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6 - EEG and MEG: forward modeling

Published online by Cambridge University Press:  05 October 2012

By
Jan C. de Munck ,
Carsten H. Wolters  and
Maureen Clerc
Edited by
Romain Brette  and
Alain Destexhe
Jan C. de Munck
Affiliation:
VU University Medical Centre, The Netherlands
Carsten H. Wolters
Affiliation:
University of Münster, Germany
Maureen Clerc
Affiliation:
INRIA Sophia Antipolis Méditerranée, France
Romain Brette
Affiliation:
Ecole Normale Supérieure, Paris
Alain Destexhe
Affiliation:
Centre National de la Recherche Scientifique (CNRS), Paris
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Summary

Introduction

The electroencephalogram (EEG) represents potential differences recorded from the scalp as function of time (Niedermayer and Lopes da Silva, 1987). The generators of the EEG consist of time-varying ionic currents generated in the brain by biochemical sources. These current sources also generate a small but measurable magnetic induction field, which can be recorded with magnetoencephalographic (MEG) equipment (Hämäläinen et al., 1993). When EEG and MEG are studied in the time or frequency domain, several rhythms can be discriminated that contain valuable information about the collective behavior of the living human brain as a neural network. In this chapter EEG and MEG are discussed in the spatial domain. We consider that these signals are recorded from multiple sensors with known positions and study the spatial distribution of EEG and MEG (in the sequel abbreviated as MEEG) in relation to the spatial distribution of the underlying sources.

More precisely, we consider the mathematical problem of predicting the spatial distribution of MEEG, from several physiological assumptions on the current sources. This problem is commonly named the “forward problem.” Solutions of the forward problem that are fast, accurate and practical are indispensable ingredients for the solution of the “inverse problem” or “backward problem,” which is the problem of extracting as much information as possible about the cerebral current sources, on the basis of MEEG data. Both the forward and the inverse problems are formulated within the framework of a certain mathematical model, wherein the underlying physiological assumptions are precisely formulated.

Type
Chapter
Information
Handbook of Neural Activity Measurement , pp. 192 - 256
Publisher: Cambridge University Press
Print publication year: 2012

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References

Akhtari, M., Bryant, H.C., Mamelak, A. N., Flynn, E. R., Heller, L., Shih, J. J. et al. (2002). Conductivities of three-layer live human skull. Brain Topogr., 14(3), 151–167.CrossRefGoogle ScholarPubMed
Awada, K. A., Jackson, S. E., Williams, J. T., Wilton, D. R., Baumann, S. B. and Papanicolaou, A. C. (1997). Computational aspects of finite element modelling in EEG source localization. IEEE Trans. Biomed. Eng., 44 (8), 736–752.CrossRefGoogle Scholar
Bangera, N. B., Schomer, D. L., Dehghani, N., Ulbert, I., Cash, S., Papavasiliou, S., Eisenberg, S. R., Dale, A. M. and Halgren, E. (2010). Experimental validation of the influence of white matter anisotropy on the intracranial EEG forward solution. J. Comput. Neurosci., 29, 371–387.CrossRefGoogle ScholarPubMed
Barnard, A. C. L., Duck, J. M. and Lynn, M. S. (1967a). The application of electromagnetic theory to electrocardiology. I. Derivation of the integral equations. Biophys. J., 7, 443–462.CrossRefGoogle ScholarPubMed
Barnard, A. C. L., Duck, J. M. and Lynn, M. S. and Timlake, W. P. (1967b). The application of electromagnetic theory to electrocardiology. II. Numerical solution of the integral equations. Biophys. J., 7, 463–491.CrossRefGoogle ScholarPubMed
Baumann, S. B., Wozny, D. R., Kelly, S. K. and Meno, F. M. (1997). The electrical conductivity of human cerebrospinal fluid at body temperature. IEEE Trans. Biomed. Eng., 44 (3), 220–223.CrossRefGoogle ScholarPubMed
