Accelerated solution method for 3D phase-based cr-MREPT

Objective.Convection-reaction equation based magnetic resonance electrical properties imaging (cr-MREPT), especially in phase-based form, is one of the most commonly used MREPT methods since it can successfully overcome internal boundary artifacts, does not rely on transceive phase approximation and is relatively easy to implement. While the partial differential equation system solved in this method introduces regularization compared to Helmholtz MREPT, it also increases the solution time especially when the method is applied in large 3D volumes and reduces the practicality of the applications.Approach.We divide the large 3D volume of interest into smaller regions (local ROIs) for which the solutions can be obtained faster, we then parallelize the solutions of the individual regions and finally combine the results to obtain the whole conductivity distribution. Sensitivities of the reconstructed conductivity at a certain voxel, to theB1phase data of nearby voxels and to the Dirichlet Boundary condition imposed at the boundary of the solution region are investigated to determine the optimum size for the small regions.Main results.Conductivity distributions for various phantoms are successfully reconstructed with significantly reduced computational times, and up to approximately 100 times acceleration of the solution is achieved using a 72-core server. This can be further increased with a high-performance computer, where theoretical limit is the solution time for a single local ROI. Significance.Multislice reconstruction of large phantoms, such as a human head, is possible within a reasonable solution time with the proposed method. These findings enhance the potential for the practical applications of phase-based cr-MREPT.