Sub-Voxel Refi nement Method forTissue Boundary Conductivities inVolume Conductor Models

摘要

The resolution and element type of the mesh used inthe Finite-Element Method modeling of transcranialdirect-current stimulation (tDCS) greatly aff ect both theaccuracy of the solution and the computational time.Tetrahedral meshing is usually used in these models as it wellapproximates curvature, but the models are slow to solve.Using a voxel grid as the mesh signifi cantly reduces thecomputational time, but the cubical elements are not the mostsuitable option for curved surfaces. Tissue boundaries can bemodeled as a layer of voxels with an average conductivityof the surrounding tissues. However, as the boundary beingmodeled only rarely divides a voxel into two equally sizedportions, this approach is often erroneous, and in particular,with low resolutions. In this paper, we propose a novelmethod for improving the accuracy of anatomically correctFinite-Element Method simulations by enhancing the tissueboundaries in voxel models. In our method, a voxel modelis created from a set of polygonal surfaces segmented frommagnetic-resonance imaging (MRI) data. This is done byfi rst voxelizing with a fi ne resolution, and then increasingthe voxel size to the target resolution, and calculating theratio of fi ne voxels in and outside the surface within eachcoarse voxel. More-accurate proportions for the volumeof a coarse voxel inside and outside the tissue boundaryare thus achieved, and the tissue boundary’s conductivitycan be better approximated. To test the performance of thismethod, a series of simulations of motor cortical tDCS wereperformed using resolutions from 0.2 mm to 2 mm, scaledto zero, two, or four times fi ner resolution. Based on theresults, the voxel size could be doubled with a cost of 3%in relative error by using our method. The model’s degreesof freedom (DOF) could thus be decreased by 87%, and thesimulation times could be decreased by 82%.