Numerische Simulation des physiologischen Kontaktes im humanen Hüftgelenk
Final Report Abstract
The role of the synovial fluid in joint function is a major focus of this project. Fluid exchange between the porous cartilage layers and the synovial gap is known to contribute to both cartilage nutrition and load transfer. Nevertheless, a detailed description of these processes is missing. Despite the well documented very low cartilage permeability, most common theories for joint function assume the fluid exchange processes to take place on the same time scale as the loading. Only in recent years, the possibility of fluid exchange processes over longer time scales like diurnal patterns has been investigated. In this project, an efficient and robust finite element model for analysing fluid exchange in the human hip joint has been developed. The overall computational strategy has been derived in this sub project, while a detailed cartilage model has been developed in a partner project at the University of Stuttgart. Material parameters for the cartilage model have been identified by measurements and material testing conducted within a second partner project at the Laboratory of Biomechanics in Hannover. For the computational strategy, two different approaches have been implemented. One option is to treat the system as a contact problem with a contact gap filled with an incompressible fiuid. A second option is to view the system as afluid-structure-interaction (FSI) problem. Both approaches have been analysed using the simplified model problem of finding the static solution of two non-porous elastic bodies separated by an incompressible fluid film. In the modified contact problem, the constraint for the contact gap is controlled by the fluid mass balance in the gap. The approach leads to an operator split scheme in which the contact problem and the fluid balance of momentum are solved alternatin gly. Due to efficiency reasons, solving the fluid balance of momentum in the gap is based on the slave surface discretisation with additional thickness information. Therefore, the investigation of different methods for solving vector valued partial differential equations on curved surfaces has been of interest this project. For the FSI approach, a staggered solution has been pursued, due to the coupling to the porous material model from the project partners. The standard algorithm for a staggered solution of FSI problems is the Dirichlet-Neumann scheme. Unfortunately, the hip joint constitutes a special case of a fluid-structure interaction, as the incompressible fluid is entirely enclosed by the deformable structure. For this case the standard scheme fails, because the Dirichlet conditions for the fluid velocities, which are derived from the solid displacements, violate the fluid's incompressibility constraint. In order to overcome this problem, a global constraint has been formulated for the volume of the fluid and enforced by the Lagrange multiplier method. The FSI approach has been extended to cover the entire hip joint system with porous cartilage layers. For this purpose, the global constraint has been formulated for the synovial gap and the cartilage layers together. These two components constitute an incompressible domain which is entirely enclosed by deformable structure. In the staggered scheme this incompressible domain plays the role of the Dirichlet partition while the surrounding elastically deformable tissues constitute the Neumann partition. Detailed parameter studies have been conducted on an example geometry representing a cut out from a synovial joint. Due to the low cartilage permeability, the consolidation process takes more than 24 hours. The assumption that diurnal/nocturnal flow patterns are present in synovial joints is supported by this result. For further analysis of these flow patterns, boundary conditions describing diurnal load patterns have to be formulated. A finite element model of the hip joint has been reconstructed from MRI data by the partner group from Stuttgart. The developed method has been applied to this model, while varying the stiffness of the labrum. A labrum resection has been approximated by a very soft labrum. The results support the theory that the labrum has a sealing function for the synovial gap. After a labrum resection there is no resistance to a fluid outflow from the gap and therefore no pressure is developed within the gap, so that increased contact of the cartilage layers has to be expected. These results indicate that a labrum resection increases the risk of osteoarthritis.
Publications
- Simulation of the Physiological Contact Pressure Distribution in the Human Hip Joint. Pamm, 9(1):149-150, December 2009
A. Lutz, K. Fietz, and U. Nackenhorst
- Numerical investigations on physiological contact in the human hip joint. Pamm, 10(1):75-76. December 2010
K. Fietz and U. Nackenhorst.
- A finite element approach for modelling hip joint contact. Pamm, 11(1 );87- 88, December 2011
K. Fietz and U. Nackenhorst
- A Finite Element Approach for Modelling Synovial Joint Contact. In W. Ehlers and B. Markert, editors, Proceedings of the 3rd GAMM Seminaron Continuum Biomechanics, pages 1-16. 2012
K. Fietz and U. Nackenhorst
- Towards a Finite Element Model for Fluid Flow in the Human Hip Joint. PhD thesis, Leibniz Universität Hannover, 2013
Kristin Fietz
