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

The resolution and element type of the mesh used in finite element method modelling of tDCS affect greatly on both the accuracy of the solution and computation time. Usually tetrahedral meshing is used in these models as they approximate curvature well but they are slow to solve. Using a voxel grid as the mesh reduces the computation time significantly but the cubical elements are not the most suitable option for curved surfaces. Tissue boundaries can be modelled as a layer of voxels with an average conductivity of the surrounding tissues. However, as the boundary being modelled only rarely divides a voxel into two equally sized portions, this approach is often erroneous. 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 MRI data 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. Thus a more accurate proportions for the volume of a coarse voxel inside and outside the tissue boundary is achieved and its 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 0, 2 or 4 times finer resolution. Based on the results, the voxel size can be doubled with a cost of 3% in relative error by using our method and thus the modelled DOFs can be decreased by 87% and the simulation times decreased by 82%.