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Title: The octapolic ellipsoidal term in magnetoencephalography
Authors: Dassios, George 
Hadjiloizi, Demetra 
Kariotou, Fotini 
Major Field of Science: Engineering and Technology
Field Category: Materials Engineering
Keywords: Bioelectronics;Neurophysiology;Magnetoencephalography;Algorithms
Issue Date: Jan-2009
Source: Journal of Mathematical Physics, 2009, vol. 50, no. 1, pp. 013508
Volume: 50
Issue: 1
Start page: 013508
End page: 013508
Journal: Journal of Mathematical Physics 
Abstract: The forward problem of magnetoencephalography (MEG) in ellipsoidal geometry has been studied by Dassios and Kariotou ["Magnetoencephalography in ellipsoidal geometry," J. Math. Phys. 44, 220 (2003)] using the theory of ellipsoidal harmonics. In fact, the analytic solution of the quadrupolic term for the magnetic induction field has been calculated in the case of a dipolar neuronal current. Nevertheless, since the quadrupolic term is only the leading nonvanishing term in the multipole expansion of the magnetic field, it contains not enough information for the construction of an effective algorithm to solve the inverse MEG problem, i.e., to recover the position and the orientation of a dipole from measurements of the magnetic field outside the head. For this task, the next multipole of the magnetic field is also needed. The present work provides exactly this octapolic contribution of the dipolar current to the expansion of the magnetic induction field. The octapolic term is expressed in terms of the ellipsoidal harmonics of the third degree, and therefore it provides the highest order terms that can be expressed in closed form using long but reasonable analytic and algebraic manipulations. In principle, the knowledge of the quadrupolic and the octapolic terms is enough to solve the inverse problem of identifying a dipole inside an ellipsoid. Nevertheless, a simple inversion algorithm for this problem is not yet known.
ISSN: 1089-7658
DOI: 10.1063/1.3036183
Rights: © American Institute of Physics
Type: Article
Affiliation: University of Patras 
Affiliation : University of Cambridge 
University of Patras 
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