A standardized boundary element method volume conductor model
Introduction
The boundary element method (BEM) improves the localization accuracy of bioelectric source reconstruction results, as compared to simple spherical shell models, by approximating the volume conductor properties of realistically shaped compartments of isotropic and homogeneous conductivities. The anisotropy and fine structure of the real tissue surrounding the electric sources to be reconstructed are purposefully neglected. These factors can in principle be treated by finite element methods (FEM), but they suffer from large computational effort and in vivo conductivity and anisotropy parameters that are mostly unknown. The BEM is a compromise between over-simplified, spherically symmetric models, that reflect only mean conductivities but not the shape of the compartments, and overly complex models for which detailed real tissue data are not available (Geddes and Baker, 1963, Law, 1993, van Burik and Peters, 2000).
Many authors have already discussed and improved the BEM (Geselowitz, 1967, Hämäläinen and Sarvas, 1989, Meijs et al., 1989, Oostendorp and van Oosterom, 1989, Cuffin, 1990, Fletcher et al., 1995, Yvert et al., 1995, Ferguson and Stroink, 1997, Fuchs et al., 1998, Fuchs et al., 2001, Musha and Okamoto, 1999, Frijns et al., 2000). The BEM requires a description of the compartment surfaces by closed triangle meshes with a limited number of nodes. It is limited by the computational power and the memory requirement for storing the huge BEM system matrix. The matrix size is proportional to the square of the total number of nodes, and the computational effort to decompose the BEM matrix is proportional to the third power of the number of nodes, whereas the accuracy of the BEM is roughly proportional to the number of nodes representing the realistic model. The computation time needed for a forward calculation of the electric potential distribution at the given electrode positions is also proportional to the number of nodes and to the number of electrodes.
In this investigation, we developed a standardized BEM model (sBEM) from averaged magnetic resonance imaging (MRI) data (Montreal Neurological Institute), having computed and stored the transfer matrix for all nodes of the outermost (skin) compartment. The measured electrode positions were transformed and scaled to the sBEM model coordinate system, which is aligned by the PreAuricular points and the Nasion (PAN system). The electric potential values at the transformed electrode positions were calculated by linear interpolation from the nodes of the sBEM model skin compartment. Finally the source reconstruction results were transformed back to the original electrode coordinate system by applying the inverse transformations.
By doing so we eliminated the need to segment an individual subject's anatomical data into the 3 main BEM model compartments, which requires sophisticated algorithms or manual interaction. If overlay of the source reconstruction results with the individual anatomy is not required, the subject's anatomical image data are not at all needed. Furthermore the time consuming BEM matrix setup and decomposition steps can be omitted. Thus an easier and much faster access to realistically shaped volume conductor models can be achieved.
Section snippets
The boundary element method
The boundary element method (BEM) allows to calculate the electric potential V of a current source in an inhomogeneous conductor by solving the following integral equation, if the conducting object is divided by closed surfaces Si (i=1,…,ns) into ns compartments, each having a different enclosed isotropic conductivity σjin. The electric potential at position is then given by (Geselowitz, 1967, Sarvas, 1987):with V0 representing the
Simulations
The spatial distributions of the localization errors for both sBEM and spherical volume conductor models using simulated data are displayed in Fig. 6. The localization errors are represented by the radii of circles centered at the true positions of the test-dipoles with the reference BEM model. For better visibility the radii are downscaled by a factor of 5 to 20% of their real size. The mean location errors averaged over all 4156 randomly distributed test-dipole positions are 6.9 mm for the
Discussion
A new realistically shaped volume conductor approximation for EEG source reconstruction is presented. The 3 compartments of the standardized BEM model are segmented from an averaged MR dataset (Fig. 1, Fig. 2). The transfer matrix for all nodes of the skin compartment is stored. The measured electrodes positions are transformed to the sBEM coordinate system by PAN landmarks and an overall scaling factor. The transformed electrode positions are projected to the closest triangles of the outer
References (24)
- et al.
Estimation of the electric conductivity from scalp measurements: feasibility and application to source localization
Clin Neurophysiol
(2000) - et al.
Boundary element method volume conductor models for EEG source reconstruction
Clin. Neurophysiology
(2001) - et al.
Improved dipole localization using local mesh refinement of realistic head geometries
Electroenceph clin Neurophysiol
(1995) Effects of head shape on EEGs and MEGs
IEEE Trans Biomed Eng
(1990)- et al.
A complete linear discretization for calculating the magnetic field using the boundary element method
IEEE Trans Biomed Eng
(1994) - et al.
Factors affecting the accuracy of the boundary element method in the forward problem I: calculating surface potentials
IEEE Trans Biomed Eng
(1997) - et al.
Improved method for computation of potentials in a realistic head shape model
IEEE Trans Biomed Eng
(1995) - et al.
Improving the accuracy of the boundary element method by the use of second-order interpolation functions
IEEE Trans Biomed Eng
(2000) - et al.
An improved boundary element method for realistic volume-conductor modeling
IEEE Trans Biomed Eng
(1998) - et al.
The specific resistance of biological material, a compendium of data for the biomedical engineer and physiologist
Med Biol Eng
(1963)
On bioelectric potentials in an inhomogeneous volume conductor
Biophys J
Realistic conductivity geometry model of the human head for interpretation of neuromagnetic data
IEEE Trans Biomed Eng
Cited by (806)
DCT based multi-head attention-BiGRU model for EEG source location
2024, Biomedical Signal Processing and ControlThe effects of synchronous and asynchronous steady-state auditory-visual motion on EEG characteristics in healthy young adults
2024, Expert Systems with ApplicationsA spontaneous dissociative episode during an EEG experiment
2024, Brain and Cognition