Beatson, R. K. and Greengard, L. (1997). A short course on fast multipole methods. In: M., Ainsworth, J., Levesley, W., Light and M., Marletta (editors), Wavelets, Multilevel Methods and Elliptic PDEs, Oxford: Oxford University Press, pp. 1–37.Google Scholar
Bénar, C. G. and Gotman, J. (2002). Modeling of post-surgical brain and skull defects in the EEG inverse problem with the boundary element method. Clin. Neurophysiol., 113, 48–56.CrossRefGoogle ScholarPubMed
Berg, P. and Scherg, M. (1994). A fast method for forward computation of multiple-shell spherical head models. Electroenceph. Clin. Neurophysiol., 90 (1), 58–64.CrossRefGoogle ScholarPubMed
Braess, D. (2007). Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Buchner, H., Knoll, G., Fuchs, M., Rienäcker, A., Beckmann, R., Wagner, M., Silny, J. and Pesch, J. (1997). Inverse localization of electric dipole current sources in finite element models of the human head. Electroenceph. Clin. Neurophysiol., 102, 267–278.CrossRefGoogle ScholarPubMed
Cheng, H., Greengard, L. and Rokhlin, V. (1999). A fast adaptive multipole algorithm in three dimensions. J. Comput. Phys., 155, 468–498.CrossRefGoogle Scholar
Clerc, M., Dervieux, A., Keriven, R., Faugeras, O., Kybic, J. and Papadopoulo, T. (2002) Comparison of BEM and FEM Methods for the E/MEG problem. Proceedings of the 13th Int.Conf. on Biomagnetism, Jena, Germany, August 10–14, pp. 688–690.Google Scholar
Cook, M. J. D. and Koles, Z. J. (2006). A high-resolution anisotropic finite-volume head model for EEG source analysis. Proc. 28th Ann. Conf. IEEE Eng. Med. Biol. Soc., pp. 4536–4539.Google Scholar
Cuffin, B. N. (1985), A comparison of moving dipole inverse solutions using EEG's and MEG's. IEEE Trans. Biomed Eng., 32 (11), 905–910.Google ScholarPubMed
Cuffin, B. N. (1991). Eccentric spheres models of the head. IEEE Trans. Biomed. Eng., 38 (9), 871–878.CrossRefGoogle Scholar
Cuffin, B. N. and Cohen, D. (1977). Magnetic fields of a dipole in special volume conductor shapes. IEEE Trans. Biomed. Eng., 24(4), 372–381.Google ScholarPubMed
Cuffin, B. N. and Cohen, D. (1983). Effects of detector coil size and configuration on measurements of the magnetoencephalogram. J. Appl. Phys., 54, 3589–3594.CrossRefGoogle Scholar
Dannhauer, M., Lanfer, B., Wolters, C. H. and Knösche, T. R. (2011). Modeling of the human skull in EEG source analysis. Human Brain Mapping, 32 (9), 1383–1399.CrossRefGoogle ScholarPubMed
Dassios, G., Giapalaki, S.N., Kandili, A. N. and Kariotou, F. (2007). The exterior magnetic field for the multilayer ellipsoidal model of the brain. Q. J. Mech. Appl. Math., 60 (1), 1–25.CrossRefGoogle Scholar
Dembart, B. and Yip, E. (1998). The accuracy of fast multipole methods for Maxwell's equations. IEEE Comput. Sci. Eng., 5 (3), 48–56.CrossRefGoogle Scholar
De Jongh, A., DeMunck, J. C., Gonçalves, S. I. and Ossenblok, P. P. W. (2005). Differences in MEG/EEG epileptic spike yields explained by regional differences in signal to noise ratios. J. Clin. Neurophysiol., 22 (2), 153–158.CrossRefGoogle ScholarPubMed
De Munck, J. C. (1988). The potential distribution in a layered anisotropic spheroidal volume conductor. J. Appl. Phys., 64 (2), 464–470.CrossRefGoogle Scholar
De Munck, J. C. (1992). A linear discretization of the volume conductor boundary integral equation using analytically integrated elements. IEEE Trans. Biomed. Eng., 39, 986–989.CrossRefGoogle ScholarPubMed
De Munck, J. C. and Peters, M. J. (1993). A fast method to compute the potential in the multi-sphere model. IEEE Trans. Biomed. Eng., 40 (11), 1166–1174.CrossRefGoogle Scholar
De Munck, J. C. and Van Dijk, B.W. (1991). Symmetry considerations in the quasistatic approximation of volume conductor theory. Phys. Med. Biol., 36 (4), 521–529.CrossRefGoogle Scholar
