Annals of Biomedical Engineering

, Volume 26, Issue 1, pp 37–47 | Cite as

A Field-Compatible Method for Interpolating Biopotentials

  • John E. Burnes
  • David C. Kaelber
  • Bruno Taccardi
  • Robert L. Lux
  • Philip R. Ershler
  • Yoram Rudy


Mapping of bioelectric potentials over a given surface (e.g., the torso surface, the scalp) often requires interpolation of potentials into regions of missing data. Existing interpolation methods introduce significant errors when interpolating into large regions of high potential gradients, due mostly to their incompatibility with the properties of the three-dimensional (3D) potential field. In this paper, an interpolation method, inverse-forward (IF) interpolation, was developed to be consistent with Laplace's equation that governs the 3D field in the volume conductor bounded by the mapped surface. This method is evaluated in an experimental heart–torso preparation in the context of electrocardiographic body surface potential mapping. Results demonstrate that IF interpolation is able to recreate major potential features such as a potential minimum and high potential gradients within a large region of missing data. Other commonly used interpolation methods failed to reconstruct major potential features or preserve high potential gradients. An example of IF interpolation with patient data is provided to illustrate its applicability in the actual clinical setting. Application of IF interpolation in the context of noninvasive reconstruction of epicardial potentials (the “inverse problem”) is also examined. © 1998 Biomedical Engineering Society.

PAC98: 8710+e, 0260Ed

Interpolation Mapping Bioelectric potentials Inverse problem Epicardial potentials Body surface potential mapping Field method Interpolating biopotentials Electrocardiogram 


