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A Novel Interpolation Method for Electric Potential Fields in the Heart during Excitation

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Abstract

In mapping the electrical activity of the heart, interpolation of electric potentials plays two important roles. First, it permits the estimation of potentials in regions that could not be sampled or where signal quality was poor, and second, it supports the construction of isopotential lines and surfaces for visualization. The difficulty in developing robust interpolation techniques for cardiac applications lies in the abrupt change in potential in the vicinity of the activation wave front. Despite the resulting nonlinearities in spatial potential distributions, simple linear interpolation methods are the current standard and the resulting errors due to aliasing can be large if electrode spacing does not lie on the order of 0.5–2 mm—the thickness of the activation wave front. We have developed a novel interpolation method that is based on two observations specific to the spread of excitation in the heart: (1) that propagation velocity changes smoothly within a region large enough to contain several measurement electrodes and (2) that electrogram morphology varies very little in the neighborhood of each sample point except for a time shift in the potential wave forms. The resulting interpolation scheme breaks the interpolation of one highly nonlinear variable—extracellular potential—into two separate interpolations of variables with much less drastic spatial variation—activation time and electrogram morphology. We have applied this method to potentials originally recorded at 1.5 mm spacing and then subsampled at a range of densities for testing of the interpolation. The results based both on reconstruction of isopotential contour maps and statistical comparison showed significant improvement of this novel approach over standard linear techniques. The applications of the new method include improved determination of electrophysiological parameters such as spatial gradients of potential and the path of cardiac activation and recovery, estimation of electrograms at desired locations, and visualization of electric potential distributions. © 1998 Biomedical Engineering Society.

PAC98: 8790+y, 0260Ed, 8710+e

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REFERENCES

  1. Alfeld, P. Scattered data interpolation in three or more variables. In: Mathematical methods in CAGD, edited by T. Lyche and L. L. Schumaker. New York: Academic, 1989, pp. 1-33.

    Google Scholar 

  2. Arisi, G., E. Macchi, S. Baruffi, S. Spaggiari, and B. Taccardi. Potential fields on the ventricular surface of the exposed dog heart during normal excitation. Circ. Res.52:706- 715, 1983.

    Google Scholar 

  3. Arisi, G., E. Macchi, C. Corradi, R. L. Lux, and B. Taccardi. Epicardial excitation during ventricular pacing: Relative independence of breakthrough sites from excitation sequence in canine right ventricle. Circ. Res.71:840-849, 1992.

    Google Scholar 

  4. Barr, R. C., T. M. Gallie, and M. S. Spach. Automated production of contour maps for electrophysiology. I. Problem definition, solution strategy, and specification of geometric model. Comput. Biomed. Res.13:142-153, 1980.

    Google Scholar 

  5. Barr, R. C., and M. S. Spach. Sampling rates required for digital recording of intracellular and extracellular cardiac potentials. Circulation55:40-48, 1977.

    Google Scholar 

  6. Bayly, P. V., E. E. Johnson, S. F. Idriss, R. E. Ideker, and W. M. Smith. Efficient electrode spacing for examining spatial organization during ventricular fibrillation. IEEE Trans. Biomed. Eng.40:1060-1066, 1993.

    Google Scholar 

  7. Berbari, E. J., P. Lander, D. B. Geselowitz, B. J. Scherlag, and R. Lazzara. The methodology of cardiac mapping. In: Cardiac Mapping, edited by M. Shenasa, M. Borggrefe, and G. Breithardt. Armonk, NY: Futura, 1993, pp. 63-77.

    Google Scholar 

  8. Berbari, E. J., P. Lander, B. J. Scherlag, R. Lazzara, and D. B. Geselowitz. Ambiguities of epicardial mapping. J. Electrocardiol. Suppl.24, 16-20, 1991.

  9. Blanchard, S. M., R. J. Damiano, W. M. Smith, R. E. Ideker, and J. E. Lowe. Interpolating unipolar epicardial potentials from electrodes separated by increasing distances. PACE12:1938-1955, 1989.

    Google Scholar 

  10. Chen, P. S., P. D. Wolf, F. J. Claydon, E. G. Dixon, H. J. Vidaillet, N. D. Danieley, T. C. Pilkington, and R. E. Ideker. The potential gradient field created by epicardial defibrillation electrodes in dogs. Circulation74:626-636, 1986.

    Google Scholar 

  11. Ciaccio, E. J., A. L. Wit, M. M. Scheinman, S. M. Dunn, M. Akay, and J. Coromilas. Predication of the location and time of spontaneous termination of reentrant ventricular tachycardia for radiofrequency catheter ablation therapy. J. Electrocardiol. Suppl.28:165-173, 1995.

    Google Scholar 

  12. Colli Franzone, P., 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. J. Cardiovasc. Electrophysiol.4:144-160, 1993.

    Google Scholar 

  13. Downey, J. M. Why the endocardium? In: Therapeutic Approches to Myocardial Infarct Size Limitation, edited by D. J. Hearse and D. M. Yellon. New York: Raven, 1984, pp. 125-138.

    Google Scholar 

  14. Farin, G. Smooth interpolation to scattered 3D data. In: Surfaces in Computer Aided Geometric Design. Amsterdam: North-Holland, 1983, pp. 43-63.

