Material properties of individual menisci and their attachments obtained through inverse FE-analysis
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 (), showed smaller variation than the parameters representing the fibers ( and ). 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).
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