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Neuroelectromagnetic Source Imaging of Brain Dynamics

  • Rey R. Ramírez
  • David Wipf
  • Sylvain Baillet
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 38)

Abstract

Neuroelectromagnetic source imaging (NSI) is the scientific field devoted to modeling and estimating the spatiotemporal dynamics of the neuronal currents that generate the electric potentials and magnetic fields measured with electromagnetic (EM) recording technologies. Unlike functional magnetic resonance imaging (fMRI), which is indirectly related to neuroelectrical activity through neurovascular coupling [e.g., the blood oxygen level-dependent (BOLD) signal], EM measurements directly relate to the electrical activity of neuronal populations. In the past few decades, researchers have developed a great variety of source estimation techniques that are well informed by anatomy, neurophysiology, and the physics of volume conduction. State-of-the-art approaches can resolve many simultaneously active brain regions and their single trial dynamics and can even reveal the spatial extent of local cortical current flows.

Keywords

Boundary Element Method Expectation Maximization Dipole Orientation Equivalent Current Dipole Gain Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Adrian, E., Mathews, B. The Berger rhythm: Potential changes from the occipital lobes in man. Brain 57, 355–385 (1934)CrossRefGoogle Scholar
  2. 2.
    Ahlfors, S.P., Ilmoniemi, R.J., Hamalainen, M.S. Estimates of visually evoked cortical currents. Electroencephalogr Clin Neurophysiol 82(3), 225–236 (1992)CrossRefGoogle Scholar
  3. 3.
    Akalin-Acar, Z., Gencer, N.G. An advanced boundary element method (BEM) implementation for the forward problem of electromagnetic source imaging. Phys Med Biol 49(21), 5011–5028 (2004)CrossRefGoogle Scholar
  4. 4.
    Attal, Y., Bhattacharjee, M., Yelnik, J., Cottereau, B., Lefvre, J., Okada, Y., Bardinet, E., Chupin, M., Baillet, S. Modeling and detecting deep brain activity with MEG & EEG. Conf Proc IEEE Eng Med Biol Soc, 4937–4940 (2007)Google Scholar
  5. 5.
    Auranen, T., Nummenmaa, A., Hamalainen, M.S., Jaaskelainen, I.P., Lampinen, J., Vehtari, A., Sams, M. Bayesian analysis of the neuromagnetic inverse problem with lp-norm priors. NeuroImage 26(3), 870–884 (2005)CrossRefGoogle Scholar
  6. 6.
    Baillet, S., Mosher, J.C., Leahy, R.M. Electromagnetic brain mapping. IEEE Signal Process Mag 18(6), 14–30 (2001)CrossRefGoogle Scholar
  7. 7.
    Bell, A.J., Sejnowski, T.J. An information-maximization approach to blind separation and blind deconvolution. Neural Comput 7(6), 1129–1159 (1995)CrossRefGoogle Scholar
  8. 8.
    Berger, H. Über das Elektroenkephalogramm des Menschen. Archiv für Psychiatrie und Nervenkrankheiten 87, 527–570 (1929)CrossRefGoogle Scholar
  9. 9.
    Bertrand, C., Ohmi, M., Suzuki, R., Kado, H. A probabilistic solution to the MEG inverse problem via MCMC methods: The reversible jump and parallel tempering algorithms. IEEE Trans Biomed Eng 48(5), 533–542 (2001)CrossRefGoogle Scholar
  10. 10.
    Bolton, J.P.R., Gross, J., Liu, A.K., Ioannides, A.A. SOFIA: Spatially optimal fast initial analysis of biomagnetic signals. Phys Med Biol 44, 87–103 (1999)CrossRefGoogle Scholar
  11. 11.
    Canolty, R.T., Edwards, E., Dalal, S.S., Soltani, M., Nagarajan, S.S., Kirsch, H.E., Berger, M.S., Barbaro, N.M., Knight, R.T. High gamma power is phase-locked to theta oscillations in human neocortex. Science 313(5793), 1626–1628 (2006)CrossRefGoogle Scholar
  12. 12.
