Towards Hyper-Reduction of Cardiac Models Using Poly-affine Transformations

This paper presents a method for frame-based finite element models in order to develop fast personalised cardiac electromechanical models. Its originality comes from the choice of the deformation model: it relies on a reduced number of degrees of freedom represented by affine transformations located at arbitrary control nodes over a tetrahedral mesh. This is motivated by the fact that cardiac motion can be well represented by such poly-affine transformations. The shape functions use then a geodesic distance over arbitrary Voronoï-like regions containing the control nodes. The high order integration of elastic energy density over the domain is performed at arbitrary integration points. This integration, which is associated to affine degrees of freedom, allows a lower computational cost while preserving a good accuracy for simple geometries. The method is validated on a cube under simple compression and preliminary results on simplified cardiac geometries are presented, reducing by a factor 100 the number of degrees of freedom.