In the last decades, various computational models have been developed to simulate cardiac electromechanics. The most common numerical tool is the finite element method (FEM). However, this method crucially depends on the mesh quality. For complex geometries such as cardiac structures, it is convenient to use tetrahedral discretisations which can be generated automatically. On the other hand, such automatic meshing with tetrahedrons together with large deformations often lead to elements distortion and volumetric locking. To overcome these difficulties, different smoothed finite element methods (S-FEMs) have been proposed in the recent years. They are known to be volumetric locking free, less sensitive to mesh distortion and so far have been used e.g. in simulation of passive cardiac mechanics. In this work, we extend for the first time node-based S-FEM (NS-FEM) towards active cardiac mechanics. Firstly, the sensitivity to mesh distortion is tested and compared to that of FEM. Secondly, an active contraction in circumferentially aligned fibre direction is modelled in the healthy and the infarcted case. We show, that the proposed method is more robust with respect to mesh distortion and computationally more efficient than standard FEM. Being furthermore free of volumetric locking problems makes S-FEM a promising alternative in modelling of active cardiac mechanics, respectively electromechanics.

在过去的几十年中，已经开发出各种计算模型来模拟心脏机电。最常用的数值工具是有限元方法（FEM）。但是，此方法主要取决于网格质量。对于复杂的几何形状（例如心脏结构），使用可以自动生成的四面体离散化会很方便。另一方面，这种与四面体的自动啮合以及较大的变形通常会导致单元变形和体积锁定。为了克服这些困难，近年来已经提出了不同的平滑有限元方法（S-FEM）。众所周知，它们是无体积锁定的，对网格变形不那么敏感，到目前为止，例如已用于被动心脏力学的仿真中。在这项工作中 我们首次将基于节点的S-FEM（NS-FEM）扩展到主动心脏力学领域。首先，测试对网格变形的敏感性并将其与FEM进行比较。其次，在健康和梗塞的病例中模拟沿圆周排列的纤维方向的主动收缩。我们表明，所提出的方法相对于网格失真更健壮，并且比标准有限元方法在计算效率上更高。此外，由于没有体积锁定问题，S-FEM在主动心脏力学或机电建模中成为有前途的替代方法。我们表明，所提出的方法相对于网格失真更健壮，并且比标准有限元方法在计算效率上更高。此外，由于没有体积锁定问题，S-FEM在主动心脏力学或机电建模中成为有前途的替代方法。我们表明，所提出的方法相对于网格失真更健壮，并且比标准有限元方法在计算效率上更高。此外，由于没有体积锁定问题，S-FEM在主动心脏力学或机电建模中成为有前途的替代方法。