De Munck, J. C., Van Dijk, B.W. and Spekreijse, H. (1988a). An analytic method to determine the effect of source modelling errors on the apparent location and direction of biological sources. J. Appl. Phys., 63 (3), 944–956.CrossRefGoogle Scholar
De Munck, J. C., Van Dijk, B.W. and Spekreijse, H. (1988b). Mathematical dipoles are adequate to describe realistic generators of human brain activity. IEEE Trans. Biomed. Eng., 35 (11), 960–966.CrossRefGoogle ScholarPubMed
De Munck, J. C., Hämäläinen, M. H. and Peters, M. J. (1991). The use of the asymptotic expansion to speed up the computation of a series of spherical harmonics. Clin. Phys. Physiol. Meas., 12A, 83–87.Google Scholar
De Munck, J. C., De Jongh, A. and Van Dijk, B.W. (2001). The localization of spontaneous brain activity: an efficient way to analyze large data sets. IEEE Trans. Biomed. Eng., 48 (11), 1221–1228.CrossRefGoogle ScholarPubMed
Drechsler, F., Wolters, C.H., Dierkes, T., Si, H. and Grasedyck, L. (2009). A full subtraction approach for finite element method based source analysis using constrained Delaunay tetrahedralisation. NeuroImage, 46 (4), 1055–1065.CrossRefGoogle ScholarPubMed
Epton, M. A. and Dembart, B. (1995). Multipole translation theory for the threedimensional Laplace and Helmholtz equations. SIAM J. Sci. Comput., 16 (4), 865–897.CrossRefGoogle Scholar
Eriksson, F. (1990). On the measure of solid angles. Math. Mag., 63 (3), 184–187.CrossRefGoogle Scholar
Ermer, J. J., Mosher, J.C., Baillet, S. and Leahy, R. M. (2001). Rapidly Re-computable EEG forward models for realistic head shapes. Phys. Med. Biol., 46 (4), 1265–1281.CrossRefGoogle ScholarPubMed
Frank, E. (1952). Electric potential produced by two point current sources in a homogeneous conducting sphere. J. Appl. Phys., 23 (11), 1225–1228.CrossRefGoogle Scholar
Friederici, A., Wang, Y., Herrmann, C., Maess, B. and Oertel, U. (2000). Localization of early syntactic processes in frontal and temporal cortical areas: an MEG study. Human Brain Mapping, 11, 1–11.3.0.CO;2-B>CrossRefGoogle Scholar
Frijns, J. H. M., De Loo, S. L. and Schoonhoven, R. (2000). Improving accuracy of the boundary element method by the use of second-order interpolation function. IEEE Trans. Biomed. Eng., 47 (10), 1336–1346.CrossRefGoogle Scholar
Fuchs, M., Drenckhahn, R., Wischmann, H. A. and Wagner, M. (1998). An improved boundary element method for realistic volume conductor modeling. IEEE Trans. Biomed. Eng., 45 (8), 980–997.CrossRefGoogle ScholarPubMed
Fuchs, M., Wagner, M. and Kastner, J. (2007). Development of volume conductor and source models to localize epileptic foci. J. Clin. Neurophysiol., 24, 101–119.CrossRefGoogle ScholarPubMed
Gencer, N. G. and Acar, C. E. (2004). Sensitivity of EEG and MEG measurements to tissue conductivity. Phys. Med. Biol., 49, 701–717.CrossRefGoogle ScholarPubMed
Geselowitz, D.B. (1970). On the magnetic field generated outside an inhomogeneous volume conductor by integral current sources. IEEE Trans. Magn., 6, 346–347.CrossRefGoogle Scholar
Golub, G. H. and Van Loan, C. F. (1989). Matrix Computations (2nd edition). Baltimore, MD: Johns Hopkins University Press.Google Scholar
Gonçalves, S. I., De Munck, J. C., Verbunt, J. P. A., Heethaar, R. M. and Lopes da Silva, F. H. (2003a). In vivo measurement of brain and skull resistivities using an EIT based method and the combined analysis of SEP/SEF data. IEEE Trans. Biomed. Eng., 50 (9), 1124–1127.CrossRefGoogle Scholar
Gonçalves, S. I., De Munck, J. C., Verbunt, J. P. A., Bijma, F., Heethaar, R.M. and Lopes da Silva, F. H. (2003b). In vivo measurement of the brain and skull resistivities using an EIT based method and realistic models for the head. IEEE Trans. Biomed. Eng., 50 (6), 754–767.CrossRefGoogle ScholarPubMed
Grynszpan, F. and Geselowitz, D.B. (1973). Model studies of the magnetocardiogram. Biophys. J., 13, 911–925.CrossRefGoogle ScholarPubMed
