Regularizing the discrete ill-posed inverse problem of electrocardiography

Elektrotehniski Vestnik/Electrotechnical Review

Volumn 63, Issue 4-5, 1996, Pages 234-240

  Hren, Rok ^a,b,c  

^a DALHOUSIE UNIVERSITY   (Canada)

^b INSTITUTE OF MATHEMATICS   (Slovenia)

^c University of Ljubljana ^*

Author keywords

Discrete ill posed problem; Electrocardiography; Inverse problem; Tikhonov regularization; Wolff Parkinson White syndrome

Indexed keywords

BOUNDARY ELEMENT METHOD; CARDIOVASCULAR SYSTEM; DISEASES; INVERSE PROBLEMS; MATHEMATICAL MODELS; PHYSIOLOGICAL MODELS;

HUMAN VENTRICULAR MYOCARDIUM; L CURVE METHOD; TIKHONOV REGULARIZATION; WOLFF PARKINSON WHITE SYNDROME;

ELECTROCARDIOGRAPHY;

EID: 0030396868     PISSN: 00135852     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. D. Gabor and C. V. Nelson. "Determination of the resultant dipole of the heart from measurements on the body surface". J. Appl. Phys., vol. 25, pp. 413-416, 1954.
2. P. Savard, G. E. Mailloux, A. R. Roberge, R. M. Gulrajani, and R. Guardo, "A simulation study of the single moving dipole representation of cardiac electrical activity", IEEE Trans. Biomed. Eng., vol. BME-29, pp. 700-707. 1982.
3. R. M. Gulrajani, "Models of the electrical activity of the heart and computer simulation of electrocardiogram", CRC Crit. Rev. Biomed. Eng., vol. 16, pp. 1-66, 1988.
4. R. Hren, X. Zhang, and G. Stroink, "The effect of conductivity inhomogeneities on the body-surface potential and magnetic-field inverse solutions", in Biomagnetism: Fundamental Research and Clinical Applications. C. Baumgartner, L. Deecke, G. Stroink, and S.J. Williamson (eds.) Amsterdam: Elsevier IOS Press. 1995, pp. 680-683.
5. R. Hren, X. Zhang, and G. Stroink, "Comparison between electrocardiographic and magnetocardiographic inverse solutions using the boundary element method", Med. Biol. Eng. Comp., vol. 34, pp. 110-114, 1996.
6. R. M. Gulrajani, H. Pham-Huy, R. A. Nadeau, P. Savard, J. de Guise, R. E. Primeau, and F. A. Roberge, "Application of the single moving dipole inverse solution to the study of the Wolff-Parkinson-White syndrome in man", J. Electrocardiol., vol. 17, pp. 271-287, 1984.
7. R. A. Nadeau, P. Savard, G. Faugére, M. Shenasa, P. Pagé, R. M. Gulrajani, R. A. Guardo, and R. Cardinal, "Localization of pre-excitation sites in the Wolff-Parkinson-White syndrome by body surface potential mapping and single moving dipole representation", in Electrocardiographic Body Surface Mapping, R. Th, van Dam and A. van Oosterom (eds.) Boston: Martinus Nijhoff, 1986, pp. 95-98.
8. R. Hren, V. Jazbinšek, R. Zimmermann, S. N. Erné, and Z. Trontelj, "Localization of complex current sources by the two-plane method", in 81th International Conference on Biomagnetism, Book of Abstracts, Münster: Westfälische Wilhelms-Universität Münster. 1991, pp. 349-350.
9. R. Hren, The Effect of Inhomogeneities on Electrocardiograiphic and Magnetocardiographic Inverse Solutions: Application in the Localization of Ventricular Preexcitation Sites, M.Sc. Thesis, Halifax: Dalhousie University. 1993.
10. Y. Rudy and B. J. Messinger-Rapport, "The inverse solution in electrocardiography: Solution in terms of epicardial potentials", CRC Crit. Rev. Biomed. Eng., vol. 16, pp. 215-268, 1988.
11. H. S. Oster and Y. Rudy, "The electrocardiographic inverse solution", in High-Performance Computing in Biomedical Research, T. C. Pilkington, B. Eoftis, and J. F. Thompson (eds.) Boca Raton: CRC Press, 1993, pp. 135-155.
12. J. A. Stratton, Electromagnetic Theory, New York: McGraw-Hill, 1941.
13. V. A. Morozov, Regularization Methods for Ill-Posed Problems, Boca Raton: CRC Press, 1993.
14. R. Hren, "Reconstruction of distributed current sources on epicardial surfaces using a regularized minimum norm estimate", Electrotechn. Rev., vol. 62, pp. 81-87, 1995.
15. A. Tikhonov, "On the solution of incorrectly posed problems and the method of regularization", Sov. Math. Dokl., vol. 4, pp. 1035-1038, 1963.
