Stable identification of sources located on the cerebral cortex from EEG over the scalp
DOI:
https://doi.org/10.31349/RevMexFis.69.050702Keywords:
Inverse problem; regularization; ill-posed problem; source identification, finite element methodAbstract
In this work, we present a stable algorithm for the inverse problem of identifying cortical sources from electroencephalographic measurements on the scalp. This inverse problem is ill-posed due to the numerical instability it presents, i.e., small changes in the measurements can produce large variations in the location of the sources. A boundary value problem is used to find correlations between the sources and measurements. In the case in which the head is modeled using two concentric spheres. We use spherical harmonics to find the solution to the inverse source cortical problem. To handle the numerical instability of this problem, we use the Tikhonov regularization method and a cut-off of the harmonic expansion series. From numerical tests, we found these parameters with which we get good approximations. Finally, we illustrate the algorithm proposed with synthetic examples
References
S. R. Nunez, PL, Electric Field of the Brain, vol. 1 (Oxford University Press: New York, 2006)
R. Plonsey, Bioelectrical Phenomena, vol. 1 (Mac Graw Hill, 1969)
A. Kirsch, An introduction to the mathematical theory of inverse problems, vol. 120 (Springer, 2011)
E. B. A and H. D. T, Some remarks on the problem of source identification from boundary measurements, Inverse Problems 14 (1998) 1
M. Morín-Castillo et al., Simplification of the inverse electroencephalographic problem to one homogeneous region with null Neumann condition, Rev. Mex. Ing. Bio. 34 (2013) 41
A. Amir, Uniqueness of the generators of brain evoked potential maps Trans. Biomed. Eng. 41 (1994) 1
M. Morín-Castillo et al., Analysis of dipolar sources in the solution of the Electroencephalographic Inverse Problem, Mathematics. 9 (2022) 1
M. Morín-Castillo et al., Stable identification of sources located on separation interfaces of two different homogeneous media., Adv. Differ. Equ. Control Process. 2019 (2019) 53
N. Tsitsas and P. Martin, Finding a source inside a sphere, Inverse Problems 28 (2012) 1
A. Papargiri, et al., Revisiting an analytical solution for the three-shell spherical human head model in electroencephalography, Partial Differential Equations in Applied Mathematics 4 (2021) 1
A. Fraguela et al., Operational statement and analysis of the inverse electroencephalographic problem, Rev. Mex. Fis. 47 (2001) 162
S. Næss et al., Corrected Four-Sphere Head Model for EEG Signals, Frontiers in human neuroscience 11 (2017) 1
F. Vatta et al., Realistic and Spherical Head Modeling for EEG Forward Problem Solution: A Comparative Cortex-Based Analysis, Comput Intell Neurosci. 2010 (2010) 1
J. J. Conde-Mones et al., Stable Numerical Identification of Sources in Non-Homogeneous Media, Mathematics. 10 (2022) 1
H. PC and P. D, The use of the L-Curve in the Regularization of Discrete Ill-Posed Problems, BIT Numerical Mathematics 30 (1990) 658
M. Morín-Castillo et al., Stable Identification of Sources Associated with Epileptic Focus on the Cerebral Cortex, Rev. Mex. Ing. Bio. 40 (2019) 1
J. J. Conde-Mones et al., Stable Identification of Sources Located on Interface of Nonhomogeneous Media, Mathematics. 9 (2021) 1.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 José Ángel Arias Cruz, María Monserrat Morín Castillo, José Jacobo Oliveros Oliveros, José Eligio Moisés Gutiérrez Arias
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
