic, Editor. Springer, New York, 1969.

    Google Scholar 

  90. Miller W.T. and D.B. Geselowitz, Simulation studies of the electrocardiogram: I The normal heart and II Ischemia and infarction. Circ. Res., 1978;4: 301–323.

    Article  Google Scholar 

  91. Tung L., A Bidomain Model for describing ischemic myocardial DC potentials. PhD thesis, M.I.T., 1978.

    Google Scholar 

  92. Roth B.J. and J.P. Wikswo, A bidomain model for the extracellular potential and magnetic field of the cardiac tissue. IEEE Trans. Biomed. Eng., 1986;33: 467–469.

    Article  CAS  PubMed  Google Scholar 

  93. Henriquez C.S. and R. Plonsey, Simulation of propagation along a cylindrical bundle of cardiac tissue–I: Mathematical formulation. IEEE Trans. Biomed. Eng., 1990;37: 850–860.

    Article  CAS  PubMed  Google Scholar 

  94. Henriquez C.S. and R. Plonsey, Simulation of propagation along a cylindrical bundle of cardiac tissue–II: Results of simulation. IEEE Trans. Biomed. Eng., 1990;37: 861–875.

    Article  CAS  PubMed  Google Scholar 

  95. Fischer G., B. Tilg, R. Moore, G.J.M. Huiskamp, J. Fetzer, W. Rucker, and P. Wach, A bidomain model based BEM-FEM coupling formulation for anisotropic cardiac tissue. Ann. Biomed. Eng., 2000;28: 1228–1243.

    Article  Google Scholar 

  96. Lines G., J. Sundnes, and A. Tveito, A domain embedding strategy for solving the bidomain equations on complicated geometries. Int. J. Bioelectromagn., 2002;4(2): 53–54.

    Google Scholar 

  97. Hopenfeld B., Stinstra J.G., and MacLeod R.S., Mechanism for ST depression associated with contiguous subendocardial ischemia. J. Cardiovasc. Electrophysiol., 2004;15(10):1200–1206.

    Article  PubMed  Google Scholar 

  98. Henriquez C.S., Simulating the electrical behavior of cardiac tissue using the bidomain model. Crit. Rev. Biomed. Eng., 1993;21(1): 1–77.

    CAS  PubMed  Google Scholar 

  99. Gardner M., Mathematical games. Scient. Amer., October 1970: 120–123.

    Google Scholar 

  100. Moe G.K., W.C. Rheinboldt, and J.A. Abildskov, A computer model of fibrillation. Am. Heart J., 1964;67: 200–220.

    Article  CAS  PubMed  Google Scholar 

  101. Abildskov J.A., Mechanism of the vulnerable period in a model of cardiac fibrillation. J. Cardiovasc. Electrophysiol., 1990;1:303–308.

    Article  Google Scholar 

  102. Restivo M., W. Craelius, W.B. Gough, and N. El-Sherif, A logical state model of reentrant ventricular activation. IEEE Trans. Biomed. Eng., 1990;37: 344–353.

    Article  CAS  PubMed  Google Scholar 

  103. Leon L.J. and B.M. Horáček, Computer model of excitation and recovery in the anisotropic myocardium: I Rectangular and cubic arrays of excitable elements. J. Electrocardiol., 1991;24: 1–15.

    Article  CAS  PubMed  Google Scholar 

  104. Grogin H.R., M.L. Stanley, S. Eisenberg, B.M. Horáček, and M.D. Lesh, Body surface mapping for localization of accessory pathways in WPW syndrome, in IEEE Comput. Cardiol.. IEEE Computer Society, 1992, p. 255.

    Google Scholar 

  105. Gharpure P.B. and C.R. Johnson, A 3-dimensional cellular automation model of the heart, in Proceedings of the IEEE Engineering in Medicine and Biology Society 15th Annual International Conference. IEEE Press, New York, 1993, pp. 752–753.

    Chapter  Google Scholar 

  106. Hren R. and Punske B.B., A comparison of simulated QRS isointegral maps resulting from pacing at adjacent sites: Implications for the spatial resolution of pace mapping using body surface potentials. J. Electrocardiol., 1998;31(Suppl): 135.

    Article  PubMed  Google Scholar 

  107. Hren R., J. Nenonen, and B.M. Horacek, Simulated epicardial potential maps during paced activation reflect myocardial fibrous structure. Ann. Biomed. Eng. 1998;26(6): 1022.

    Article  CAS  PubMed  Google Scholar 

  108. Bailie A.H., R.H. Mithchell, and J. McCAnderson, A computer model of re-entry in cardiac tissue. Comp. in Biol. & Med. 1990, 20: 47–54.

    Article  CAS  Google Scholar 

  109. Saxberg B.E. and R.J. Cohen, Cellular automata models for reentrant arrhythmias. J. Electrocardiol., 199023(Suppl): 95.

    Article  PubMed  Google Scholar 

  110. Leon L.J. and Horáček B.M., Computer model of excitation and recovery in the anisotropic myocardium: II Excitation in the simplified left ventricle. J. Electrocardiol., 1991;24: 17–31.

    Article  CAS  PubMed  Google Scholar 

  111. Leon L.J. and B.M. Horáček, Computer model of excitation and recovery in the anisotropic myocardium: III Arrhythmogenic conditions in the simplified left ventricle. J. Electrocardiol., 1991;24: 33–41.

    Article  CAS  PubMed  Google Scholar 

  112. Wei D., O. Okazaki, K. Harumi, E. Harasawa, and H. Hosaka, Comparative simulation of excitation and body surface electrocardiogram with isotropic and anisotropic computer heart models. IEEE Trans. Biomed. Eng., 1995;42(4): 343–357.

    Article  CAS  PubMed  Google Scholar 

  113. Weixue L. and X. Ling, Computer simulation of epicardial potentials using a heart-torso model with realistic geometry. IEEE Trans. Biomed. Eng., 1996;43(2): 211–217.

