Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid

Andrei Irimia

Applications of Mathematics (2008)

  • Volume: 53, Issue: 2, page 131-142
  • ISSN: 0862-7940

Abstract

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The bioelectric current dipole model is important both theoretically and computationally in the study of electrical activity in the brain and stomach due to the resemblance of the shape of these two organs to an ellipsoid. To calculate the magnetic field 𝐁 due to a dipole in an ellipsoid, one must evaluate truncated series expansions involving ellipsoidal harmonics 𝔼 n m , which are products of Lamé functions. In this article, we extend a strictly analytic model (G. Dassios and F. Kariotou, J. Math. Phys. 44 (2003), 220–241), where 𝐁 was computed from an ellipsoidal harmonic expansion of order 2. The present derivations show how the field can be evaluated to arbitrary order using numerical procedures for evaluating the roots of Lamé polynomials of degree 5 or higher. This can be accomplished using an optimization technique for solving nonlinear systems of equations, which allows one to acquire an understanding of the truncation error associated with the harmonic series expansion used for the calculation.

How to cite

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Irimia, Andrei. "Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid." Applications of Mathematics 53.2 (2008): 131-142. <http://eudml.org/doc/33314>.

@article{Irimia2008,
abstract = {The bioelectric current dipole model is important both theoretically and computationally in the study of electrical activity in the brain and stomach due to the resemblance of the shape of these two organs to an ellipsoid. To calculate the magnetic field $\{\mathbf \{B\}\}$ due to a dipole in an ellipsoid, one must evaluate truncated series expansions involving ellipsoidal harmonics $\mathbb \{E\}_n^m$, which are products of Lamé functions. In this article, we extend a strictly analytic model (G. Dassios and F. Kariotou, J. Math. Phys. 44 (2003), 220–241), where $\{\mathbf \{B\}\}$ was computed from an ellipsoidal harmonic expansion of order 2. The present derivations show how the field can be evaluated to arbitrary order using numerical procedures for evaluating the roots of Lamé polynomials of degree 5 or higher. This can be accomplished using an optimization technique for solving nonlinear systems of equations, which allows one to acquire an understanding of the truncation error associated with the harmonic series expansion used for the calculation.},
author = {Irimia, Andrei},
journal = {Applications of Mathematics},
keywords = {magnetic field; dipole; ellipsoid; magnetic field; dipole; ellipsoid},
language = {eng},
number = {2},
pages = {131-142},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid},
url = {http://eudml.org/doc/33314},
volume = {53},
year = {2008},
}

TY - JOUR
AU - Irimia, Andrei
TI - Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 2
SP - 131
EP - 142
AB - The bioelectric current dipole model is important both theoretically and computationally in the study of electrical activity in the brain and stomach due to the resemblance of the shape of these two organs to an ellipsoid. To calculate the magnetic field ${\mathbf {B}}$ due to a dipole in an ellipsoid, one must evaluate truncated series expansions involving ellipsoidal harmonics $\mathbb {E}_n^m$, which are products of Lamé functions. In this article, we extend a strictly analytic model (G. Dassios and F. Kariotou, J. Math. Phys. 44 (2003), 220–241), where ${\mathbf {B}}$ was computed from an ellipsoidal harmonic expansion of order 2. The present derivations show how the field can be evaluated to arbitrary order using numerical procedures for evaluating the roots of Lamé polynomials of degree 5 or higher. This can be accomplished using an optimization technique for solving nonlinear systems of equations, which allows one to acquire an understanding of the truncation error associated with the harmonic series expansion used for the calculation.
LA - eng
KW - magnetic field; dipole; ellipsoid; magnetic field; dipole; ellipsoid
UR - http://eudml.org/doc/33314
ER -

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