Elastostatic, Acoustic and Time-reversed Simulation of Bones by Non-standard Fictitious Domain Methods

In recent years, non-standard fictitious domain techniques [1] like the Finite Cell Method (FCM) have gained increasing interest in the context of high order methods or the integration of engineering design and numerical analysis [2]. One of the most important advantages of these methods compared to mesh-based finite element schemes is the possibility to circumvent any time-consuming mesh generation and to directly couple them to different types of geometric models. This feature yields the FCM particularly attractive for simulation of biomechanical structures, as these are often geometrically very complicated and thus difficult to mesh into finite elements. A very efficient implementation of the FCM is possible by pre-computation of (sub-)cell matrices, under the condition that material properties are constant in the corresponding geometric entities. As this is a natural assumption for each individual voxel of a geometric model obtained by e.g. quantitative Computer Tomography (qCT), the FCM has been successfully applied in a computational steering system for preoperative planning, i.e. an integrated software to interactively simulate positioning of an artificial hip joint in a human femur.