    Article  CAS  PubMed  Google Scholar 

  114. Hren R., R.S. MacLeod, G. Stroink, and B.M. Horáček, Assessment of spatial resolution of body surface potentials maps in localizing ventricular tachycardia foci. Biomed. Technik, 1997;42(Suppl): 41–44.

    Article  Google Scholar 

  115. Hren R. and B.M. Horacek, Value of simulated body surface potential maps as templates in localizing sites of ectopic activation for radiofrequency ablation. Physiol. Measur., 1997;18(4): 373.

    Article  CAS  Google Scholar 

  116. Spitzer V., M.J. Ackerman, A.L. Scherzinger, and D. Whitlock, The visible human male: a technical report. J Am Med Inform Assoc, 1996;3(2): 118–130.

    Article  CAS  PubMed  Google Scholar 

  117. Sachse F.B., C.D. Werner, K. Meyer-Waarden, and O. Dossel, Development of a human body model for numerical calculation of electrical fields. Comput Med Imaging Graph, 2000;24(3): 165–171.

    Article  CAS  PubMed  Google Scholar 

  118. Freudenberg J., T. Schiemann, U. Tiede, and K.H. Hohne, Simulation of cardiac excitation patterns in a three-dimensional anatomical heart atlas. Comput Biol Med, 2000;30(4): 191–205.

    Article  CAS  PubMed  Google Scholar 

  119. Okajima M., T. Fujino, T. Kobayashi, and K. Yamada, Computer simulation of the propagation process in excitation of the ventricles. Circ. Res., 1968;23(2): 203–211.

    Article  CAS  PubMed  Google Scholar 

  120. Solomon J.C. and R.H. Selvester, Simulation of measured activation sequence in the human heart. Am Heart J, 1973;85(4): 518–524.

    Article  CAS  PubMed  Google Scholar 

  121. Lorange M. and Gulrajani R.M., Computer simulation of the Wolff–Parkinson–White preexcitation syndrome with a modified miller-geselowitz heart model. IEEE Trans. Biomed. Eng., 1986;33: 862–873.

    Article  CAS  PubMed  Google Scholar 

  122. Saxberg B.E., M.P. Grumbach, and R.J. Cohen, A time dependent anatomically detailed model of cardiac conduction. Comput Cardiol, 1985;12: 401–404.

    CAS  PubMed  Google Scholar 

  123. Plonsey R. and R.C. Barr, Mathematical modeling of electrical activity of the heart. J. Electrocardiol., 1987;20: 219–226.

    Article  CAS  PubMed  Google Scholar 

  124. Keener J.P., An eikonal-curvature equation for action potential propagation in myocardium. J Math Biol, 1991;29(7): 629–651.

    Article  CAS  PubMed  Google Scholar 

  125. Hooks D.A., K.A. Tomlinson, S.G. Marsden, I.J. LeGrice, B.H. Smaill, A.J. Pullan, and P.J. Hunter, Cardiac microstructure: implications for electrical propagation and defibrillation in the heart. Circ. Res., 2002;91(4): 331–338.

    Article  CAS  PubMed  Google Scholar 

  126. Colli Franzone P., L. Guerri, and B. Taccardi, Potential distributions generated by point stimulation in a myocardial volume: Simulation studies in a model of anisotropic ventricular muscle. J. Cardiovasc. Electrophysiol., 1993;4: 438–458.

    Article  CAS  PubMed  Google Scholar 

  127. Colli Franzone P., L. Guerri, and B. Taccardi, Spread of excitation in a myocardial volume: Simulation studies in a model of anisotropic ventricula muscle activated by point stimulation. J. Cardiovasc. Electrophysiol., 1993;4: 144–160.

    Article  Google Scholar 

  128. Colli Franzone P., L. Guerri, M. Pennacchio, and B. Taccardi, Spread of excitation in 3-d models of the anisotropic cardiac tissue. iii. effects of ventricular geometry and fiber structure on the potential distribution. Math Biosci, 1998;151(1): 51–98.

    Article  CAS  PubMed  Google Scholar 

  129. Colli-Franzone P., L. Guerri, and B. Taccardi, Modeling ventricular excitation: axial and orthotropic anisotropy effects on wavefronts and potentials. Math Biosci, 2004;188: 191–205.

    Article  PubMed  Google Scholar 

  130. Colli Franzone P., L.F. Pavarino, and B. Taccardi, Simulating patterns of excitation, repolarization and action potential duration with cardiac bidomain and monodomain models. Math Biosci, 2005;197(1): 35–66.

    Article  CAS  PubMed  Google Scholar 

  131. Taccardi B., B.B. Punske, F. Sachse, X. Tricoche, P. Colli-Franzone, L.F. Pavarino, and C. Zabawa, Intramural activation and repolarization sequences in canine ventricles. experimental and simulation studies. J. Electrocardiol., Oct 2005;38(4 Suppl): 131–137.

    Article  PubMed  Google Scholar 

  132. Pullan A., L. Cheng, R. Yassi, and M. Buist, Modelling gastrointestinal bioelectric activity. Prog. Biophys. Mol. Biol., 2004;85(2–3): 523–550.

    Article  PubMed  Google Scholar 

  133. Fitzhugh R., Impulses and physiological states in theoretical models of nerve membranes. Biophys. J., 1961;1: 445–466.

    Article  CAS  PubMed  Google Scholar 

  134. Nagumo J., S. Arimoto, and S. Yoshizawa, An active pulse transmission line simulating nerve axons. Proc. IRL, 1960;50: 2061–2070.

    Article  Google Scholar 

  135. Rogers J.M. and A.D. McCulloch, A collocation–galerkin finite element model of cardiac action potential propagation. IEEE Trans. Biomed. Eng., 1994;41(8): 743–757.

