How the stiffness of meniscal attachments and meniscal material properties affect tibio-femoral contact pressure computed using a validated finite element model of the human knee joint
Introduction
In an effort to prevent degeneration of the articular cartilage caused by meniscectomies (Bolano and Grana, 1993; Fauno and Nielson, 1992; Rangger et al., 1995), both meniscal allografts (De Boer and Koudstaal, 1991; Siegel and Roberts, 1993; Stone, 1993;Veltri et al., 1994) and synthetic replacements (Kollias and Fox, 1996; Messner, 1994; Stone et al., 1992) have been previously investigated. However, the clinical success of meniscal allografts has been varied (Arnoczky et al., 1990; De Boer and Koudstaal, 1991; Garrett and Stevensen, 1991; Jackson et al., 1992; Kohn et al., 1992; Mikic et al., 1993; Milachowski et al., 1989). The mixed results may be due in part to a failure of the replacement to satisfy the biomechanical criteria necessary for proper meniscal function.
Among the most important biomechanical factors that determine the relative success of a meniscal replacement are the material properties of the tissue. Meniscal collagen fibers are arranged predominantly in the circumferential direction. These fibers function to support the large hoop stresses that are important to the distribution of contact pressures within the knee joint. Previous studies have demonstrated that the radial modulus is influenced by the presence of radial tie fibers (Skaggs et al., 1994); however, the modulus in the radial and axial directions is approximately 10 times less than that of the circumferential direction (Tissakht and Ahmed, 1995). Therefore, it appears that a transversely isotropic constitutive relationship is appropriate to represent the meniscal tissue. Mathematical models of load transmission of the tibio-femoral joint, which have modeled the meniscus as transversely isotropic, suggest that the circumferential tensile modulus is critical to achieving proper distribution of contact pressure (Schreppers et al., 1990; Spilker and Donzelli, 1992). However, a transversely isotropic constitutive relation requires five independent parameters, and the relative importance of the remaining four parameters, in addition to the circumferential modulus, on the contact pressure distribution is at the present unknown.
Another factor that may be important to the success of meniscal replacements is the attachment of the meniscus to the surrounding tissues. The anterior and posterior horns of each meniscus are connected to the tibial plateau either by means of ligaments or by direct insertion (Arnoczky et al., 1987). In addition, the posterior fibers of the anterior horn of the medial meniscus merge with the transverse ligament, which then connects to the anterior horn of the lateral meniscus. The medial meniscus is more firmly attached than the lateral meniscus to the femur and tibia by a thickening in the joint capsule known as the deep medial collateral ligament (MCL). While the function of these various attachments is to provide restraints that limit the relative movement of the meniscus on the tibial plateau when it bears load (Tissakht et al., 1989), the relative importance of each attachment on the contact pressure distribution is at present unknown.
Currently, tissue banks do not consider material properties in selecting meniscal allografts, and those developing synthetic replacements are not guided by any design criteria for restoring meniscal function. In addition, during meniscal replacement surgery, a question that remains to be answered is what specific attachments must be restored since attaching the horns alone does not restore normal meniscal function (Alhalki et al., 1999). Therefore, the objectives of the current study were to (1) determine whether a transversely isotropic, linearly elastic, homogeneous constitutive relationship is necessary to achieve a normal contact pressure distribution on the tibial plateau, (2) determine material parameters and attachment parameters to which the contact pressure distribution of the tibial plateau is most sensitive, and (3) determine tolerances on material and attachment parameters that will restore the contact pressure distribution to within a specified difference from normal.
Section snippets
Determination of experimental contact variables
One human, fresh-frozen, cadaveric, right knee was obtained from a 30-year-old male. Antero-posterior and lateral roentgenograms of the knee were obtained to ensure that there was no joint space narrowing, osteophytes, chondrocalcinosis, meniscal tears, or history of knee surgery. The knee was then aligned in a specialized load application system for the testing of joints (Bach and Hull, 1995). The knee was aligned using a functional-axes approach, which has been shown to exhibit good
Results
When the constitutive relation for the meniscal material was considered to be transversely isotropic, an RMSNE of 5.4% was obtained by the first optimization (Table 2). The minimization resulted in values for each of the nine parameters as follows:
- 1.
Grθ=Gzθ=57.7 MPa,
- 2.
stiffness of transverse ligament=900 N/mm,
- 3.
total stiffness of horn attachment=2000 N/mm,
- 4.
nonlinear stiffness of medial collateral ligament bundles=4000 N,
- 5.
reference strain of medial collateral ligament bundles=0.00,
- 6.
νrθ=νzθ=0.3,
- 7.
νrz=0.2,
- 8.
Er=Ez
Discussion
The purpose of this study was to establish a set of criteria to aid in the design and/or selection of meniscal replacements. To fulfill this purpose, a finite element model of a single cadaveric knee was used in a sensitivity analysis to identify both material and attachment parameters that are the most important determinants of the contact pressure distribution and therefore would influence the long-term success of the replacement. One key finding of this study was that a transversely
Acknowledgements
The authors are grateful to the Whitaker Foundation for providing the financial support to undertake this project.
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