Factors affecting the accuracy of the boundary element method in the forward problem-I: Calculating surface potentials

IEEE Transactions on Biomedical Engineering

Volumn 44, Issue 11, 1997, Pages 1139-1155

  Ferguson, A S ^a   Stroink, G ^a  

^a DALHOUSIE UNIVERSITY   (Canada)

Author keywords

Boundary element method; Electrocardiography; Electroencephalography; Forward solution; Inverse problems; Magnetocardiography; Magnetoencephalography; Surface potentials

Indexed keywords

APPROXIMATION THEORY; BIOELECTRIC POTENTIALS; BOUNDARY ELEMENT METHOD; ELECTROCARDIOGRAPHY; ELECTROENCEPHALOGRAPHY; ERROR ANALYSIS; INVERSE PROBLEMS;

MAGNETOCARDIOGRAPHY; MAGNETOENCEPHALOGRAPHY; SURFACE POTENTIALS;

BIOMEDICAL ENGINEERING;

ARTICLE; DIAGNOSTIC ACCURACY; ELECTRIC POTENTIAL; ELECTROCARDIOGRAM; ELECTROENCEPHALOGRAM; MAGNETOCARDIOGRAPHY; SURFACE PROPERTY;

BODY SURFACE POTENTIAL MAPPING; CHI-SQUARE DISTRIBUTION; DATA DISPLAY; ELECTROCARDIOGRAPHY; ELECTROENCEPHALOGRAPHY; HUMANS; LINEAR MODELS; MODELS, STATISTICAL; RANDOM ALLOCATION; SURFACE PROPERTIES;

EID: 0031282144     PISSN: 00189294     EISSN: None     Source Type: Journal    
DOI: 10.1109/10.641342     Document Type: Article

References (29)

