跳至主要内容

On the Inverse MEG Problem with a 1-D Current Distribution

Read  full  paper  at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53063#.VLSP88nQrzE

ABSTRACT
The inverse problem of magnetoencephalography (MEG) seeks the neuronal current within the conductive brain that generates a measured magnetic flux in the exterior of the brain-head system. This problem does not have a unique solution, and in particular, it is not even possible to identify the support of the current if it extends over a three-dimensional set. However, a localized current supported on a zero-, one- or two-dimensional set can in principle be identified. In the present work, we demonstrate an analytic algorithm that is able to recover a one-dimensional distribution of current from the knowledge of the exterior magnetic flux field. In particular, we consider a neuronal current that is supported on a small line segment of arbitrary location and orientation in space, and we reduce the identification of its characteristics to a nonlinear algebraic system. A series of numerical tests show that this system has a unique real solution. A special case is easily solved via the use of trivial algebraic operations.
 
Cite this paper
Dassios, G. and Satrazemi, K. (2015) On the Inverse MEG Problem with a 1-D Current Distribution. Applied Mathematics, 6, 95-105. doi: 10.4236/am.2015.61010.
 
References
[1]Hamalainen, M., Hari, R., Ilmoniemi, R.J., Knuutila, J. and Lounasmaa, O. (1993) Magnetoencephalography—Theory, Instrumentation, and Applications to Noninvasive Studies of the Working Human Brain. Reviews of Modern Physics, 65, 413.
http://dx.doi.org/10.1103/RevModPhys.65.413
 
[2]Malmivuo, J. and Plonsey, R. (1995) Bioelectromagnetism. Oxford University Press, New York.
 
[3]Helmholtz, H. (1853) Ueber einige Gesetze der Vertheilung elektrischer Str ome in k orperlichen Leitern mit Anwendung auf die thierisch-elektrischen Versuche. Annalen der Physik und Chemie, 89, 211-233, 353-377.
 
[4]Dassios, G. and Fokas, A.S. (2013) The Definitive Non Uniqueness Results for Deterministic EEG and MEG Data. Inverse Problems, 29, 1-10.
http://dx.doi.org/10.1088/0266-5611/29/6/065012
 
[5]Albanese, R. and Monk, P.B. (2006) The Inverse Source Problem for Maxwell’s Equations. Inverse Problems, 22, 1023-1035.
http://dx.doi.org/10.1088/0266-5611/22/3/018
 
[6]Landau, L.D. and Lifshitz, E.M. (1960) Electrodynamics of Continuous Media. Pergamon Press, London.
 
[7]Plonsey, R. and Heppner, D.B. (1967) Considerations of Quasi-Stationarity in Electrophysiological Systems. Bulletin of Mathematical Biophysics, 29, 657-664.
http://dx.doi.org/10.1007/BF02476917
 
[8]Sarvas, J. (1987) Basic Mathematical and Electromagnetic Concepts of the Biomagnetic Inverse Problems. Physics in Medicine and Biology, 32, 11-22.
http://dx.doi.org/10.1088/0031-9155/32/1/004
 
[9]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.
http://dx.doi.org/10.1109/TMAG.1970.1066765
 
[10]Dassios, G. (2009) Electric and Magnetic Activity of the Brain in Spherical and Ellipsoidal Geometry. Mathematical Modeling in Biomedical Imaging I Lecture Notes in Mathematics, 133-202.
 
[11]Dassios, G. (2012) Ellipsoidal Harmonics. Theory and Applications. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9781139017749
 
[12]Dassios, G. and Fokas, A.S. (2009) Electro-Magneto-Encephalography and Fundamental Solutions. Quarterly of Applied Mathematics, 67, 771-780.
 
[13]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, Article ID: 035001.
http://dx.doi.org/10.1088/0266-5611/25/3/035001
 
[14]Morse, P.M. and Feshbach, H. (1953) Methods of Theoretical Physics, Volume I. McGraw-Hill, New York.
 
[15]Brand, L. (1947) Vector and Tensor Analysis. John Wiley and Sons, New York.                 eww150113lx
标签：

评论

发表评论

此博客中的热门博文