    Cohen, D. Magnetoencephalography: Evidence of magnetic fields produced by alpha-rhythm currents. Science 161, 784–786 (1968)CrossRefGoogle Scholar
  13. 13.
    Cohen, D. Magnetoencephalography: Detection of the brain's electrical activity with a superconducting magnetometer. Science 175, 664–666 (1972)CrossRefGoogle Scholar
  14. 14.
    Cotter, S.F., Rao, B.D., Engan, K., Kreutz-Delgado, K. Sparse solutions to linear inverse problems with multiple measurement vectors. IEEE Trans Signal Process 53(7), 2477–2488 (2005)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Dale, A.M., Liu, A.K., Fischl, B.R., Buckner, R.L., Belliveau, J.W., Lewine, J.D., Halgren, E. Dynamic statistical parametric mapping: Combining fMRI and MEG for high-resolution imaging of cortical activity. Neuron 26(1), 55–67 (2000)CrossRefGoogle Scholar
  16. 16.
    Darvas, F., Ermer, J.J., Mosher, J.C., Leahy, R.M. Generic head models for atlas-based EEG source analysis. Hum Brain Mapp 27(2), 129–143 (2006)CrossRefGoogle Scholar
  17. 17.
    Dogdas, B., Shattuck, D.W., Leahy, R.M. Segmentation of skull and scalp in 3-D human MRI using mathematical morphology. Hum Brain Mapp 26(4), 273–285 (2005)CrossRefGoogle Scholar
  18. 18.
    Friston, K.J., Penny, W., Phillips, C., Kiebel, S., Hinton, G., Ashburner, J. Classical and Bayesian inference in neuroimaging: Theory. NeuroImage 16(2), 465–483 (2002)CrossRefGoogle Scholar
  19. 19.
    Fuchs, M., Kastner, J., Wagner, M., Hawes, S., Ebersole, J.S. A standardized boundary element method volume conductor model. Clin Neurophysiol 113(5), 702–712 (2002)CrossRefGoogle Scholar
  20. 20.
    Fuchs, M., Wagner, M., Kohler, T., Wischmann, H.A. Linear and nonlinear current density reconstructions. J Clin Neurophysiol 16(3), 267–295 (1999)CrossRefGoogle Scholar
  21. 21.
    Gencer, N.G., Williamson, S.J. Differential characterization of neural sources with the bimodal truncated SVD pseudo-inverse for EEG and MEG measurements. IEEE Trans Biomed Eng 45(7), 827–838 (1998)CrossRefGoogle Scholar
  22. 22.
    George, J.S., Aine, C.J., Mosher, J.C., Schmidt, D.M., Ranken, D.M., Schlitt, H.A., Wood, C.C., Lewine, J.D., Sanders, J.A., Belliveau, J.W. Mapping function in the human brain with magnetoencephalography, anatomical magnetic resonance imaging, and functional magnetic resonance imaging. J Clin Neurophysiol 12(5), 406–431 (1995)CrossRefGoogle Scholar
  23. 23.
    Golub, G.H. , van Loan, C.F. Matrix Computations, 3rd edn. Johns Hopkins University Press, Baltimore, MD (1996)MATHGoogle Scholar
  24. 24.
    Goncalves, S.I., deMunck, J.C., Verbunt, J.P.A., Bijma, F., Heethaar, R.M., da Silva, F.L. 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 (2003)CrossRefGoogle Scholar
  25. 25.
    Gorodnitsky, I., Rao, B.D. Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm. IEEE Trans Signal Process 45(3), 600–616 (1997)CrossRefGoogle Scholar
  26. 26.
    Gorodnitsky, I.F., George, J.S., Rao, B.D. Neuromagnetic source imaging with FOCUSS: A recursive weighted minimum norm algorithm. Electroencephalogr Clin Neurophysiol 95(4), 231–251 (1995)CrossRefGoogle Scholar
  27. 27.
