[en] Distributed linear solutions have frequently been used to solve the source localization problem in EEG. Here we introduce an approach based on the weighted minimum norm (WMN) method that imposes constraints using anatomical and physiological information derived from other imaging modalities. The anatomical constraints are used to reduce the solution space a priori by modeling the spatial source distribution with a set of basis functions. These spatial basis functions are chosen in a principled way using information theory. The reduced problem is then solved with a classical WMN method. Further (functional) constraints can be introduced in the weighting of the solution using fMRI brain responses to augment spatial priors. We used simulated data to explore the behavior of the approach over a range of the model's hyperparameters. To assess the construct validity of our method we compared it with two established approaches to the source localization problem, a simple weighted minimum norm and a maximum smoothness (Loreta-like) solution. This involved simulations, using single and multiple sources that were analyzed under different levels of confidence in the priors. (C) 2002 Elsevier Science (USA).
Disciplines :
Neurosciences & behavior
Author, co-author :
Phillips, Christophe ; Université de Liège - ULiège > Centre de recherches du cyclotron
Rugg, Michael D
Friston, Karl J
Language :
English
Title :
Anatomically informed basis functions for EEG source localization : Combining functional and anatomical constraints
Publication date :
July 2002
Journal title :
NeuroImage
ISSN :
1053-8119
eISSN :
1095-9572
Publisher :
Academic Press Inc Elsevier Science, San Diego, United States - California
Aine C., Huang M., Stephen J., Christner R. (2000) Multistart algorithms for MEG empirical data analysis reliably characterize locations and time courses of multiple sources. NeuroImage , doi:10.1006/nimg.2000.0616; 12:159-172.
Ashburner J., Friston K.J. (1997) Multimodal image coregistration and partitioning - A unified framework. NeuroImage , doi:10.1006/nimg.1997.0290; 6:209-217.
Backus G.E., Gilbert J.F. (1970) Uniqueness in the inversion of inacurate gross earth data. Phil. Trans. R. Soc. 266:123-192.
Baillet S., Garnero L. (1997) A Bayesian approach to introducing anatomo-functional priors in the EEG/MEG inverse problem. IEEE Trans. Biomed. Eng. 44:374-385.
Baillet S., Garnero L., Marin G., Hugonin J.-P. (1999) Combined MEG and EEG source imaging by minimization of mutual information. IEEE Trans. Biomed. Eng. 46:522-534.
Brooks D.H., Ahmad G.F., MacLeod R.S., Maratos G.M. (1999) Inverse electrocardiography by simultaneous imposition of multiple constraints. IEEE Trans. Biomed. Eng. 46:3-17.
Dale A.M., Sereno M.I. (1993) Improved localisation of cortical activity by combining EEG and MEG with MRI cortical surface reconstruction: A linear approach. J. Cogn. Neurosci. 5:162-176.
Dale A.M., Liu A.K., Fischl B.R., Buckner R.L., Belliveau J.W., Lewine J.D., Halgren E. (2000) Dynamic statistical parametric mapping: Combining fMRI and MEG for high-resolution imaging of cortical activity. Neurone 26:55-67.
Dempster A.P., Laird N.M., Rubin D.B. (1977) Maximum likelihood estimation from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B 39:1-38.
Ferguson A.S., Stroink G. (1997) Factors affecting the accuracy of the boundary element method in the forward problem - I: Calculating surface potential. IEEE Trans. Biomed. Eng. 44:1139-1155.
Fischl B., Dale A.M. (2000) Mesuring the thickness of the human cerebral cortex from magnetic resonance images. Proc. Natl. Acad. Sci. USA 97:11050-11055.
Frackowiak R.S.J., Friston K.J., Frith C.D., Dolan R., Mazziotta J.C. Human Brain Function, Academic Press, San Diego; 1997.
Fuchs M., Wagner M., Wischmann H.-A., Köhler T., Tiessen A., Drenckhahn R., Buchner H. (1998) Improving source reconstructions by combining bioelectric and biomagnetic data. Electroencephalogr. Clin. Neurophysiol. 107:93-111.
George J.S., Aine C.J., Mosher J.C., Ranken D.M., Chlitt H.A., Wood C.C., Lewine J.D., Sanders J.A., Belliveau J.W. (1995) Mapping function in the human brain with MEG, anatomical MRI, and functional MRI. J. Clin. Neurophysiol. 12:406-431.
Goebel R. Brain Voyager 2000, Version 4.22000. http://www.brainvoyager.de
Grave de Peralta Menendez R., Gonzalez Andino S. (1998) A critical analysis of linear inverse solutions to the neuroelectromagnetic inverse problem. IEEE Trans. Biomed. Eng. 45:440-448.
Grave de Peralta Menendez R., Gonzalez Andino S. (1999) Backus and Gilbert method for vector fields. Human Brain Mapp. 7:161-165.
