Saeedizadeh N, Kermani S, Rabbani H
Department of Medical Physics and Medical Engineering, Isfahan University of Medical Sciences, Isfahan, Iran (email:
J Med Signals Sens. 2011 Jul;1(3):200-5.
In this study, a hp-version of Finite Element Method (FEM) was applied for forward modeling in image reconstruction of Electrical Impedance Tomography (EIT). The EIT forward solver is normally based on the conventional Finite Element Method (h-FEM). In h-FEM, the polynomial order (p) of the element shape functions is constant and the element size (h) is decreasing. To have an accurate simulation with the h-FEM, a mesh with large number of nodes and elements is usually needed. In order to overcome this problem, the high order finite element method (p-FEM) was proposed. In the p-version, the polynomial order is increasing and the mesh size is constant. Combining the advantages of two previously mentioned methods, the element size (h) was decreased and the polynomial order (p) was increased, simultaneously, which is called the hp-version of Finite Element Method (hp-FEM). The hp-FEM needs a smaller number of nodes and consequently, less computational time and less memory to achieve the same or even better accuracy than h-FEM. The SNR value is 42db for hp-FEM and is 9db for h-FEM. The numerical results are presented and verified that the performance of the hp-version is better than of the h-version in image reconstruction of EIT.
在本研究中，有限元方法（FEM）的hp版本被应用于电阻抗断层成像（EIT）图像重建的正向建模。EIT正向求解器通常基于传统有限元方法（h-FEM）。在h-FEM中，单元形状函数的多项式阶数（p）是恒定的，而单元尺寸（h）在减小。为了使用h-FEM进行精确模拟，通常需要一个具有大量节点和单元的网格。为了克服这个问题，提出了高阶有限元方法（p-FEM）。在p版本中，多项式阶数增加而网格尺寸恒定。结合上述两种方法的优点，同时减小单元尺寸（h）并增加多项式阶数（p），这被称为有限元方法的hp版本（hp-FEM）。与h-FEM相比，hp-FEM需要的节点数量更少，因此，在获得相同甚至更好精度的情况下，计算时间更短，内存占用更少。hp-FEM的SNR值为42dB，h-FEM的SNR值为9dB。给出了数值结果并验证了在EIT图像重建中hp版本比h版本的性能更好。
