Ider Y Ziya, Onart Serkan, Lionheart William R B
Department of Electrical and Electronics Engineering, Bilkent University, Ankara, Turkey.
Physiol Meas. 2003 May;24(2):591-604. doi: 10.1088/0967-3334/24/2/368.
Magnetic resonance-electrical impedance tomography (MR-EIT) was first proposed in 1992. Since then various reconstruction algorithms have been suggested and applied. These algorithms use peripheral voltage measurements and internal current density measurements in different combinations. In this study the problem of MR-EIT is treated as a hyperbolic system of first-order partial differential equations, and three numerical methods are proposed for its solution. This approach is not utilized in any of the algorithms proposed earlier. The numerical solution methods are integration along equipotential surfaces (method of characteristics), integration on a Cartesian grid, and inversion of a system matrix derived by a finite difference formulation. It is shown that if some uniqueness conditions are satisfied, then using at least two injected current patterns, resistivity can be reconstructed apart from a multiplicative constant. This constant can then be identified using a single voltage measurement. The methods proposed are direct, non-iterative, and valid and feasible for 3D reconstructions. They can also be used to easily obtain slice and field-of-view images from a 3D object. 2D simulations are made to illustrate the performance of the algorithms.
磁共振电阻抗断层成像（MR-EIT）于1992年首次被提出。从那时起，人们提出并应用了各种重建算法。这些算法以不同组合使用外围电压测量和内部电流密度测量。在本研究中，MR-EIT问题被视为一阶偏微分方程的双曲型系统，并提出了三种数值方法来求解。这种方法在早期提出的任何算法中都未被采用。数值求解方法是沿等势面积分（特征线法）、在笛卡尔网格上积分以及对由有限差分公式导出的系统矩阵进行求逆。结果表明，如果满足一些唯一性条件，那么使用至少两种注入电流模式，除了一个乘法常数外，可以重建电阻率。然后可以使用单个电压测量来识别这个常数。所提出的方法是直接的、非迭代的，并且对于三维重建是有效且可行的。它们还可以用于从三维物体轻松获得切片和视野图像。进行了二维模拟以说明算法的性能。