    Grave de Peralta Menendez, R., Gonzalez Andino, S.L. Backus and Gilbert method for vector fields. Hum Brain Mapp 7(3), 161–165 (1999)CrossRefGoogle Scholar
  28. 28.
    Gross, J., Ioannides, A.A. Linear transformations of data space in MEG. Phys Med Biol 44(8), 2081–2097 (1999)CrossRefGoogle Scholar
  29. 29.
    Gross, J., Kujala, J., Hamalainen, M., Timmermann, L., Schnitzler, A., Salmelin, R. Dynamic imaging of coherent sources: Studying neural interactions in the human brain. Proc Natl Acad Sci USA 98(2), 694–699 (2001)CrossRefGoogle Scholar
  30. 30.
    Halchenko, Y.O., Hanson, S.J., Pearlmutter, B.A. Multimodal integration: fMRI, MRI, EEG, MEG. In: Landini, L., Positano, V., Santarelli, M.F. (eds.) Advanced Image Processing in Magnetic Resonance Imaging, Signal Processing and Communications, pp. 223–265. Dekker, New York (2005)CrossRefGoogle Scholar
  31. 31.
    Hamalainen, M., Hari, R., Ilmoniemi, R., Knuutila, J., Lounasmaa, O. Magnetoencephalography – theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev Mod Phys 65(2), 413–497 (1993)CrossRefGoogle Scholar
  32. 32.
    Hamalainen, M., Sarvas, J. Feasibility of the homogenous head model in the interpretation of the magnetic fields. Phys Med Biol 32, 91–97 (1987)CrossRefGoogle Scholar
  33. 33.
    von Helmholtz, H. Ueber einige Gesetze der Vertheilung elektrischer Strome in korperlichen Leitern, mit Anwendung auf die thierisch-elektrischen Versuche. Ann Phys Chem 89, 211–233, 353–377 (1853)Google Scholar
  34. 34.
    Hillebrand, A., Barnes, G.R. The use of anatomical constraints with MEG beamformers. NeuroImage 20(4), 2302–2313 (2003)CrossRefGoogle Scholar
  35. 35.
    Huang, M., Aine, C.J., Supek, S., Best, E., Ranken, D., Flynn, E.R. Multi-start downhill simplex method for spatio-temporal source localization in magnetoencephalography. Electroencephalogr Clin Neurophysiol 108(1), 32–44 (1998)CrossRefGoogle Scholar
  36. 36.
    Huang, M.X., Mosher, J.C., Leahy, R.M. A sensor-weighted overlapping-sphere head model and exhaustive head model comparison for MEG. Phys Med Biol 44(2), 423–440 (1999)CrossRefGoogle Scholar
  37. 37.
    Hubbard, J.I., Llinás, R.R., Quastel, D.M.J. Electrophysiological Analysis of Synaptic Transmission. Edward Arnold, London (1969)Google Scholar
  38. 38.
    Ioannides, A.A., Bolton, J.P., Clarke, C.J.S. Continuous probabilistic solutions to the biomagnetic inverse problem. Inverse Probl 6, 523–542 (1990)MATHCrossRefGoogle Scholar
  39. 39.
    Jerbi, K., Mosher, J.C., Baillet, S., Leahy, R.M. On MEG forward modelling using multipolar expansions. Phys Med Biol, 47(4), 523–555 (Feb 2002)CrossRefGoogle Scholar
  40. 40.
    Lachaux, J.P., Rudrauf, D., Kahane, P. Intracranial EEG and human brain mapping. J Physiol (Paris) 97, 613–628 (2003)CrossRefGoogle Scholar
  41. 41.
    Liu, A.K., Dale, A.M., Belliveau, J.W. Monte Carlo simulation studies of EEG and MEG localization accuracy. Hum Brain Mapp 16(1), 47–62 (2002)CrossRefGoogle Scholar
  42. 42.
    Liu, L., Ioannides, A.A., Streit, M. Single trial analysis of neurophysiological correlates of the recognition of complex objects and facial expressions of emotion. Brain Topogr 11(4), 291–303 (1999)CrossRefGoogle Scholar
  43. 43.
