Realistic tDCS Head Modeling with Multimodal MRI

For a tDCS simulation study, a realistic FE model of the head was generated from a T1-weighted, a T2-weighted and a diffusion-tensor (DT)-magnetic resonance image (MRI) of a healthy 26-year-old male subject. In a first step, the T2-MRI was rigidly registered onto the T1-MRI using a mutual information based cost-function (Jenkinson and Smith, 2001 (link)). Segmentation into tissue compartments skin, skull compacta, skull spongiosa, cerebrospinal fluid (CSF), brain gray (GM), and white matter (WM) was then performed using the FSL software¹ (Zhang et al., 2001 (link); Smith, 2002 (link); Jenkinson et al., 2005 ). Segmentation started with the generation of initial masks for skin, inner and outer skull, and brain using both T1- and T2-MRI. In a second step, the T1-MRI served for GM and WM segmentation, while the T2-MRI allowed for a segmentation of skull compacta, skull spongiosa, and CSF space (see Figure 1). For the compartments of skin, skull compacta, skull spongiosa, and CSF, we used the isotropic conductivity values of 0.43, 0.007, 0.025, and 1.79 S/m, respectively (Baumann et al., 1997 (link); Akhtari et al., 2002 (link); Dannhauer et al., 2011 (link)). For the modeling of white matter conductivity anisotropy, the diffusion-weighted images were first artifact-corrected using our reversed-gradient approach introduced in Olesch et al. (2010 ). Diffusion tensors were then determined and the result was registered onto the structural images using the FSL routine vecreg². In a last step, the conductivity anisotropy in GM and WM was computed from the registered DTI using an effective medium approach (Tuch et al., 2001 (link); Rullmann et al., 2009 (link)). This resulted in mean conductivities of 0.19 and 0.24 S/m for WM and GM.
Two electrode patches with a size of 7 cm × 5 cm, thickness of 4 mm, and saline like conductivity of 1.4 S/m are modeled. A total current of 1 mA is injected at the red patch (anode) and removed at the blue one (cathode). For field modeling of this stimulation throughout the volume conductor, a quasistatic approximation of Maxwell’s equations (Plonsey and Heppner, 1967 (link)) was used, resulting in a Laplace equation for the electric potential Φ with inhomogeneous Neumann boundary conditions at the head surface. An isoparametric FE approach is used for the computation of Φ in a 1 mm geometry-adapted hexahedral mesh (Wolters et al., 2007a (link),b (link)), resulting in a large sparse linear equation system with 2.255 million unknowns, which is solved using an algebraic multigrid preconditioned conjugate gradient approach (Wolters et al., 2002 (link); Lew et al., 2009 (link)). In a last step, the current density J = σ grad Φ is computed with σ being the 3 × 3 conductivity tensor. For simulation, we used our software SimBio³.
In all subsequent figures, slices of the current density distribution through the cortex are presented. The amplitude of J is coded by means of a linear color-scale. The current density distributions were computed in the 1 mm geometry-adapted hexahedral head model and the software SciRun⁴ was used for visualization.