Sub-voxel refinement method for tissue boundary conductivities in volume conductor models

摘要

The resolution and element type of the mesh used in the Finite-Element Method modeling of transcranial direct-current stimulation (tDCS) greatly affect both the accuracy of the solution and the computational time. Tetrahedral meshing is usually used in these models as it well approximates curvature, but the models are slow to solve. Using a voxel grid as the mesh significantly reduces the computational time, but the cubical elements are not the most suitable option for curved surfaces. Tissue boundaries can be modeled as a layer of voxels with an average conductivity of the surrounding tissues. However, as the boundary being modeled only rarely divides a voxel into two equally sized portions, this approach is often erroneous, and in particular, with low resolutions. In this paper, we propose a novel method for improving the accuracy of anatomically correct Finite-Element Method simulations by enhancing the tissue boundaries in voxel models. In our method, a voxel model is created from a set of polygonal surfaces segmented from magnetic-resonance imaging (MRI) data. This is done by first voxelizing with a fine resolution, and then increasing the voxel size to the target resolution, and calculating the ratio of fine voxels in and outside the surface within each coarse voxel. More-accurate proportions for the volume of a coarse voxel inside and outside the tissue boundary are thus achieved, and the tissue boundary's conductivity can be better approximated. To test the performance of this method, a series of simulations of motor cortical tDCS were performed using resolutions from 0.2 mm to 2 mm, scaled to zero, two, or four times finer resolution. Based on the results, the voxel size could be doubled with a cost of 3% in relative error by using our method. The model's degrees of freedom (DOF) could thus be decreased by 87%, and the simulation times could be decreased by 82%.