Stresses and Strains in the Medial Meniscus of an ACL Deficient Knee under Anterior Loading: A Finite Element Analysis with Image-Based Experimental Validation

Abstract

The menisci are believed to play a stabilizing role in the ACL-deficient knee, and are known to be at risk for degradation in the chronically unstable knee. Much of our understanding of this behavior is based on ex vivo experiments or clinical studies in which we must infer the function of the menisci from external measures of knee motion. More recently, studies using magnetic resonance (MR) imaging have provided more clear visualization of the motion and deformation of the menisci within the tibio-femoral articulation. In this study, we used such images to generate a finite element model of the medial compartment of an ACL-deficient knee to reproduce the meniscal position under anterior loads of 45, 76, and 107 N. Comparisons of the model predictions to boundaries digitized from images acquired in the loaded states demonstrated general agreement, with errors localized to the anterior and posterior regions of the meniscus, areas in which large shear stresses were present. Our model results suggest that further attention is needed to characterize material properties of the peripheral and horn attachments. Although overall translation of the meniscus was predicted well, the changes in curvature and distortion of the meniscus in the posterior region were not captured by the model, suggesting the need for refinement of meniscal tissue properties.

Subject-Specific Finite Element Modeling of the Tibiofemoral Joint Based on CT, Magnetic Resonance Imaging and Dynamic Stereo-Radiography Data in Vivo

“…The menisci were therefore modeled as linearly elastic, transversely isotropic materials [1,2,4,9,10,16,25,30,[34][35][36]39,[43][44][45]52], where the modulus and Poisson's ratio were 20 MPa and 0.2, respectively, in the radial and axial directions, and 140 MPa and 0.3, respectively, in the circumferential direction [4,30,45,52]. Time dependent effects of the cartilage and menisci properties were not considered due to the quasi-static nature of the models [4,7,8,23,30,32,35,[40][41][42]48,53,54].…”

“…For the model in the DSX-based standing position, since the prescribed position of the femur relative to tibia is a final, known position from the experimental data, the only DOF permitted was an axial translation, allowing the femur to settle into its final position in response to the force applied. The femoral and tibial cartilage components were tied to the femur and tibia surfaces, respectively, while hard, frictionless contact was assumed for cartilage-cartilage and cartilage-meniscus interfaces [1,4,16,23,30,[32][33][34][35][37][38][39]42,43,45,46,48,55]. In all models, a large-strain formulation was used [38,46] to account for potentially substantial strains in the soft tissue components.…”

“…It has been shown that under this condition, the biphasic response of cartilage can be negligible and the single-phase linear isotropic constitutive law be applicable [40,41]. Therefore, cartilage was modeled as a homogeneous, elastic, linearly isotropic material [1,2,[4][5][6][7]9,16,23,25,30,32,33,[35][36][37][38][39][42][43][44][45][46] with a modulus of 15 MPa [4,9,25,30,35,45] and a Poisson's ratio of 0.46 [31][32][33]47,48].…”

“…The femur and tibia were modeled as rigid structures, which greatly reduced the computational time and has been shown to have minimal effect on the model predictions [1,4,6,9,23,[29][30][31][32][33][34][35][36][37][38][39]. Articular cartilage is known to be an anisotropic, biphasic material with a time constant approaching 1500 s [40,41].…”

“…The accuracy of FE model solutions depends on well-defined anatomical geometry, material properties and boundary conditions [1]. Given the considerable inter-subject variability in tissue structure morphology, personalized analyses and insights would require subject-specific FE modeling [2].…”