Grave de Peralta Menendez R., Hauk O., Gonzalez Andino S., Vogt H., Michel C. (1997) Linear inverse solutions with optimal resolution kernels applied to electromagnetic tomography. Human Brain Mapp. 5:454-467.
Greenblatt R.E. (1993) Probabilistic reconstruction of multiple sources in the bioelectromagnetic inverse problem. Inverse Problems 9:271-284.
Hämäläinen M.S., Ilmoniemi R.J. (1994) Interpreting magnetic fields of the brain: Minimum norm estimates. Med. Biol. Eng. Comput. 32:35-42.
Hämäläinen M.S., Sarvas J. (1989) Realistic conductivity geometry model of the human head for interpretation of neuromagnetic data. IEEE Trans. Biomed. Eng. 36:165-171.
Hämäläinen M.S., Hari R., Ilmoniemi R.J., Knuutila J., Lounasmaa O.V. (1993) Magentoencephalography - Theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev. Modern Phys. 65:413-497.
Harville D.A. (1974) Bayesian inference for variance components using only error contrasts. Biometrika 61:383-385.
Huang M., Aaron R., Shiffman C.A. (1997) Maximum entropy method for magnetoencephalography. IEEE Trans. Biomed. Eng. 44:98-102.
Jones D.S. Elementary Information Theory, Clarendon, Oxford; 1979.
Liu A.K., Belliveau J.W., Dale A.M. (1998) Spatiotemporal imaging of human brain activity using functional MRI constrained magentoencephalography data: Monte Carlo simulations. Proc. Nat. Acad. Sci. USA 95:8945-8950.
Malmivuo J., Plonsey R. Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields, Oxford Univ. Press, London; 1995.
Miltner W., Braun C., Johnson R., Simpson G.V., Ruchkni D.S. (1994) A test of brain electrical source analysis (BESA): A simulation study. Electroencephalogr. Clin. Neurophysiol. 91:295-310.
Mosher J.C., Lewis P.S., Leahy R.M. (1992) Multiple dipole modelling and localization from spatio-temporal MEG data. IEEE Trans. Biomed. Eng. 39:541-557.
Nunez P.L. Electric Fields of the Brain: The Neurophysics of EEG, Oxford Univ. Press, New York; 1981.
Opitz B., Mecklinger A., Friederici A.D., Von Cramon D.Y. (1999) The functional neuroanatomy of novelty processing: Integrating ERP and fMRI results. Cerebral Cortex 9:379-391.
Pascual-Marqui R.D. (1995) Reply to comments by M. Hämäläinen, R. Ilmoniemi and P. Nunez. Source Localization: Continuing Discussion of the Inverse Prolem , W. Skrandies, Ed. ISBET Newsletter, No. 6; 16-28.
Pascual-Marqui R.D. (1999) Review of methods for solving the EEG inverse problem. Int. J. Bioelectromagn. 1:75-86.
Pascual-Marqui R.D., Michel C.M., Lehmann D. (1994) Low resolution electromagnetic tomography: A new method for localizing electrical activity in the brain. Int. J. Psychophysiol. 18:49-65.
Patterson H.D., Thompson R. (1971) Recovery of inter-block information when block sizes are unequal. Biometrika 58:545-554.
Perona P., Malik J. (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intelligence 12:629-639.
Phillips C., Rugg M.D., Friston K.J. Systematic Noise Regularisation for Linear Inverse Solution of the Source Localisation Problem in EEG2002.
Rao C.R., Mitra S.K. (1973) Theory and application of constrained inverse of matrices. SIAM J. Appl. Math. 24:473-488.
Rugg M.D. (1998) Convergent approaches to electrophysiological and haemodynamics investigations of memory. Human Brain Mapp. 6:394-398.
Rugg M.D. (1999) Functional neuroimaging in cognitive neuroscience. The Neurocognition of Language , C. M. Brown and P. Hagoort, Eds. Oxford Univ. Press, Oxford; 15-36.
Sarvas J. (1987) Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. Phys. Med. Biol. 32:11-22.
Scherg M., Ebersole J.S. (1994) Brain source imaging of focal and multifocal epileptiform EEG activity. Clin. Neurophysiol. 24:51-60.
Scherg M., Bast T., Berg P. (1999) Multiple source analysis of interictal spikes: Goals, requirements, and clinical value. J. Clin. Neurophysiol. 16:214-224.
Tikhonov A.N., Arsenin V.Y. Solutions of Ill-Posed Problems, Wiley, New York; 1977.
Uutela K., Hämäläinen M.S., Somersalo E. (1999) Visualization of magnetoencephalographic data using minimum current estimates. NeuroImage , doi:10.1006/nimg.1999.0454; 10:173-180.
Von Helmholtz H.L.F. (1853) Ueber einige gesetze der vertheilung elektrischer ströme in köperlichen leitern mit anwendung auf die thierisch-elektrischen versuche. Ann. Phys. Chem. 89:211-233.