Numerical simulations of intra-voxel dephasing effects and signal voids in gradient echo MR imaging using different sub-grid sizes.

Signal void artifacts in gradient echo imaging are caused by the intra-voxel dephasing of the spins. Intra-voxel dephasing can be estimated by computing the field distribution on a sub-grid inside each picture element, followed by integration of all magnetization components. The strategy of computing the artifacts based on the integration of the sub-voxel signal components is presented here for different sub-grids. The coarseness of the sub-grid is directly related to computational effort. The possibility to save memory space and computing time for the dipole model by computing the field only on a sub-grid is addressed in the presented article. It is investigated as to how far computational time and memory space can be reduced by using an appropriate sub-grid. Numerical results for a model of a partially diamagnetically coated needle shaft are compared to experimental findings. In the case of a pure titanium needle, it is shown as being sufficient to compute the field distribution on a sub-grid that is at least four times coarser in each direction than the grid used to discretize the object in the related MR image. Due to three nested loops over the 3D grid, the need for memory space and time is saved by a factor 64. Deviations between measurements and simulations for the broad side of the artifact (uncompensated) and for the small side of the artifact (compensated) were 15.5%, respectively, 19.1% for orientation parallel to the exterior field, and 22.7%, respectively, 23.1% for orientation perpendicular to the exterior field.