Güllmar, D., Haueisen, J., Eiselt, M., Giessler, F., Flemming, L., Anwander, A., Knösche, T. R., Wolters, C. H., Dümpelmann, M., Tuch, D. S., and Reichenbach, J. R. (2006). Influence of anisotropic conductivity on EEG source reconstruction: investigations in a rabbit model. IEEE Trans. Biomed. Eng., 53 (9), 1841–1850.CrossRefGoogle Scholar
Güllmar, D., Haueisen, J. and Reichenbach, J. R. (2010). Influence of anisotropic electrical conductivity in white matter tissue on the EEG/MEG forward and inverse solution. A high resolution whole head simulation study. NeuroImage, 51, 145–163.CrossRefGoogle ScholarPubMed
Gutiérrez, D. and Nehorai, A. (2008). Array response kernels for EEG and MEG in multilayer ellipsoidal geometry. IEEE Trans. Biomed. Eng., 55 (3), 1103–1111.CrossRefGoogle ScholarPubMed
Hackbusch, W. (1994). Iterative Solution of Large Sparse Systems of Linear Equations, Applied Mathematical Sciences, Vol. 95. New York: Springer Verlag.CrossRefGoogle Scholar
Hackbusch, W. and Nowak, Z. K. (1989). On the fast matrix multiplication in the boundary element method by panel clustering. Numer. Math., 54, 463–491.CrossRefGoogle Scholar
Hallez, H. (2008). Incorporation of anisotropic conductivities in EEG source analysis. Dissertation, Universiteit Gent, Biomedical Engineering, ISBN 978-90-8578-229-2.Google Scholar
Hallez, H., Vanrumste, B., Van Hese, P., D'Asseler, Y., Lemahieu, I. and Van de Walle, R. (2005). A finite difference method with reciprocity used to incorporate anisotropy in electroencephalogram dipole source localization, Phys. Med. Biol., 50, 3787–3806.CrossRefGoogle ScholarPubMed
Hämäläinen, M. S. and Sarvas, J. (1989). Realistic conductivity geometry model of the human head for interpretation of neuromagnetic data. IEEE Trans. Biomed. Eng., 36, 165–171.CrossRefGoogle ScholarPubMed
Hämäläinen, M. S., Hari, R., Ilmoniemi, R. J., Knuutila, J. and Lounasmaa, O.V. (1993). Magnetoencephalography theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev. Mod. Phys., 65, 413–497.CrossRefGoogle Scholar
Haueisen, J., Tuch, D. S., Ramon, C., Schimpf, P. H., Wedeen, V. J., George, J. S. and Belliveau, J.W. (2002). The influence of brain tissue anisotropy on human EEG and MEG. NeuroImage, 15, 159–166.CrossRefGoogle ScholarPubMed
Hosek, R. S., Sances, A., Jodat, R.W. and Larson, S. J. (1978). The contributions of intracerebral currents to the EEG and evoked potentials. IEEE Trans. Biomed. Eng., 25 (5), 405–413.Google ScholarPubMed
Huang, M. X., Mosher, J.C. and Leahy, R. M. (1999). “A sensor-weighted overlappingsphere head model and exhaustive head model comparison for MEG. Phys. Med. Biol., 423–440.Google ScholarPubMed
Huang, M. X., Song, T., Hagler, D. J., Podgorny, I., Jousmaki, V., Cui, L., Gaa, K., Harrington, D. L., Dale, A. M., Lee, R. R., Elman, J. and Halgren, E. (2007). A novel integrated MEG and EEG analysis method for dipolar sources. NeuroImage, 37, 731–748.CrossRefGoogle ScholarPubMed
Ilmoniemi, R. J. (1995). Radial anisotropy added to a spherically symmetric conductor does not affect the external magnetic field due to internal sources. Europhys. Lett., 30 (5), 313–326.CrossRefGoogle Scholar
Ilmoniemi, R. J., Hämäläinen, M. S. and Knuutila, J. (1985). The forward and inverse problems in the spherical model. In: H., Weinberg, G., Stroink and T., Katila (editors), Biomagnetism: Applications and Theory. Oxford: Pergamon Press, pp. 278–282.Google Scholar
Jackson, J. D. (1962). Classical Electrodynamics. New York: Wiley.Google Scholar
Kariotou, F. (2004). Electroencephalography in ellipsoidal geometry. J. Math. Anal. Appl., 290, 324–342.CrossRefGoogle Scholar
Kybic, J., Clerc, M., Faugeras, O., Keriven, R. and Papadopoulo, T. (2005a). Fast multipole acceleration of the MEG/EEG boundary element method. Phys. Med. Biol., 50, 4695–4710.CrossRefGoogle ScholarPubMed
Kybic, J., Clerc, M., Abboud, T., Faugeras, O., Keriven, R. and Papadopoulo, T. (2005b). A common formalism for the integral formulations of the forward EEG problem. IEEE Trans. Med. Im., 24, 12–28.CrossRefGoogle ScholarPubMed
