Patient-specific simulation of dynamic stress distribution in the human knee

Abstract

We present a method for efficient, high-resolution, patient-specific simulation of the loads and stresses in a human knee joint during a gait cycle. Femur and tibia are modelled using first-order finite elements on a grid generated semi-automatically from a CT scan of the patient. We therefore obtain patient-specific information which can be very useful in operation and therapy planning. A new stabilized Newmark time scheme allows the time integration of Newton's equations of motion with arbitrarily large time steps. At each time step a large minimization problem has to be solved. Additional difficulty arises from the non-penetration condition imposed on the bones, which lead to inequality constaints for the minimization problem. A generalization of standard multigrid solvers, the so-called monotone multigrid solver, can solve such contact problems with optimal efficiency. Knee ligaments are modelled as nonlinear Cosserat rods. These are physically correct one-dimensional objects and allow to capture bending and twisting phenomena. They are coupled to the three-dimensional bone-models using equality of mechanical work as the coupling condition. We show numerical results for test problems with analytically known solutions as well as real-world examples using the Visible-Human data set.