    Google Scholar 

  15. Hodgkin, A. L., and A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. (London)117:500-544, 1952.

    Google Scholar 

  16. Ideker, R. E., W. M. Smith, S. M. Blanchard, S. L. Reiser, E. V. Simpson, P. D. Wolf, and N. D. Danieley. The assumptions of isochronal cardiac mapping. PACE12:456-478, 1989.

    Google Scholar 

  17. Idriss, S. F., S. B. Melnick, P. D. Wolf, W. M. Smith, and R. E. Ideker. Predicting the potential gradient field in ventricular fibrillation from shocks delivered in paced rhythm. Am. J. Physiol.268:H2336-H2344, 1995.

    Google Scholar 

  18. Janse, M. J., A. G. Kleber, A. Capucci, R. Coronel, and F. Wilms-Schopman. Electrophysiological basis for arrhythmias caused by acute ischemia: Role of subendocardium. J. Mol. Cell. Cardiol., 18:339-355, 1986.

    Google Scholar 

  19. MacLeod, R. S., and C. R. Johnson. Map3d: Interactive scientific visualization for bioengineering data. In: Proceedings of the IEEE Engineering in Medicine and Biology Society 15th Annual International Conference. New York: IEEE, 1993, pp. 30-31.

    Google Scholar 

  20. MacLeod, R. S., R. L. Lux, and B. Taccardi. Translation of body surface maps between different electrode configurations using a three-dimensional interpolation scheme. In: Electrocardiology' 93: Proceedings of the International Congress on Electrocardiology, XXth Annual Meeting, edited by P. W. MacFarlane. Singapore: World Scientific, 1993, pp. 179-182.

    Google Scholar 

  21. Monro, D. M. Interpolation methods for surface mapping. Comput. Program Biomed.11:145-157, 1980.

    Google Scholar 

  22. Oostendorp, T. F., A. van Oosterom, and G. J. Huiskamp. Interpolation on a triangulated 3D surface. J. Comput. Phys.80:331-343, 1989.

    Google Scholar 

  23. Roberts, D. E., L. T. Hersh, and A. M. Scher. Influence of cardiac fiber orientation on wavefront voltage, conduction velocity, and tissue resistivity in the dog. Circ. Res.44:701- 712, 1979.

    Google Scholar 

  24. Roberts, D. E., and A. M. Scher. Effect of tissue anisotropy on extracellular potential fields in canine myocardium in situ. Circ. Res.50:342-351, 1982.

    Google Scholar 

  25. Rudy, Y., and R. Plonsey. A comparison of volume conductor and source geometry on body surface and epicardial potentials. Circ. Res.46:283-291, 1980.

    Google Scholar 

  26. Savard, P., G. Bonneau, G. Tremblay, R. A. Leblanc, R. Cardinal, P. Pagé, and R. A. Nadeau. Interactive cardiac mapping system for antiarrhythmia surgery. In: IEEE Engineering in Medicine and Biology Society 8th Annual International Conference. New York: IEEE, 1986, pp. 1286- 1288.

    Google Scholar 

  27. Schijvenaars, B. J. A., J. A. Kors, G. van Herpen, F. Kornreich, and J. H. van Bemmel. Interpolation of body surface potential maps. J. Electrocardiol. Suppl.28:104-109, 1996.

    Google Scholar 

  28. Spach, M. S., and P. C. Dolber. Relating extracellular potentials and their derivatives to anisotropic propagation at a microscopic level in human cardiac muscle. Circ. Res.58:356-371, 1986.

    Google Scholar 

  29. Spach, M. S., P. C. Dolber, and J. F. Heidlage. Influence of the passive anisotropic properties on directional differences in propagation following modification of the sodium conductance in human atrial muscle: A model of reentry based on anisotropic discontinuous propagation. Circ. Res.62:811- 832, 1988.

    Google Scholar 

  30. Spach, M. S., W. T. Miller, D. B. Geselowitz, R. C. Barr, J. M. Kootsey, and E. A. Johnson. The discontinuous nature of propagation in normal canine cardiac muscle: Evidence for recurrent discontinuities of intracellular resistance that affect the membrane currents. Circ. Res.48:39-54, 1981.

    Google Scholar 

  31. Taccardi, B., R. L. Lux, P. R. Ershler, R. S. Macleod, C. Zabawa, and Y. Vyhmeister. Potential distributions and excitation time maps recorded with high spatial resolution from the entire ventricular surface of exposed dog hearts. In: Computers in Cardiology. Los Alamitos, CA: IEEE Computer Press, 1992, pp. 1-4.

    Google Scholar 

  32. 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- 3090, 1994.

    Google Scholar 

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Authors and Affiliations

  1. Nora Eccles Harrison Cardiovascular Research and Training Institute, University of Utah, Salt Lake City, UT

    Quan Ni, Robert S. MacLeod, Robert L. Lux & Bruno Taccardi

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  1. Quan Ni
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  2. Robert S. MacLeod
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  3. Robert L. Lux
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  4. Bruno Taccardi
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Ni, Q., MacLeod, R.S., Lux, R.L. et al. A Novel Interpolation Method for Electric Potential Fields in the Heart during Excitation. Annals of Biomedical Engineering 26, 597–607 (1998). https://doi.org/10.1114/1.41

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