Mathematische Planung orthopädischer Operationen скачать в хорошем качестве

Mathematische Planung orthopädischer Operationen

The mathematical modelling and simulation of human motion in the context of computer assisted surgery is a challenging task. For example, the design of fixation devices in surgery and joint prostheses requires a realistic modelling of the healing process and a quantitative description of displacements and stresses during different gaits, e.g., walking and stair climbing. A realistic physical and mathematical modelling in combination with efficient simulation techniques would open exciting medical perspectives far beyond osteotomic surgery. Mathematical models coupling all possibly relevant biomechanical aspects of human motion are clearly not manageable. Existing musculo-skeletal models for human motion are typically based on a rigid body approximation of human bones leading to multibody systems of differential-algebraic equations (DAEs). Joints and muscles are incorporated by simple models. To study the local elastic behavior of bones, finite element methods (FEM) are used for 3D partial differential equations (PDEs). In applications such as prostheses or fixation devices, mechanical contact problems occur. Quite often, contact problems are just neglected for computational complexity reasons. If at all, they are usually treated via penalty methods or heuristic techniques. Heterogeneous dynamical DAE/PDE models, which would actually be required, seem to be not available yet.