Calcul des potentiels électriques et des champs magnétiques par la méthode des intégrales de surface
Keywords:
Surface meshing, mesh simplification, BEM, EEG,, MEG, source localizationAbstract
This paper describes a full data processing sequences from image processing by magnetic resonance (IRM) to the computation of electrical potentials and magnetic fields generated by cerebral activity using the boundary element method (BEM) applied to a realistic anatomical model of the head. This latter is constituted by a set of surfaces dividing mediums with different electrical conductivity, namely the brain, the skull and the scalp. A new fast method to generate approximate regular surface meshes from IRM is introduced as a surface mesh simplification approach based on Hausdorff distance allowing to satisfy the constraints specified by the BEM regarding the number of mesh elements as well as the anatomy.
Downloads
References
[ART 70] ARTHUR R.M., GESELOWITZ D.B., « Effect of inhomogeneities on the apparent
locations and magnitude of a cardiac dipole source », IEEE Trans. Biomed. Eng., vol. 17,
, p. 141-146.
[ARY 81] ARY J.P, KLEIN S.A., FENDER D.H., « Location of sources of evoked scalp potentials
: corrections for skull and scalp thiknesses », IEEE Trans. Biomed. Eng., vol. 6,
, p. 447-452.
[BAR 77] BARR C., RAMSEY III M., SPACH M.S., « Relating epicarcial to body surface
potential distributions by means of transfer coefficients based on geometry measurements »,
IEEE Trans. Biomed. Eng., vol. 24, 1977, p. 1-11.
[BAR 67a] BARNARD A.C.L.,DUCK I.M., LYNN M.S., « The application of electromagnetic
theory to electrocardiography. I : Derivation of the integral equations », Biophys. J., vol. 7,
, p. 443-462.
[BAR 67b] BARNARD A.C.L., DUCK I.M., LYNN M.S., TIMLAKE W.P., « The application
of electromagnetic theory to electrocardiography. II : The numerical solution to the integral
equations », Biophys. J., vol. 7, 1967, p. 463-491.
[BOR 99] BOROUCHAKI H., « Simplification des maillages de surfaces basée sur la distance
de Hausdorff », C.R. Acad. Sci. Paris, t. 329, Série I, 1999, p. 641-646.
[CUF 79] CUFFIN B.N., COHEN D., « Comparison of the magnetoencephalogram and electroencephalogram
», Electroenceph. Clin. Neurophysiol., vol. 47, 1979, p. 132-146.
[CUF 90] CUFFIN B.N., « Effects of Head Shape on EEG’s and MEG’s », IEEE Trans. Biomed.
Eng., vol. 37, 1990, p. 44-52.
[CUF 91] CUFFIN B.N., « Eccentric spheres models of the head », IEEE Trans. Biomed. Eng.,
vol. 38, 1991, p. 871-878.
[CUP 84] CUPPEN J., VAN OOSTEROM A., « Model Studies with the Inversely Calculated
Isochrones of Ventricular Depolarization », IEEE Trans. Biomed. Eng., vol. 31, 1984,
p. 652-653.
[MUN 92] DE MUNCK J.C., « A linear discretization of the volume conductor boundary integral
equation using analytically integrated elements », IEEE Trans. Biomed. Eng., vol. 39,
, p. 986-990.
[FER 94] FERGUSON A.S., ZHANG X., STROINK G., « A complete linear discretization for
calculating the magnetic field using the boundary element method », IEEE Trans. Biomed.
Eng., vol. 41, 1994, p. 455-459.
[FRI 00] FRIJNS J.H.M., DE SNOO S.L., SCHOONHOVEN R., « Improving the Accuracy
of the Boundary Element Method by Use of Second-Order Interpolation », IEEE Trans.
Biomed. Eng., vol. 47, 2000, p. 1336-1346.
[FUC 00] FUCHS M., WAGNER M., KASTNER J., « Optimized node distribution for realistically
shaped boundary element method volume conductor models », Proceedings of the
ISBET congress, Frankfurt, Nov. 2000.
[FUC 01] FUCHS M., WAGNER M., KASTNER J., « Boundary element method volume
conductor models for EEG source reconstruction », Electroenceph. Clin. Neurophysiol.,
vol. 112, 2001, p. 1400-1407.
[GED 67] GEDDES L.A., BAKER L.E., « The specific resistance of biological materials – a
compendium of data of the biomedical engineer and physiologist », Med. Biol. Eng., vol. 5,
, p. 271-293.