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  1. 1.
    Barr, R. C., M. S. Spach, and G. S. Herman-Giddens. Selection of the number and positions of measuring locations for electrocardiography. IEEE Trans. Biomed. Eng.18:125-38, 1971.Google Scholar
  2. 2.
    Brebbia, C. A., J. C. F. Telles, and L. C. Wrobel. Boundary Element Techniques. Theory and Applications in Engineering. Berlin: Springer-Verlag, 1984.Google Scholar
  3. 3.
    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.77:353-96, 1985.Google Scholar
  4. 4.
    De Ambroggi, L., E. Musso, and B. Taccardi. Body Surface Mapping. In: Comprehensive Electrocardiography. Theory and Practice in Health and Disease, edited by P. W. MacFarlane and T. D. V. Lawrieed. New York: Pergamon, 1989, pp. 1015-45.Google Scholar
  5. 5.
    Gulrajani, R. M., P. Savard, and F. A. Roberge. The inverse problem in electrocardiography: Solutions in terms of equivalent sources. Crit. Rev. Biomed. Eng.16:171-214, 1988.Google Scholar
  6. 6.
    Harder, R. L., and R. N. Desmarais. Interpolation using surface splines. J. Aircr.9:189-91, 1972.Google Scholar
  7. 7.
    Heringa, A., G. J. H. Uijen, R. T. van Dam, and J. P. J. de Valk. The display of body surface maps. In: Electrocardiographic Body Surface Mapping, edited by R. T. van Dam and A. van Oosterom, 1st ed. Boston: Martinus Nijhoff, 1986, pp. 171-5.Google Scholar
  8. 8.
    Hoekema, R., G. J. M. Huiskamp, T. F. Oostendorp, G. J. H. Uijen, and A. van Oosterom. Lead system transformation for pooling of body surface map data: A surface Laplacian approach. J. Electrocardiol. 28:344-345, 1995.Google Scholar
  9. 9.
    Hubley-Kozey, C. L., L. B. Mitchell, M. J. Gardner, J. W. Warren, C. J. Penney, E. R. Smith, and B. M. Horacek. Spatial features in body-surface potential maps can identify patients with a history of sustained ventricular tachycardia. Circulation92:1825-38, 1995.Google Scholar
  10. 10.
    Huiskamp, G. J., and A. van Oosterom. The depolarization sequence of the human heart surface computed from measured body surface potentials. IEEE Trans. Biomed. Eng.35:1047-59, 1989.Google Scholar
  11. 11.
    Ilmoniemi, R. J. Models of source currents in the brain. Brain Topogr.5:331-6, 1993.Google Scholar
  12. 12.
    Jackson, J. D. Classical Electrodynamics, 2nd ed. New York: Wiley, 1975.Google Scholar
  13. 13.
    Kaelber, D., J. Haaga, and Y. Rudy. Non-invasive in vivodetermination of body surface and epicardial geometries for electrocardiographic imaging. In: Proceedings of the 16th annual International Conference of the IEEE Engineering in Medicine and Biology Society. Engineering advances: New Opportunities for Biomedical Engineers, edited by N. F. Sheppard, Jr., M. Eden, and G. Kantor. Piscataway, NJ: IEEE Press, 1994, Vol. 16, pp. 153-154.Google Scholar
  14. 14.
    Klug, D., A. Ferracci, F. Molin, M Dubuc, P. Savard, T. Kus, F. Helie, R. Cardinal, and R. Nadeau. Body surface potential distributions during idiopathic ventricular tachycardia. Circulation91:2002-9, 1995.Google Scholar
  15. 15.
    Liebman, J., J. A. Zeno, B. Olshansky, A. S. Geha, C. W. Thomas, Y. Rudy, R. W. Henthorn, M. Cohen, and A. L. Waldo. Electrocardiographic body surface potential mapping in the Wolff-Parkinson-White syndrome. Noninvasive determination of the ventricular insertion sites of accessory atrioventricular connections. Circulation83:886-901, 1991.Google Scholar
  16. 16.
    Lopes da Silva, F. H. A critical review of clinical applications of topographic mapping of brain potentials. J. Clin. Neurophysiol.7:535-51, 1990.Google Scholar
  17. 17.
    Lux, R. L., C. R. Smith, R. F. Wyatt, and J. A. Abildskov. Limited lead selection for estimation of body surface potential maps in electrocardiography. IEEE Trans. Biomed. Eng.25:270-6, 1978.Google Scholar
  18. 18.
    MacLeod, R. S., M. Gardner, R. M. Miller, and B. M. Horacek. Application of an electrocardiographic inverse solution to localize ischemia during coronary angioplasty. J. Cardiovasc. Electrophysiol.6:2-18, 1995.Google Scholar
  19. 19.
    Messinger Rapport, B. J., and Y. Rudy. Regularization of the inverse problem in electrocardiography. A model study. Math. Biosci.89:79-118, 1988.Google Scholar
  20. 20.
    Messinger Rapport, B. J., and Y. Rudy. Noninvasive recovery of epicardial potentials in a realistic heart-torso geometry. Normal sinus rhythm. Circ. Res.66:1023-39, 1990.Google Scholar
  21. 21.
    Oostendorp, T. F., A. van Oosterom, and G. Huiskamp. Interpolation of a triangulated 3D surface. Comput. Phys.80:331-43, 1989.Google Scholar
  22. 22.
    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.Google Scholar
  23. 23.
    Perrin, F., J. Pernier, O. Bertrand, M. H. Giard, and J. F. Echallier. Mapping of scalp potentials by surface spline interpolation. Electroencephalogr. Clin. Neurophysiol.66:75- 81, 1987.Google Scholar
  24. 24.
    Rudy, Y., and B. J. Messinger Rapport. The inverse problem in electrocardiography: Solutions in terms of epicardial potentials. Crit. Rev. Biomed. Eng.16:215-68, 1988.Google Scholar
  25. 25.
    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.41:249-56, 1994.Google Scholar
  26. 26.
    Sippensgroenewegen, A., H. Spekhorst, N. M. van Hemel, J. H. Kingma, R. N. Hauer, J. M. de Bakker, C. A. Grimbergen, M. J. Janse, and A. J. Dunning. Value of body surface mapping in localizing the site of origin of ventricular tachycardia in patients with previous myocardial infarction. J. Am. Coll. Cardiol.24:1708-24, 1994.Google Scholar
  27. 27.
    Soufflet, L., M. Toussaint, R. Luthringer, J. Gresser, R. Minot, and J. P. Macher. A statistical evaluation of the main interpolation methods applied to 3-dimensional EEG mapping. Electroencephalogr. Clin. Neurophysiol.79:393-402, 1991.Google Scholar
  28. 28.
    Taccardi, B., E. Macchi, R. L. Lux, P. R. Ershler, S. Spaggiari, S. Baruffi, and Y. Vyhmeister. Effect of myocardial fiber direction on epicardial potentials. Circulation90:3076- 90, 1994.Google Scholar

Copyright information

© Biomedical Engineering Society 1998

Authors and Affiliations

  • John E. Burnes
    • 1
  • David C. Kaelber
    • 1
  • Bruno Taccardi
    • 2
  • Robert L. Lux
    • 2
  • Philip R. Ershler
    • 2
  • Yoram Rudy
    • 1
  1. 1.Cardiac Bioelectricity Research and Training Center, Department of Biomedical EngineeringCase Western Reserve UniversityCleveland
  2. 2.Cardiovascular Research and Training InstituteUniversity of UtahSalt Lake City

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