Kybic, J., Clerc, M., Faugeras, O., Keriven, R. and Papadopoulo, T. (2006). Generalized head models for MEG/EEG: boundary element method beyond nested volumes. Phys. Med. Biol., 51, 1333–1346.CrossRefGoogle ScholarPubMed
Lanfer, B. (2007) Validation and comparison of realistic head modelling techniques and application to tactile somatosensory evoked EEG and MEG data. Diploma Thesis in Physics, Fachbereich Physik, Westfaelische Wilhelms-Universitaet Muenster.Google Scholar
Lanfer, B., Wolters, C. H., Demokritov, S. O. and Pantev, C. (2007). Validating finite element method based EEG and MEG forward computations. Proc. 41. Jahrestagung der DGBMT, Deutsche Gesellschaft fuer Biomedizinische Technik im VDE, Aachen, Germany, September 26–29, pp. 140–141. ISSN: 0939-4990, www.bmt2007.de.Google Scholar
Lew, S., Wolters, C. H., Anwander, A., Makeig, S. and MacLeod, R. S. (2009a). Improved EEG source analysis using low resolution conductivity estimation in a four-compartment finite element head model. Human Brain Mapping, 30 (9), 2862–2878.CrossRefGoogle Scholar
Lew, S., Wolters, C. H., Röer, C., Dierkes, T. and MacLeod, R. S. (2009b). Accuracy and run-time comparison for different potential approaches and iterative solvers in finite element method based EEG source analysis. Appl. Numer. Math., 59 (8), 1970–1988.CrossRefGoogle ScholarPubMed
Lopes da Silva, F. H. and Van Rotterdam, A. (1982). Biophysical aspects of EEG and MEG generation. In: E., Niedermeyer and F. H. Lopes da, Silva (editors), Electroencephalography: Basic Principles, Clinical Applications and Related Fields, (4th edition). Munich: Urban & Schwarzenberg, pp. 93–109.Google Scholar
Lynn, M. S. and Timlake, W. P. (1968a). The numerical solution of singular integral equations of potential theory. Numer. Math., 11, 77–98.Google Scholar
Lynn, M. S. and Timlake, W. P. (1968b). The use of multiple deflations in the numerical solution of singular systems of equations, with applications to potential theory. SIAM J. Numer. Anal., 5 (2), 303–322.CrossRefGoogle Scholar
Marin, G., Guerin, C., Baillet, S., Garnero, L. and Meunier, G. (1998). Influence of skull anisotropy for the forward and inverse problem in EEG: simulation studies using the FEM on realistic head models. Human Brain Mapping, 6, 250–269.3.0.CO;2-2>CrossRefGoogle ScholarPubMed
Meijs, J.W.H., Weier, O.W., Peters, M. J. and Van Oosterom, A. (1989). On the numerical accuracy of the boundary element method. IEEE Trans. Biomed. Eng., 36, 1038–1049.CrossRefGoogle ScholarPubMed
Merzbacher, E. (1961). Quantum Mechanics. New York: Wiley.Google Scholar
Mohr, M. (2004). Simulation of bioelectric fields: the forward and inverse problem of electroencephalographic source analysis. Dissertation, Friedrich-Alexander-Universitaet Erlangen-Nuernberg, Arbeitsberichte des Instituts fuer Informatik, Band 37, Nummer 6, ISSN 1611–4205.Google Scholar
Mohr, M. and Vanrumste, B. (2003). Comparing iterative solvers for linear systems associated with the finite difference discretisation of the forward problem in electroencephalographic source analysis. Med. Biol. Eng. Comput., 41, 75–84.CrossRefGoogle Scholar
Moon, P. and Spencer, D. E. (1988). The Field Theory Handbook. Berlin: Springer-Verlag.Google Scholar
Morse, P. M. and Feshbach, H. (1953). Methods of Theoretical Physics, Vol I and II. New York: McGraw-Hill.Google Scholar
Mosher, J.C., Leahy, R. M. and Lewis, P. S. (1999). EEG and MEG: forward solutions for inverse methods. IEEE Trans. Biomed. Eng., 46 (3), 245–259.CrossRefGoogle ScholarPubMed
Murakami, S. and Okada, Y. (2006). Contributions of principal neocortical neurons to magnetoencephalography and electroencephalography signals. J. Physiol., 575 (3), 925–936.CrossRefGoogle ScholarPubMed
Niedermayer, E. and Lopes da Silva, F. (editors) (1987). Electroencephalography. Basic Principles, Clinical Applications and Related Fields, (2nd edition). Baltimore, MD: Urban and Schwarzenberg.
