Elsevier

Journal of Biomechanics

Volume 48, Issue 8, 1 June 2015, Pages 1343-1349
Journal of Biomechanics

Material properties of individual menisci and their attachments obtained through inverse FE-analysis

https://doi.org/10.1016/j.jbiomech.2015.03.014Get rights and content

Abstract

Meniscal properties for computational methods have already been proposed. However, it is well known that there is high intra subject variability in the material properties of soft tissues and that disruption of the fiber network alters the biomechanics of the meniscus. Therefore, the objective of this study was to establish a non invasive method to determine the material properties of the individual menisci and their attachments using inverse FE-analyses.

In a previous study, the 3D displacements of the meniscus and its attachments under axial joint loads were determined for intact porcine knees. To simulate the experimental response in individual FE-analyses (n=5), an anisotropic, hyperelastic meniscus matrix was embedded in a poroelastic model. During a particle swarm optimization, the difference between the force applied to the meniscus during the experiment and the femoral surface reaction force of the FE model at equilibrium was minimized by varying four material parameters. Afterwards, a prediction error was determined to describe how well the material parameter fit to each of the three displacement directions. Additionally, the stresses occurring in the meniscus were evaluated.

The error of the material parameter optimization was on average 6.5±4.4%. The best fitting material parameter combination revealed an error of 1.2%. The highest stresses occurred in the region between the pars intermedia and posterior horn of the meniscus.

The individual material properties of the meniscus were successfully obtained with a combination of previously reported, noninvasively measured 3D displacements and inverse FE-analyses. The methodology presented in this study is a promising contribution to the detection of degeneration within the meniscus.

Introduction

The menisci in the knee joint are essential for load transmission, joint lubrication and joint stability (Masouros et al., 2008). To accommodate these functions, the meniscus is a biphasic structure composed of a fluid phase consisting of water and electrolytes (60–70%) and a solid phase consisting of collagen type I (15–25%), proteoglycans (1–2%), other proteins and chondrocytes (Mow and Huiskes, 2005). The collagen fibers are primarily arranged circumferentially (14%) with a sparse occurrence of radial fibers (2.5%) (Shirazi et al., 2008), accounting for the anisotropy. This structural composition of the meniscus, in combination with the firm fixation via its ligamentous attachments, limits the radial protrusion from the knee joint and resists circumferential tension (hoop stresses) generated under axial joint compression.

Due to the complex structural organization of the meniscus and its important load distribution function in the knee joint, the in depth knowledge of the non isotropic meniscal material properties is important for basic research as well as for the development and improvement of meniscal replacements. Several experimental and numerical studies have attempted to elucidate the biomechanical behavior and the material properties of the meniscus and its attachments. Experimental studies primarily investigated the tensile (Proctor et al., 1989, Tissakht and Ahmed, 1995, Lechner et al., 2000, Villegas et al., 2007, Abraham et al., 2011) and compressive creep or relaxation properties of these tissues (Proctor et al., 1989, Sweigart et al., 2004, Maes and Donahue, 2006, Chia and Hull, 2008, Seitz et al., 2013), mostly using standardized specimens obtained from specific locations within the meniscus and its attachments. However, disruption of the fiber network alters the biomechanics of the meniscus (Lee et al., 2006, Bedi et al., 2010, Seitz et al., 2012). Therefore, it is likely that, in standardized samples with a discontinuous fiber network, the mechanics are altered.

Numerical studies commonly use such experimental data to define the material properties of the whole meniscus in simulation models. Homogenous, linear elastic, and isotropic or transversely isotropic material laws were typically applied to investigate effects of meniscal tears, meniscectomy, and contact pressure distributions in meniscus models (Haut Donahue et al., 2003, Meakin et al., 2003, Pena et al., 2005, Zielinska and Donahue, 2006, Pena et al., 2008, Mononen et al., 2012). A single-phase material formulation may be sufficient for specific aims if experimental data confirm the FE analysis results such as for a specific load case. However, one should be aware that insufficient material properties (e.g. too stiff or too soft) can lead to an over-or underestimation of the stresses, those acting on the articular cartilage for example. Thus, different studies elucidated the influence of material properties (Sauren et al., 1984, Aspden, 1985, Haut Donahue et al., 2003, Meakin et al., 2003, Yao et al., 2006), geometry (Aspden, 1985, Meakin et al., 2003) and load conditions (Spilker et al., 1992, Haut Donahue et al., 2002) on the outcome of the FE analysis. These studies either lacked subject-specific meniscal geometries along with experimental assessment of the individual response to validate the model (Sauren et al., 1984, Aspden, 1985, Spilker et al., 1992, Meakin et al., 2003), or they performed their analysis on only one specimen (Haut Donahue et al., 2002, Haut Donahue et al., 2003, Yao et al., 2006), which might not be representative of the wider spectrum. The material properties of biological tissue are highly variable (Sweigart et al., 2004) and thus different individuals might have material properties substantially different from the average values. Therefore, the objective of this study was to establish a method to accurately determine the individual material properties of the meniscus entity as a whole from in vitro MRI data of intact knee joints.