[GES 67] GESELOWITZ D.B., « On bioelectric potentials in a inhomogeneous volume
conductor », Biophys. J., vol. 7, 1967, p. 1-17.
[GOR 89] GORDON D., UDUPA J.K., « Fast surface tracking in three-dimensionnal binary
images », Computer Vision, Graphics, And Image Processing, vol. 45, 1989, p. 196-214.
[HAM 87] HÄMÄLAÏNEN M.S., SARVAS J., « Feasibility of the homogeneous head model in
the interpretation of neuromagnetic data », Phys. Med. Biol., vol. 32, 1987, p. 91-97.
[HUI 99] HUISKAMP G., VROEIJENSTIJN M., VAN DICK R.,WIENEKE G., VAN HUFFELEN
A.C., « The need for correct realistic geometry in the inverse EEG problem », IEEE Trans.
Biomed. Eng., vol. 46, 1999, p. 1281-1287.
[ILM 85] ILMONIEMI R.J., HÄMÄLAÏNEN M.S., KNUUTILA J., « The forward and inverse
problems in the spherical model », In Biomagnetism : Applications & Theory, Weinberg,
H., Stoink, G. and Katila, T. Eds. Pergamon Press, New York, 1985, p. 278-282.
[LOR 87] LORENSEN W.E., CLINE H.E., « Marching cubes : a high resolution 3D surface
construction algorithm », Comput. Graphics, vol. 21, no 4, 1987, p. 163-169.
[MAB 98] MABIN F.H., MONGENET C., « A Parallel Algorithm to Reconstruct Bounding
Surfaces in 3D Images », The Journal of Superconducting, vol. 12, 1998, p. 137-155.
[MAR 98] MARIN G., GUÉRIN C., BAILLET S., GARNERO L., « Influence of skull anisotropy
for the forward and inverse problem in EEG : Simulation studies using FEM on realistic
head models », Human Brain Mapping, vol. 6, no 4, 1998, p. 250-269.
[MEI 89] MEIJS J.W.H.,WEIER O.W., PETERS M.J., VAN OOSTEROM A., « On the numerical
accuracy of the boundary element method », IEEE Trans. Biomed. Eng., vol. 36, 1989,
p. 1038-1049.
[RUS 69] RUSH S., DRISCOLL D.A., « EEG electrode sensitivity – and application of reciprocity
», IEEE Trans. Biomed. Eng., vol. 16, 1969, p. 15-22.
[SMI 00] SMITH S., « Robust automated brain extraction », Abstracts of the Sixth Int. Conf.
on Functional Mapping of the Human Brain, 2000, p. 625.
[SOU 93] SOUFFLET L., BOLO N.R., NÉDÉLEC J-F.J., MACHER J-P., « 3-D reconstruction
with facet representation of cerebral structures fromMRI sections », Abstracts of the twelfth
annual meeting of the Society of Magnetic Resonance in Medicine, New York, 1993.
[SRE 96] SREBRO S., « A modified boundary element method for the estimation of potential
fields on the scalp », IEEE Trans. Biomed. Eng., vol. 43, 1996, p. 650-653.
[TAU 95] TAUBIN G., « A signal processing approach to fair surface design », Computer
Graphics, Proceeding SIGGRAPH’95, 1995, p. 351-358.
[THE 91] THÉVENET M., BERTRAND O., PERRIN F., DUMONT J., PERNIER J., « The finite
element method for a realistic head model of electrical brain activities : preliminary
results », Clin. Phys. Physiol. Meas., vol. 12, Suppl. A, 1991, p. 89-94.
[THE 92] THÉVENET M., « Modélisation de l’activité électrique cérébrale par la méthode des
éléments finis », Ph. D. Dissertation, Lyon, France, 1992.
[YVE 95] YVERT B., BERTRAND O., ECHALLIER J.F., PERNIER J., « Improved forward
EEG calculations using local mesh refinement of realistic head geometries », Electroenceph.
Clin. Neurophysiol., vol. 95, 1995, p. 381-392.
[ZHO 92] ZHOU H., VAN OOSTEROM A., « Computation of the potential distribution in a
four-layer anisotropic concentric spherical volume conductor », IEEE Trans. Biomed. Eng.,
vol. 39, 1992, p. 154–158.
