A Method for Electrical Property Tomography Based on a Three-Dimensional Integral Representation of the Electric Field
A Method for Electrical Property Tomography Based on a Three-Dimensional Integral Representation of the Electric Field
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DOI：
10.1109/tmi.2021.3139455
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发表时间：
2022-06-01
影响因子：
10.6
通讯作者：
Nara, Takaaki
中科院分区：
文献类型：
--
作者：
Eda, Naohiro;Fushimi, Motofumi;Nara, Takaaki
磁共振电性质断层扫描（MREPT）无创重建高分辨率的电性质（EP）地图使用MRI扫描仪，是有用的诊断癌组织。然而，传统的MREPT方法存在数值拉普拉斯运算对噪声敏感、三维EPs重构困难、迭代过程不保证收敛性等缺点。我们提出了一种新的、迭代的三维重建MREPT方法，而不需要数值拉普拉斯运算。我们利用麦克斯韦方程组的亥姆霍兹分解推导出电场的积分表示，假设EPs在感兴趣区域的边界上已知，近似不可测量的磁场分量为零。然后，用理论上保证收敛性的凸投影算法求解由积分表示和安培定律组成的联立方程组。通过数值模拟和仿真实验验证了该方法的有效性。结果表明，该方法能有效地重建三维EPs，对噪声具有较强的鲁棒性。结果表明，采用不可测分量H-的方法提高了背景下EPs的精度；采用所有磁场分量的方法除所有电场分量接近于零外，减少了切片中心的伪影。
Magnetic resonance electrical properties tomography (MREPT) noninvasively reconstructs high-resolution electrical property (EP) maps using MRI scanners and is useful for diagnosing cancerous tissues. However, conventional MREPT methods have limitations: sensitivity to noise in the numerical Laplacian operation, difficulty in reconstructing three-dimensional (3D) EPs and convergence not guaranteed in the iterative process. We propose a novel, iterative 3D reconstruction MREPT method without a numerical Laplacian operation. We derive an integral representation of the electric field using its Helmholtz decomposition with Maxwell's equations, under the assumption that the EPs are known on the boundary of the region of interest with the approximation that the unmeasurable magnetic field components are zero. Then, we solve the simultaneous equations composed of the integral representation and Ampere's law using a convex projection algorithm whose convergence is theoretically guaranteed. The efficacy of the proposed method was validated through numerical simulations and a phantom experiment. The results showed that this method is effective in reconstructing 3D EPs and is robust to noise. It was also shown that our proposed method with the unmeasurable component H- enhances the accuracy of the EPs in a background and that with all the components of the magnetic field reduces the artifacts at the center of the slices except when all the components of the electric field are close to zero.