The Application of hybrid BEM / FEM methods to solve Electrical Impedance Tomography ’ s forward problem for the human head
The Application of hybrid BEM / FEM methods to solve Electrical Impedance Tomography ’ s forward problem for the human head
复制标题
应用边界元/有限元混合方法解决人体头部电阻抗断层扫描的前向问题
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
L. Horeshb
中科院分区：
文献类型：
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作者：
J. Sikora;S. R. Arridgeb;R. H. Bayfordc;L. Horeshb
电阻抗成像（EIT）中的正问题需要精确估计其解。虽然存在有限数量的情况下的解析解，有没有合适的分析解决方案的几何形状的人的头部。通常采用的方法是使用有限元法（FEM）。然而，人的头部由层组成，包括头皮和CSF，其厚度约为1 mm。网格化这些层在技术上是困难的，并且在解决方案中引入了显著的误差。一个有趣的替代方法是使用混合方法结合边界元法和有限元法。边界元法是有限元法的一种替代方法。该方法本质上使用绿色定理来将边界分布映射到边界分布，使用绿色函数的显式形式。虽然边界元法有密集矩阵的缺点，并假设该区域是均匀的，它将是很大的优势，如头皮和CSF，这是均匀的人的薄层。较大的区域更适合于有限元法，这是由非均匀的电导率分布。正问题的一个合理的解决方法是将边界元法和有限元法联合收割机产生混合代码，该代码假定某些区域具有接触值。我们目前的结果为2D球，并讨论所需的修改边界元，以提高相对较高的误差在界面上，我们还表明，与一定的离散化解决方案的误差为1毫米的薄层可以减少的领域。
The forward problem in Electrical Impedance Tomography (EIT) requires an accurate estimation of its solution. Although analytical solutions exist for a limited number of cases, there is no suitable analytical solution for the geometry of the human head. A commonly adopted method is the use of Finite Element Methods (FEM). However, the human head consists of layers, which include the scalp and CSF, which are approximately 1 mm thick. Meshing these layers is technically difficult and introduces significant errors in to the solution. An interesting alternative is the use of hybrid methods combining both BEM and FEM. The Boundary Element Method (BEM) is an alterative to FEM. This method essentially uses Green’s theorem to map boundary distributions to boundary distributions, using the explicit form of the Green’s functions. Although BEM has the disadvantage of dense matrices, and assumes the region is homogenous, it would be of great advantage for the thin layer of the human such as the scalp and CSF, which are homogenous. The larger regions are better suited to FEM, which are composed of non-uniform conductivity distribution. A logical approach for this forward problem is to combine the BEM and FEM to produce hybrid code, which assumes some region, have contact values. We present results for 2D spheres and discuss the required modifications of BEM in order to improve relatively high error at the interface, we also show for spheres that with certain discretization solution error for a 1mm thin layer could be reduced.