    Article  CAS  PubMed  Google Scholar 

  136. Pertsov A.M., J.M. Davidenko, R. Salomonsz, W.T. Baxter, and J. Jalife, Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle. Circ. Res., 1993;72(3): 631–650.

    Article  CAS  PubMed  Google Scholar 

  137. Starmer C.F., D.N. Romashko, R.S. Reddy, Y.I. Zilberter, J. Starobin, A.O. Grant, and V.I. Krinsky, Proarrhythmic response to potassium channel blockade. numerical studies of polymorphic tachyarrhythmias. Circ., 1995;92(3): 595–605.

    Article  CAS  Google Scholar 

  138. Karma A., Electrical alternans and spiral wave breakup in cardiac tissue. CHAOS, 1994;4(3): 461–472.

    Article  PubMed  Google Scholar 

  139. Aliev R.R. and A.V. Panfilov, Modeling of heart excitation patterns caused by a local inhomogeneity. J Theor Biol, 1996;181(1): 33–40.

    Article  CAS  PubMed  Google Scholar 

  140. Fenton F. and A. Karma, Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation. Chaos, 1998;8(1): 20–47.

    Article  PubMed  Google Scholar 

  141. Stinstra J.G., B. Hopenfeld, and R.S. MacLeod, On the passive cardiac conductivity. Ann. Biomed. Eng., 2005;33: 1743–1751.

    Article  PubMed  Google Scholar 

  142. Stinstra J.G. , S. Shome, B. Hopenfeld, C.S. Henriquez, and R.S. MacLeod, Modeling the passive cardiac conductivity during ischemia. Comp. in Biol. & Med., 2005;43(6): 776–782.

    Article  CAS  Google Scholar 

  143. Shome S., J.G. Stinstra, B. Hopenfeld, B.B. Punske, and R.S. MacLeod, A study of the dynamics of cardiac ischemia using experimental and modeling approaches, in Proceedings of the IEEE Engineering in Medicine and Biology Society 26th Annual International Conference. IEEE EMBS, IEEE Press, New York, 2004.

    Google Scholar 

  144. Muzikant A.L. and C.S. Henriquez, Paced activation mapping reveals organization of myocardial fibers: A simulation study. J. Cardiovasc. Electrophysiol., 1997;8: 281–294.

    Article  CAS  PubMed  Google Scholar 

  145. Muzikant A.L. and C.S. Henriquez, Bipolar stimulation of a three-dimensional bidomain incorporating rotational anisotropy. IEEE Trans. Biomed. Eng., 1998;45(4): 449–462.

    Article  CAS  PubMed  Google Scholar 

  146. Harrild D.M., R.C. Penland, and C.S. Henriquez, A flexible method for simulating cardiac conduction in three-dimensional complex geometries. J. Electrocardiol., 2000;33(3): 241–251.

    Article  Google Scholar 

  147. Tranquillo J.V., M.R. Franz, B.C. Knollmann, A.P. Henriquez, D.A. Taylor, and C.S. Henriquez, Genesis of the monophasic action potential: role of interstitial resistance and boundary gradients. Am. J. Physiol., Apr 2004;286(4): H1370–H1381.

    CAS  Google Scholar 

  148. Tranquillo J.V., D.O. Burwell, and C.S. Henriquez, Analytical model of extracellular potentials in a tissue slab with a finite bath. IEEE Trans. Biomed. Eng., Feb 2005;52(2): 334–338.

    Article  PubMed  Google Scholar 

  149. Weinstein D.M., C.R. Johnson, J. Tranquillo, C. Henriquez, R.S. MacLeod, and C.R. Johnson, BioPSE case study: Modeling, simulation, and visualization of three dimensional mouse heart propagation. Int. J. Bioelectromagnet., 2003;5(1):(in press).

    Google Scholar 

  150. Sampson K.J. and C.S. Henriquez, Electrotonic influences on action potential duration dispersion in small hearts: a simulation study. Am. J. Physiol., 2005;289(1): H350–H360.

    CAS  Google Scholar 

  151. Hopenfeld B., J.G. Stinstra, and R.S. MacLeod, The effect of conductivity on ST segment epicardial potentials arising from subendocardial ischemia. Ann. Biomed. Eng., 2005;33(6): 751–763.

    Article  PubMed  Google Scholar 

  152. Frazier D.W., W. Krassowska, P.S. Chen, P.D. Wolf, E.G. Dixon, W.M. Smith, and R.E. Ideker, Extracellular field required for excitation in three-dimensional anisotropic canine myocardium. Circ. Res., 1988;63: 147–164.

    Article  CAS  PubMed  Google Scholar 

  153. Trayanova N., K. Skouibine, and F. Aguel, The role of cardiac tissue structure in defibrillation. Chaos, 1998;8(1): 221–233.

    Article  PubMed  Google Scholar 

  154. Trayanova N. and J. Eason, Shock-induced arrhythmogenesis in the myocardium. Chaos, 2002;12(3): 962–972.

    Article  PubMed  Google Scholar 

  155. Trayanova N.A., R.A. Gray, D.W. Bourn, and J.C. Eason, Virtual electrode-induced positive and negative graded responses: new insights into fibrillation induction and defibrillation. J. Cardiovasc. Electrophysiol., Jul 2003;14(7): 756–763.

    Article  PubMed  Google Scholar 

  156. Rodriguez B., L. Li, J.C. Eason, I.R. Efimov, and N.A. Trayanova, Differences between left and right ventricular chamber geometry affect cardiac vulnerability to electric shocks. Circ. Res., Jul 2005;97(2): 168–175.

    Article  CAS  PubMed  Google Scholar 

  157. Trayanova N., Defibrillation of the heart: insights into mechanisms from modelling studies. Exp Physiol, 2006;91(2): 323–337.

