Effect of Head Shape Variations Among Individuals on the EEG/MEG Forward and Inverse Problems

We study the effect of the head shape variations on the EEG/magnetoencephalography (MEG) forward and inverse problems. We build a random head model such that each sample represents the head shape of a different individual and solve the forward problem assuming this random head model, using a polynomial chaos expansion. The random solution of the forward problem is then used to quantify the effect of the geometry when the inverse problem is solved with a standard head model. The results derived with this approach are valid for a continuous family of head models, rather than just for a set of cases. The random model consists of three random surfaces that define layers of different electric conductivity, and we built an example based on a set of 30 deterministic models from adults. Our results show that for a dipolar source model, the effect of the head shape variations on the EEG/MEG inverse problem due to the random head model is slightly larger than the effect of the electronic noise present in the sensors. The variations in the EEG inverse problem solutions are due to the variations in the shape of the volume conductor, while the variations in the MEG inverse problem solutions, larger than the EEG ones, are caused mainly by the variations of the absolute position of the sources in a coordinate system based on anatomical landmarks, in which the magnetometers have a fixed position.

[1]  J. P. Ary,et al.  Location of Sources of Evoked Scalp Potentials: Corrections for Skull and Scalp Thicknesses , 1981, IEEE Transactions on Biomedical Engineering.

[2]  William H. Press,et al.  Numerical recipes , 1990 .

[3]  Ting-Zhu Huang,et al.  Estimation of ||A-1||∞ and the smallest singular value , 2008, Comput. Math. Appl..

[4]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[5]  C. Grimbergen,et al.  Investigation into the origin of the noise of surface electrodes , 2002, Medical and Biological Engineering and Computing.

[6]  Katrina Wendel,et al.  Correlation between Live and Post Mortem Skull Conductivity Measurements , 2006, 2006 International Conference of the IEEE Engineering in Medicine and Biology Society.

[7]  Henryk Wozniakowski,et al.  Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems , 1995, J. Complex..

[8]  H. Spekreijse,et al.  Mathematical dipoles are adequate to describe realistic generators of human brain activity , 1988, IEEE Transactions on Biomedical Engineering.

[9]  B.N. Cuffin,et al.  Effects of head shape on EEGs and MEGs , 1990, IEEE Transactions on Biomedical Engineering.

[10]  W. van Drongelen,et al.  Estimation of in vivo brain-to-skull conductivity ratio in humans. , 2006, Applied physics letters.

[11]  H. Wilf.  Mathematics for the Physical Sciences , 1976 .

[12]  Shizuo Kakutani,et al.  Spectral Analysis of Stationary Gaussian Processes , 1961 .

[13]  J. D. Munck.  A linear discretization of the volume conductor boundary integral equation using analytically integrated elements (electrophysiology application) , 1992 .

[14]  Amanda L. Kaas,et al.  A fast method to derive realistic BEM models for E/MEG source reconstruction , 2001, IEEE Trans. Biomed. Eng..

[15]  G. Huiskamp,et al.  The need for correct realistic geometry in the inverse EEG problem , 1999, IEEE Transactions on Biomedical Engineering.

[16]  B.N. Cuffin,et al.  Effects of local variations in skull and scalp thickness on EEG's and MEG's , 1993, IEEE Transactions on Biomedical Engineering.

[17]  M. E. Spencer,et al.  Error bounds for EEG and MEG dipole source localization. , 1993, Electroencephalography and clinical neurophysiology.

[18]  Thom F. Oostendorp,et al.  The conductivity of the human skull: results of in vivo and in vitro measurements , 2000, IEEE Transactions on Biomedical Engineering.

[19]  Carlos H. Muravchik,et al.  EEG/MEC error bounds for a static dipole source with a realistic head model , 2001, IEEE Trans. Signal Process..

[20]  Carlos H. Muravchik,et al.  Effects of geometric head model perturbations on the EEG forward and inverse problems , 2006, IEEE Transactions on Biomedical Engineering.

[21]  S. Sato,et al.  How well does a three-sphere model predict positions of dipoles in a realistically shaped head? , 1993, Electroencephalography and clinical neurophysiology.

[22]  J J Riera,et al.  Evaluation of inverse methods and head models for EEG source localization using a human skull phantom , 2001, Physics in medicine and biology.

[23]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[24]  Onno W. Weier,et al.  On the numerical accuracy of the boundary element method (EEG application) , 1989, IEEE Transactions on Biomedical Engineering.

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

[26]  Viktor Winschel,et al.  Estimation with Numerical Integration on Sparse Grids , 2006 .

[27]  L. Heller,et al.  Evaluation of boundary element methods for the EEG forward problem: effect of linear interpolation , 1995, IEEE Transactions on Biomedical Engineering.

[28]  Lourens J. Waldorp,et al.  Spatiotemporal EEG/MEG source analysis based on a parametric noise covariance model , 2002, IEEE Transactions on Biomedical Engineering.

[29]  B. Radich,et al.  EEG dipole localization bounds and MAP algorithms for head models with parameter uncertainties , 1995, IEEE Transactions on Biomedical Engineering.

[30]  David M. Allen,et al.  The Relationship Between Variable Selection and Data Agumentation and a Method for Prediction , 1974 .

[31]  N. Wiener.  The Homogeneous Chaos , 1938 .

[32]  Shuang-Ren Zhao,et al.  Interpolation of Magnetic Fields and their Gradients for MEG Data with 3D Spline Functions , 1996, Bildverarbeitung für die Medizin.

[33]  M. Fuchs,et al.  A standardized boundary element method volume conductor model , 2002, Clinical Neurophysiology.

[35]  J. Pernier,et al.  A systematic evaluation of the spherical model accuracy in EEG dipole localization. , 1997, Electroencephalography and clinical neurophysiology.