Nolte, G. and Curio, G. (1997). On the calculation of magnetic fields based on multipole modeling of focal biological current sources. Biophys. J., 73, 1253–1262.CrossRefGoogle ScholarPubMed
Nolte, G. and Curio, G. (1999). Perturbative solutions of the electric forward problem for realistic volume conductors. J. Appl. Phys., 86 (5), 2800–2812.CrossRefGoogle Scholar
Nolte, G., Fieseler, T. and Curio, G. (2001). Perturbative analytical solutions of the magnetic forward problem for realistic volume conductors. J. Appl. Phys., 89 (4), 2360–2370.CrossRefGoogle Scholar
Of, G., Steinbach, O. and Wendland, W. L. (2002). A fast multipole boundary element method for the symmetric boundary integral formulation. In: Proceedings of IABEM, Austin, TX, 2002.Google Scholar
Olivi, E., Clerc, M., Papadopoulo, T. and Vallaghé, S. (2010). Domain decomposition for coupling finite and boundary element methods in EEG. In: Proceedings of International Conference on Biomagnetism.Google Scholar
Olesch, J., Ruthotto, L., Kugel, H., Skare, S., Fischer, B. and Wolters, C. H. (2010). A variational approach for the correction of field-inhomogeneities in EPI sequences. SPIE Medical Imaging, Image Processing, 7623(1), 8 pages, San Diego, CA. doi: 10.1117/12.844375.CrossRefGoogle Scholar
Ollikainen, J., Vaukhonen, M., Karjalainen, P. A. and Kaipio, J. P. (1999). Effects of local skull inhomogeneities on EEG source estimation. Med. Eng. Phys., 21, 143–154.CrossRefGoogle ScholarPubMed
Oostenveld, R. and Oostendorp, T. F. (2002). Validating the boundary element method for forward and inverse EEG computations in the presence of a hole in the skull. Human Brain Mapping, 17 (3), 179–192.CrossRefGoogle ScholarPubMed
Ossenblok, P., De Munck, J. C., Drolsbach, W., Colon, A. and Boon, P. (2007). The advantages of interictal MEG compared to EEG in case of frontal lobe epilepsy. Epilepsia, 48 (11), 2139–2149.Google Scholar
Plonsey, R. and Heppner, D. (1967). Considerations of quasistationarity in electrophysiological systems. Bull. Math. Biophys., 29, 657–664.CrossRefGoogle Scholar
Peters, M. J. and Elias, P. J. H. (1988). On the magnetic field and the electric potential generated by biological sources in an anisotropic volume conductor. Med. Biol. Eng. Comput., 26, 617–623.CrossRefGoogle Scholar
Pruis, G.W., Guilding, B. H. and Peters, M. J. (1993). A comparison of different numerical methods for solving the forward problem of EEG and MEG. Physiol. Meas., 14, A1–A9.CrossRefGoogle ScholarPubMed
Pursiainen, S. (2008). Computational methods in electromagnetic biomedical inverse problems. Thesis, Helsinki University of Technology, Faculty of Information and Natural Sciences, Institute of Mathematics.Google Scholar
Pursiainen, S., Lucka, F. and Wolters, C. H. (2012). Complete electrode model in EEG: relationship and differences to the point electrode model. Phys. Med. Biol., 57, 999–1017.CrossRefGoogle ScholarPubMed
Rahola, J. (1998). Experiments on iterative methods and the fast multipole method in electromagnetic scattering calculations. Technical Report TR/PA/98/49, CERFACS, 98.Google Scholar
Ramon, C., Schimpf, P., Haueisen, J., Holmes, M. and Ishimaru, A. (2004). Role of soft bone, CSF and gray matter in EEG simulations. Brain Topography, 16 (4), 245–248.Google ScholarPubMed
Roberts, T., Poeppel, D. and Rowley, H. (1998). Magnetoencephalography and magnetic source imaging. Neuropsych. Behav. Neurol., 11, 49–64.Google ScholarPubMed
Rosenfeld, M., Tanami, R. and Abboud, S. (1996). Numerical solution of the potential due to dipole sources in volume conductors with arbitrary geometry and conductivity. IEEE Trans. Biomed. Eng., 43 (7), 679–0689.CrossRefGoogle ScholarPubMed
Rudy, R. and Plonsey, R. (1979). The eccentric spheres model as the basis for a study of the role of geometry and inhomogeneities in electrocardiography. IEEE Trans. Biomed. Eng., 26 (7), 392–399.Google ScholarPubMed
Rullmann, M., Anwander, A., Dannhauer, M., Warfield, S. K., Duffy, F. H. and Wolters, C. H. (2009). EEG source analysis of epileptiform activity using a 1mm anisotropic hexahedra finite element head model. NeuroImage, 44, 399–410.CrossRefGoogle Scholar
Sadleir, R. J. and Argibay, A. (2007). Modeling skull electrical properties. Ann. Biomed. Eng., 35 (10), 1699–1712.CrossRefGoogle ScholarPubMed
