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Can ECG Recordings and Mathematics tell the Condition of Your Heart?

  • Bjørn Fredrik Nielsen
  • Marius Lysaker
  • Per Grøttum
  • Kent-André Mardal
  • Aslak Tveito
  • Christian Tarrou
  • Kristina Hermann Haugaa
  • Andreas Abildgaard
  • Jan Gunnar Fjeld
Chapter

Abstract

If a coronary artery supplying blood to the heart becomes blocked, the heart will not receive sufficient oxygen, causing an ischemic region. If the condition persists, it will eventually lead to permanent damage, that is, myocardial infarction. Coronary artery disease is one of the most common diseases in the Western world, causing millions of deaths each year. For example, in the United States 18 per cent of deaths in 2005 were due to coronary artery disease [76], while in Denmark around eight per cent of the population experiences poor health because of the disease [77].

Keywords

Inverse Problem Ischemic Heart Disease Transmembrane Potential Colour Version Ischemic Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    G. Fischer, F. Hanser, B. Pfeifer, M. Seger, C. Hintermüller, 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 of Information in Medicine, 44(4):508–515, 2005. Google Scholar
  2. [2]
    L. K. Cheng, G. B. Sands, R. L. French, S. J. Withy, S. P. Wong, M. E. Legget, W. M. Smith, and A. J. Pullan. Rapid construction of a patient-specific torso model from 3D ultrasound for non-invasive imaging of cardiac electrophysiology. Medical & Biological Engineering & Computing, 43:325–330, 2005. CrossRefGoogle Scholar
  3. [3]
    M. R. Franz, J. T. Flaherty, E. V. Platia, B. H. Bulkley, and M. L. Weisfeldt. Localization of regional myocardial ischemia by recording of monophasic action potentials. Circulation, 69:593–604, 1984. Google Scholar
  4. [4]
    W. E. Cascio, H. Yang, T. A. Johnson, B. J. Muller-Borer, and J. J. Lemasters. Electrical properties and conduction in reperfused papillary muscle. Circulation Research, 89:807–814, 2001. CrossRefGoogle Scholar
  5. [5]
    E. Downar, M. J. Janse, and D. Durrer. The effect of acute coronary artery occlusion on subepicardial transmembrane potentials in the intact porcine heart. Circulation, 56:217–224, 1977. Google Scholar
  6. [6]
    A. G. Kleber, M. J. Janse, F. J. van Capelle, and D. Durrer. 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. Circulation Research, 42:603–613, 1978. Google Scholar
  7. [7]
    F. J. Vetter and A. D. McCulloch. Three-dimensional analysis of regional cardiac function: a model of rabbit ventricular anatomy. Progress in Biophysics & Molecular Biology, 69:157–183, 1998. CrossRefGoogle Scholar
  8. [8]
    P. M.F. Nielsen, I. J.L. Grice, B. H. Smaill, and P. J. Hunter. Mathematical model of geometry and fibrous structure of the heart. American Journal of Physiology, 260:1365–1378, 1991. Google Scholar
  9. [9]
    B. F. Nielsen, O. M. Lysaker, C. Tarrou, A. Abildgaard, M. MacLachlan, and A. Tveito. On the use of st-segment shifts and mathematical models for identifying ischemic heart disease. Computers in Cardiology 2005, Lyon, France, September 25-28, pages 1005–1008. IEEE, 2005. Google Scholar
  10. [10]
    D. N. Arnold, R. S. Falk, and R. Winther. Preconditioning discrete approximations of the Reissner-Mindlin plate model. Mathematical Modeling and Numerical Analysis, 31(4):517–557, 1997. zbMATHMathSciNetGoogle Scholar
  11. [11]
    K.-A. Mardal and R. Winther. Uniform preconditioners for the time dependent Stokes problem. Numerische Mathematik, 98(2):305–327, 2004. zbMATHMathSciNetCrossRefGoogle Scholar
