Smoothed finite element methods in modelling and simulation of cardiac electromechanics

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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.