Noninvasive electrocardiographic imaging (ECGI): Application of the generalized minimal residual (GMRes) method

Annals of Biomedical Engineering

Volumn 31, Issue 8, 2003, Pages 981-994

  Ramanathan, Charulatha ^a   Jia, Ping ^a   Ghanem, Raja ^a   Calvetti, Daniela ^b   Rudy, Yoram ^a,b  

^a Case Western Reserve University   (United States)

^b CASE WESTERN RESERVE UNIVERSITY   (United States)

Author keywords

Electrocardiographic inverse problem; Noninvasive arrhythmia diagnosis; Tikhonov regularization

Indexed keywords

BIOELECTRIC POTENTIALS; CARDIOVASCULAR SYSTEM; COMPUTER AIDED DIAGNOSIS; COMPUTER SIMULATION; DISEASES; ELECTROPHYSIOLOGY; IMAGE RECONSTRUCTION; INVERSE PROBLEMS; NONINVASIVE MEDICAL PROCEDURES;

GENERALIZED MINIMAL RESIDUAL METHOD; INFARCTED HEART; NONINVASIVE ELECTROCARDIOGRAPHIC IMAGING; TKHONOV SOLUTION;

ELECTROCARDIOGRAPHY;

ACTION POTENTIAL; ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPARATIVE STUDY; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; DOG; ELECTROCARDIOGRAPHY; EVALUATION; HEART INFARCTION; HEART MUSCLE CONDUCTION SYSTEM; HEART PACING; HEART VENTRICLE TACHYCARDIA; INNERVATION; METHODOLOGY; PATHOPHYSIOLOGY; PERICARDIUM; VALIDATION STUDY;

ACTION POTENTIALS; ALGORITHMS; ANIMALS; BODY SURFACE POTENTIAL MAPPING; CARDIAC PACING, ARTIFICIAL; COMPUTER SIMULATION; DIAGNOSIS, COMPUTER-ASSISTED; DOGS; ELECTROCARDIOGRAPHY; HEART CONDUCTION SYSTEM; MODELS, CARDIOVASCULAR; MODELS, NEUROLOGICAL; MYOCARDIAL INFARCTION; PERICARDIUM; TACHYCARDIA, VENTRICULAR;

EID: 0042878627     PISSN: 00906964     EISSN: None     Source Type: Journal    
DOI: 10.1114/1.1588655     Document Type: Article

References (33)