  12. [12]
    E. Haug and R. Winther. A domain embedding preconditioner for the Lagrange multiplier system. Mathematics of Computation, 69(229):65–82, 1999. MathSciNetCrossRefGoogle Scholar
  13. [13]
    O. Axelsson and G. Lindskog. On the eigenvalue distribution of a class of preconditioning methods. Numerische Mathematik, 48(5):479–498, 1986. zbMATHMathSciNetCrossRefGoogle Scholar
  14. [14]
    O. Axelsson and G. Lindskog. On the rate of convergence of the preconditioned conjugate gradient method. Numerische Mathematik, 48(5):499–523, 1986. zbMATHMathSciNetCrossRefGoogle Scholar
  15. [15]
    O. Axelsson. Iterative Solution Methods. Cambridge University Press, 1994. Google Scholar
  16. [16]
    A. M. Bruaset. A Survey of Preconditioned Iterative Methods, volume 324. Addison-Wesley Longman (currently CRC Press), 1995. Google Scholar
  17. [17]
    B. F. Nielsen, T. S. Ruud, G. T. Lines, and A. Tveito. Optimal monodomain approximations of the bidomain equations. Applied Mathematics and Computation, 184(2):276–290, 2007. MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    T. S. Ruud, B. F. Nielsen, O. M. Lysaker, and J. Sundnes. A computationally efficient method for determining the size and location of myocardial ischemia. IEEE Transactions on Biomedical Engineering, 56(2):263–272, 2009. CrossRefGoogle Scholar
  19. [19]
    B. F. Nielsen and K.-A. Mardal. Efficient preconditioners for optimality systems arising in connection with inverse problems. Submitted to journal for publication, 2008. Google Scholar
  20. [20]
    F. Greensite. Myocardial activation imaging. Computational inverse problems in electrocardiography, pages 143–190. WIT Press, 2001. Google Scholar
  21. [21]
    J. Cuppen and A. van Oosterom. Model studies with inversly calculated isochrones of ventricular depolarization. IEEE Transactions on Biomedical Engineering, BME-31:652–659, 1984. CrossRefGoogle Scholar
  22. [22]
    K.-A. Mardal, B. F. Nielsen, X. Cai, and A. Tveito. An order optimal solver for the discretized bidomain equations. Numerical Linear Algebra with Applications, 14(2):83–98, 2007. zbMATHMathSciNetCrossRefGoogle Scholar
  23. [23]
    B. Tilg, G. Fischer, R. Modre, F. Hanser, B. Messnarz, M. Schocke, C. Kremser, T. Berger, F. Hintringer, and F. X. Roithinger. Model-based imaging of cardiac electrical excitation in humans. IEEE Transactions on Medical Imaging, 21(9):1031–1039, 2002. CrossRefGoogle Scholar
  24. [24]
    R. Modre, B. Tilg, G. Fischer, and P. Wach. Noninvasive myocardial activation time imaging: a novel inverse algorithm applied to clinical ECG mapping data. IEEE Transactions on Biomedical Engineering, 49(10):1153–1161, 2002. CrossRefGoogle Scholar
  25. [25]
    P. Pedregal. Introduction to optimization. Springer-Verlag, 2004. Google Scholar
  26. [26]
    B. Messnarz, M. Seger, R. Modre, G. Fischer, F. Hanser, and B. Tilg. A comparison of noninvasive reconstruction of epicardial versus transmembrane potentials in consideration of the null space. IEEE Transactions on Biomedical Engineering, 51(9):1609–1618, 2004. CrossRefGoogle Scholar
  27. [27]
    A. J. Pullan, L. K. Cheng, M. P. Nash, C. P. Bradley, and D. J. Paterson. Noninvasive electrical imaging of the heart: Theory and model development. Annals of Biomedical Engineering, 29(10):817–836, 2001. CrossRefGoogle Scholar
  28. [28]
