On the resolution of synchronous dipolar excitations via MEG measurements
Authors:
George Dassios, Michael Doschoris and Konstantia Satrazemi
Journal:
Quart. Appl. Math. 76 (2018), 39-45
MSC (2010):
Primary 35Q61, 35R30, 35J25
DOI:
https://doi.org/10.1090/qam/1476
Published electronically:
June 28, 2017
MathSciNet review:
3733093
Full-text PDF
Abstract |
References |
Similar Articles |
Additional Information
Abstract: In the present work we provide a mathematical analysis that leads to an algorithm which decides whether a set of magnetoencephalographic data represents a single or a multiple simultaneous excitation of equivalent current dipoles. The very special case where this identification is not possible is analyzed in detail.
References
- George Dassios, Electric and magnetic activity of the brain in spherical and ellipsoidal geometry, Mathematical modeling in biomedical imaging. I, Lecture Notes in Math., vol. 1983, Springer, Berlin, 2009, pp. 133–202. MR 2581900, DOI https://doi.org/10.1007/978-3-642-03444-2_4
- G. Dassios and A. S. Fokas, Electro-magneto-encephalography for a three-shell model: dipoles and beyond for the spherical geometry, Inverse Problems 25 (2009), no. 3, 035001, 20. MR 2480171, DOI https://doi.org/10.1088/0266-5611/25/3/035001
- G. Dassios, M. Doschoris, and K. Satrazemi, Localizing Brain Activity from Multiple Distinct Sources via EEG, Journal of Applied Mathematics, vol.2014, Article ID232747. 2014.
- George Dassios and A. S. Fokas, The definite non-uniqueness results for deterministic EEG and MEG data, Inverse Problems 29 (2013), no. 6, 065012, 10. MR 3056085, DOI https://doi.org/10.1088/0266-5611/29/6/065012
- R. Grech, T. Cassar, J. Muscat, K. P. Camilleri, S. G. Fabri, M. Zervakis, P. Xanthopoulos, V. Sakkalis, and B. Vanrumste, Review on solving the inverse problem in EEG source analysis, Journal of Neuro-Engineering and Rehabilitation, 5(25), 2008.
- P. L. Nunez and R. Srinivasan, Electric Fields of the Brain: The Neurophysics of EEG, 2nd Edition. Oxford University Press. 2006.
- R. Plonsey and D. B. Heppner, Considerations of quasi-stationary in electrophysiological systems, Buletin of Mathematical Biophysics, 29, 657-664, 1967.
- J. Sarvas, Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem, Physics in Medicine and Biology, 32, 11-22, 1987.
References
- George Dassios, Electric and magnetic activity of the brain in spherical and ellipsoidal geometry, Mathematical modeling in biomedical imaging. I, Lecture Notes in Math., vol. 1983, Springer, Berlin, 2009, pp. 133–202. MR 2581900, DOI https://doi.org/10.1007/978-3-642-03444-2_4
- G. Dassios and A. S. Fokas, Electro-magneto-encephalography for a three-shell model: dipoles and beyond for the spherical geometry, Inverse Problems 25 (2009), no. 3, 035001, 20. MR 2480171, DOI https://doi.org/10.1088/0266-5611/25/3/035001
- G. Dassios, M. Doschoris, and K. Satrazemi, Localizing Brain Activity from Multiple Distinct Sources via EEG, Journal of Applied Mathematics, vol.2014, Article ID232747. 2014.
- George Dassios and A. S. Fokas, The definite non-uniqueness results for deterministic EEG and MEG data, Inverse Problems 29 (2013), no. 6, 065012, 10. MR 3056085, DOI https://doi.org/10.1088/0266-5611/29/6/065012
- R. Grech, T. Cassar, J. Muscat, K. P. Camilleri, S. G. Fabri, M. Zervakis, P. Xanthopoulos, V. Sakkalis, and B. Vanrumste, Review on solving the inverse problem in EEG source analysis, Journal of Neuro-Engineering and Rehabilitation, 5(25), 2008.
- P. L. Nunez and R. Srinivasan, Electric Fields of the Brain: The Neurophysics of EEG, 2nd Edition. Oxford University Press. 2006.
- R. Plonsey and D. B. Heppner, Considerations of quasi-stationary in electrophysiological systems, Buletin of Mathematical Biophysics, 29, 657-664, 1967.
- J. Sarvas, Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem, Physics in Medicine and Biology, 32, 11-22, 1987.
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC (2010):
35Q61,
35R30,
35J25
Retrieve articles in all journals
with MSC (2010):
35Q61,
35R30,
35J25
Additional Information
George Dassios
Affiliation:
Department of Chemical Engineering, University of Patras, Caratheodory 1, University Campus, GR 265 04 Patras, Hellas , and FORTH/ICE-HT, 26504 Patras, Hellas
MR Author ID:
54715
Email:
gdassios@chemeng.upatras.gr; gdassios@otenet.gr
Michael Doschoris
Affiliation:
Department of Chemical Engineering, University of Patras, Caratheodory 1, University Campus, GR 265 04 Patras, Hellas , and FORTH/ICE-HT, 26504 Patras, Hellas
MR Author ID:
921586
Email:
mdoscho@chemeng.upatras.gr
Konstantia Satrazemi
Affiliation:
Department of Chemical Engineering, University of Patras, Caratheodory 1, University Campus, GR 265 04 Patras, Hellas
MR Author ID:
1104775
Email:
satrazemik@chemeng.upatras.gr
Received by editor(s):
February 22, 2017
Published electronically:
June 28, 2017
Article copyright:
© Copyright 2017
Brown University