    Luck, S.J. An Introduction to the Event-Related Potential Technique. MIT Press, Cambridge, MA (2005)Google Scholar
  44. 44.
    Mackay, D.J.C. Bayesian interpolation. Neural Comput 4(3), 415–447 (1992)CrossRefGoogle Scholar
  45. 45.
    MacKay, D.J.C. Comparison of approximate methods for handling hyperparameters. Neural Comput 11(5), 1035–1068 (1999)CrossRefGoogle Scholar
  46. 46.
    Makeig, S., Jung, T.P., Bell, A.J., Ghahremani, D., Sejnowski, T.J. Blind separation of auditory event-related brain responses into independent components. Proc Natl Acad Sci USA 94(20), 10979–10984 (1997)CrossRefGoogle Scholar
  47. 47.
    Makeig, S., Ramírez, R.R. Neuroelectromagnetic source imaging (NSI) toolbox and EEGLAB module. Proceedings of the 37th Annual Meeting of the Society for Neuroscience, San Diego, CA (2007)Google Scholar
  48. 48.
    Makeig, S., Westerfield, M., Jung, T.P., Enghoff, S., Townsend, J., Courchesne, E., Sejnowski, T.J. Dynamic brain sources of visual evoked responses. Science 295(5555), 690–694 (2002)CrossRefGoogle Scholar
  49. 49.
    Matsuura, K., Okabe, Y. Selective minimum-norm solution of the biomagnetic inverse problem. IEEE Trans Biomed Eng 42(6), 608–615 (1995)CrossRefGoogle Scholar
  50. 50.
    Mattout, J., Phillips, C., Penny, W.D., Rugg, M.D., Friston, K.J. MEG source localization under multiple constraints: An extended Bayesian framework. NeuroImage 30(3), 753–767 (2006)CrossRefGoogle Scholar
  51. 51.
    Mitra, P.P., Maniar, H. Concentration maximization and local basis expansions (LBEX) for linear inverse problems. IEEE Trans Biomed Eng 53(9), 1775–1782 (2006)CrossRefGoogle Scholar
  52. 52.
    Mosher, J.C., Leahy, R.M. Recursive MUSIC: A framework for EEG and MEG source localization. IEEE Trans Biomed Eng 45(11), 1342–1354 (1998)CrossRefGoogle Scholar
  53. 53.
    Mosher, J.C., Lewis, P.S., Leahy, R.M. Multiple dipole modeling and localization from spatio-temporal MEG data. IEEE Trans Biomed Eng 39(6), 541–557 (1992)CrossRefGoogle Scholar
  54. 54.
    Murakami, S., Okada, Y. Contributions of principal neocortical neurons to magnetoencephalography and electroencephalography signals. J Physiol 575(Pt 3), 925–936 (2006)CrossRefGoogle Scholar
  55. 55.
    Neal, R.M. Bayesian Learning for Neural Networks. Springer, New York; Secaucus, NJ (1996)CrossRefGoogle Scholar
  56. 56.
    Nguyen, N., Milanfar, P., Golub, G. Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement. IEEE Trans Image Process 10(9), 1299–1308 (2001)MathSciNetMATHCrossRefGoogle Scholar
  57. 57.
    Nicholson, C., Llinas, R. Field potentials in the alligator cerebellum and theory of their relationship to Purkinje cell dendritic spikes. J Neurophysiol 34(4), 509–531 (1971)Google Scholar
  58. 58.
    Niedermeyer, E., Lopes da Silva, F. Electroencephalography: Basic Principles, Clinical Applications, and Related Fields. Williams ' Wilkins, Philadelphia, PA (2005)Google Scholar
  59. 59.
    Nummenmaa, A., Auranen, T., Hamalainen, M.S., Jaaskelainen, I.P., Lampinen, J., Sams, M., Vehtari, A. Hierarchical Bayesian estimates of distributed MEG sources: Theoretical aspects and comparison of variational and MCMC methods. NeuroImage 35(2), 669–685 (2007)CrossRefGoogle Scholar
  60. 60.
