Abstract
In Yeh, Martinek and de Beaumont (Bull. Math. Biophysics,20, 203–16, 1958), a method is presented for determining successively better central multipole representations of the current generators in a homogeneous conducting sphere by measuring surface potentials at a successively increasing number of points. This paper generalizes the method such that the multipoles may be located at any chosen point in the conductor. The spherical harmonic expansion is advantageously used and the “interior sphere theorem” of Ludford, Martinek and Yeh (Proc. Cambridge Philos. Soc.,51, 389–93, 1955) makes possible disturbance potential expressions in closed forms. A method for approximate determination of the eccentricity is also presented. In the theory of electrocardiography, the eccentric multipoles can more accurately represent the heart as a current generator with fewer surface potential measurements than the central multipoles.
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Literature
Ludford, G. S. S., J. Martinek and G. C. K. Yeh. 1955. “The Sphere Theorem in Potential Theory.”Proc. Cambridge Philos. Soc.,51, 389–393.
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Yeh, G. C. K., and J. Martinek. 1959. “Multipole Representation of an Eccentric Dipole and an Eccentric Double-layer.”Bull. Math. Biophysics,21, 33–60.
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This investigation was supported by The National Heart Institute under Research Grant H-2263(c-4).
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Yeh, G.C.K. Eccentric multipole representations of current generators in a spherical volume conductor. Bulletin of Mathematical Biophysics 23, 263–276 (1961). https://doi.org/10.1007/BF02476740
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DOI: https://doi.org/10.1007/BF02476740