Hierarchical Bayesian inference for the EEG inverse problem using realistic FE head models: Depth localization and source separation for focal primary currents

NeuroImage

Volumn 61, Issue 4, 2012, Pages 1364-1382

  Lucka, Felix ^a   Pursiainen, Sampsa ^b   Burger, Martin ^a   Wolters, Carsten H ^a  

^a UNIVERSITY OF MÜNSTER   (Germany)

^b TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

Author keywords

Current density reconstruction; Depth localization; EEG inverse problem; Fully Bayesian inference; Hierarchical Bayesian modeling; Wasserstein distance

Indexed keywords

ARTICLE; BAYES THEOREM; BRAIN DEPTH STIMULATION; ELECTROENCEPHALOGRAM; FINITE ELEMENT ANALYSIS; HUMAN; INTERMETHOD COMPARISON; MAGNETOENCEPHALOGRAPHY; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; NEUROIMAGING; NEUROPHYSIOLOGY; NUCLEAR MAGNETIC RESONANCE IMAGING; PRIORITY JOURNAL; SYSTEMATIC ERROR; VALIDATION PROCESS;

ALGORITHMS; ANIMALS; BAYES THEOREM; BRAIN; BRAIN MAPPING; ELECTROENCEPHALOGRAPHY; HUMANS; MAGNETOENCEPHALOGRAPHY; MODELS, NEUROLOGICAL; NEUROPHYSIOLOGY; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 84861361414     PISSN: 10538119     EISSN: 10959572     Source Type: Journal    
DOI: 10.1016/j.neuroimage.2012.04.017     Document Type: Article

References (101)