    A. J. Pullan, M. L. Buist, and L. K. Cheng. Mathematically Modelling the Electrical Activity of the Heart: From Cell to Body Surface and Back. World Scientific Publishing Company, 2005. Google Scholar
  29. [29]
    D. Braess. Finite elements. Theory, fast solvers, and applications in solid mechanics. Cambridge University Press, second edition, 2001. Google Scholar
  30. [30]
    O. M. Lysaker and B. F. Nielsen. Towards a level set framework for infarction modeling: An inverse problem. International Journal of Numerical Analysis and Modeling, 3(4):377–394, 2006. zbMATHMathSciNetGoogle Scholar
  31. [31]
    B. F. Nielsen, O. M. Lysaker, and A. Tveito. On the use of the resting potential and level set methods for identifying ischemic heart disease; an inverse problem. Journal of Computational Physics, 220(2):772–790, 2007. zbMATHMathSciNetCrossRefGoogle Scholar
  32. [32]
    M. C. MacLachlan, B. F. Nielsen, O. M. Lysaker, and A. Tveito. Computing the size and location of myocardial ischemia using measurements of st-segment shift. IEEE Transactions on Biomedical Engineering, 2005. Google Scholar
  33. [33]
    F. Santosa. A level-set approach for inverse problems involving obstacles. ESAIM: Control, Optimisation and Calculus of Variations, 1:17–33, 1996. zbMATHMathSciNetCrossRefGoogle Scholar
  34. [34]
    S. Osher and J. Sethian. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79:12–49, 1988. zbMATHMathSciNetCrossRefGoogle Scholar
  35. [35]
    S. Osher and R. Fedkiw. Level Set Methods and Dynamic Implicit Surfaces, volume 153 of Applied Mathematical Sciences. Springer, 2003. Google Scholar
  36. [36]
    Z. Qu and A. Garfinkel. An advanced algorithm for solving partial differential equation in cardiac conduction. IEEE Transactions on Biomedical Engineering, 46(9):1166–1168, 1999. CrossRefGoogle Scholar
  37. [37]
    K. Skouibine and W. Krassowska. Increasing the computational efficiency of a bidomain model of defibrillation using a time-dependent activating function. Annals of Biomedical Engineering, 28:772–780, 2000. CrossRefGoogle Scholar
  38. [38]
    J. Sundnes, G. T. Lines, X. Cai, B. F. Nielsen, K. A. Mardal, and A. Tveito. Computing the Electrial Activity in the Heart. Springer-Verlag, 2006. Google Scholar
  39. [39]
    J. Sundnes, B. F. Nielsen, K. A. Mardal, X. Cai, G. T. Lines, and A. Tveito. On the computational complexity of the bidomain and the monodomain models of electrophysiology. Annals of Biomedical Engineering, 34(7):1088–1097, 2006. CrossRefGoogle Scholar
  40. [40]
    R. L. Winslow, J. Rice, S. Jafri, E. Marban, and B. O’Rourke. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, II, model studies. Circulation Research, 84:571–586, 1999. Google Scholar
  41. [41]
    E. Carmeliet. Cardiac ionic currents and acute ischemia: From channels to arrhythmias. Physiol. Rev., 79:917–1017, 1999. Google Scholar
  42. [42]
    J. T. Marti. Introduction to Sobolev Spaces and Finite Element Solution of Elliptic Boundary Value Problems. Academic Press, 1986. Google Scholar
  43. [43]
    C. W. Groetsch. Inverse Problems in the Mathematical Sciences. Vieweg, 1993. Google Scholar
  44. [44]
    A. Kirsch. An Introduction to the Mathematical Theory of Inverse Problems. Springer, 1996. Google Scholar
  45. [45]
    H. W. Engl, M. Hanke, and A. Neubauer. Regularization of Inverse Problems. Kluwer Academic Publishers, 1996. Google Scholar
  46. [46]
    Computational Inverse Problems in Electrocardiography. WIT Press, 2001. Google Scholar
  47. [47]
