Dept. of Electr. and Electron. Eng., Middle East Tech. Univ., Ankara.
IEEE Trans Med Imaging. 1990;9(1):49-59. doi: 10.1109/42.52982.
An algorithm is developed for electrical impedance tomography (EIT) of finite cylinders with general cross-sectional boundaries and translationally uniform conductivity distributions. The electrodes for data collection are assumed to be placed around a cross-sectional plane; therefore, the axial variation of the boundary conditions and the potential field are expanded in Fourier series. For each Fourier component a two-dimensional (2-D) partial differential equation is derived. Thus the 3-D forward problem is solved as a succession of 2-D problems, and it is shown that the Fourier series can be truncated to provide substantial savings in computation time. The finite element method is adopted and the accuracy of the boundary potential differences (gradients) thus calculated is assessed by comparison to results obtained using cylindrical harmonic expansions for circular cylinders. A 1016-element and 541-node mesh is found to be optimal. The algorithm is applied to data collected from phantoms, and the errors incurred from the several assumptions of the method are investigated.
本文提出了一种适用于具有任意截面边界和均匀平移电导率分布的有限长圆柱体的电阻抗断层成像（EIT）的算法。假设用于数据采集的电极位于一个横截面平面周围，因此边界条件和电位场的轴向变化可以展开为傅里叶级数。对于每个傅里叶分量，都推导出一个二维（2-D）偏微分方程。因此，3-D 正问题被解耦为一系列 2-D 问题，并且可以证明傅里叶级数可以截断以显著节省计算时间。采用有限元法，通过与圆柱谐展开方法获得的结果进行比较，评估了由此计算得到的边界电位差（梯度）的准确性。发现一个具有 1016 个元素和 541 个节点的网格是最优的。该算法应用于从体模中收集的数据，并研究了该方法的几个假设所带来的误差。
