Gradient‐based electrical conductivity imaging usingMRphase

Purpose To develop a fast, practically applicable, and boundary artifact free electrical conductivity imaging method that does not use transceive phase assumption, and that is more robust against the noise. Theory Starting from the Maxwell's equations, a new electrical conductivity imaging method that is based solely on the MR transceive phase has been proposed. Different from the previous phase based electrical properties tomography (EPT) method, a new formulation was derived by including the gradients of the conductivity into the equations. Methods The governing partial differential equation, which is in the form of a convection‐reaction‐diffusion equation, was solved using a three‐dimensional finite‐difference scheme. To evaluate the performance of the proposed method numerical simulations, phantom and in vivo human experiments have been conducted at 3T. Results Simulation and experimental results of the proposed method and the conventional phase–based EPT method were illustrated to show the superiority of the proposed method over the conventional method, especially in the transition regions and under noisy data. Conclusion With the contributions of the proposed method to the phase‐based EPT approach, a fast and reliable electrical conductivity imaging appears to be feasible, which is promising for clinical diagnoses and local SAR estimation. Magn Reson Med 77:137–150, 2017. © 2016 Wiley Periodicals, Inc.