The effect of brain tissue anisotropy on the electric field caused by transcranial electric stimulation: Sensitivity analysis and magnetic resonance electrical impedance tomography

Calculations of the electric field (E-field) are important for addressing the variability in the physical dose of transcranial electric stimulation (tES). These calculations rely on precise knowledge of the individual head and brain anatomy and on choosing the appropriate ohmic conductivities for the different tissue compartments. In particular, the conductivity of brain white matter and to a lesser extent gray matter is anisotropic. Consensus on the importance to account for the conductivity anisotropy of the brain in the E-field calculations is still lacking. Most simulation studies use isotropic conductivities, which avoids the need for diffusion tensor imaging (DTI) data and lowers practical complexity. On the other hand, in magnetic resonance electrical impedance tomography (MREIT) that employs measurements of the tiny magnetic fields caused by the tES-induced current flow, diffusion anisotropy measured by DTI has been put forward as a key parameter for the reconstruction of the brain conductivity at the individual level. Here, we conducted a series of three sub-studies to systematically assess the effect of brain anisotropy on the tES-induced E-field in cortical gray matter and to compare in-vivo MREIT data with simulated data from isotropic and anisotropic head models. In sub-study 1, we employed simulations to demonstrate that sparse knowledge of the ohmic tissue conductivities is the main source of uncertainty, while the modeling of brain anisotropy has comparatively small effects on the simulated E-field. In sub-study 2, we compared simulations with in-vivo MREIT data and found that optimizing the conductivities of the modeled tissue compartments enhanced the agreement between simulated and measured data. Modeling brain conductivity as anisotropic had no impact on this optimization process. In sub-study 3, we used simulations to test how the differences in the tES-induced current flow caused by isotropic versus anisotropic brain conductivities affect the results of the "DT-MREIT" algorithm, which enables voxel-wise reconstructions of brain tissue conductivity. The algorithm performed similarly in both cases. On the other hand, the results were worse in a more realistic scenario where the reconstruction was based on simulated MREIT data (rather than simulated current densities). Together, our findings underscore the relevance of an accurate knowledge of the tissue conductivities for calculations of the tES-induced E-field. When cortical gray matter is the target for tES, modeling brain conductivity as anisotropic based on DTI data does not add substantial benefit. While in-vivo MREIT data generally show promise for refining the conductivity estimates of biological tissue at low frequencies, MREIT appears to be only weakly sensitive to the conductivity anisotropy of brain tissue.