    Article  PubMed  Google Scholar 

  158. Jolley M., J. Triedman, C.F. Westin, D.M. Weinstein, R.S. Macleod, and D.H. Brooks, Image based modeling of defibrillation in children, in Proceedings of the IEEE Engineering in Medicine and Biology Society 28th Annual International Conference. IEEE, IEEE Press, New York, 2006, pp. 2564–2567.

    Google Scholar 

  159. Wilson F.N. and R.H. Bayley, The electric field of an eccentric dipole in a homogeneous spherical conducting medium. Circ., 1950;1: 84–92.

    Article  CAS  Google Scholar 

  160. Frank E., Electric potential produiced by two point current sources in homogeneous coducting sphere. J. Appl. Phys., 1952;23: 1225–1228.

    Article  Google Scholar 

  161. Burger H.C., H.A. Tolhoek, and F.G. Backbier, The potential distribition on the body surface caused by a heart vector. calculations on some simple models. Am. Heart J., 1954;48: 249–263.

    Article  CAS  PubMed  Google Scholar 

  162. Okada R.H., Potentials produced by an eccentric current dipole in a finite-length circular conducting cylinder. IRE Trans. Med. Electron., 1956;7: 14–19.

    Article  Google Scholar 

  163. Bayley R.H. and P.M. Berry, The electrical field produced by the eccentric current dipole in the nonhomogeneous conductor. Am. Heart J., 1962;63: 808–820.

    Article  CAS  PubMed  Google Scholar 

  164. Bayley R.H. and P.M. Berry, The arbitrary electromotive double layer in the eccentric “heart” of the nonhomogeneous circular lamina. IEEE Trans. Biomed. Eng., 1964;11.

    Google Scholar 

  165. Bayley R.H., J.M. Kalbfleisch, and P.M. Berry, Changes in the body’s QRS surface potentials produced by alterations in certain compartments of the nonhomogeneous conducting model. Am. Heart J., 1969;77.

    Google Scholar 

  166. Rudy Y. and R. Plonsey, The eccentric spheres model as the basis for a study of the role of geometry and inhomogeneities in electrocardiography. IEEE Trans. Biomed. Eng., 1979;26:392–399.

    Article  CAS  PubMed  Google Scholar 

  167. Rudy Y. and R. Plonsey, The effects of variations in conductivity and geometrical parameters on the electrocardiogram, using an eccentric spheres model. Circ. Res., 1979;44(1):104–111.

    Article  CAS  PubMed  Google Scholar 

  168. Rudy Y. and R. Plonsey, A comparison of volume conductor and source geometry effects on body surface and epicardial potentials. Circ. Res., 1980;46: 283–291.

    Article  CAS  PubMed  Google Scholar 

  169. Throne R.D., L.G. Olson, T.J. Hrabik, and J.R. Windle, Generalized eigensystem techniques for the inverse problem of electrocardiography applied to a realistic heart-torso geometry. IEEE Trans. Biomed. Eng., 1997;44(6): 447.

    Article  CAS  PubMed  Google Scholar 

  170. Iakovidis I. and R.M. Gulrajani, Regularization of the inverse epicardial solution using linearly constrained optimization, in Proceedings of the IEEE Engineering in Medicine and Biology Society 13th Annual International Conference. IEEE Press, New York, 1991, pp. 698–699.

    Google Scholar 

  171. Throne R. and L. Olsen, A generalized eigensystem aproach to the inverse problem of electrocardiography. IEEE Trans. Biomed. Eng., 1994;41: 592–600.

    Article  CAS  PubMed  Google Scholar 

  172. Throne R. and L. Olsen, The effect of errors in assumed conductivities and geometry on numerical solutions to the inverse problem of electrocardiography. IEEE Trans. Biomed. Eng., 1995;42: 1192–1200.

    Article  CAS  PubMed  Google Scholar 

  173. He S., Frequency series expansion of an explicit solution for a dipole inside a conducting sphere at low frequencies. IEEE Trans. Biomed. Eng., 1998;45(10): 1249–1258.

    Article  CAS  PubMed  Google Scholar 

  174. Barr R.C. and M.S. Spachm Inverse calculation of QRS-T epicardial potentials from body surface potential distributions for normal and ectopic beats in the intact dog. Circ. Res., 1978;42: 661–675.

    Article  CAS  PubMed  Google Scholar 

  175. Pollard A. and Barr R.C. Computer simulations in an anatomically based model of the human ventricular conduction system. IEEE Trans. Biomed. Eng., 1991; 38: 982.

    Article  CAS  PubMed  Google Scholar 

  176. Pollard A.E., M.J. Burgess, and K.W. Spitzer, Computer simulations of three-dimensional propagation in ventricular myocardium. Effects of intramural fiber rotation and inhomogeneous conductivity on epicardial activation. Circ. Res., 1993; 72(4): 744–756.

    Article  CAS  PubMed  Google Scholar 

  177. Budgett D.M., D.M. Monro, S.W. Edwards, and R.D. Stanbridge, Comparison of measured and computed epicardial potentials from a patient-specific inverse model. J. Electrocardiol., 1993; 26(Suppl): 165–173.

    PubMed  Google Scholar 

  178. Sachse F.B., C. Werner, K. Meyer-Waarden, and O. Dössel, Comparison of solution to the forward problem in electrophysiology with homogeneous, heterogeneous and anisotropic impedance models. Biomed. Technik, 1997; 42(Suppl): 277–280.

    Google Scholar 

  179. Geselowitz D.B. and J.E. Ferrara, Is accurate recording of the ECG surface laplacian feasible? IEEE Trans. Biomed. Eng., April 1999 46(4): 377–381.

    Article  CAS  PubMed  Google Scholar 

  180. Wu D., H.C. Tsai, and B. He, On the estimation of the laplacian electrocardiogram during ventricular activation. Ann. Biomed. Eng., 1999; 27(6): 731–745.

