A full subtraction approach for finite element method based source analysis using constrained Delaunay tetrahedralisation

NeuroImage

Volumn 46, Issue 4, 2009, Pages 1055-1065

  Drechsler, F ^a   Wolters, C H ^b   Dierkes, T ^b   Si, H ^c   Grasedyck, L ^a  

^a MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

^b UNIVERSITY OF MÜNSTER   (Germany)

^c WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Cerebrospinal fluid; Conductivity anisotropy; Constrained Delaunay tetrahedralisation; Dipole; Electroencephalography; Finite element method; Full subtraction approach; Projected subtraction approach; Source reconstruction; Transfer matrix; Validation in four layer sphere models

Indexed keywords

ANALYTICAL ERROR; ANISOTROPY; ARTICLE; CEREBROSPINAL FLUID; DIPOLE; FINITE ELEMENT ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PRIORITY JOURNAL; VALIDATION PROCESS;

ALGORITHMS; BRAIN; BRAIN MAPPING; COMPUTER SIMULATION; ELECTROENCEPHALOGRAPHY; FINITE ELEMENT ANALYSIS; IMAGE PROCESSING, COMPUTER-ASSISTED; MODELS, NEUROLOGICAL;

EID: 67349276103     PISSN: 10538119     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neuroimage.2009.02.024     Document Type: Article

References (46)

