Anatomically Informed Basis Functions for EEG Source Localization: Combining Functional and Anatomical Constraints

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.

[1]  A. Dale,et al.  Improved Localizadon of Cortical Activity by Combining EEG and MEG with MRI Cortical Surface Reconstruction: A Linear Approach , 1993, Journal of Cognitive Neuroscience.

[2]  G. Backus,et al.  Uniqueness in the inversion of inaccurate gross Earth data , 1970, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[3]  M Wagner,et al.  Improving source reconstructions by combining bioelectric and biomagnetic data. , 1998, Electroencephalography and clinical neurophysiology.

[4]  M. Scherg,et al.  Brain source imaging of focal and multifocal epileptiform EEG activity , 1994, Neurophysiologie Clinique/Clinical Neurophysiology.

[5]  J. Fermaglich.  Electric Fields of the Brain: The Neurophysics of EEG , 1982 .

[6]  A K Liu,et al.  Spatiotemporal imaging of human brain activity using functional MRI constrained magnetoencephalography data: Monte Carlo simulations. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[7]  A. Dale,et al.  Cortical Surface-Based Analysis II: Inflation, Flattening, and a Surface-Based Coordinate System , 1999, NeuroImage.

[8]  A. S. Ferguson,et al.  Factors affecting the accuracy of the boundary element method in the forward problem. I. Calculating surface potentials , 1997, IEEE Transactions on Biomedical Engineering.

[9]  Colin M. Brown,et al.  The neurocognition of language , 2000 .

[10]  E. Halgren,et al.  Dynamic Statistical Parametric Mapping Combining fMRI and MEG for High-Resolution Imaging of Cortical Activity , 2000, Neuron.

[11]  M D Rugg.  Convergent approaches to electrophysiological and hemodynamic investigations of memory , 1998, Human brain mapping.

[12]  A. Friederici,et al.  The functional neuroanatomy of novelty processing: integrating ERP and fMRI results. , 1999, Cerebral cortex.

[13]  H. D. Patterson,et al.  Recovery of inter-block information when block sizes are unequal , 1971 .

[14]  Karl J. Friston,et al.  Anatomically Informed Basis Functions , 2000, NeuroImage.

[15]  J. Ashburner,et al.  Multimodal Image Coregistration and Partitioning—A Unified Framework , 1997, NeuroImage.

[16]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[17]  G. V. Simpson,et al.  A test of brain electrical source analysis (BESA): a simulation study. , 1994, Electroencephalography and clinical neurophysiology.

[18]  Robert Plonsey,et al.  Bioelectromagnetism: Principles and Applications of Bioelectric and Biomagnetic Fields , 1995 .

[19]  A M Dale,et al.  Measuring the thickness of the human cerebral cortex from magnetic resonance images. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[20]  Karl J. Friston,et al.  Systematic noise regularisation for linear inverse solution of the source localisation problem in EEG , 2001, NeuroImage.

[21]  D. S. Jones,et al.  Elementary information theory , 1979 .

[22]  C. Michel,et al.  Linear inverse solutions with optimal resolution kernels applied to electromagnetic tomography , 1997, Human brain mapping.

[23]  M. Hämäläinen,et al.  Realistic conductivity geometry model of the human head for interpretation of neuromagnetic data , 1989, IEEE Transactions on Biomedical Engineering.

[24]  Sujit Kumar Mitra,et al.  Theory and Application of Constrained Inverse of Matrices , 1973 .

[25]  Sylvain Baillet,et al.  A Bayesian approach to introducing anatomo-functional priors in the EEG/MEG inverse problem , 1997, IEEE Transactions on Biomedical Engineering.

[26]  R. Aaron,et al.  Maximum entropy method for magnetoencephalography , 1997, IEEE Transactions on Biomedical Engineering.

[27]  R. Leahy,et al.  Multiple Dipole Modeling and Localization from , 1992 .

[28]  M Rugg,et al.  Functional neuroimaging in cognitive neurosicence , 1999 .

[29]  L. Garnero,et al.  Combined MEG and EEG source imaging by minimization of mutual information , 1999, IEEE Transactions on Biomedical Engineering.

[30]  E. Somersalo,et al.  Visualization of Magnetoencephalographic Data Using Minimum Current Estimates , 1999, NeuroImage.

[31]  Rob S. MacLeod,et al.  Inverse electrocardiography by simultaneous imposition of multiple constraints , 1999, IEEE Transactions on Biomedical Engineering.

[32]  D. Lehmann,et al.  Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain. , 1994, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[33]  H. Helmholtz.  Ueber einige Gesetze der Vertheilung elektrischer Ströme in körperlichen Leitern mit Anwendung auf die thierisch‐elektrischen Versuche , 1853 .

[34]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[35]  S. Gonzalez-Andino,et al.  A critical analysis of linear inverse solutions to the neuroelectromagnetic inverse problem , 1998, IEEE Transactions on Biomedical Engineering.

[36]  P Berg,et al.  Multiple source analysis of interictal spikes: goals, requirements, and clinical value. , 1999, Journal of clinical neurophysiology : official publication of the American Electroencephalographic Society.

[37]  Anders M. Dale,et al.  Cortical Surface-Based Analysis I. Segmentation and Surface Reconstruction , 1999, NeuroImage.

[38]  Karl J. Friston,et al.  Human Brain Function , 1997 .

[39]  R. Pascual-Marqui.  Review of methods for solving the EEG inverse problem , 1999 .

[40]  R. Greenblatt.  Probabilistic reconstruction of multiple sources in the bioelectromagnetic inverse problem , 1993 .

[41]  C. Aine,et al.  Multistart Algorithms for MEG Empirical Data Analysis Reliably Characterize Locations and Time Courses of Multiple Sources , 2000, NeuroImage.

[42]  Rolando Grave de Peralta Menendez,et al.  Backus and gilbert method for vector fields , 1999 .

[43]  D. Harville.  Bayesian inference for variance components using only error contrasts , 1974 .

[44]  J. Sarvas.  Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. , 1987, Physics in medicine and biology.

[45]  R. Ilmoniemi,et al.  Magnetoencephalography-theory, instrumentation, and applications to noninvasive studies of the working human brain , 1993 .

[46]  C C Wood,et al.  Mapping function in the human brain with magnetoencephalography, anatomical magnetic resonance imaging, and functional magnetic resonance imaging. , 1995, Journal of clinical neurophysiology : official publication of the American Electroencephalographic Society.