    Article  CAS  PubMed  Google Scholar 

  181. Trew M., I. Le Grice, B. Smaill, and A. Pullan, A finite volume method for modeling discontinuous electrical activation in cardiac tissue. Ann. Biomed. Eng., 2005; 33(5):590–602.

    Article  PubMed  Google Scholar 

  182. Barr R.C., T.C. Pilkington, J.P. Boineau, and M.S. Spach, Determining surface potentials from current dipoles, with application to electrocardiography. IEEE Trans. Biomed. Eng., 1966; 13: 88–92.

    Article  CAS  PubMed  Google Scholar 

  183. Messinger-Rapport B.J. and Y. Rudy, The inverse problem in electrocardiography: A model study of the effects of geometry and conductivity parameters on the reconstruction of epicardial potentials. IEEE Trans. Biomed. Eng., 1986; 33: 667–676.

    Article  CAS  PubMed  Google Scholar 

  184. Rudy Y. and B.J. Messinger-Rapport, The inverse solution in electrocardiography: Solutions in terms of epicardial potentials. Crit. Rev. Biomed. Eng., 1988; 16: 215–268.

    CAS  PubMed  Google Scholar 

  185. Derfus D.L., T.C. Pilkington, and R.E. Ideker, Calculating intracavitary potentials from measured endocardial potentials, in Proceedings of the IEEE Engineering in Medicine and Biology Society 12th Annual International Conference. IEEE Press, New York. 1990, p. 635.

    Google Scholar 

  186. Charulatha R. and Y. Rudy, Electrocardiographic imaging:I. effect of torso inhomgeneities on body surface electrocardiographic potentials. J. Cardiovasc. Electrophysiol., 2001;12: 229–240.

    Article  Google Scholar 

  187. Colli Franzone P., B. Taccardi, and C. Viganotti, An approach to inverse calculation of epicardial potentials from body surface maps. Adv. Cardiol., 1978; 21: 50–54.

    Google Scholar 

  188. Colli Franzone P., L. Guerri, C. Viganotti, E. Macchi, S. Baruffi, S. Spaggiari, and B. Taccardi, Potential fields generated by oblique layers modeling excitation wavefronts in the anisotropic myocardium. Circ. Res., 1982;51: 330–346.

    Article  CAS  PubMed  Google Scholar 

  189. Yamashita Y. and T. Takahashi, Use of the finite element method to determine epicardial from body surface potentials under a realistic torso model. IEEE Trans. Biomed. Eng., 1984; 31: 611–621.

    Article  CAS  PubMed  Google Scholar 

  190. Hunter P.J., A.D. McCulloch, P.M.F. Nielsen, and B.H. Smaill, A finite element model of passive ventricular mechanics. ASME BED, 1988; 9: 387–397.

    Google Scholar 

  191. Sepulveda N.G., J.P. Wikswo, and D.S. Echt, Finite element analysis of cardiac defibrillation current distributions. IEEE Trans. Biomed. Eng., 1990; 37: 354–365.

    Article  CAS  PubMed  Google Scholar 

  192. Nielsen P.M.F., I.J. Le Grice, B.H. Smaill, and P.J. Hunter, Mathematical model of geometry and fibrous structure of the heart. Am. J. Physiol., 1991;260: H1365–H1378.

    CAS  PubMed  Google Scholar 

  193. Panfilov A.V. and J.P. Keener, Modelling re-entry in a finite element model of the heart. J. Physiol., 1993;467: 152.

    Google Scholar 

  194. Hunter P.J., P.M.F. Nielsen, B.H. Smaill, and I.J. LeGrice, An anatomical heart model with application in myocardial activation and ventricular mechanics, in High Performance Computing in Biomedical Research, chapter 1, T.C. Pilkington, B. Loftis, J. F. Thompson, S. L-Y Woo, T.C. Palmer, and T.F. Budinger, Editors. CRC Press, Boca Raton, 1993, pp. 3–26.

    Google Scholar 

  195. Klepfer R.N., C.R. Johnson, and R.S. MacLeod, The effects of inhomogeneities and anisotropies on electrocardiographic fields: A three-dimensional finite element study. IEEE Trans. Biomed. Eng., 1997; 44(8): 706–719.

    Article  CAS  PubMed  Google Scholar 

  196. Ramon C., Y. Wang, J. Haueisen, P. Schimpf, S. Jaruvatanadilok, and A. Ishimaru, Effect of myocardial anisotropy on the torso current flow patterns, potentials and magnetic fields. Phys Med Biol, 2000; 45(5): 1141–1150.

    Article  CAS  PubMed  Google Scholar 

  197. Hopenfeld B., Spherical harmonic-based finite element meshing scheme for modelling current flow within the heart. Med. – Biol. Eng. – Comp., 2004; 42(6): 847–851.

    Article  CAS  Google Scholar 

  198. Stanley P.C. and T.C. Pilkington, The combination method: A numerical technique for electrocardiographic calculations. IEEE Trans. Biomed. Eng., 1989; 36: 456–461.

    Article  CAS  PubMed  Google Scholar 

  199. Pullan A., A high-order coupled finite/boundary element torso model. IEEE Trans. Biomed. Eng., 1996; 43(3):292– 298.

    Article  CAS  PubMed  Google Scholar 

  200. Pullan A., M.L. Buist, and L.K. Cheng, Mathematically Modeling the electrical activity of the heart. World Scientific Co, Singapore, 2005.

    Google Scholar 

  201. Phillips G.M., Numerical integration in two and three dimensions. Comput. J., 1967; 10(2): 202–204.

    Article  Google Scholar 

  202. Oostendorp T.F. and A. van Oosterom, Source parameter estimation in inhomogeneous volume conductors of arbitrary shape. IEEE Trans. Biomed. Eng., 1989; 36: 382–391.