1. Acar Z.A., Makeig S. Neuroelectromagnetic forward head modeling toolbox. J. Neurosci. Methods 2010, 190:258-270.
2. Ahlfors S.P., Ilmoniemi R.J., Hämäläinen M. Estimates of visually evoked cortical currents. Electroencephalogr. Clin. Neurophysiol. 1992, 82:225-236.
3. Akhtari M., Bryant H., Mamelak A., Flynn E., Heller L., Shih J., Mandelkem M., Matlachov A., Ranken D.M., Best E., et al. Conductivities of three-layer live human skull. Brain Topogr. 2002, 14:151-167.
4. Ambrosio L., Gigli N., Savaré G. Gradient Flows in Metric Spaces and in the Spaces of Probability Measures 2008, Birkhäuser, Basel, 2nd edition.
5. Aubert G., Kornprobst P. Mathematical problems in image processing. Applied Mathematical Sciences 2006, vol. 147. Springer. 2nd edition.
6. Baillet S., Garnero L. A Bayesian approach to introducing anatomo-functional priors in the EEG/MEG inverse problem. IEEE Trans. Biomed. Eng. 1997, 44:374-385.
7. Bertrand O., Thévenet M., Perrin F. 3D finite element method in brain electrical activity studies. Biomagnetic Localization and 3D Modelling 1991, 154-171. Helsinki University of Technology, Helsinki. J. Nenonen, H. Rajala, T. Katila (Eds.).
8. Bruno P., Vatta F., Mininel S., Inchingolo P. Head model extension for the study of bioelectric phenomena. Biomed. Sci. Instrum. 2003, 39:59-64.
9. Bruno P., Vatta F., Minimel S., Inchingolo P. Referenced EEG and head volume conductor model: geometry and parametrical setting. Conf Proc IEEE Eng Med Biol Soc, San Francisco, USA 2004.
10. Buchner H., Knoll G., Fuchs M., Rienäcker A., Beckmann R., Wagner M., Silny J., Pesch J. Inverse localization of electric dipole current sources in finite element models of the human head. Electroencephalogr. Clin. Neurophysiol. 1997, 102:267-278.
11. Calvetti D., Somersalo E. A Gaussian hypermodel to recover blocky objects. Inverse Probl. 2007, 23:733-754.
12. Calvetti D., Somersalo E. Introduction to Bayesian scientific computing. Surveys and Tutorials in the Applied Mathematical Sciences. 2007, vol. 2. Springer, New York.
13. Calvetti D., Somersalo E. Hypermodels in the Bayesian imaging framework. Inverse Probl. 2008, 24:034013. (20 pp.).
14. Calvetti D., Somersalo E. Recovery of shapes: hypermodels and Bayesian learning. J. Phys. Conf. Ser. 2008, 012014. IOP Publishing.
15. Calvetti D., Hakula H., Pursiainen S., Somersalo E. Conditionally Gaussian hypermodels for cerebral source localization. SIAM J. Imaging Sci. 2009, 2:879-909.
16. Dalal S., Guggisberg A., Edwards E., Sekihara K., Findlay A., Canolty R., Berger M., Knight R., Barbaro N., Kirsch H., Nagarajan S. Five-dimensional neuroimaging: localization of the time-frequency dynamics of cortical activity. NeuroImage 2008, 40:1686-1700.
17. Dalal S., Jerbi K., Bertrand O., Adam C., Ducorps A., Schwartz D., Garnero L., Baillet S., Martinerie J., Lachaux J. Insights from simultaneous recording of MEG and intracranial EEG. Front. Neurosci. Conference Abstract: Biomag 2010 - 17th International Conference on Biomagnetism 2010.
18. Dale A.M., Sereno M.I. Improved localization of cortical activity by combining EEG and MEG with MRI cortical surface reconstruction: a linear approach. J. Cogn. Neurosci. 1993, 5:162-176.
19. Dannhauer M., Lanfer B., Wolters C., Knösche T. Modeling of the human skull in EEG source analysis. Hum. Brain Mapp. 2011, 32:1383-1399.
20. de Munck J.C., van Dijk B.W., Spekreijse H. Mathematical dipoles are adequate to describe realistic generators of human brain activity. IEEE Trans. Biomed. Eng. 1988, 35:960-966.
21. Drechsler F., Wolters C.H., Dierkes T., Si H., Grasedyck L. A full subtraction approach for finite element method based source analysis using constrained Delaunay tetrahedralisation. NeuroImage 2009, 46:1055-1065.
22. Durka P.J., Matysiak A., Montes E.M., Sosa P.V., Blinowska K.J. Multichannel matching pursuit and EEG inverse solutions. J. Neurosci. Methods 2005, 148:49-59.
23. Ebersole J.S., Ebersole S.M. Combining MEG and EEG source modeling in epilepsy evaluations. J. Clin. Neurophysiol. 2010, 27:360-371.
24. Engl H., Hanke-Bourgeois M., Neubauer A. Regularization of inverse problems. Mathematics and Its Applications 1996, Springer, Netherland, Berlin.
25. Friston K.J., Mattout J., Trujillo-Barreto N.J., Ashburner J., Penny W.D. Variational free energy and the Laplace approximation. NeuroImage 2007, 34:220-234.
