Abstract
Recently a theorem for representing current generators in a volume conductor by the superposition of a central dipole, quadrupole, octopole, etc., has been established by G. C. K. Yeh, J. Martinek, and H. de Beaumont (Bull. Math. Biophysics,20, 203–16, 1958). This theorem makes possible the representation of any discrete or line, surface- or volume-distributed current source by a unique model which can be determined for each given case by surface potential measurements and closed form analysis. In this paper the multipole representations of an eccentric dipole and an eccentric double-layer are obtained in terms of the various parameters of the assumed singularities, and the contributions to surface potentials due to each of the multipoles are compared. Certain numerical results corresponding to those of E. Frank (Amer. Heart J.,46, 364–78, 1953) are carried out and compared. Furthermore, the multipole representation of a partially damaged double-layer is also determined and compared with that of an undamaged one. It is concluded that within the range of parameters corresponding to human subjects the higher-order multipoles can contribute significantly to the surface potentials compared with the dipole.
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Literature
Frank, E. 1953. “A Comparative Analysis of the Eccentric Double-Layer Representation of the Human Heart.”Amer. Heart J.,46, 364–78.
Lamb, H. 1932.Hydrodynamics. Sixth Edition. Cambridge: Cambridge University Press.
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.
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.
—, J. Martinek, and H. de Beaumont. 1958. “Multipole Representations of Current Generators in a Volume Conductor.”Bull. Math. Biophysics,20, 203–16.
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This investigation was supported by the National Heart Institute under a research grant H-2263(c).
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Yeh, G.C.K., Martinek, J. Multipole representation of an eccentric dipole and an eccentric double-layer. Bulletin of Mathematical Biophysics 21, 33–60 (1959). https://doi.org/10.1007/BF02476457
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DOI: https://doi.org/10.1007/BF02476457