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Oliver Sander:

Multidimensional coupling in a human knee model


The thesis presents a new model for the numerical simulation of the mechanics of the human knee. In this model bones are described using linear elasticity. Ligaments instead are modelled as one-dimensional Cosserat rods. The simulations give insight into the mechanical behavior of human joints. This can be helpful for a number of applications. For example, it is possible to estimate the long-term effect of certain surgical interventions. Also, the design of prosthetic devices can be improved. The main mathematical focus is on the correct formulation of the coupling conditions between one- and three- dimensional objects. Starting from the case of two three-dimensional objects, for which coupling conditions can be derived rigorously, conditions for the multidimensional case are formulated. A solution algorithm for this coupled problem is presented, and the existence of solutions is shown under certain symmetry assumptions. For the subproblems, large contact problems and minimization problems on Riemannian manifolds have to be solved. For both problems, robust and efficient numerical methods are introduced. Numerical experiments show the applicability for real-world problems.

Academic Advisor
Prof. Dr. Ralf Kornhuber
Sep 25, 2008