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. 1998 Dec 7;6(4):250–269. doi: 10.1002/(SICI)1097-0193(1998)6:4<250::AID-HBM5>3.0.CO;2-2

Influence of skull anisotropy for the forward and inverse problem in EEG: Simulation studies using FEM on realistic head models

Gildas Marin 1, Christophe Guerin 2, Sylvain Baillet 1, Line Garnero 1,✉, Gérard Meunier 3
PMCID: PMC6873358  PMID: 9704264

Abstract

For the sake of realism in the description of conduction from primary neural currents to scalp potentials, we investigated the influence of skull anisotropy on the forward and inverse problems in brain functional imaging with EEG. At present, all methods available for cortical imaging assume a spherical geometry, or when using realistic head shapes do not consider the anisotropy of head tissues. However, to our knowledge, no study relates the implication of this simplifying hypothesis on the spatial resolution of EEG for source imaging.

In this paper, a method using finite elements in a realistic head geometry is implemented and validated. The influence of erroneous conductivity values for the head tissues is presented, and results show that the conductivities of the brain and the skull in the radial orientation are the most critical ones.

In the inverse problem, this influence has been evaluated with simulations using a distributed source model with a comparison of two regularization techniques, with the isotropic model working on data sets produced by a nonisotropic model. Regularization with minimum norm priors produces source images with spurious activity, meaning that the errors in the head model totally annihilate any localization ability. But nonlinear regularization allows the accurate recovery of simultaneous spots of activity, while the restoration of very close active regions is profoundly disabled by errors in the head model.

We conclude that for robust cortical source imaging with EEG, a realistic head model taking anisotropy of tissues into account should be used. Hum. Brain Mapping 6:250–269, 1998. © 1998 Wiley‐Liss, Inc.

