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Towards an efficient numerical simulation of complex 3D knee joint motion

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Computing and Visualization in Science

Abstract

We present a time-dependent finite element model of the human knee joint of full 3D geometric complexity together with advanced numerical algorithms needed for its simulation. The model comprises bones, cartilage and the major ligaments, while patella and menisci are still missing. Bones are modeled by linear elastic materials, cartilage by linear viscoelastic materials, and ligaments by one-dimensional nonlinear Cosserat rods. In order to capture the dynamical contact problems correctly, we solve the full PDEs of elasticity with strict contact inequalities. The spatio-temporal discretization follows a time layers approach (first time, then space discretization). For the time discretization of the elastic and viscoelastic parts we use a new contact-stabilized Newmark method, while for the Cosserat rods we choose an energy-momentum method. For the space discretization, we use linear finite elements for the elastic and viscoelastic parts and novel geodesic finite elements for the Cosserat rods. The coupled system is solved by a Dirichlet–Neumann method. The large algebraic systems of the bone–cartilage contact problems are solved efficiently by the truncated non-smooth Newton multigrid method.

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Notes

  1. http://www.netlib.org/ode/ddassl.f.

  2. An adaptive time step control for the contact-stabilized Newmark method has been presented in [23, 26].

  3. http://www.amira.com.

  4. http://www.dune-project.org.

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Authors and Affiliations

  1. Freie Universität Berlin Institut für Mathematik, Arnimallee 6, 14195 , Berlin, Germany

    Oliver Sander, Jonathan Youett & Ralf Kornhuber

  2. Zuse Institute Berlin (ZIB), Takustraße 7, 14195 , Berlin, Germany

    Corinna Klapproth & Peter Deuflhard

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  1. Oliver Sander
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  2. Corinna Klapproth
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  5. Peter Deuflhard
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Correspondence to Oliver Sander.

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Communicated by: Gabriel Wittum.

This work has been funded in part by the DFG research center Matheon.

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Sander, O., Klapproth, C., Youett, J. et al. Towards an efficient numerical simulation of complex 3D knee joint motion. Comput. Visual Sci. 16, 119–138 (2013). https://doi.org/10.1007/s00791-014-0227-6

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