1. Awada K., Jackson D., Williams J., Wilton D., Baumann S., and Papanicolaou A. Computational aspects of finite element modeling in EEG source localization. IEEE Trans. Biomed. Eng. 44 8 (1997) 736-751
2. Baumann S., Wozny D., Kelly S., and Meno F. The electrical conductivity of human cerebrospinal fluid at body temperature. IEEE Trans. Biomed. Eng. 44 3 (1997) 220-223
3. Bertrand O., Thévenet M., and Perrin F. 3D finite element method in brain electrical activity studies. In: Nenonen J., Rajala H., and Katila T. (Eds). Biomagnetic Localization and 3D Modelling. Report of the Dep. of Tech.Physics (1991), Helsinki University of Technology 154-171
4. Braess D. Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics (2007), Cambridge Univ. Press
5. Buchner H., Knoll G., Fuchs M., Rienäcker A., Beckmann R., Wagner M., Silny J., and Pesch J. Inverse localization of electric dipole current sources in finite element models of the human head. Electroencephalogr. Clin. Neurophysiol. 102 (1997) 267-278
6. Calvetti D., Hakula H., Pursiainen S., Somersalo E., 2008: Conditionally Gaussian hypermodels for cerebral source localization, submitted for publication.
7. Cook M., and Koles Z. A high-resolution anisotropic finite-volume head model for EEG source analysis. Proc. of the 28th Annual Int. Conf. of the IEEE Engineering in Medicine and Biology Society (2006) 4536-4539
8. Dahmen W., and Reusken A. Numerik für Ingenieure und Naturwissenschaftler (2008), Springer-Lehrbuch ISBN 978-3-540-76492-2
9. de Munck J., and Peters M. A fast method to compute the potential in the multi sphere model. IEEE Trans. Biomed. Eng. 40 11 (1993) 1166-1174
10. de Munck J., van Dijk B., and Spekreijse H. Mathematical dipoles are adequate to describe realistic generators of human brain activity. IEEE Trans. Biomed. Eng. 35 11 (1988) 960-966
11. Gencer N., and Acar C. Sensitivity of EEG and MEG measurements to tissue conductivity. Phys. Med. Biol. 49 (2004) 701-717
12. Haase G., Kuhn M., and Reitzinger S. Parallel AMG on distributed memory computers. SIAM J. Sci. Comput. 24 2 (2002) 410-427
13. Hackbusch W. Elliptic Differential Equations. Theory and Numerical Treatment (1992), Springer-Verlag, Berlin
14. Hackbusch W. Iterative Solution of Large Sparse Systems of Equations. Appl. Math. Sci. 95 (1994), Springer Verlag
15. Hallez H., Vanrumste B., Hese P.V., D'Asseler Y., Lemahieu I., and de Walle R.V. A finite difference method with reciprocity used to incorporate anisotropy in electroencephalogram dipole source localization. Phys. Med. Biol. 50 (2005) 3787-3806
16. Hämäläinen M., Hari R., Ilmoniemi R., Knuutila J., and Lounasmaa O. Magnetoencephalography: theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev. Mod. Phys. 65 (1993) 413-497
17. Kybic J., Clerc M., Abboud T., Faugeras O., Keriven R., and Papadopoulo T. A common formalism for the integral formulations of the forward eeg problem. IEEE Trans. Med. Imag. 24 1 (2005) 12-18
18. Marin G., Guerin C., Baillet S., and Garnero L.G.M. Influence of skull anisotropy for the forward and inverse problem in EEG: simulation studies using the FEM on realistic head models. Hum. Brain Mapp. 6 (1998) 250-269
19. Meijs J., Weier O., Peters M., and van Oosterom A. On the numerical accuracy of the boundary element method. IEEE Trans. Biomed. Eng. 36 (1989) 1038-1049
20. Michel C., Murray M., Lantz G., Gonzalez S., Spinelli L., and de Peralta R. EEG source imaging. Clin. Neurophysiol. 115 (2004) 2195-2222 invited review
21. Murakami S., and Okada Y. Contributions of principal neocortical neurons to magnetoencephalography and electroencephalography signals. J. Physiol. 575 3 (2006) 925-936
22. Plonsey R., and Heppner D. Considerations on quasi-stationarity in electro-physiological systems. Bull. Math. Biophys. 29 (1967) 657-664
23. Plummer C., Harvey A., and Cook M. Eeg source localization in focal epilepsy: where are we now?. Epilepsia 49 2 (2008) 201-218
24. Pursiainen S. EEG/MEG forward simulation through h- and p-type finite elements. Journal of Physics: Conference Series, Proceedings of Applied Inverse Problems (AIP) (2007) 1-11
25. Pursiainen S. (2008): Computational methods in electromagnetic biomedical inverse problems. Ph.D. thesis, at the Helsinki University of Technology, Faculty of Information and Natural Sciences, Institute of Mathematics.
26. Ramon C., Schimpf P., Haueisen J., Holmes M., and Ishimaru A. Role of soft bone, CSF and gray matter in EEG simulations. Brain Topogr. 16 4 (2004) 245-248
27. Rullmann M., Anwander A., Dannhauer M., Warfield S., Duffy F., Wolters C., (2009). EEG source analysis of epileptiform activity using a 1 mm anisotropic hexahedra finite element head model. NeuroImage 44 (2), 399-410. http://dx.doi.org/10.1016/j.neuroimage.2008.09.009.
28. Sarvas J. Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. Phys. Med. Biol. 32 1 (1987) 11-22
29. Schimpf P., Ramon C., and Haueisen J. Dipole models for the EEG and MEG. IEEE Trans. Biomed. Eng. 49 5 (2002) 409-418
30. Shimony J.S., McKinstry R., Akbudak E., Aronovitz J.A., Snyder A.Z., Lori N.F., Cull T.S., and Conturo T.E. Quantitative diffusion-tensor anisotropy brain MR imaging: Normative human data and anatomic analysis. Radiology 212 (1999) 770-784
31. Si H. (2004): TetGen, a quality tetrahedral mesh generator and three-dimensional delaunay triangulator, v1.3, user's manual. Tech. Rep. 9, Weierstrass Institute for Applied Analysis and Stochastics.
32. Si H. (2007): TetView. http://tetgen.berlios.de/tetview.html.
33. Si H. Adaptive tetrahedral mesh generation by constrained Delaunay refinement. Int. J. Numer. Methods Eng. 75 7 (2008) 856-880
34. Si H., and Gärtner K. Meshing piecewise linear complexes by constrained Delaunay tetrahedralizations. Proc. 14th International Meshing Roundtable (2005), Sandia National Laboratories 147-163
35. Stroud A.H. Approximate Calculation of Multiple Integrals (1971), Prentice-Hall, Inc
36. Tanzer O., Järvenpää S., Nenonen J., and Somersalo E. Representation of bioelectric current sources using Whitney elements in finite element method. Phys. Med. Biol. 50 (2005) 3023-3039
37. Tuch D., Wedeen V., Dale A., George J., and Belliveau J. Conductivity tensor mapping of the human brain using diffusion tensor MRI. Proc. Natl. Acad. Sci. U. S. A. 98 20 (2001) 11697-11701
38. van den Broek S. (1997): Volume conduction effects in EEG and MEG. Ph.D. thesis, Proefschrift Universiteit Twente Enschede, The Netherlands.
39. Wang K., Zhu S., Mueller B., Lim K., Liu Z., and He B. A new method to derive white matter conductivity from diffusion tensor MRI. IEEE Trans. Biomed. Eng. 55 10 (2008) 2481-2486
40. Wendel K., Narra N., Hannula M., Kauppinen P., and Malmivuo J. The influence of CSF on EEG sensitivity distributions of multilayered head models. IEEE Trans. Biomed. Eng. 55 4 (2008) 1454-1456
41. Wolters C., Kuhn M., Anwander A., and Reitzinger S. A parallel algebraic multigrid solver for finite element method based source localization in the human brain. Comp. Vis. Sci. 5 3 (2002) 165-177
42. Wolters C.H., Grasedyck L., and Hackbusch W. Efficient computation of lead field bases and influence matrix for the FEM-based EEG and MEG inverse problem. Inverse Probl. 20 4 (2004) 1099-1116
43. Wolters C., Köstler H., Möller C., Härtlein J., Grasedyck L., and Hackbusch W. Numerical mathematics of the subtraction method for the modeling of a current dipole in EEG source reconstruction using finite element head models. SIAM J. Sci. Comput. 30 1 (2007) 24-45
44. Wolters C.H., Anwander A., Berti G., and Hartmann U. Geometry-adapted hexahedral meshes improve accuracy of finite element method based EEG source analysis. IEEE Trans. Biomed. Eng. 54 8 (2007) 1446-1453
45. Yan Y., Nunez P., and Hart R. Finite-element model of the human head: Scalp potentials due to dipole sources. Med. Biol. Eng. Comput. 29 (1991) 475-481
46. Zhang Y., Ding L., van Drongelen W., Hecox K., Frim D., and He B. A cortical potential imaging study from simultaneous extra- and intra-cranial electrical recordings by means of the finite element method. NeuroImage 31 4 (2006) 1513-1524