Incorporating and Compensating Cerebrospinal Fluid in Surface-Based Forward Models of Magneto- and Electroencephalography

Abstract

MEG/EEG source imaging is usually done using a three-shell (3-S) or a simpler head model. Such models omit cerebrospinal fluid (CSF) that strongly affects the volume currents. We present a four-compartment (4-C) boundary-element (BEM) model that incorporates the CSF and is computationally efficient and straightforward to build using freely available software. We propose a way for compensating the omission of CSF by decreasing the skull conductivity of the 3-S model, and study the robustness of the 4-C and 3-S models to errors in skull conductivity. We generated dense boundary meshes using MRI datasets and automated SimNIBS pipeline. Then, we built a dense 4-C reference model using Galerkin BEM, and 4-C and 3-S test models using coarser meshes and both Galerkin and collocation BEMs. We compared field topographies of cortical sources, applying various skull conductivities and fitting conductivities that minimized the relative error in 4-C and 3-S models. When the CSF was left out from the EEG model, our compensated, unbiased approach improved the accuracy of the 3-S model considerably compared to the conventional approach, where CSF is neglected without any compensation (mean relative error < 20% vs. > 40%). The error due to the omission of CSF was of the same order in MEG and compensated EEG. EEG has, however, large overall error due to uncertain skull conductivity. Our results show that a realistic 4-C MEG/EEG model can be implemented using standard tools and basic BEM, without excessive workload or computational burden. If the CSF is omitted, compensated skull conductivity should be used in EEG.

Fig 1. Boundary meshes and the resulting four-compartment model.

Below each boundary mesh, the used mesh densities in terms of mean triangle-side length TSL are listed; the TSL of the shown mesh is printed in boldface. EEG electrodes and magnetometer pickup coils are marked with black points and transparent blue squares, respectively.

Fig 2. Example on signal topographies and comparison metrics.

At the top, two example source positions are shown on the cortex model. Below, the EEG and MEG topography maps computed for these sources using four-compartment (reference) and uncompensated three-shell (test) models are visualized; also the values for Relative Error RE and Correlation CC between the reference and test topographies are shown. All EEG plots are in the same scale as well as all the MEG plots. Contour lines have spacing of 0.1 times the maximum absolute value of the strongest topography; zero line is drawn in black, and yellow/red and blue mark positive and negative values, respectively.

Fig 3. Multi-resolution verification of four-compartment head model in MEG (top row) and EEG (bottom row) using LG and LC BEM approaches (red and blue plots).

The plots on the left side show the median and 16^th & 84^th percentiles of the Relative Error (RE) metric computed for all topographies, and the plots on the right show the corresponding plots of the Correlation (CC) metric.

Fig 4. Median RE and CC between the reference four-compartment model and test four-compartment (left) and three-shell (right) models as function of the skull resistivity ratio K for a) MEG and b) EEG.

The black dots show the best values for equivalent K in three-shell models. Note that color scales for MEG and EEG are not the same.

Fig 5. Errors due to skull conductivity mismatch between the reference and test models.

The median, 16^th percentile, and 84^th percentile of RE and CC metrics between the reference four-compartment (4-C) model and test 4-C and three-shell (3-S) models are plotted as function of the skull resistivity ratio K of the reference model. The 4-C and 3-S test models have the overall-best skull resistivity ratios of K_opt = 50 and K_equi = 100, respectively.

Fig 6. Expected RE and CC of four-compartment (4-C) (models 1–5) and three-shell (3-S) test models, when the true skull resistivity ratio is known to be between 20 and 80.

The 4-C test models have the skull resistivity ratio K = K_opt = 50, the 3-S test model has K = K_equi = 100. The plots show the median, 16^th percentile and 84^th percentile of the expected value of metrics for both LG and LC BEMs for different test models. Test models 1–5 are those described in Table 1, and model 3-S is the 3-S model that corresponds to test model 4.

Fig 7. The effect of numerical errors, conductivity errors, and the omission of CSF: expected RE and CC of four-compartment (4-C) and three-shell (3-S) test models for all sources, when the true skull resistivity ratio is known to be between 20 and 80.

Test models are built using the LC BEM. The 4-C test model (model 4 in Table 1 and Fig 6) has the skull resistivity ratio K = K_opt = 50, and the 3-S test model (the same as in Fig 6) has K = K_equi = 100. The numbers below the plots show median value and 16^th & 84^th percentiles of the plotted metrics. Results for MEG and EEG are shown on the left and side of the plot, respectively. The first row contains the RE results and the second row the CC results.