Section snippets

Study outline

A finite element analysis in combination with experimental data and optimization routines was utilized to determine the anisotropic, hyperelastic properties of the medial meniscus and its attachments (Fig. 1). In a previous study, five porcine knee joints were scanned in a magnetic resonance imaging (MRI) device with and without axial load (Freutel et al., 2013). The geometry and displacement of the individual medial menisci under load were experimentally determined and utilized for this finite

Mesh sensitivity

The coarse mesh revealed an axial reaction force (RF) of 310 N with 18,930 elements. The evaluation of the standard voxel mesh with 40,925 elements resulted in a RF of 372 N and the fine mesh with 81,850 elements had an RF of 384 N. The change between coarse and standard mesh was 13.5% higher than the change between standard and fine mesh. Therefore, the standard mesh was determined to be sufficiently mesh-independent.

Material parameter

Five individual meniscus models with their adjacent attachments were created and

Discussion

With previously obtained experimental data, it was possible to determine the subject-specific material properties of the meniscus and its attachments. The optimization of the subject-specific material properties resulted in normalized root mean square errors (NRMSE) lower than the threshold value of 15% in all cases and as low as 1.2%. The two parameters describing the properties of the matrix (C10andD), showed smaller variation than the parameters representing the fibers (k1 and k2). The

Conflict of interest statement

In the name of the authors of the manuscript I declare that we do not have any financial or personal relationship with other people or organizations that could have inappropriately influenced this study.

Acknowledgments

This study was funded by the German Research Foundation (DFG: DU254/5-2).

References (49)

  • E. Pena et al.

    Finite element analysis of the effect of meniscal tears and meniscectomies on human knee biomechanics

    Clin. Biomech.

    (2005)
  • A.M. Seitz et al.

    Stress-relaxation response of human menisci under confined compression conditions

    J. Mech. Behav. Biomed. Mater.

    (2013)
  • R. Shirazi et al.

    Analysis of articular cartilage as a composite using nonlinear membrane elements for collagen fibrils

    Med. Eng. Phys.

    (2005)
  • R. Shirazi et al.

    Role of cartilage collagen fibrils networks in knee joint biomechanics under compression

    J. Biomech.

    (2008)
  • R.L. Spilker et al.

    A transversely isotropic biphasic finite element model of the meniscus

    J. Biomech.

    (1992)
  • C. Stehling et al.

    Loading of the knee during 3.0 T MRI is associated with significantly increased medial meniscus extrusion in mild and moderate osteoarthritis

    Eur. J. Radiol.

    (2012)
  • W.R. Taylor et al.

    Tibio-femoral joint contact forces in sheep

    J. Biomech.

    (2006)
  • M. Tissakht et al.

    Tensile stress–strain characteristics of the human meniscal material

    J. Biomech.

    (1995)
  • D.F. Villegas et al.

    Failure properties and strain distribution analysis of meniscal attachments

    J. Biomech.

    (2007)
  • Z.A. Zarins et al.

    Cartilage and meniscus assessment using T1rho and T2 measurements in healthy subjects and patients with osteoarthritis

    Osteoarthr. Cartil.

    (2010)
  • R.M. Aspden

    A model for the function and failure of the meniscus

    Eng. Med.

    (1985)
  • A. Bedi et al.

    Dynamic contact mechanics of the medial meniscus as a function of radial tear, repair, and partial meniscectomy

    J. Bone Jt. Surg. Am.

    (2010)
  • H.N. Chia et al.

    Compressive moduli of the human medial meniscus in the axial and radial directions at equilibrium and at a physiological strain rate

    J. Orthop. Res.

    (2008)
  • Dynardo, 2011. Optislang: the optimizing structural language—software documentation. DYNARDO GmbH, Weimar,...
  • Cited by (22)

    • Hyperelastic parameter identification of human articular cartilage and substitute materials

      2022, Journal of the Mechanical Behavior of Biomedical Materials
      Citation Excerpt :

      Dusfour et al., 2020) In an even more complex procedure, a whole joint can be used to inversely identify material parameters. ( Freutel et al., 2015) In this work, we evaluate the suitability of material parameters determined through direct and inverse PI, respectively, for numerical simulations.

    • Mechanical properties of meniscal circumferential fibers using an inverse finite element analysis approach

      2022, Journal of the Mechanical Behavior of Biomedical Materials
      Citation Excerpt :

      Numerous studies have been conducted to understand the complex behavior of the meniscus and to develop appropriate constitutive models to predict this behavior (Kazemi et al., 2013). Several solutions, mostly depending on the loading condition considered, have been proposed including; poroelastic (Haemer et al., 2012; Morejon et al., 2021), poro-viscoelastic (Seitz et al., 2013), poro-hyper-viscoelastic (Seitz et al., 2013), fibril-reinforced poro-hyper-viscoelastic (Quiroga et al., 2014), transversely isotropic biphasic linear elastic (LeRoux and Setton, 2002), transversely isotropic poro-hyperelastic (Freutel et al., 2015), and transversely isotropic poro-hyper-viscoelastic (Seyfi et al., 2018). The present contribution focused on the mechanical characterization of the circumferential collagen fibers in the meniscus.

    • Development of particle swarm and topology optimization-based modeling for mandibular distractor plates

      2020, Swarm and Evolutionary Computation
      Citation Excerpt :

      The optimal miniplate-miniscrew configuration offers less screw-loosening risk, minimal implant volume and better callus stability. In the recent years, there has been a significant rise in the interest of both Topology Optimization and several metaheuristic optimization techniques such as Genetic Algorithm (GA) [23–25] Simulated Annealing (SA) [26], Particle Swarm Optimization (PSO) [27,28], in the field of biomechanics. While topology optimization offers the best material distribution in a design space, the previously mentioned metaheuristic approaches provides less computational cost compared to numerical optimization methods since they are derivative-free algorithms.

    View all citing articles on Scopus
    View full text