Dipole estimation errors due to differences in modeling anisotropic conductivities in realistic head models for EEG source analysis

To improve the EEG source localization in the brain, the conductivities used in the head model play a very important role. In this study, we focus on the modeling of the anisotropic conductivity of the white matter. The anisotropic conductivity profile can be derived from diffusion weighted magnetic resonance images (DW-MRI). However, deriving these anisotropic conductivities from diffusion weighted MR images of the white matter is not straightforward. In the literature, two methods can be found for calculating the conductivity from the diffusion weighted images. One method uses a fixed value for the ratio of the conductivity in different directions, while the other method uses a conductivity profile obtained from a linear scaling of the diffusion ellipsoid. We propose a model which can be used to derive the conductivity profile from the diffusion tensor images. This model is based on the variable anisotropic ratio throughout the white matter and is a combination of the linear relationship as stated in the literature, with a constraint on the magnitude of the conductivity tensor (also known as the volume constraint). This approach is stated in the paper as approach A. In our study we want to investigate dipole estimation differences due to using a more simplified model for white matter anisotropy (approach B), while the electrode potentials are derived using a head model with a more realistic approach for the white matter anisotropy (approach A). We used a realistic head model, in which the forward problem was solved using a finite difference method that can incorporate anisotropic conductivities. As error measures we considered the dipole location error and the dipole orientation error. The results show that the dipole location errors are all below 10 mm and have an average of 4 mm in gray matter regions. The dipole orientation errors ranged up to 66.4 degrees, and had a mean of, on average, 11.6 degrees in gray matter regions. In a qualitative manner, the results show that the orientation and location error is dependent on the orientation of the test dipole. The location error is larger when the orientation of the test dipole is similar to the orientation of the anisotropy, while the orientation error is larger when the orientation of the test dipole deviates from the orientation of the anisotropy. From these results, we can conclude that the modeling of white matter anisotropy plays an important role in EEG source localization. More specifically, accurate source localization will require an accurate modeling of the white matter conductivity profile in each voxel.