    Article  CAS  PubMed  Google Scholar 

  203. Barr R.C., T.C. Pilkington, J.P. Boineau, and C.L. Rogers, An inverse electrocardiographic solution with an on-off model. IEEE Trans. Biomed. Eng., 1970; 17: 49–57.

    Article  CAS  PubMed  Google Scholar 

  204. Zickler P., Cardiac mapping. Biomed Instrum Technol (BTI), 1997; 31(2): 173–175.

    CAS  Google Scholar 

  205. Smeets J., S. Ben Haim, L. Rodriguez, C. Timmermans, and H. Wellens, New method for nonfluoroscopic endocardial mapping in humans. Circ., 1998; 97: 2426–2432

    Article  CAS  Google Scholar 

  206. Callans D.J., J.F. Ren, J. Michele, F.E. Marchlinski, and S.M. Dillon, Electroanatomic left ventricular mapping in the porcine model of healed anterior myocardial infarction. correlation with intracardiac echocardiography and pathological analysis. Circ., 1999; 100: 1744–1750.

    Article  CAS  Google Scholar 

  207. Rao L., C. Ding, and D.S. Khoury, Nonfluoroscopic localization of intracardiac electrode-catheters combined with noncontact electrical-anatomical imaging. Ann. Biomed. Eng., 2004; 32(12): 1654–1661.

    Article  PubMed  Google Scholar 

  208. Ding C., L. Rao, S.F. Nagueh, and D.S. Khoury, Dynamic three-dimensional visualization of the left ventricle by intracardiac echocardiography. Ultrasound Med. Biol., 2005; 31(1): 15–21.

    Article  PubMed  Google Scholar 

  209. Ghanem R.N., C. Ramanathan, P. Jia, and Y. Rudy, Heart-surface reconstruction and ECG electrodes localization using fluoroscopy, epipolar geometry and stereovision: application to noninvasive imaging of cardiac electrical activity. IEEE Trans. Med. Imaging, 2003;22(10): 1307–1318.

    Article  PubMed  Google Scholar 

  210. Jezzard P. and R.S. Balaban, Correction for geometric distortion in echo planar images from B0 field variations. Mag. Res. Med., 1995; 34(1): 65–73.

    Article  CAS  Google Scholar 

  211. Ernst T., O. Speck, L. Ittl, and L. Chang, Simultaneous correction for interdscan patient motion and geometric distortion in echoplanar imaging. Mag. Res. Med., 1999; 42: 201–205.

    Article  CAS  Google Scholar 

  212. Studholme C., T. Constable, and J.S. Duncan, A phantom based investigation of non-rigid registration constraints in mapping fMRI to anatomical MRI, in Medical Imaging 2000: Image Processing, 2000, 2000.

    Google Scholar 

  213. Sosa E., M. Scanavacca, A. D’avila, and F. Pilleggi, A new technique to perform epicardial mapping in the electrophysiology laboratory. J. Cardiovasc. Electrophysiol., 1996; 7: 531–536.

    Article  CAS  PubMed  Google Scholar 

  214. Sosa E., M. Scanavacca, A. D’avila, J. Piccioni, O. Sanchez, J.L. Velarde, M. Silva, and B. Reolao, Endocardial and epicardial ablation guided by nonsurgical transthoracic epicardial mapping to treat recurrent of ventricular tachycardia. J. Cardiovasc. Electrophysiol., 1998; 9: 229–239.

    Article  CAS  PubMed  Google Scholar 

  215. Sosa E., M. Scanavacca, A. D’Avila, F. Oliviera, and J.A.F Ramires, Nonsurgical transthoracic epicardial ablation to treat recurrent of ventricular tachycardia. J. Am. Coll. Cardiol., 2000; 35(1): 1442–1449.

    Article  CAS  PubMed  Google Scholar 

  216. Spoor C.W. and F.E. Veldpaus, Rigid body motion calculated from spatial co-ordinates of markers. J. Biomech., 1980; 13:391–393.

    Article  CAS  PubMed  Google Scholar 

  217. Challis J.H., A procedure for determining rigid body transformation parameters. J. Biomechanics, 1995; 28(6): 733–737.

    Article  CAS  Google Scholar 

  218. Horáček B.M., The Effect on Electrocardiographic Lead Vectors of Conductivity Inhomogeneities in the Human Torso. PhD thesis, Dalhousie University, Halifax, N.S., Canada, 1971.

    Google Scholar 

  219. MacLeod R.S., C.R. Johnson, and P.R. Ershler, Construction of an inhomogeneous model of the human torso for use in computational electrocardiography, in Proceedings of the IEEE Engineering in Medicine and Biology Society 13th Annual International Conference. IEEE Press, New York, 1991, pp. 688–689.

    Google Scholar 

  220. MacLeod R.S., R.M. Miller, M.J. Gardner, and B.M. Horáček, Application of an electrocardiographic inverse solution to localize myocardial ischemia during percutaneous transluminal coronary angioplasty. J. Cardiovasc. Electrophysiol., 1995; 6:2–18.

    Article  CAS  PubMed  Google Scholar 

  221. Modre R., B. Tilg, G. Fischer, F. Hanser, B. Messnarz, F.X. Roithinger, and F. Hintringer, A clinical pilot study on the accessory pathway localization accuracy applying ECG mapping, in Proceedings of the IEEE Engineering in Medicine and Biology Society 24th Annual International Conference, vol. 2, 2002, pp. 1381–1382.

    Google Scholar 

  222. Fischer G., B. Pfeifer, M. Seger, C. Hintermuller, F. Hanser, R. Modre, B. Tilg, T. Trieb, C. Kremser, F.X. Roithinger, and F. Hintringer, Computationally efficient noninvasive cardiac activation time imaging. Methods Inf. Med., 2005; 44(5): 674–686.

