Frequency series expansion of an explicit solution for a dipole inside a conducting sphere at low frequency.

The electromagnetic field generated by a current dipole situated at an arbitrary position inside a conducting sphere is derived using the expansions of the spherical vector wave functions. The first few terms in a series expansion of this field with respect to the frequency are given for the normal magnetic field (used in magnetoencephalogram) and the tangential electric field (used in electroencephalogram) outside the conducting sphere at low frequency. It is shown that the first correction term to the static solution is linear in the frequency omega (the second correction term is proportional to omega 3/2) and, thus, the static solution can be used as a good approximation for the solution at a very low frequency.

[1]  B. Neil Cuffin,et al.  Magnetic Fields of a Dipole in Special Volume Conductor Shapes , 1977, IEEE Transactions on Biomedical Engineering.

[2]  Dietrich Lehmann,et al.  Evaluation of Methods for Three-Dimensional Localization of Electrical Sources in the Human Brain , 1978, IEEE Transactions on Biomedical Engineering.

[3]  Gerhard Kristensson,et al.  Scattering from buried inhomogeneities—a general three‐dimensional formalism , 1978 .

[4]  F. Roberge,et al.  Application of the single moving dipole inverse solution to the study of the Wolff-Parkinson-White syndrome in man. , 1984, Journal of electrocardiology.

[5]  J. Sarvas.  Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. , 1987, Physics in medicine and biology.

[6]  M. Hämäläinen,et al.  Realistic conductivity geometry model of the human head for interpretation of neuromagnetic data , 1989, IEEE Transactions on Biomedical Engineering.

[7]  Alexander G. Ramm,et al.  Dissipative Maxwell's equations at low frequencies , 1990 .

[8]  M. Scherg.  Fundamentals if dipole source potential analysis , 1990 .

[9]  Norbert Weck,et al.  Low‐frequency asymptotics for dissipative Maxwell's equations in bounded domains , 1990 .

[10]  T. Katila,et al.  Magnetocardiographic functional localization using current multipole models , 1991, IEEE Transactions on Biomedical Engineering.

[11]  Anders E Boström,et al.  Transformation properties of plane, spherical and cylindrical scalar and vector wave functions , 1991 .

[12]  R. Ilmoniemi,et al.  Estimates of visually evoked cortical currents. , 1992, Electroencephalography and clinical neurophysiology.

[13]  R. Ilmoniemi,et al.  Magnetoencephalography-theory, instrumentation, and applications to noninvasive studies of the working human brain , 1993 .

[14]  Sailing He,et al.  Identification of dipole sources in a bounded domain for Maxwell's equations , 1998 .