26. Friston K.J., Harrison L., Daunizeau J., Kiebel S.J., Phillips C., Trujillo-Barreto N.J., Henson R.N., Flandin G., Mattout J. Multiple sparse priors for the M/EEG inverse problem. NeuroImage 2008, 39:1104-1120.
27. Fuchs M., Drenckhahn R., Wischmann H., Wagner M. An improved boundary element method for realistical volume conductor modeling. IEEE Trans. Biomed. Eng. 1998, 45:980-997.
28. Fuchs M., Wagner M., Köhler T., Wischmann H.A. Linear and nonlinear current density reconstructions. J. Clin. Neurophysiol. 1999, 16:267.
29. Galka A., Yamashita O., Ozaki T., Biscay R., Valdés-Sosa P. A solution to the dynamical inverse problem of EEG generation using spatiotemporal Kalman filtering. NeuroImage 2004, 23:435-453.
30. Gelman A., Carlin J.B., Stern H.S., Rubin D.B., Gelman A., Carlin J.B., Stern H.S., Rubin D.B. Bayesian data analysis. Chapman and Hall/CRC Texts in Statistical Science 2003, CRC Press, 2nd edition. 2nd edition.
31. 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. 1998, 45:827-838.
32. Gramfort A., Strohmeier D., Haueisen J., Hämäläinen M., Kowalski M. Functional brain imaging with M/EEG using structured sparsity in time-frequency dictionaries. Inf. Process. Med. Imaging 2011, 600-611. Springer.
33. Grave de Peralta R., Hauk O., Gonzalez S.L. The neuroelectromagnetic inverse problem and the zero dipole localization error. Comput. Intell. Neurosci. 2009, 11 pages. doi:10.1155/2009/659247 (Article ID 659247).
34. Greenblatt R.E., Ossadtchi A., Pflieger M.E. Local linear estimators for the bioelectromagnetic inverse problem. IEEE Trans. Signal Process. 2005, 53:3403-3412.
35. Hallez, H., 2008. Incorporation of Anisotropic Conductivities in EEG Source Analysis. Ph.D. thesis. Faculteit Ingenieurswetenschappen, Universiteit Gent, Belgium.
36. Hämäläinen M., Ilmoniemi R.J. Interpreting measured magnetic fields of the brain: minimum norm estimates of current distributions. Helsinki University of Technology, Technical Report TKK-F-A559 1984.
37. Hämäläinen M., Ilmoniemi R.J. Interpreting magnetic fields of the brain: minimum norm estimates. Med. Biol. Eng. Comput. 1994, 32:35-42.
38. Hämäläinen M., Haario H., Lehtinen M. Inference about sources of neuromagnetic fields using Bayesian parameter estimation. Helsinki University of Technology, Technical Report TKK-F-A620 1987.
39. Hämäläinen M., Hari R., Ilmoniemi R.J., Knuutila J., Lounasmaa O.V. Magnetoencephalography - theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev. Mod. Phys. 1993, 65:413-497.
40. Haueisen J., Tuch D.S., Ramon C., Schimpf P.H., Wedeen V.J., George J.S., Belliveau J.W. The influence of brain tissue anisotropy on human EEG and MEG. NeuroImage 2002, 15:159-166.
41. Henson R.N., Mattout J., Phillips C., Friston K.J. Selecting forward models for MEG source-reconstruction using model-evidence. NeuroImage 2009, 46:168-176.
42. Henson R.N., Mouchlianitis E., Friston K.J. MEG and EEG data fusion: simultaneous localisation of face-evoked responses. NeuroImage 2009, 47:581-589.
43. Henson R.N., Flandin G., Friston K.J., Mattout J. A parametric empirical Bayesian framework for fMRI-constrained MEG/EEG source reconstruction. Hum. Brain Mapp. 2010, 31:1512-1531.
44. Hufnagel A., Elger C.E., Pels H., Zentner J., Wolf H.K., Schramm J., Wiestler O.D. Prognostic significance of ictal and interictal epileptiform activity in temporal lobe epilepsy. Epilepsia 1994, 35:1146-1153.
45. Ioannides A.A., Bolton J.P.R., Clarke C.J.S. Continuous probabilistic solutions to the biomagnetic inverse problem. Inverse Probl. 1990, 6:523-542.
46. Janszky J., Jokeit H., Schulz R., Hoppe M., Ebner A. EEG predicts surgical outcome in lesional frontal lobe epilepsy. Neurology 2000, 54:1470-1476.
47. Jun S.C., George J.S., Kim W., Paré-Blagoev J., Plis S.M., Ranken D.M., Schmidt D.M. Bayesian brain source imaging based on combined MEG/EEG and fMRI using MCMC. NeuroImage 2008, 40:1581-1594.
48. Kaipio J.P., Somersalo E. Statistical and computational inverse problems. Applied Mathematical Sciences 2005, vol. 160. Springer, New York.
49. Kantorovich L. On the translocation of masses. Dokl. Akad. Nauk SSSR 1942, 37:227-229.
50. Kantorovich L., Gavurin M. The application of mathematical methods in problems of freight flow analysis. Collection of Problems Concerned with Increasing the Effectiveness of Transports 1949, 110-138.
