School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, QLD 4072, Australia.
Phys Med Biol. 2018 Jul 16;63(14):145013. doi: 10.1088/1361-6560/aacc35.
Magnetic resonance electrical property tomography (MR-EPT) reconstructs electrical properties (EPs) from measured magnetic fields in magnetic resonance imaging (MRI) systems. In this study, an MR-EPT method was proposed that utilized a new finite difference approximation of the involved differential wave equation. Compared with existing MR-EPT approaches, the construction of the system matrix involves applying the first derivative twice based on a larger number of neighbouring finite-difference grids, which is different from a standard Laplacian operator on a regular grid structure, leading to a better conditioned linear inverse problem. With improved noise robustness, more faithful EPs can be obtained by the proposed method, particularly at tissue boundaries and regions with a poorly measured magnetic field (low signal-to-noise ratio). Numerical simulations with a specially designed multi-slice phantom and an anatomically accurate head model (Duke) have demonstrated that the proposed method can provide a more faithful reconstruction of EPs compared to existing methods, which usually offer unreliable solutions associated with traditional finite difference approximation of the central wave equation and unrealistic assumptions. Experiments on a 9.4 T MRI system have been conducted to validate the simulations.
磁共振电阻抗断层成像（MR-EPT）通过磁共振成像（MRI）系统中测量的磁场来重建电特性（EP）。在这项研究中，提出了一种利用所涉及的微分波动方程的新有限差分逼近的 MR-EPT 方法。与现有的 MR-EPT 方法相比，系统矩阵的构建涉及基于更多相邻有限差分网格应用两次一阶导数，这与规则网格结构上的标准拉普拉斯算子不同，从而导致线性逆问题的条件更好。通过所提出的方法，可以获得更好的噪声鲁棒性，更真实的 EP，特别是在组织边界和磁场测量较差的区域（低信噪比）。使用专门设计的多切片体模和解剖精确的头部模型（Duke）进行的数值模拟已经证明，与通常提供与中心波动方程的传统有限差分逼近相关的不可靠解决方案和不切实际的假设的现有方法相比，所提出的方法可以提供更真实的 EP 重建。已经在 9.4 T MRI 系统上进行了实验以验证模拟。