    CAS  PubMed  Google Scholar 

  223. Fischer G., F. Hanser, B. Pfeifer, M. Seger, C. Hintermuller, R. Modre, B. Tilg, T. Trieb, T. Berger, F.X. Roithinger, and F. Hintringer, A signal processing pipeline for noninvasive imaging of ventricular preexcitation. Methods Inf. Med., 2005; 44(4): 508–515.

    CAS  PubMed  Google Scholar 

  224. Pfeifer B., G. Fischer, F. Hanser, M. Seger, C. Hintermuller, R. Modre-Osprian, T. Trieb, and B. Tilg, Atrial and ventricular myocardium extraction using model-based techniques. Methods Inf. Med., 2006; 45(1): 19–26.

    CAS  PubMed  Google Scholar 

  225. Patterson R.R., Projective transformations os the parameter of a Bernstein-Bézier curve. ACM Trans. Graph., 1985; 4(4): 276–290.

    Article  Google Scholar 

  226. Robeson S.M., Spherical methods for spatial interpolation: Review and evaluation. Cartog. Geog. Inf. Sys., 1997; 24(1): 3–20.

    Article  Google Scholar 

  227. Mercer R.R., G.M. McCauley, and S. Anjilvel, Approximation of surfaces in a quantitative 3-D reconstruction system. IEEE Trans. Biomed. Eng., 1990; 37: 1136–1146.

    Article  CAS  PubMed  Google Scholar 

  228. Vesely I., B. Eickmeier, and G. Campbell, Automated 3-D reconstruction of vascular structures from high definition casts. IEEE Trans. Biomed. Eng., 1991;38: 1123–1129.

    Article  CAS  PubMed  Google Scholar 

  229. MacLeod R.S., C.R. Johnson, and M.A. Matheson, Visualization tools for computational electrocardiography. In Visualization in Biomedical Computing, Bellingham, Wash., 1992. Proceedings of the SPIE #1808, pp. 433–444.

    Google Scholar 

  230. Weinstein D., Scanline surfacing: Building separating surfaces from planar contours, in Proceeding of IEEE Visualization 2000, 2000, pp. 283–289.

    Google Scholar 

  231. Hren R. and G. Stroink, Application of the surface harmonic expansions for modeling the human torso. IEEE Trans. Biomed. Eng., 1995; 42(5): 521.

    Article  Google Scholar 

  232. Bradley C.P., A.J. Pullan, and P.J. Hunter, Geometric modeling of the human torso using cubic hermite elements. Ann. Biomed. Eng., 1997; 25: 96–111.

    Article  CAS  PubMed  Google Scholar 

  233. Gumhold S., X. Wang, and R.S. MacLeod, Feature extraction from point clouds, in Proceedings, 10th International Meshing Roundtable. Sandia National Laboratories, 2001, pp. 293–305.

    Google Scholar 

  234. Bern M. and D. Eppstein, Mesh generation and optimal triangulation, in Computing in Euclidean Geomtry, F.K. Hwang and D.Z. Du, Editors. World Scientific, Singapore, 1992.

    Google Scholar 

  235. Lee D.T. and B.J. Schachter, Two algorithms for constructing a Delaunay triangulation. Int. J. Comp. Inf. Sci., 1980; 9: 219–242.

    Article  Google Scholar 

  236. Schumaker L.L., Triangularization methods, in Topics in Multivariate Analysis. Academic Press, London, 1987, pp. 219–232.

    Google Scholar 

  237. Schmidt J.A., C.R. Johnson, J.A. Eason, and R.S. MacLeod, Applications of automatic mesh generation and adaptive methods in computational medicine, in Modeling, Mesh Generation, and Adaptive Methods for Partial Differential Equations, J. Flaherty and I. Babuska, Editors. Springer, Berlin, 1994, pp. 367–394.

    Google Scholar 

  238. Schimpf P.H., D.R. Haynor, and Y. Kim, Object-free adaptive meshing in highly heterogeneous 3-D domains. Int. J. Biomed. Comput., 1996; 40(3): 209–225.

    Article  CAS  PubMed  Google Scholar 

  239. Peraire J. and K. Morgan, Unstructured mesh generation including directional refinement for aerodynamic flow simulation. Finite Elements Anal. Design, 1997; 25: 343.

    Article  Google Scholar 

  240. Alliez P., D. Cohen-Steiner, M. Yvinec, and M. Desbrun, Variational tetrahedral meshing, in International Conference on Computer Graphics and Interactive Techniques. ACM Press, New York, NY, USA, 2005, pp. 617–625.

    Google Scholar 

  241. Yu F. and C. R. Johnson, An automatic adaptive refinement and derefinement method, in Proceedings of the 14th IMACS World Congress, 1944, pp. 1555–1557.

    Google Scholar 

  242. Livnat Y. and Johnson C.R., The effects of adaptive refinement on ill-posed inverse problems. Personal communication, 1997.

    Google Scholar 

  243. Schimpf P.H., Y. Wang, D.R. Haynor, and Y. Kim, Sensitivity of transvenous defibrillation models to adaptive mesh density and resolution: the potential for interactive solution times. Int. J. Med. Inf., 1997; 45(3): 193–207.

    Article  CAS  Google Scholar 

  244. Lines G., P. Grottum, and A. Tveito, Modeling the electrical activity of the heart –A bidomain model of the ventricles embedded in a torso. Comput. – Vis. Sci., 2003;5(4): 195–213.

    Article  Google Scholar 

  245. Missan S. and T. F. McDonald, CESE: Cell Electrophysiology Simulation Environment. Appl. Bioinformat., 2005; 4(2): 155–156.