    L. K. Cheng, J. M. Bodely, and J. Pullan. Comparison of potential- and activation-based formulations for the inverse problem of electrocardiology. IEEE Transactions on Biomedical Engineering, 50(1):11–22, January 2003. CrossRefGoogle Scholar
  48. [48]
    G. Huiskamp and A. van Oosterom. The depolarization sequence of the human heart surface computed from measured body surface potentials. IEEE Transactions on Biomedical Engineering, 35:1047–1058, 1988. CrossRefGoogle Scholar
  49. [49]
    F. Greensite and G. Huiskamp. An improved method for estimating epicardial potentials from the body surface. IEEE Transactions on Biomedical Engineering, 45(1):98–104, January 1998. CrossRefGoogle Scholar
  50. [50]
    G. Huiskamp and F. Greensite. A new method for myocardial activation imaging. IEEE Transactions on Biomedical Engineering, 44(6):433–446, 1997. CrossRefGoogle Scholar
  51. [51]
    R. S. MacLeod and D. H. Brooks. Recent progress in inverse problems in electrocardiology. IEEE Engineering in Medicine and Biology, 17(1):73–83, January 1998. CrossRefGoogle Scholar
  52. [52]
    B. Hopenfeld, J. G. Stinstra, and R. S. Macleod. Mechanism for ST depression associated with contiguous subendocardial ischemia. Journal of Cardiovascular Electrophysiology, 15:1200–1206, 2004. CrossRefGoogle Scholar
  53. [53]
    M. P. Nash and A. J. Pullan. Challenges facing validation of noninvasive electrical imaging of the heart. The Annals of Noninvasive Electrocardiology, 10(1):73–82, 2005. CrossRefGoogle Scholar
  54. [54]
    R. M. Gulrajani. Forward and inverse problems of electrocardiography. IEEE Engineering in Medicine and Biology, 17(5):84–101, September 1998. CrossRefGoogle Scholar
  55. [55]
    O. Dössel. Inverse problem of electro- and magnetocardiography: Review and recent progress. International Journal of Bioelectromagnetism, 2(2), 2000. Google Scholar
  56. [56]
    Y. Rudy and B. J. Messinger-Rapport. The inverse problem in electrocardiography: Solutions in terms of epicardial potentials. Critical Reviews in Biomedical Engineering, 16:215–268, 1988. Google Scholar
  57. [57]
    Y. Rudy and H. S. Oster. The electrocardiographic inverse problem. Critical Reviews in Biomedical Engineering, 20:25–45, 1992. Google Scholar
  58. [58]
    C. P. Franzone, L. Guerri, S. Tentonia, C. Viganotti, and S. Baruffi. A mathematical procedure for solving the inverse potential problem of electrocardiography: Analysis of the time-space accuracy from in vitro experimental data. Mathematical Biosciences, 77:353–396, 1985. zbMATHMathSciNetCrossRefGoogle Scholar
  59. [59]
    J. Lau, J. P. Ioannidis, E. M. Balk, C. Milch, N. Terrin, P. W. Chew, and D. Salem. Diagnosing acute cardiac ischemia in the emergency department: a systematic review of the accuracy and clinical effect of current technologies. Ann. Emerg. Med., 37:453–460, 2001. CrossRefGoogle Scholar
  60. [60]
    Y. Birnbaum and B. J. Drew. The electrocardiogram in ST elevation acute myocardial infarction: correlation with coronary anatomy and prognosis. Postgrad. Med. J., 79, 2003. Google Scholar
  61. [61]
    J. Keener and J. Sneyd. Mathematical Physiology. Springer-Verlag, 1998. Google Scholar
  62. [62]
    M. C. MacLachlan, J. Sundnes, and G. T. Lines. Simulation of ST segment changes during subendocardial ischemia using a realistic 3D cardiac geometry. IEEE Transactions on Biomedical Engineering, 52(5):799–807, May 2005. CrossRefGoogle Scholar
  63. [63]
    W. T. Miller and D. B. Geselowitz. Simulation studies of the electrocardiogram: II. ischemia and infarction. Circ. Res., 43:315–323, 1978. Google Scholar
