Geodesic
Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid
Applications of Mathematics, Tome 53 (2008) no. 2, pp. 131-142.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.1007/s10492-008-0016-y
Classification : 78A25, 92C50
Keywords: magnetic field; dipole; ellipsoid 
@article{10_1007_s10492_008_0016_y,
     author = {Irimia, Andrei},
     title = {Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid},
     journal = {Applications of Mathematics},
     pages = {131--142},
     publisher = {mathdoc},
     volume = {53},
     number = {2},
     year = {2008},
     doi = {10.1007/s10492-008-0016-y},
     mrnumber = {2399902},
     zbl = {1187.78010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-008-0016-y/}
}
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
SP  - 131
EP  - 142
VL  - 53
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-008-0016-y/
DO  - 10.1007/s10492-008-0016-y
LA  - en
ID  - 10_1007_s10492_008_0016_y
ER  - 
%0 Journal Article
%A Irimia, Andrei
%T Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid
%J Applications of Mathematics
%D 2008
%P 131-142
%V 53
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-008-0016-y/
%R 10.1007/s10492-008-0016-y
%G en
%F 10_1007_s10492_008_0016_y
Irimia, Andrei. Calculation of the magnetic field due to a bioelectric current dipole in an ellipsoid. Applications of Mathematics, Tome 53 (2008) no. 2, pp. 131-142. doi : 10.1007/s10492-008-0016-y. http://geodesic.mathdoc.fr/articles/10.1007/s10492-008-0016-y/

Cité par Sources :