JAMP  Vol.2 No.8 , July 2014
Inversion of Meg Data for a 2-D Current Distribution
Abstract: The support of a localized three-dimensional neuronal current distribution, within a conducting medium, is not identifiable from knowledge of the exterior magnetic flux density, obtained via Magnetoencephalographic (MEG) measurements. However, this is not true if the neuronal current is supported on a set with dimensionality less than three. That is, the support of a dipolar current distribution can be recovered if it is a set of isolated points, a segment of a curve, or a surface patch. In this work we provide an analytic algorithm for this inverse MEG problem and apply it to the case where the current is supported on a localized disk having arbitrary position and size within the brain tissue. The proposed recovery algorithm reduces the identification of the characteristics of the current to the solution of a nonlinear algebraic system, which can be handled numerically.
Cite this paper: Dassios, G. and Satrazemi, K. (2014) Inversion of Meg Data for a 2-D Current Distribution. Journal of Applied Mathematics and Physics, 2, 771-782. doi: 10.4236/jamp.2014.28085.

[1]   Dassios, G. and Kariotou, F. (2003) Magnetoencephalography in Ellipsoidal Geometry. Journal of Mathematical Physics, 44, 220-241.

[2]   Hamalainen, M., Hari, R., Ilmoniemi, R.J., Knuutila, J. and Lounasmaa, O.V. (1993) Magnetoencephalography-Theory, Instrumentation, and Applications to Noninvasive Studies of the Working Human Brain. Reviewed Modern Physics, 65, 413-497.

[3]   Malmivuo, J. and Plonsey, R. (1995) Bioelectromagnetism. Oxford University Press, New York.

[4]   Helmholtz, H. (1853) Ueber einige Gesetze der Vertheilung elektrischer Strme in k orperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche. Annalen der Physik und Chemie, 89, 211-233,353-377.

[5]   Fokas, A.S. (2008) Electro-Magneto-Encephalography for the Three-Shell Model: Distributed Current in Arbitrary, Spherical and Ellipsoidal Geometries. Journal of the Royal Society Interface, 6, 479-488.

[6]   Dassios, G. and Fokas, A.S. (2013) The Definitive Non Uniqueness Results for Deterministic EEG and MEG Data. Inverse Problems, 29, 1-10.

[7]   Albanese, R. and Monk, P.B. (2006) The Inverse Source Problem for Maxwell’s Equations. Inverse Problems, 22, 1023-1035.

[8]   Landau, L.D. and Lifshitz, E.M. (1960) Electrodynamics of Continuous Media. Pergamon Press, London.

[9]   Plonsey, R. and Heppner, D.B. (1967) Considerations of Quasi-Stationarity in Electrophysiological Systems. Bulletin of Mathematical Biophysics, 29, 657-664.

[10]   Sarvas, J. (1987) Basic Mathematical and Electromagnetic Concepts of the Biomagnetic Inverse Problems. Physics in Medicine and Biology, 32, 11-22.

[11]   Geselowitz, D.B. (1970) On the Magnetic Field Generated outside an Inhomogeneous Volume Conductor by Internal Current Sources. IEEE Transactions in Biomagnetism, 6, 346-347.

[12]   Dassios, G. (2009) Electric and Magnetic Activity of the Brain in Spherical and Ellipsoidal Geometry. In: Ammari, H., Ed., Mathematical Modeling in Biomedical Imaging, Mathematical Biosciences Subseries, Springer-Verlag, 183, 133-202.

[13]   Dassios, G. (2012) Ellipsoidal Harmonics. Theory and Applications. Cambridge University Press, Cambridge.

[14]   Dassios, G. and Fokas, A.S. (2009) Electro-Magneto-Encephalography and Fundamental Solutions. Quarterly of Applied Mathematics, 67, 771-780.

[15]   Dassios, G. and Fokas, A.S. (2009) Electro-Magneto-Encephalography for the Three-Shell Model: Dipoles and Beyond for the Spherical Geometry. Inverse Problems, 25, 1-20.

[16]   Brand, L. (1947) Vector and Tensor Analysis. John Wiley and Sons, New York.

[17]   Morse, P.M. and Feshbach, H. (1953) Methods of Theoretical Physics. McGraw-Hill, New York.