    Nummenmaa, A., Auranen, T., Hamalainen, M.S., Jaaskelainen, I.P., Sams, M., Vehtari, A., Lampmen, J. Automatic relevance determination based hierarchical Bayesian MEG inversion in practice. NeuroImage 37(3), 876–889 (2007)CrossRefGoogle Scholar
  61. 61.
    Nunez, P.L., Srinivasan, R. Electric Fields of the Brain: The Neurophysics of EEG. Oxford University Press, New York (2006)CrossRefGoogle Scholar
  62. 62.
    Okada, Y. Empirical bases for constraints in current-imaging algorithms. Brain Topogr 5(4), 373–377 (1993)CrossRefGoogle Scholar
  63. 63.
    Okada, Y.C., Wu, J., Kyuhou, S. Genesis of MEG signals in a mammalian CNS structure. Electroencephalogr Clin Neurophysiol 103(4), 474–485 (1997)CrossRefGoogle Scholar
  64. 64.
    Parra, L.C., Spence, C.D., Gerson, A.D., Sajda, P. Recipes for the linear analysis of EEG. NeuroImage 28(2), 326–341 (2005)CrossRefGoogle Scholar
  65. 65.
    Pascual-Marqui, R.D. Standardized low-resolution brain electromagnetic tomography (sLORETA): Technical details. Methods Find Exp Clin Pharmacol 24 Suppl D, 5–12 (2002)Google Scholar
  66. 66.
    Pascual-Marqui, R.D., Lehmann, D., Koenig, T., Kochi, K., Merlo, M.C., Hell, D., Koukkou, M. Low resolution brain electromagnetic tomography (LORETA) functional imaging in acute, neuroleptic-naive, first-episode, productive schizophrenia. Psychiatry Res 90(3), 169–179 (1999)CrossRefGoogle Scholar
  67. 67.
    Penfield, W., Jasper, H.H. Epilepsy and the Functional Anatomy of the Human Brain. Little, Brown, Boston (1954)Google Scholar
  68. 68.
    Phillips, C., Mattout, J., Rugg, M.D., Maquet, P., Friston, K.J. An empirical Bayesian solution to the source reconstruction problem in EEG. NeuroImage 24(4), 997–1011 (2005)CrossRefGoogle Scholar
  69. 69.
    Ramírez, R.R. Neuromagnetic Source Imaging of Spontaneous and Evoked Human Brain Dynamics. PhD thesis, New York University School of Medicine, New York (2005)Google Scholar
  70. 70.
    Ramírez, R.R., Makeig, S. Neuroelectromagnetic source imaging using multiscale geodesic neural bases and sparse Bayesian learning. Proceedings of the 12th Annual Meeting of the Organization for Human Brain Mapping, Florence, Italy (2006)Google Scholar
  71. 71.
    Ramírez, R.R., Makeig, S. Neuroelectromagnetic source imaging of spatiotemporal brain dynamical patterns using frequency-domain independent vector analysis (IVA) and geodesic sparse Bayesian learning (gSBL). Proceedings of the 13th Annual Meeting of the Organization for Human Brain Mapping, Chicago, IL (2007)Google Scholar
  72. 72.
    Ramírez, R.R., Makeig, S. Neuroelectromagnetic source imaging using multiscale geodesic basis functions with sparse Bayesian learning or MAP estimation. Neural Comput (In preparation) (2010)Google Scholar
  73. 73.
    Ramírez, R.R., Wipf, D., Rao, B., Makeig, S. Sparse Bayesian learning for estimating the spatial orientations and extents of distributed sources. Biomag 2006 – Proceedings of the 15th International Conference on Biomagnetism, Vancouver, BC, Canada (2006)Google Scholar
  74. 74.
    Rao, B.D., Engan, K., Cotter, S.F., Palmer, J., Kreutz-Delgado, K. Subset selection in noise based on diversity measure minimization. IEEE Trans Signal Process 51(3), 760–770 (2002)CrossRefGoogle Scholar
  75. 75.
