Repository: Freie Universit├Ąt Berlin, Math Department

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

Deuflhard, P. and Ertel, S. and Kornhuber, R. and Krause, R. and Sander, O. (2006) Patient-specific simulation of dynamic stress distribution in the human knee. Journal of Biomechanics, 39 . p. 47. ISSN 0021-9290

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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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:1946
Deposited By: Ekaterina Engel
Deposited On:08 Sep 2016 08:18
Last Modified:08 Sep 2016 08:18

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