Saleheen, H. I. and Kwong, T. N. (1997). New finite difference formulations for general inhomogeneous anisotropic bioelectric problems. IEEE Trans. Biomed. Eng., 44 (9), 800–809.CrossRefGoogle ScholarPubMed
Sarvas, J. (1987). Basic mathematical and electromagnetic concepts of the basic biomagnetic inverse problem. Phys. Med. Biol., 32 (1), 11–22.CrossRefGoogle ScholarPubMed
Schimpf, P. H. (2007). Application of quasi-static magnetic reciprocity to finite element models of the MEG lead-field. IEEE Trans. Biomed. Eng., 54 (11), 2082–2088.CrossRefGoogle ScholarPubMed
Schimpf, P. H., Ramon, C. and Haueisen, J. (2002). Dipole models for the EEG and MEG. IEEE Trans. Biomed. Eng., 49 (5), 409–418.CrossRefGoogle ScholarPubMed
Tanzer, O., Järvenpää, S., Nenonen, J. and Somersalo, E. (2005). Representation of bioelectric current sources using Whitney elements in finite element method. Phys. Med. Biol., 50, 3023–3039.CrossRefGoogle ScholarPubMed
Taulu, S. and Simola, J. (2006). Spatiotemporal signal space separation method for rejecting nearby interference in MEG measurements. Phys. Med. Biol., 51, 1759–68.CrossRefGoogle ScholarPubMed
Taulu, S., Simola, J. and Kajola, M. (2005). Applications of the signal space separation method. IEEE Trans. Signal Process., 53, 3359–72.CrossRefGoogle Scholar
Tuch, D. S., Wedeen, V. J., Dale, A. M., George, J. S. and Belliveau, J.W. (2001). Conductivity tensor mapping of the human brain using diffusion tensor MRI. Proc. Natl. Acad. Sci. USA, 98 (20), 11697–11701.CrossRefGoogle ScholarPubMed
Uutela, K., Taulu, S. and Hämäläinen, M. (2010). Detecting and correcting for head movements in neuromagnetic measurements. NeuroImage, 14, 1424–1431.Google Scholar
Vallaghé, S. and Clerc, M. (2009). A global sensitivity analysis of three- and four-layer EEG conductivity models. IEEE Trans. Biomed. Eng., 56 (4), 988–995.CrossRefGoogle ScholarPubMed
Vallaghé, S. and Papadopoulo, T. (2010). A trilinear immersed finite element method for solving the EEG forward problem. SIAM J. Sci. Comput., 32, 2379–2394.CrossRefGoogle Scholar
Vallaghé, S., Clerc, M. and Badier, J.-M. (2007). In vivo conductivity estimation using somatosensory evoked potentials and cortical constraints on the sources. Proceedings of 4th IEEE International Symposium on Biomedical Imaging: from Nano to Macro, pp. 1036–1039.Google Scholar
Vallaghé, S., Papadopoulo, T. and Clerc, M. (2009). The adjoint method for general EEG and MEG sensor-based lead field equations. Phys. Med. Biol., 54, 135–147.CrossRefGoogle ScholarPubMed
Van Oosterom, A. and Strackee, J. (1983). The solid angle of a plane triangle. IEEE Trans. Biomed. Eng., 30 (2), 125–126.Google ScholarPubMed
Van 't Ent, D., De Munck, J. C. and Kaas, A. L. (2001). An automated procedure for deriving realistic volume conductor models for MEG/EEG source localization. IEEE Trans. Biomed. Eng., 48 (12), 1434–1443.Google Scholar
Vorwerk, J. (2011). Comparison of numerical approaches to the EEG forward problem, Master's thesis, Mathematics, Münster.Google Scholar
Waberski, T., Buchner, H., Lehnertz, K., Hufnagel, A., Fuchs, M., Beckmann, R. and Rienäcker, A. (1998). The properties of source localization of epileptiform activity using advanced headmodelling and source reconstruction. Brain Topography, 10 (4), 283–290.CrossRefGoogle ScholarPubMed
Wagner, M., Fuchs, M., Wischmann, H. A., Ottenberg, K. and Dössel, O. (1995). Cortex segmentation from 3D MR images for MEG reconstructions. In: C., Baumgartner et al. (editors), Biomagnetism: Fundamental Research and Clinical Applications. Amsterdam: Elsevier/IOS Press, pp. 433–438.Google Scholar
Wagner, M., Fuchs, M., Drenckhahn, R., Wischmann, H.-A., Koehler, T. and Theissen, A. (2000). Automatic generation of BEM and FEM meshes from 3D MR data. NeuroImage, 3, S168.CrossRefGoogle Scholar
Wang, K., Zhu, S., Mueller, B., Lim, K. O., Liu, Z. and He, B. (2008). A new method to derive white matter conductivity from diffusion tensor MRI. IEEE Trans. Biomed. Eng., 55 (10), 2481–2486.Google ScholarPubMed
Weinstein, D., Zhukov, L. and Johnson, C. (2000). Lead-field bases for electroencephalography source imaging. Ann. of Biomed. Eng., 28 (9), 1059–1066.CrossRefGoogle ScholarPubMed
Wehner, D. T., Hämäläinen, M. S., Mody, M. and Ahlfors, S. P. (2008). Head movements of children in MEG: quantification, effects on source estimation, and compensationNeuroImage, 40 (2), 541–550.CrossRefGoogle ScholarPubMed
