Smoothed finite element methods in modelling and simulation of cardiac electromechanics

在心脏电力学建模中，目前常用的方法是有限元方法。然而，它的性能关键取决于网格质量。由于心脏复杂的个性化几何形状，在大多数情况下，只能自动生成四面体网格。然而，具有成本效益的线性四面体单元与几乎不可压缩的材料和大变形相结合，受到体积锁定的影响。作为替代，可以使用六面体网格、高阶单元或无网格法。然而，第一种方法大多需要手动调整，而第二种方法和第三种方法计算成本较高。另一方面，光滑有限元方法(S有限元)具有体积无锁定、对网格变形不敏感等优点，目前已成功地应用于被动心脏力学的模拟。为了克服上述困难，建议进一步开发S-FEMS，以应用于主动心脏力学、电生理学及其相互耦合。这项工作的总体目标是在S-FEMS的框架内提供计算成本高且准确的心脏仿真模型，该模型可以很好地用于自动生成四面体网格。该工作被分成五个数学工作包。首先，实现了基于节点的三维S有限元方法。然后，将NS-有限元与基于面的S有限元相结合，得到选择性的NS/FS-有限元。然后将S-有限元方法扩展到主动心脏力学、电生理学和完全耦合的电机学。在此基础上，进一步将心脏电机学的重要成分纳入S-有限元模型。最后，将模拟结果与临床数据和我们以前的有限元结果进行了比较。

In modelling of cardiac electromechanics, so far the finite element method (FEM) is the commonly utilised technique. However, its performance crucially depends on the mesh quality. Due to the complex personalised cardiac geometries, in most cases only tetrahedral meshes can be generated automatically. Nevertheless, the cost efficient linear tetrahedral elements in combination with a nearly incompressible material and large deformations suffer from volumetric locking. As alternatives, hexahedral meshes, high order elements or meshless methods can be used. However, the first ones mostly require manual adjustments, whereas the second and third ones are computationally expensive. On the other hand, smoothed finite element methods (S-FEM) are known to be volumetric locking free, less sensitive to mesh distortion and so far, have been successfully used e.g. in simulation of passive cardiac mechanics. To overcome the mentioned difficulties, S-FEMs are proposed to be further developed for the application to active cardiac mechanics, electrophysiology and their coupling.The overall objective of this work is to provide computationally cost efficient but also accurate cardiac simulation models within the framework of S-FEMs which work well on automatically generated tetrahedral meshes.The proposed work is grouped into five thematical work packages. Firstly, node-based S-FEM (NS-FEM) for 3D is implemented. Then, NS-FEM is combined with face-based S-FEM (FS-FEM) in order to obtain the selective NS/FS-FEM. The S-FEM approach is then extended to active cardiac mechanics, electrophysiology and fully coupled electromechanics. After that, further important ingredients for cardiac electromechanics are included into the S-FEM model. Finally the simulation results are compared to clinical data and our previous results using FEM.