Magnetic Resonance-Electrical Properties Tomography by Directly Solving Maxwell's Curl Equations

Magnetic Resonance-Electrical Properties Tomography (MR-EPT) is a method to reconstruct the electrical properties (EPs) of bio-tissues from the measured radiofrequency (RF) field in Magnetic Resonance Imaging (MRI). Current MR-EPT approaches reconstruct the EP profile by solving a second-order partial differential wave equation problem, which is sensitive to noise and can induce large reconstruction artefacts near tissue boundaries and areas with inaccurate field measurements. In this paper, a novel MR-EPT approach is proposed, which is based on a direct solution to Maxwell's curl equations. The distribution of EPs is calculated by iteratively fitting the RF field calculated by the finite-difference-time-domain (FDTD) technique to the measured values. To solve the time-consuming problem of the iterative fitting, a graphics processing unit (GPU) is used to accelerate the FDTD technique to process the field calculation kernel. The new EPT method was evaluated by investigating a numerical head phantom, and it was found that EP values can be accurately calculated and were relatively insensitive to simulated RF field errors. The feasibility of the proposed method was further validated using phantom-based experimental data collected from a 9.4 Tesla (T) Magnetic Resonance Imaging (MRI) system. The results also indicated that more accurate EP values could be reconstructed from the new method compared with conventional methods. Moreover, even in the absence of phase information of the RF field, the proposed approach is still capable of offering robust EPT solutions, thus having improved practicality for potential clinical applications.