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

https://doi.org/10.1016/S0021-9290(02)00305-6Get rights and content

Abstract

In an effort to prevent degeneration of articular cartilage associated with meniscectomies, both meniscal allografts and synthetic replacements are subjects of current interest and investigation. The objectives of the current study were to (1) determine whether a transversely isotropic, linearly elastic, homogeneous material model of the meniscal tissue is necessary to achieve a normal contact pressure distribution on the tibial plateau, (2) determine which material and boundary condition (attachments) parameters affect the contact pressure distribution most strongly, and (3) set tolerances on these parameters to restore the contact pressure distribution to within a specified error. To satisfy these objectives, a finite element model of the tibio-femoral joint of a human cadaveric knee (including both menisci) was used to study the contact pressure distribution on the tibial plateau. To validate the model, the contact pressure distribution on the tibial plateau was measured experimentally in the same knee used to create the model. Within physiologically reasonable bounds on five material parameters and four attachment parameters associated with a meniscal replacement, an optimization was performed under 1200 N of compressive load on the set of nine parameters to minimize the difference between the experimental and model results. The error between the experimental and model contact variables was minimized to 5.4%. The contact pressure distribution of the tibial plateau was sensitive to the circumferential modulus, axial/radial modulus, and horn stiffness, but relatively insensitive to the remaining six parameters. Consequently, both the circumferential and axial/radial moduli are important determinants of the contact pressure distribution, and hence should be matched in the design and/or selection of meniscal replacements. In addition, during surgical implantation of a meniscal replacement, the horns should be attached with high stiffness bone plugs, and the attachments of the transverse ligament and deep medial collateral ligament should be restored to minimize changes in the contact pressure distribution, and thereby possibly prevent the degradation of articular cartilage.

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.

    G=G=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.

    ν=ν=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.

References (62)

  • M.G. Siegel et al.

    Meniscal allografts

    Clinics in Sports Medicine

    (1993)
  • K.R. Stone et al.

    Surgical technique of meniscal replacement

    Arthroscopy

    (1993)
  • M. Tissakht et al.

    Tensile stress–strain characteristics of the human meniscal material

    Journal of Biomechanics

    (1995)
  • J. Wismans et al.

    A three-dimensional mathematical model of the knee joint

    Journal of Biomechanics

    (1980)
  • A.M. Ahmed et al.

    In-vitro measurement of static pressure distribution in synovial joints—Part Itibial surface of the knee

    Journal of Biomechanical Engineering

    (1983)
  • M.M. Alhalki et al.

    How three methods for fixing a medial meniscal autograft affect tibial contact mechanics

    American Journal of Sports Medicine

    (1999)
  • P.R. Allen et al.

    Late degenerative changes after meniscectomy. Factors effecting the knee after operation

    Journal of Bone and Joint Surgery [Br]

    (1984)
  • S.P. Arnoczky et al.

    Meniscus

  • S.P. Arnoczky et al.

    The effect of cryopreservation on canine meniscia biochemical, morphologic, and biomechanical evaluation

    Journal of Orthopedic Research

    (1988)
  • S.P. Arnoczky et al.

    Meniscal replacement using a cryopreserved allograftan experimental study in the dog

    Clinical Orthopedics and Related Research

    (1990)
  • J.M. Bach et al.

    A new load application system for in vitro study of ligamentous injuries to the human knee joint

    Journal of Biomechanical Engineering

    (1995)
  • M.E. Baratz et al.

    Meniscal tearsthe effect of meniscectomy and of repair on intraarticular contact areas and stress in the human knee. A preliminary report

    American Journal of Sports Medicine

    (1986)
  • G.S. Berns et al.

    Implementation of a five degree of freedom automated system to determine knee flexibility in vitro

    Journal of Biomechanical Engineering

    (1990)
  • L.E. Bolano et al.

    Isolated arthroscopic partial meniscectomyfunctional radiographic evaluation at five years

    American Journal of Sports Medicine

    (1993)
  • H.H. De Boer et al.

    The fate of meniscus cartilage after transplantation of cryopreserved nontissue-antigen-matched allograft. A case report

    Clinical Orthopedics and Related Research

    (1991)
  • S.G. Elias et al.

    A correlative study of the geometry and anatomy of the distal femur

    Clinical Orthopaedics and Related Research

    (1990)
  • D.C. Fithian et al.

    Human meniscus tensile propertiesregional variation and biochemical correlation

    Transactions of ORS

    (1989)
  • T. Fukubayashi et al.

    The contact area and pressure distribution pattern of the knee. A study of normal and osteoarthrotic knee joints

    Acta Orthopedica Scandanavia

    (1980)
  • J.J. Garcia et al.

    An approach for the stress analysis of transversely isotropic biphasic cartilage under impact load

    Journal of Biomechanical Engineering

    (1998)
  • T.L. Haut et al.

    A high accuracy three-dimensional coordinate digitizing system for recontructing the geometry of diarthrodial joints

    Journal of Biomechanics

    (1997)
  • T.L. Haut et al.

    Use of roentgenography and MRI to predict meniscal geometry determined with a three-dimensional coordinate digitizing system

    Journal of Orthopedic Research

    (2000)
  • Cited by (0)

    View full text