51. Kiebel S.J., Garrido M.I., Moran R., Chen C.C., Friston K.J. Dynamic causal modeling for EEG and MEG. Hum. Brain Mapp. 2009, 30:1866-1876.
52. Klenke A. Probability Theory: A Comprehensive Course 2008, Springer, London. 1st edition.
53. Kybic J., Clerc M., Abboud T., Faugeras O., Keriven R., Papadopoulo T. A common formalism for the integral formulations of the forward EEG problem. IEEE Trans. Med. Imaging 2005, 24:12-28.
54. Lanfer B., Scherg M., Dannhauer M., Knösche T., Wolters C. Influence of deficiencies in segmenting the skull on EEG source modeling. Proc. of the 16th Annual Meeting of the Organization for Human Brain Mapping, Barcelona, Spain, June 6-10 2010.
55. Lew S., Wolters C.H., Dierkes T., Röer C., MacLeod R.S. Accuracy and run-time comparison for different potential approaches and iterative solvers in finite element method based EEG source analysis. Appl. Numer. Math. 2009, 59:1970-1988.
56. Lin F.H., Witzel T., Ahlfors S.P., Stufflebeam S.M., Belliveau J.W., Hämäläinen M. Assessing and improving the spatial accuracy in MEG source localization by depth-weighted minimum-norm estimates. NeuroImage 2006, 31:160-171.
57. Lucka, F., 2011. Hierarchical Bayesian Approaches to the Inverse Problem of EEG/MEG Current Density Reconstruction. Master's thesis. University of Muenster, Germany.
58. MacKay D. Information Theory, Inference, and Learning Algorithms 2003, Cambridge University Press. 1st edition.
59. Mattout J., Phillips C., Penny W.D., Rugg M.D., Friston K.J. MEG source localization under multiple constraints: an extended Bayesian framework. NeuroImage 2006, 30:753-767.
60. Molins A., Stufflebeam S.M., Brown E.N., Hämäläinen M. Quantification of the benefit from integrating MEG and EEG data in minimum l2-norm estimation. NeuroImage 2008, 42:1069-1077.
61. Mosher J.C., Lewis P.S., Leahy R.M. Multiple dipole modeling and localization from spatio-temporal MEG data. IEEE Trans. Biomed. Eng. 1992, 39:541-557.
62. Niedermeyer E., Lopez da Silva F.L. Electroencephalography: Basic Principles, Clinical Applications, and Related Fields 2004, Lippincot Williams & Wilkins, Philadelphia. 5th edition.
63. Nummenmaa A., Auranen T., Hämäläinen M., Jääskeläinen 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 2007, 35:669-685.
64. Nummenmaa A., Auranen T., Hämäläinen M., Jääskeläinen I.P., Sams M., Vehtari A., Lampinen J. Automatic relevance determination based hierarchical Bayesian MEG inversion in practice. NeuroImage 2007, 37:876-889.
65. Nunez P.L., Srinivasan R. Electric Fields of the Brain: The Neurophysics of EEG 2005, Oxford University Press, USA. 2nd edition.
66. Oostenveld R., Oostendorp T. Validating the boundary element method for forward and inverse EEG computations in the presence of a hole in the skull. Hum. Brain Mapp. 2002, 17:179-192.
67. Ou W., Hämäläinen M.S., Golland P. A distributed spatio-temporal EEG/MEG inverse solver. NeuroImage 2009, 44:932-946.
68. Parkkonen L., Fujiki N., Mäkelä J. Sources of auditory brainstem responses revisited: contribution by magnetoencephalography. Hum. Brain Mapp. 2009, 30:1772-1782.
69. Pascual-Marqui R.D. Review of methods for solving the EEG inverse problem. Int. J. Bioelectromagn. 1999, 1:75-86.
70. Pascual-Marqui R.D. Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details. Methods Find. Exp. Clin. Pharmacol. 2002, 24:5-12. Suppl. D.
71. Phillips C., Mattout J., Rugg M.D., Maquet P., Friston K.J. An empirical Bayesian solution to the source reconstruction problem in EEG. NeuroImage 2005, 24:997-1011.
72. Ramon C., Schimpf P.H., Haueisen J. Influence of head models on EEG simulations and inverse source localizations. Biomed. Eng. Online 2006, 5:10. (13 pp.).
73. Rampp S., Stefan H. Magnetoencephalography in presurgical epilepsy diagnosis. Expert Rev. Med. Devices 2007, 4:335-347.
74. Rullmann M., Anwander A., Dannhauer M., Warfield S.K., Duffy F.H., Wolters C.H. EEG source analysis of epileptiform activity using a 1mm anisotropic hexahedra finite element head model. NeuroImage 2009, 44:399-410.
75. Sander T.H., Knösche TR, Schl̈gl A, Kohl F, Wolters CH, Haueisen J, Trahms L. Recent advances in modeling and analysis of bioelectric and biomagnetic sources. Biomed. Tech. (Berl) 2010, 55:65-76.