Keywords: EEG, FEM, forward problem, inverse problem, anisotropic conductivity

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References

  1. Awada KA, Jackson DR, Williams JW, Wilton JR, Baumann SB, Papanicolaou AC (1997): Computational aspects of finite element modeling in EEG source localization. IEEE Trans Biomed Eng 44: 736–751. [DOI] [PubMed] [Google Scholar]
  2. Baillet S, Garnero L (1997): A Bayesian approach to introducing anatomo‐functional priors in the EEG/MEG inverse problem. IEEE Trans Biomed Eng 44: 374–385. [DOI] [PubMed] [Google Scholar]
  3. Bertrand O, Thevenet M, Perrin F (1991): 3D finite element method in brain electrical activity studies In: Nenonen J, Rajala HM, Katila T. (eds): Biomagnetic Localization and 3D Modelling, Report of the Department of Technical Physics, Helsinski University, pp 154–171. [Google Scholar]
  4. Buchner H, Knoll G, Fuchs M, Rienaäcker A, Beckmann R, Wagner M, Silny J, Jörg P (1997): Inverse localization localization of electric dipole current sources in finite element models of the human head. Electroencephalogr Clin Neurophysiol 102: 267–278. [DOI] [PubMed] [Google Scholar]
  5. Dale AM, Sereno MI (1993): Improved localization of cortical activity by combining EEG and ME Gwith MRI cortical surface reconstruction: Alinear approach. J Cogn Neurosci 5: 162–176. [DOI] [PubMed] [Google Scholar]
  6. De Munck JC (1988): The potential distribution in a layered anisotropic spheroidal volume conductor. J Appl Physiol 64: 464–470. [Google Scholar]
  7. Gorodnitsky IF, George JS, Rao BD, (1995): Neuromagnetic imaging with FOCUSS: A recursive weighted minimu‐norm algorithm. Electroencephalogr Clin Neurophysiol 79: 211–226. [DOI] [PubMed] [Google Scholar]
  8. Hämäläinen MS, Ilmnoniemi RJ (1994): Interpreting magnetic fields of the brain: Minimum norm estimated. Med Biol Eng Comp 32: 35–42. [DOI] [PubMed] [Google Scholar]
  9. Hämäläinen MS, Sarvas J (1989): Realistic conductivity geometry model of the human head for interpretation of neuromagnetic data. IEEE Trans Biomed Eng 86: 165–171. [DOI] [PubMed] [Google Scholar]
  10. Haueisen J, Ramon C, Czapski P, Eiselt M (1995): On the influence of volume currents and extended sources on neuromagnetic fields: Asimulation study. Ann Biomed Eng 25: 728–739. [DOI] [PubMed] [Google Scholar]
  11. Haueisen J, Ramon C, Eiselt M, Brauer H, Nowak H (1997): Influence of tissues resistivities on neuromagnetic fields and electric potentials studied with a finite element model of the head. IEEE Trans Biomed Eng 44: 727–735. [DOI] [PubMed] [Google Scholar]
  12. Meijs JWH, Weier OW, Peters MJ, Oosterom AV (1989): On the numerical accuracy of the boundary element method. IEEE Trans Biomed Eng 36: 1038–1049. [DOI] [PubMed] [Google Scholar]
  13. Miller CE, Henriquez CS (1990): Finite element analysis of bioelectric phenomena. Crit Rev Biomed Eng 18: 207–233. [PubMed] [Google Scholar]
  14. Pascual‐Marqui RD, Michel CM, Lehmann D (1994): Low resolution electromagnetic tomography: Anew method for localizing electrical activity of the brain. Int J Psychophysiol 18: 49–65. [DOI] [PubMed] [Google Scholar]
  15. Peters MJ, de Munck JC (1990): The influence of model parameters on the inverse solution based on MEGs and EECs. Acta Otolaryngol [Suppl] (Stockh) 491: 61–69. [DOI] [PubMed] [Google Scholar]
  16. Rao CR, Mitra SK (1973): Theory and application of constrained inverses of matrices. SIAM J Appl Math 24: 476–488. [Google Scholar]
  17. Sarvas J (1987): Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. Phys Med Biol 32: 11–22. [DOI] [PubMed] [Google Scholar]
  18. Sherg M, Buchner H (1993): Somatosensory evoked potentials and magnetic fields: Separation of multiple source activity. Physiol Measurements [Suppl] 14: 35–39. [DOI] [PubMed] [Google Scholar]
  19. Simkin J, Trowbridge CW (1979): On the use of the total scalar potential in the numerical solution of fields problems in electromagnetics. Int J Num Methods Eng 14: 423–440. [Google Scholar]
  20. Thevenet M (1992): Modélisation de l'activité électrique cérébrale par la méthode des éléments finis. Thèse, no. d'ordre 92 ISAL 0036.
  21. Tikhonov A, Arsenin V (1977): Solutions of Ill‐Posed Problems. Washington, DC: Winston. [Google Scholar]
  22. Wang JZ, Williamson SJ, Kaufman L (1992): Magnetic source images determined by a lead‐field analysis: The unique minimum‐norm least‐squares estimation. IEEE Trans Biomed Eng 39: 665–675. [DOI] [PubMed] [Google Scholar]
  23. Wikswo JR, Gevims A, Williamson SJ (1993): The future of EEG and MEG, Electroenceph Clin Neurophysiol 87: 1–9. [DOI] [PubMed] [Google Scholar]
  24. Yan Y, Nunez PL, Hart RT (1991): Finite element model of the human head: Scalp potentials due to dipole sources. Med Biol Eng Comp, 1991 29: 475–481. [DOI] [PubMed] [Google Scholar]
  25. Zhou H, van Oosterom A (1992): Computation of the potential distribution in a four‐layer anisotropic concentric spherical volume conductor. IEEE Trans Biomed Eng 39: 154–158. [DOI] [PubMed] [Google Scholar]
  26. Zienkiewicz OC (1977): The Finite Element Method in Engineering Science. McGraw‐Hill, New York. [Google Scholar]
  27. Zubal IG, Harrell CR, Smith EO, Rattner Z, Gindi GR, Hoffer PB (1994): Computerized three‐dimensional segmented human anatomy. Med Phys 21: 299–302. [DOI] [PubMed] [Google Scholar]

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