1. W. W. Sutherling, P. H. Crandall, T. M. Darcey, D. P. Becker, M. F. Levesque, and D. S. Barth.The magnetic and electric fields agree with intracranial localizations of somatosensory cortex," Neural., vol. 38, pp. 1705-1714, 1988.
2. G. Stroink.Cardiomagnetic imaging," in Frontiers in Cardiovascular Imaging, B. L. Zaret, L. Kaufman, A. S. Berson, and R. A. Dünn, Eds. New York: Ravenl993, pp. 161-177.
3. D. L. Derfus and T. C. Pilkington.Assessing the effect of uncertainty in intracavitary electrode position on endocardial potential estimates," IEEE Trans. Biomed. Eng., vol. 39, no. 8, pp. 676-681, 1992.
4. B. He, T. Musha, Y. Okamoto, S. Homma, Y. Nakajima, and T. Sato.Electric dipole tracing in the brain by means of the boundary element method and its accuracy," IEEE Trans. Biomed. Eng., vol. BME-34, pp. 40614, 1987.
5. E. Frank.Electric potential produced by two point current sources in a homogeneous conducting sphere," J. Appl. Phys., vol. 11, pp. 1225-1228, 1952.
6. P. M. Berry.Appendix: N, M space harmonics of the oblate spheroid," Annals NY Acad. Sei, vol. 65, pp. 1126-1134, 1956.
7. Ph. Lambin and J. Troquet.Complete calculation of the electric potential produced by a pair of current source and sink energizing a circular finite-length cylinder," J. Appl. Phys., vol. 54, pp. 41741184, 1983.
8. A. S. Ferguson and G. Stroink.The potential generated by current sources located in an insulated rectangular volume conductor", J. Appl. Phys., vol. 76, pp. 7671-7676, 1994.
9. J. W. H. Meijs, O. W. Weier, M. J. Peters, and A. van Oosterom.On the numerical accuracy of the boundary element method," IEEE Trans. Biomed. Eng., vol. 36, pp. 1038-1049, 1989.
10. L. Heller, R. Aaron, E. D. Best, H. A. Schlitt, and D. M. Ranken.Mesh generation issues in the EEG and MEG forward problems," in Recent Advances in Biomagnetism, Abstracts of 9th Int. Conf. Biomag. (Vienna), L. Deecke, C. Baumgartner, G. Stroink, and S. J. Williamson, Eds., 1993, p. 199.
11. H. Schutt, L. Heller, R. Aaron, E. Best, and D. Ranken.Evaluation of boundary element methods for the EEG forward problem: Effect of linear interpolation," IEEE Trans. Biomed. Eng., vol. 42, no. 1, pp. 52-58, 1995.
12. J. C. de Munck.A linear discretization of the volume conductor boundary integral equation using analytically integrated elements," IEEE Trans. Biomed. Eng., vol. 39, pp. 986-990, 1992.
13. L. Heller.Computation of the return current in encephalography: The auto solid angle," in Digital Image Synthesis and Inverse Optics, Proc. SPIE 1351, A. F. Gmitro, P. S. Well, and I. J. LaHaie, Eds., 1990, pp. 376-390.
14. M. Thevenet, O. Bertrand, F. Perrin, T. Dumont, and J. Pernier.The finite element method for a realistic head model of electrical brain activities: preliminary results," Clin. Phys. Physiol. Meas., vol. 12, pp. 89-94, 1991.
15. P. Savard, A. Ackaoui, R. M. Gulrajani, R. A. Nadeau, F. A. Roberge, R. Guardo, and B. Dube.Localization of cardiac ectopic activity in man by a single moving dipole: Comparison of different computation techniques,"/ Electrocardiol., vol. 18, pp. 211-222, 1985.
16. J. C. deMunck, B. W. Van Dijk, and H. Spekreijse.Mathematical dipoles are adequate to describe realistic generators of human brain activity," IEEE Trans. Biomed. Eng., vol. 35, pp. 960-966, 1988.
17. E. Nyssen.Potentiaalkaarten in de elektrokardiologie: Een zoektocht naar technieken voor de verbetering van hun klinische toepassing," Ph.D. thesis, Vrije Univ. Brüssel, Brussels, Belguim, 1986.
18. P. P. Silvester and R. L. Ferrari, Finite Elements for Electrical Engineers. Cambridge, U.K.: Cambridge Univ. Press, 1983, ch. 3.
19. M. S. Lynn and W. P. Timlake.The use of multiple deflations in the numerical solution of singular systems of equations, with applications to potential theory," SIAM J. Numer. Anal., vol. 5, pp. 303-322, 1968.
20. A. C. Barnard, I. M. Duck, M. S. Lynn, and W. P. Timlake.The application of electromagnetic theory to electrocardiography II: The numerical solution to the integral equations," Biophys. J., vol. 7, pp. 46391, 1967.
21. J. Radon.Zur mechanischen Kubatur," Monat. Mathematik, vol. 52, pp. 286-300, 1948.
22. C. J. Purcell, G. Stroink, and B. M. Horacek.Effect of torso boundaries on electric potential and magnetic field of a dipole," IEEE Trans. Biomed. Eng., vol. 35, pp. 671-678, 1988.
23. J. J. M. Cuppen and A. van Oosterom.Model studies with the inversely calculated isochrones of ventricular depolarization," IEEE Trans. Biomed. Eng., vol. BME-31, pp. 652-659, 1984.
24. B. N. Cuffin.A method for localizing EEG sources in realistic head models," IEEE Trans. Biomed. Eng., vol. 42, no. 1, pp. 68-71, 1995.
25. C. Purcell, T. Mashiko, K. Odaka, and K. Ueno.Describing head shape with surface harmonic expansions," IEEE Trans. Biomed. Eng., vol. 38, pp. 303-306, 1991.
26. R. Hren and G. Stroink.Application of the surface harmonic expansion for modeling the human torso," IEEE Trans. Biomed. Eng., vol. 42, no. 5, pp. 521-524, 1995.
27. R. C. Barr, M. Ramsey, III, and M. S. Spach.Relating epicardial to body surface potential distributions by means of transfer coefficients based on geometry measurements," IEEE Trans. Biomed. Eng., vol. BME-24, pp. 1-11, 1977.
28. D. J. Fletcher, A. Amir, D. L. Jewett, and G. Fein.Improved method for computation of potentials in a realistic head shape model," IEEE Trans. Biomed. Eng., vol. 42, no. 11, pp. 1094-1104, 1995.
29. S. D. Conte and C. de Boor, Elementary Numerical Analysis, 3rd ed. New York: McGraw Hill, 1980, pp. 303-310.