    Rao, B.D., Kreutz-Delgado, K. An affine scaling methodology for best basis selection. IEEE Trans Signal Process 1, 187–202 (1999)MathSciNetCrossRefGoogle Scholar
  76. 76.
    Ribary, U., Ioannides, A.A., Singh, K.D., Hasson, R., Bolton, J.P., Lado, F., Mogilner, A., Llinas, R. Magnetic field tomography of coherent thalamocortical 40-Hz oscillations in humans. Proc Natl Acad Sci USA 88(24), 11037–11041 (1991)CrossRefGoogle Scholar
  77. 77.
    Sarnthein, J., Morel, A., von Stein, A., Jeanmonod, D. Thalamic theta field potentials and EEG: High thalamocortical coherence in patients with neurogenic pain, epilepsy and movement disorders. Thalamus Related Syst 2(3), 231–238 (2003)Google Scholar
  78. 78.
    Sarvas, J. Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. Phys Med Biol 32(1), 11–22 (1987)CrossRefGoogle Scholar
  79. 79.
    Sato, M., Yoshioka, T., Kajihara, S., Toyama, K., Naokazu, G., Doya, K., Kawatoa, M. Hierarchical Bayesian estimation for MEG inverse problem. NeuroImage 23, 806–826 (2004)CrossRefGoogle Scholar
  80. 80.
    Scherg, M., Berg, P. Use of prior knowledge in brain electromagnetic source analysis. Brain Topogr 4(2), 143–150 (1991)CrossRefGoogle Scholar
  81. 81.
    Schimpf, P.H., Liu, H., Ramon, C., Haueisen, J. Efficient electromagnetic source imaging with adaptive standardized LORETA/FOCUSS. IEEE Trans Biomed Eng 52(5), 901–908 (2005)CrossRefGoogle Scholar
  82. 82.
    Schmidt, D.M., George, J.S., Wood, C.C. Bayesian inference applied to the electromagnetic inverse problem. Hum Brain Mapp 7(3), 195–212 (1999)CrossRefGoogle Scholar
  83. 83.
    Sekihara, K., Nagarajan, S., Poeppel, D., Miyashita, Y. Time-frequency MEG-music algorithm. IEEE Trans Med Imaging 18(1), 92–97 (1999)CrossRefGoogle Scholar
  84. 84.
    Tallon-Baudry, C., Bertrand, O., Delpuech, C., Pernier, J. Stimulus specificity of phaselocked and non-phase-locked 40 Hz visual responses in human. J Neurosci 16(13), 4240–4249 (1996)Google Scholar
  85. 85.
    Tang, A.C., Pearlmutter, B.A., Malaszenko, N.A., Phung, D.B., Reeb, B.C. Independent components of magnetoencephalography: Localization. Neural Comput 14(8), 1827–1858 (2002)MATHCrossRefGoogle Scholar
  86. 86.
    Taulu, S., Kajola, M., Simola, J. Suppression of interference and artifacts by the signal space separation method. Brain Topogr 16(4), 269–275 (2004)CrossRefGoogle Scholar
  87. 87.
    Taylor, J.G., Ioannides, A.A., Muller-Gartner, H.W. Mathematical analysis of lead field expansions. IEEE Trans Med Imaging 18(2), 151–163 (1999)CrossRefGoogle Scholar
  88. 88.
    Tesche, C.D. Non-invasive detection of ongoing neuronal population activity in normal human hippocampus. Brain Res 749(1), 53–60 (1997)CrossRefGoogle Scholar
  89. 89.
    Tipping, M.E. Sparse Bayesian learning and the relevance vector machine. J Mach Learn Res 1, 211–244 (2001)MathSciNetMATHGoogle Scholar
  90. 90.
    Tuch, D.S., Wedeen, V.J., Dale, A.M., George, J.S., Belliveau, J.W. Conductivity tensor mapping of the human brain using diffusion tensor MRI. Proc Natl Acad Sci USA 98(20), 11697–11701 (2001)CrossRefGoogle Scholar
  91. 91.