1. Abildskov, J. A., A. K. Evans, R. L. Lux, and M. J. Burgess. Ventricular recovery properties and qrst deflection area in cardiac electrograms. Am. J. Physiol. 239:H227-H231, 1980.
2. Burnes, J. E., B. Taccardi, R. S. MacLeod, and Y. Rudy. Noninvasive ECG imaging of electrophysiologically abnormal substrates in infarcted hearts: A model study. Circulation 101:533-540, 2000.
3. Burnes, J. E., B. Taccardi, and Y. Rudy. A noninvasive imaging modality for cardiac arrhythmias. Circulation 102:2152-2158, 2000.
4. Burnes, J. E., B. Taccardi, P. R. Ershler, and Y. Rudy. Noninvasive electrocardiographic imaging of substrate and intramural ventricular tachycardia in infarcted hearts. J. Am. Coll. Cardiol. 38:2071-2078, 2001.
5. Calvetti, D., L. Reichel, F. Sgallari, and G. Spaletta. An iterative method for image reconstruction from projections. In: Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, edited by J. G. Lewis, Philadelphia, 1994, pp. 92-96.
6. Calvetti, D., B. Lewis, and L. Reichel. Restoration of images with spatially invariant blur by the GMRes method. Proc. SPIE 4116:364-374, 2000.
7. Calvetti, D., B. Lewis, and L. Reichel. Gmres, L curves, and discrete ill-posed problems. BIT 42:44-65, 2002.
8. Colli Franzone, P., L. Guerri, S. Tentoni, C. Viganotti, S. Baruffi, S. Spaggiari, and B. Taccardi. Mathematical procedure for solving the inverse problem of electrocardiography. Math. Biosci. 77:353-396, 1985.
9. Ghanem, R. N., J. E. Burnes, A. L. Waldo, and Y. Rudy. Imaging dispersion of myocardial repolarization. II. Noninvasive reconstruction of epicardial measures. Circulation 104:1306-1312, 2001.
10. Hanke, M. Limitations of the L-curve method in ill-posed problems. BIT 36:287-301, 1996.
11. Hansen, P. C., and D. P. O'Leary. The use of the L curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput. (USA) 14:1487-1503, 1993.
12. Hansen, P. C. Rank-deficient and discrete ill-posed problems: Numerical Aspects of Linear Inversion. Philadelphia: Society for Industrial and Applied Mathematics (SIAM), 1998, 247 pp.
13. http://www.americanheart.org.
14. http://www.imm.dtu.dk/~pch/Regutools/regutools.html.
15. Jia, P., B. Punske, B. Taccardi, and Y. Rudy. Electrophysicologic endocardial mapping from a noncontact nonexpandable catheter: A validation study of a geometry-based concept. J. Cardiovasc. Electrophysiol. 11:1238-1251, 2000.
16. Jia, P., B. Punske, B. Taccardi, and Y. Rudy. Endocardial mapping of electrophysiologically abnormal substrates and cardiac arrhythmias using a noncontact nonexpandable catheter. J. Cardiovasc. Electrophysiol. 13:1238-1251, 2002.
17. Johnston, P. R., and R. M. Gulrajani. A new method for regularization parameter determination in the inverse problem of electrocardiography. IEEE Trans. Biomed. Eng. 44:19-39, 1997.
18. Khoury, D. S., B. Taccardi, R. L. Lux, P. R. Ershler, and Y. Rudy. Reconstruction of endocardial potentials and activation sequences from intracavitary probe measurements. Localization of pacing sites and effects of myocardial structure. Circulation 91:845-863, 1995.
19. Liu, Z. W., P. Jia, P. R. Ershler, B. Taccardi, R. L. Lux, D. S. Khoury, and Y. Rudy. Noncontact endocardial mapping: Reconstruction of electrograms and isochrones from intracavitary probe potentials. J. Cardiovasc. Electrophysiol. 8:415-431, 1997.
20. Liu, Z. W., P. Jia, L. A. Biblo, B. Taccardi, and Y. Rudy. Endocardial potential mapping from a noncontact nonexpandable catheter: A feasibility study. Ann. Biomed. Eng. 26:994-1009, 1998.
21. Messinger-Rapport, B. J., and Y. Rudy. Noninvasive recovery of epicardial potentials in a realistic heart-torso geometry. Normal sinus rhythm. Circ. Res. 66:1023-1039, 1990.
22. Mirvis, D. M. Body Surface Electrocardiographic Mapping. Boston, MA: Kluwer Academic, 1988.
23. Montague, T. J., E. R. Smith, D. A. Cameron, P. M. Rautaharju, G. A. Klassen, C. S. Felmington, and B. M. Horacek. Isointegral analysis of body surface maps: Surface distribution and temporal variability in normal subjects. Circulation 63:1163-1172, 1981.
24. 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. Circulation 96:1012-1024, 1997.
25. 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. Circulation 97:1496-1507, 1998.
26. Plonsey, R. A contemporary view of the ventricular gradient of wilson. J. Electrocardiol. 12:337-341, 1979.
27. Ramanathan, C. and Y. Rudy. Electrocardiographic imaging. I. Effect of torso inhomogeneities on body surface electro-cardiographic potentials. J. Cardiovasc. Electrophysiol. 12:229-240, 2001.
28. Ramanathan, C., and Y. Rudy. Electrocardiographic imaging. II. Effect of torso inhomogeneities on noninvasive reconstruction of epicardial potentials, electrograms, and isochrones. J. Cardiovasc. Electrophysiol. 12:241-252, 2001.
29. Rudy, Y., and B. J. Messinger-Rapport. The inverse problem in electrocardiography: Solutions in terms of epicardial potentials. Crit. Rev. Biomed. Eng. 16:215-268, 1988.
30. Rudy, Y., and H. S. Oser. The electrocardiographic inverse problem. Crit. Rev. Biomed. Eng. 20:25-45, 1992.
31. Rudy, Y., and J. E. Burnes. Noninvasive electrocardiographic imaging. Ann. Noninvasive Electrocardiol. 4:340-358, 1999.
32. Saad, Y., and M. H. Schultz. Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7:856-869, 1986.
33. Tikhonov, A. N., and V. Y. Arsenin. Solutions of Ill-posed Problems. New York: Wiley, 1977.