16. A. Tikhonov and V. Arsenin, Solution of Ill-posed Problems, Washington, DC: Winston, 1977.
17. R. Hren, "Solution of the inverse problem in electrocardiography using Tikhonov regularization method", Electrotechn. Rev., vol. 62, pp. 73-80, 1995.
18. J. C. De Munck, "A linear discretization of the volume conductor boundary integral equation using analytically integrated elements", IEEE Trans. Biomed. Eng., vol. BME-39, pp. 986-990, 1992.
19. A. S. Ferguson, X. Zhang, and G. Stroink, "A complete linear discretization for calculating the magnetic field usine the boundary element method", IEEE Trans. Biomed. Eng., vol. BME-41, pp. 455-460, 1994.
20. C. F. van Loan, "Generalizing the singular value decomposition", SIAM J. Numer. Anal., vol. 13, pp. 76-83, 1976.
21. G. H. Golub and C. F. van Loan, Matrix Computations. Baltimore: John Hopkins University Press, 1983.
22. R. Hren and B. M. Horáček, "A three dimensional model of anisotropic ventricular myocardium: Simulation of normal activation sequence", in Proc. 3rd Electrotechn. Comp. Sci. Conf. ERK'94 Vol. B. B. Zajc and F. Solina (eds.) Portorož, 1994, pp. 367-369.
23. R. Hren, "Comparison between complex and singledipole source models: Application in the localization of ventricular pre-excitation sites", in Proc. 3rd Electrotechn. Comp. Sci. Conf. ERK'94 Vol. B. B. Zajc and F. Solina (eds.) Portorož, 1994, pp. 370-372.
24. K. Hren, J. Nenonen, P. MacInnis, and B. M. Horáček. "Simulated activation from endocardial pacing sites in an anisotropic model of human ventricles", in Building Bridges in Electrocardiology. A. van Oosterom, T. F. Oostendorp, and G. J. H. Uijen (eds.) Nijmegen: University Press Nijmegen, 1995, pp. 156-157.
25. R. Hren, J. Nenonen, P. MacInnis, and B. M. Horáček. "Simulated body-surface potential maps for paced activation sequences in human ventricles", in Computers in Cardiology 1995, A. Murray and R. Arzbaecher (eds.) Piscataway: IEEE Press, 1995, pp. 95-98.
26. R. Hren and B. M. Horáček, "A model study of the effect of ventricular fibrous structure on epicardial potentials", in Life Sciences 1995, Book of Abstracts, S. Ribarič and R. Zorec (eds.) Ljubljana: Physiological Society of Slovenia, 1995, pp. 66.
27. R. Hren, A Realistic Model of the Human Ventricular Myocardium: Application to the Study of Ectopic Activation, Ph.D. Dissertation, Halifax: Dalhousie University, 1996.
28. P. C. Hansen, "Analysis of discrete ill-posed problems by means of the L-curve", SIAM Review, vol. 34, pp. 561-580, 1992.
29. P. C. Hansen and D. P. O'Leaty, "The use of the L-curve in the regularization of discrete ill-posed problems", SIAM J. Sci. Statist. Comput., vol. 14, pp. 1487-1503, 1993.
30. R. Hren and G. Stroink, "Application of the surface harmonic expansions for modelling the human torso", IEEE Trans. Biomed. Eng., vol. BME-42, pp. 521-524, 1995.
31. T. F. Oostendorp, A. van Oosterom, and G. Huiskamp, "Interpolation on a triangulated 3D surface", J. Comp. Physics, vol. 80, pp. 331-343, 1989.
32. E. Anderson, Z. Bai, C. Bischof, J. W. Demmel, J. J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen, LAPACK User's Guide, Philadelphia: Society for Industrial and Applied Mathematics, 1992.
33. The Numerical Algorithms Group Ltd., The NAG Fortran Library Manual - Murk 13, Oxford: The Numerical Algorithms Group Ltd., 1988.
34. M. S. Spach, R. C. Barr and C. F. Lanning, "Experimental basis for QRS and T wave potentials in the WPW syndrome: The relation of epicardial to body surface potentials in the intact chimpanzee", Circ. Res., vol. 42, pp. 103-118, 1978.
35. B. Taccardi, E. Macchi, R. L. Lux, P. E. Ershler, S. Spaggiari, S. Baruffi, and Y. Vyhmeister, "Effect of myocardial liber direction on epicardial potentials", Circulation, vol. 90, pp. 3076-3090, 1994.
36. A. V. Shahidi, P. Savard and R. Nadeau, "Forward and inverse problems of electrocardiography: Modeling and recovery of epicardial potentials in humans", IEEE Trans. Biomed. vol. BME-41, pp. 249-256, 1994.