    Ulbert, I., Halgren, E., Heit, G., Karmos, G. Multiple microelectrode-recording system for human intracortical applications. J Neurosci Methods 106(1), 69–79 (2001)CrossRefGoogle Scholar
  92. 92.
    Uusitalo, M.A., Ilmoniemi, R.J. Signal-space projection method for separating MEG or EEG into components. Med Biol Eng Comput 35(2), 135–140 (1997)CrossRefGoogle Scholar
  93. 93.
    Uutela, K., Hamalainen, M., Salmelin, R. Global optimization in the localization of neuromagnetic sources. IEEE Trans Biomed Eng 45(6), 716–723 (1998)CrossRefGoogle Scholar
  94. 94.
    Uutela, K., Hamalainen, M., Somersalo, E. Visualization of magnetoencephalographic data using minimum current estimates. NeuroImage 10(2), 173–180 (1999)CrossRefGoogle Scholar
  95. 95.
    Van Veen, B.D., van Drongelen, W., Yuchtman, M., Suzuki, A. Localization of brain electrical activity via linearly constrained minimum variance spatial filtering. IEEE Trans Biomed Eng 44(9), 867–880 (1997)CrossRefGoogle Scholar
  96. 96.
    Volkmann, J., Joliot, M., Mogilner, A., Ioannides, A.A., Lado, F., Fazzini, E., Ribary, U., Llinas, R. Central motor loop oscillations in parkinsonian resting tremor revealed by magnetoencephalography. Neurology 46(5), 1359–1370 (1996)CrossRefGoogle Scholar
  97. 97.
    Vrba, J., Robinson, S.E. Signal processing in magnetoencephalography. Methods 25(2), 249–271 (2001)CrossRefGoogle Scholar
  98. 98.
    Wang, J.Z., Williamson, S.J., Kaufman, L. Magnetic source images determined by a leadfield analysis: The unique minimum-norm least-squares estimation. IEEE Trans Biomed Eng 39(7), 665–675 (1992)CrossRefGoogle Scholar
  99. 99.
    Wipf, D.P., Ramírez, R.R., Palmer, J.A., Makeig, S., Rao, B.D. Analysis of empirical Bayesian methods for neuroelectromagnetic source localization. In: Schlkopf, B., Platt, J., Hoffman, T. (eds.), Advances in Neural Information Processing Systems, vol. 19. MIT Press, Cambridge, MA (2007)Google Scholar
  100. 100.
    Wipf, D.P., Rao, B.D. Sparse Bayesian learning for basis selection. IEEE Trans Signal Process 52, 2153–2164 (2004)MathSciNetCrossRefGoogle Scholar
  101. 101.
    Wipf, D.P., Rao, B.D. An empirical Bayesian strategy for solving the simultaneous sparse approximation problem. IEEE Trans Signal Process 55(7), 3704–3716 (2007)MathSciNetCrossRefGoogle Scholar
  102. 102.
    Wolters, C.H., Anwander, A., Tricoche, X., Weinstein, D., Koch, M.A., MacLeod, R.S. Influence of tissue conductivity anisotropy on EEG/MEG field and return current computation in a realistic head model: A simulation and visualization study using high-resolution finite element modeling. NeuroImage 30(3), 813–826 (2006)CrossRefGoogle Scholar
  103. 103.
    Zimmerman, J.E., Frederick, N.V. Miniature ultrasensitive superconducting magnetic gradiometer and its use in cardiography and other applications. Appl Phys Lett 19(1), 16–19 (1971)CrossRefGoogle Scholar
  104. 104.
    Zumer, J.M., Attias, H.T., Sekihara, K., Nagarajan, S.S. A probabilistic algorithm integrating source localization and noise suppression for MEG and EEG data. NeuroImage 37, 102–115 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.MEG Program, Department of NeurologyMedical College of Wisconsin and Froedtert HospitalMilwaukeeUSA
  2. 2.Biomagnetic Imaging LaboratoryUniversity of California San FranciscoSan FranciscoUSA

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