  64. [64]
    P. R. Johnston. A cylindrical model for studying subendocardial ischemia in the left ventricle. Mathematical Biosciences, 186(1):43–61, 2003. zbMATHMathSciNetCrossRefGoogle Scholar
  65. [65]
    P. R. Johnston and D. Kilpatrick. The effect of conductivity values on st segment shift in subendocardial ischaemia. IEEE Trans. Biomed. Eng., 50:150–158, 2003. CrossRefGoogle Scholar
  66. [66]
    P. R. Johnston, D. Kilpatrick, and C. Y. Li. The importance of anisotropy in modeling ST segment shift in subendocardial ischaemia. IEEE Trans. Biomed. Eng., 48:1366–1376, 2001. CrossRefGoogle Scholar
  67. [67]
    D. Kilpatrick, P. R. Johnston, and D. S. Li. Mechanisms of ST change in partial thickness ischemia. J. Electrocardiol., 36:7–12, 2003. CrossRefGoogle Scholar
  68. [68]
    D. Li, C. Y. Li, A. C. Yong, and D. Kilpatrick. Source of electrocardiographic ST changes in subendocardial ischemia. Circulation Research, 82:957–970, 1998. Google Scholar
  69. [69]
    B. Hopenfeld, J. G. Stinstra, and R. S. MacLeod. A mechanism for ST depression associated with contiguous subendocardial ischemia. J. Cardiovasc. Electrophysiol., 15:1200–1206, October 2004. CrossRefGoogle Scholar
  70. [70]
    K. R. Foster and H. P. Schwan. Dielectric properties of tissues and biological materials: a critical review. Critical Reviews in Biomedical Engineering, 17:25–104, 1989. Google Scholar
  71. [71]
    L. Clerc. Directional differences of impulse spread in trabecular muscle from mammalian heart. The Journal of Physiology, 255(2):335–346, 1976. Google Scholar
  72. [72]
    D. E. Roberts and A. M. Scher. Effect of tissue anisotropy on extracellular potential fields in canine myocardium in situ. Circulation Research, 50(3):342–351, 1982. Google Scholar
  73. [73]
    F. Hanser, M. Seger, B. Tilg, R. Modre, G. Fischer, B. Messnarz, F. Hintringer, T. Berger, and F. X. Roithinger. Influence of ischemic and infarcted tissue on the surface potential. Computers in Cardiology, 30:789–792, 2003. Google Scholar
  74. [74]
    P. C. Franzone, L. Guerri, and B. Taccardi. Spread of excitation in a myocardial volume: Simulation studies in a model of anisotropic ventricular muscle activated by point stimulation. Journal of Cardiovascular Electrophysiology, 4(2):144–160, 1993. CrossRefGoogle Scholar
  75. [75]
    B. F. Nielsen, X. Cai, and O. M. Lysaker. On the possibility for computing the transmembrane potential in the heart with a one shot method; an inverse problem. Mathematical Biosciences, 210(2):523–553, 2007. zbMATHMathSciNetCrossRefGoogle Scholar
  76. [76]
    H. Kung, D. Hoyert, J. Xu, and S. Murphy. Final data for 2005. National vital statistics reports. Technical Report vol 56 no 10, National Center for Health Statistics, 2005. Google Scholar
  77. [77]
    Statens Institut for Folkesundhed. Sundheds- og sygelighedsundersøgelsen 2000. Technical report, Statens Institut for Folkesundhed, 2001. Google Scholar
  78. [78]
    P. Ginn, B. Jamieson, and M. Mendoza. Clinical inquiries. How accurate is the use of ECGs in the diagnosis of myocardial infarct? The Journal of Family Practice, 55:539–40, 2006. Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Bjørn Fredrik Nielsen
    • 1
  • Marius Lysaker
  • Per Grøttum
  • Kent-André Mardal
  • Aslak Tveito
  • Christian Tarrou
  • Kristina Hermann Haugaa
  • Andreas Abildgaard
  • Jan Gunnar Fjeld
  1. 1.CBCSimula Research LaboratoryOsloNorway

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