Wendel, K., Narra, N. G., Hannula, M., Kauppinen, P. and Malmivuo, J. (2008). The influence of CSF on EEG sensitivity distributions of multilayered head models. IEEE Trans. Biomed. Eng., 55 (4), 1454–1456.CrossRefGoogle ScholarPubMed
Willemse, R. B., De Munck, J. C., Van 't Ent, D., Ris, P., Baayen, J. C., Stam, C. J. and Vandertop, W. P. (2007). Magnetoencephalographic study of posterior tibial nerve stimulation in patients with intracranial lesions around the central sulcus. Neurosurgery, 61 (6), 1209–1218.CrossRefGoogle ScholarPubMed
Wilson, F. N. and Bayley, R. H. (1950). The electric field of an eccentric dipole in a homogeneous spherical conducting medium. Circulation, 1, 84–92.CrossRefGoogle Scholar
Wolters, C. H. (2003). Influence of tissue conductivity inhomogeneity and anisotropy on EEG/MEG based source localization in the human brain. MPI of Cognitive Neuroscience Leipzig, MPI Series in Cognitive Neuroscience, No. 39, ISBN 3-936816-11-5 (http://lips.informatik.uni-leipzig.de/pub/2003-33).Google Scholar
Wolters, C. H. (2008). Finite element method based electro- and magnetoencephalography source analysis in the human brain. Habilitation, Fachbereich für Mathematik und Informatik, Westfälische Wilhelms-Universität Münster.Google Scholar
Wolters, C. H. and De Munck, J. C. (2007). Volume conduction, Scholarpedia, 2 (3), 1738, www.scholarpedia.org/article/Volume_conduction.CrossRefGoogle Scholar
Wolters, C. H., Beckmann, R. F., Rienäcker, A. and Buchner, H. (1999). Comparing regularized and non-regularized nonlinear dipole fit methods: A study in a simulated sulcus structure. Brain Topography, 12 (1), 3–18.CrossRefGoogle Scholar
Wolters, C. H., Anwander, A., Koch, M., Reitzinger, S., Kuhn, M. and Svensen, M. (2001). Influence of head tissue conductivity anisotropy on human EEG and MEG using fast high resolution finite element modeling, based on a parallel algebraic multigrid solver. In: T., Plesser and V., Macho (editors), Contributions to the Heinz-Billing Award, pp. 111–157. Gesellschaft für wissenschaftliche Datenverarbeitung mbH. Forschung und wissenschaftliches Rechnen, ISSN: 0176-2516, www.billingpreis.mpg.de.Google Scholar
Wolters, C. H., Kuhn, M., Anwander, A. and Reitzinger, S. (2002). A parallel algebraic multigrid solver for fininite element methods based source localization methods in the human brain. Comput. Vis. Sci., 5 (3), 165–177.CrossRefGoogle Scholar
Wolters, C. H., Graesdyck, L. and Hackbush, W. (2004). Efficient computation of lead field bases and influence matrix for the FEM-based EEG and MEG inverse problem. Inverse Problems, 20, 1099–1116.CrossRefGoogle Scholar
Wolters, C. H., Anwander, A., Weinstein, D., Koch, M., Tricoche, X. and MacLeod, R. S. (2006). Influence of tissue conductivity anisotropy on EEG/MEG field and return current computation in a realistiuc head model: a simulation and visualization study using high-resolution finite element modeling. NeuroImage, 30 (3), 813–826.CrossRefGoogle Scholar
Wolters, C. H., Köstler, H., Möller, C., Härtlein, J., Grasedyck, L. and Hackbusch, W. (2007a). 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), 24–45.Google Scholar
Wolters, C. H., Anwander, A., Berti, G. and Hartmann, U. (2007b). Geometry-adapted hexahedral meshes improve accuracy of finite element method based EEG source analysis. IEEE Trans. Biomed. Eng., 54 (8), 1446–1453.CrossRefGoogle ScholarPubMed
Wolters, C. H., Lew, S., MacLeod, R. S. and Hämäläinen, M. S. (2010). Combined EEG/MEG source analysis using calibrated finite element head models. Proc. 44th Annual Meeting of the DGBMT, Rostock-Warnemünde, Germany, http://conference.vde.com/bmt-2010, to appear.Google Scholar
Yan, Y., Nunez, P. L., Hart, R. T. (1991). Finite element model of the human head: scalp potentials due to dipole sources. Med. Biol. Eng. Comput., 29, 475–481.CrossRefGoogle ScholarPubMed
Yvert, B., Crouzeix-Cheylus, A. and Pernier, J. (2001). Fast realistic modelling in bioelectromagnetism using lead field interpolation. Human Brain Mapping, 14, 48–63.CrossRefGoogle Scholar
Zhang, Z. (1995). A fast method to compute the surface potentials generated by dipoles within multilayer anisotropic spheres. Phys. Med. Biol., 40, 335–349.CrossRefGoogle ScholarPubMed

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