Rapidly recomputable EEG forward models for realistic head shapes

Abstract

With the increasing availability of surface extraction techniques for magnetic resonance and x-ray computed tomography images, realistic head models can be readily generated as forward models in the analysis of electroencephalography (EEG) and magnetoencephalography (MEG) data. Inverse analysis of this data, however, requires that the forward model be computationally efficient. We propose two methods for approximating the EEG forward model using realistic head shapes. The 'sensor-fitted sphere' approach fits a multilayer sphere individually to each sensor, and the 'three-dimensional interpolation' scheme interpolates using a grid on which a numerical boundary element method (BEM) solution has been precomputed. We have characterized the performance of each method in terms of magnitude and subspace error metrics, as well as computational and memory requirements. We have also made direct performance comparisons with traditional spherical models. The approximation provided by the interpolative scheme had an accuracy nearly identical to full BEM, even within 3 mm of the inner skull surface. Forward model computation during inverse procedures was approximately 30 times faster than for a traditional three-shell spherical model. Cast in this framework, high-fidelity numerical solutions currently viewed as computationally prohibitive for solving the inverse problem (e.g. linear Galerkin BEM) can be rapidly recomputed in a highly efficient manner. The sensor-fitting method has a similar one-time cost to the BEM method, and while it produces some improvement over a standard three-shell sphere, its performance does not approach that of the interpolation method. In both methods, there is a one-time cost associated with precomputing the forward solution over a set of grid points.

Hearing Faces: How the Infant Brain Matches the Face It Sees with the Speech It Hears

“…EEG forward modeling was computed using the overlapping-sphere analytical model with three shells (scalp, skull, and CSF). This technique has proven to reach comparable accuracy as numerical Boundary Element Model's, although with greater computational efficiency (Ermer, Mosher, Baillet, & Leah, 2001). All sphere and conductivity parameters were adjusted to the typical infants' head tissue properties which contain more water than the adult head tissues (Gibson, Bayford, & Holder, 2000).…”

Numerical Simulations of EEG Fields in Three Head Models

“…But the draw back of BEM is still the computational cost and the singularity in the vicinity of a surface separating two compartments. Most work of BEM is devoted to improving the accuracy [15]- [17].Currently, the efficiency of EEG forward solutions for non-spherical head models is limited [18]. We use Point of Least Squares (PLS) with compactly supported trial functions.…”

“…Spherical head models [1] - [3] have been commonly used in EEG problems. However, some key drawbacks are shown using spherical head models in [4], [5]. Nonspherical head models, such as ellipsoid models [5]- [7] and realistic head shape [8]- [10] are also applied.…”

Synthetic neuronal datasets for benchmarking directed connectivity metrics

“…As the scope of this work is to simulate a generic EEG signal we can adopt a simpler model of the skull like the three layer sphere with isotropic conductivities (Berg & Scherg, 1994) where the problem of volume conduction is observed. Following (Berg & Scherg, 1994;Zhang, 1995) Details about the computation of the "Berg parameters" can be found in (Zhang, 1995) and other methods for EEG forward models in (Mosher, Leahy & Lewis, 1999;Ermer & Mosher, 2001;Darvas et al, 2004). The Brainstorm application offers several methods for the EEG forward model among others (Tadel et al, 2011).…”