76. Santiuste M., Nowak R., Russi A., Tarancon T., Oliver B., Ayats E., Scheler G., Graetz G. Simultaneous magnetoencephalography and intracranial EEG registration: technical and clinical aspects. J. Clin. Neurophysiol. 2008, 25:331-339.
77. Sarvas J. Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. Phys. Med. Biol. 1987, 32:11-22.
78. Sato M., Yoshioka T., Kajihara S., Toyama K., Goda N., Doya K., Kawato M. Hierarchical Bayesian estimation for MEG inverse problem. NeuroImage 2004, 23:806-826.
79. Scherg M., Buchner H. Somatosensory evoked potentials and magnetic fields: separation of multiple source activities. Physiol. Meas. 1993, 14:A35.
80. Scherg M., Cramon D.V. Two bilateral sources of the late AEP as identified by a spatio-temporal dipole model. Electroencephalogr. Clin. Neurophysiol. 1985, 62:32-44.
81. Schiffbauer H., Berger M., Ferrari P., Freudenstein D., Rowley H., Roberts T. Preoperative magnetic source imaging for brain tumor surgery: a quantitative comparison with intraoperative sensory and motor mapping. J. Neurosurg. 2002, 97:1333-1342.
82. Schimpf P., Ramon C., Haueisen J. Dipole models for the EEG and MEG. IEEE Trans. Biomed. Eng. 2002, 49:409-418.
83. Schmitt U., Louis A.K., Wolters C.H., Vauhkonen M. Efficient algorithms for the regularization of dynamic inverse problems: II. Applications. Inverse Probl. 2002, 18:659-676.
84. Sekihara K., Nagarajan S.S. Adaptive spatial filters for electromagnetic brain imaging. Series in Biomedical Engineering 2008, Springer. 1st edition.
85. Sekihara K., Sahani M., Nagarajan S.S. Localization bias and spatial resolution of adaptive and non-adaptive spatial filters for MEG source reconstruction. NeuroImage 2005, 25:1056-1067.
86. Stefan H., Hummel C., Scheler G., Genow A., Druschky K., Tilz C., Kaltenhauser M., Hopfengartner R., Buchfelder M., Romstock J. Magnetic brain source imaging of focal epileptic activity: a synopsis of 455 cases. Brain 2003, 126:2396-2405.
87. Tao J.X., Ray A., Hawes-Ebersole S., Ebersole J.S. Intracranial EEG substrates of scalp EEG interictal spikes. Epilepsia 2005, 46:669-676.
88. Taubin G. A signal processing approach to fair surface design. Proceedings of the 22nd annual conference on Computer graphics and interactive techniques 1995, 351-358. ACM.
89. Trujillo-Barreto N.J., Aubert-Vázquez E., Valdés-Sosa P.A. Bayesian model averaging in EEG/MEG imaging. NeuroImage 2004, 21:1300-1319.
90. Trujillo-Barreto N.J., Aubert-Vázquez E., Penny W.D. Bayesian M/EEG source reconstruction with spatio-temporal priors. NeuroImage 2008, 39:318-335.
91. Vallaghé S., Papadopoulo T. A trilinear immersed finite element method for solving the electroencephalography forward problem. SIAM J. Sci. Comput. 2010, 32:2379-2394.
92. Van den Broek S., Reinders F., Donderwinkel M., Peters M. Volume conduction effects in EEG and MEG. Electroencephalogr. Clin. Neurophysiol. 1998, 106:522-534.
93. Vese L.A., Chan T.F. A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. Comput. Vis. 2002, 50:271-293.
94. Vorwerk, J., 2011. Comparison of Numerical Approaches to the EEG Forward Problem. Master's thesis. University of Muenster, Germany.
95. Wagner M., Fuchs M., Kastner J. Evaluation of sLORETA in the presence of noise and multiple sources. Brain Topogr. 2004, 16:277-280.
96. Wang J.Z., Williamson S.J., Kaufman L. Magnetic source images determined by a lead-field analysis: the unique minimum-norm least-squares estimation. IEEE Trans. Biomed. Eng. 1992, 39:665-675.
97. Weinstein D., Zhukov L., Johnson C. Lead-field bases for electroencephalography source imaging. Ann. Biomed. Eng. 2000, 28:1059-1065. 10.1114/1.1310220.
98. Wipf D., Nagarajan S.S. A unified Bayesian framework for MEG/EEG source imaging. NeuroImage 2009, 44:947-966.
99. Wolters C.H., Grasedyck L., Hackbusch W. Efficient computation of lead field bases and influence matrix for the FEM-based EEG and MEG inverse problem. Inverse Probl. 2004, 20:1099-1116.
100. Wolters C.H., Köstler H., Möller C., Härdtlein J., Anwander A. Numerical approaches for dipole modeling in finite element method based source analysis. Int. Congr. Ser. 2007, 1300:189-192. ISBN-13:978-0-444-52885-8. http://dx.doi.org/10.1016/j.ics.2007.02.014.
101. Wolters C.H., Köstler H., Möller C., Härtlein J., Grasedyck L., 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. 2007, 24-45.