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The bulletin of mathematical biophysics

, Volume 21, Issue 1, pp 61–70 | Cite as

The inconsistencies of present-day mathematical-physical methods pertaining to current generators in volume conductors used in electrocardiography

  • J. Martinek
  • G. C. K. Yeh
  • H. de Beaumont
Article
  • 34 Downloads

Abstract

The present-day practices of electrocardiography and vectorardiography are based upon the theory that the surface potential differences can be assumed to be due to a single dipole inside the body. It is shown in this paper that a dipole cannot account for all the surface potentials due to realistic current generators, and hence the determination of the current generator from surface potential measurements based upon such a theory will lead to inconsistent representations of the heart for one and the same subject.

To demonstrate this point two eccentric dipoles of different strengths and locations representing two muscle fibers are taken to be the current generator in a homogeneous spherical conductor. The exact surface potentials are then expressed by means of the “interior sphere theorem” of the authors. With these expressions the magnitude, direction, and location of the resultant dipole are determined by the method of D. Gabor and C. V. Nelson (J. App. Physics,25, 413–16, 1954). The surface potentials due to this resultant dipole are again exactly expressed by means of the “interior sphere theorem” and compared with those due to the eccentric dipoles assumed. It can be seen that the differences can be considerable.

It is suggested that the multipole model of the authors (Bull. Math. Biophysics,20, 203–16, 1958) be used as a more accurate and the only unique representation of the heart.

Keywords

Surface Potential Current Generator Volume Conductor Central Dipole Single Dipole 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature

  1. Gabor, D., and C. V. Nelson. 1954. “Determination of the Resultant Dipole of the Heart from Measurements on the Body Surface.”J. App. Physics,25, 413–16.CrossRefGoogle Scholar
  2. Ludford, G. S. S., J. Martinek, and G. C. K. Yeh. 1955. “The Sphere Theorem in Potential Theory.”Proc. Cambridge Philos. Soc.,51, 389–93.MATHMathSciNetCrossRefGoogle Scholar
  3. Okada, R. H. 1958. “Multiple Dipole Representation of the Human Heart for Vectorcardiography.”Science,127, 240–41.Google Scholar
  4. Yeh, G. C. K., J. Martinek, and G. S. S. Ludford. 1955. “The Potentials due to Certain Singularities in the Presence of a Fixed Sphere.”J. Soc. Indust. App. Math.,3, 142–52.MATHMathSciNetCrossRefGoogle Scholar
  5. Yeh, G. C. K., J. Martinek, and H. de Beaumont. 1958. “Multipole Representations of Current Generators in a Volume Conductor.”Bull. Math. Biophysics,20, 203–16.Google Scholar

Copyright information

© University of Chicagol 1958

Authors and Affiliations

  • J. Martinek
    • 1
  • G. C. K. Yeh
    • 1
  • H. de Beaumont
    • 1
  1. 1.Staff ScientistsReed Research FoundationWashington, D. C.

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