    Article  CAS  Google Scholar 

  246. Tomita M., K. Hashimoto, K. Takahashi, T.S. Shimizu, Y. Matsuzaki, F. Miyoshi, K. Saito, S. Tanida, K. Yugi, J.C. Venter, and C.A. Hutchison. E-CELL: software environment for whole-cell simulation. Bioinformatics, 1999; 15(1): 72–84.

    Article  CAS  PubMed  Google Scholar 

  247. van Oosterom A. and T.F. Oostendorp, ECGSIM: an interactive tool for studying the genesis of QRST waveforms. Heart, 2004; 90(2): 165–168.

    Article  CAS  PubMed  Google Scholar 

  248. SCIRun: A Scientific Computing Problem Solving Environment, Scientific Computing and Imaging Institute (SCI), 2006.

    Google Scholar 

  249. BioPSE: Problem Solving Environment for modeling, simulation, image processing, and visualization for biomedical computing applications. Scientific Computing and Imaging Institute (SCI), 2006.

    Google Scholar 

  250. Weinstein D.M., S.G. Parker, and C.R. Johnson, A physically based mesh generation algorithm: Applications in computational medicine, in IEEE Engineering in Medicine and Biology Society 16th Annual International Conference. IEEE Press, New York,1994, pp. 718–719.

    Chapter  Google Scholar 

  251. Weinstein D.M., L. Zhukov, and C.R. Johnson, Lead-field bases for EEG source imaging. Ann. Biomed. Eng., 2000; 28(9): 1059–1065.

    Article  CAS  PubMed  Google Scholar 

  252. Weinstein D.M., L. Zhukov, and C.R. Johnson, An inverse EEG problem solving environment and its applications to EEG source localization. NeuroImage (suppl.), 2000: 921.

    Google Scholar 

  253. MacLeod R.S. and C.R. Johnson, Map3d: Interactive scientific visualization for bioengineering data, in Proceedings of the IEEE Engineering in Medicine and Biology Society 15th Annual International Conference. IEEE Press, New York, 1993, pp. 30–31. http://software.sci.utah.edu/map3d.html.

  254. Clancy C.E. and Y. Rudy, Linking a genetic defect to its cellular phenotype in a cardiac arrhythmia. Nature, 1999 400(6744): 566–509.

    Article  CAS  PubMed  Google Scholar 

  255. Venter J.C., M.D. Adams, E.W. Myers, and P.W. Li, The sequence of the human genome. Science, 2001 291(5507): 1304–1351.

    Article  CAS  PubMed  Google Scholar 

  256. Hunter P.J. and T.K. Borg, Integration from proteins to organs: the physiome project. Nat. Rev. Mol. Cell. Biol., 2003;4(3): 237–243.

    Article  CAS  PubMed  Google Scholar 

  257. Hunter P.J., The iups physiome project: a framework for computational physiology. Prog. Biophys. Mol. Biol., 2004; 85(2–3): 551–569.

    Article  CAS  PubMed  Google Scholar 

  258. H.C. Burger and van Milaan J.B., Heart-vector and leads. Part I. Br. Heart J., 1946; 8: 157–61.

    Article  Google Scholar 

  259. Sundnes J., G.T. Lines, X. Cai, B.F. Nielsen, K.A. Mardal, and A. Tveito, Computing the Electrical Activity in the Heart. Spinger, Berlin, 2006.

    Google Scholar 

  260. Potse M., B. Dube, J. Richer, A. Vinet, and R.M. Gulrajani, A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart. IEEE Trans. Biomed. Eng., 2006; 53(12): 2425–2435.

    Article  PubMed  Google Scholar 

  261. Austin T.M., M.L. Trew, and A.J. Pullan, Solving the cardiac bidomain equations for discontinuous conductivities. IEEE Trans. Biomed. Eng., 2006; 53(7): 1265–1272.

    Article  PubMed  Google Scholar 

  262. Austin T., D. Hooks, P. Hunter, D. Nickerson, A.J. Pullan, G. Sands, B. Maaill, and M. Trew, Modelling cardiac electrical activity at the cell and tissue levels, in Interactive and Integrative Cardiology, vol. 1080, S. Sideman, R. Beyar, and A. Landesberg, Editors. Annals of NY Academy of Sciences, 2006; 1080: 334–347.

    Google Scholar 

  263. Trew M.L., B.J. Caldwell, G.B. Sands, D.A. Hooks, D.C. Tai, T.M. Austin, I.J. LeGrice, A.J. Pullan, and B.H. Smaill, Cardiac electrophysiology and tissue structure: bridging the scale gap with a joint measurement and modelling paradigm. Exp Physiol, 2006; 91(2): 355–370.

    Article  PubMed  Google Scholar 

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Authors and Affiliations

  1. University of Utah, Salt Lake City, UT, USA

    Rob MacLeod

  2. National University of Singapore, Singapore, Singapore

    Martin Buist

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  1. Rob MacLeod
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  2. Martin Buist
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Editor information

Editors and Affiliations

  1. University of Glasgow, Glasgow, UK

    Peter W. Macfarlane

  2. Radboud University Nijmegen, Nijmegen, The Netherlands

    A. van Oosterom

  3. Lund University, Lund, Sweden

    Olle Pahlm

  4. Weill Cornell Medical College, New York, NY, USA

    Paul Kligfield

  5. University of Amsterdam, Amsterdam, The Netherlands

    Michiel Janse

  6. St. George's, University of London, London, UK

    John Camm

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MacLeod, R., Buist, M. (2010). The Forward Problem of Electrocardiography. In: Macfarlane, P.W., van Oosterom, A., Pahlm, O., Kligfield, P., Janse, M., Camm, J. (eds) Comprehensive Electrocardiology. Springer, London. https://doi.org/10.1007/978-1-84882-046-3_8

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  • DOI: https://doi.org/10.1007/978-1-84882-046-3_8

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84882-045-6

  • Online ISBN: 978-1-84882-046-3

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