Stress-relaxation response of human menisci under confined compression conditions

Abstract

The objective of this study was to determine the viscoelastic properties of human meniscal tissue during stress-relaxation under confined compression conditions. Lateral and medial longitudinal meniscus plugs of 25 donor knees (ntotal=150) were exposed to stress-relaxation tests under confined compression conditions at three compression levels (ε=0.1; 0.15; 0.2). Mathematical modelling using an exponential 1D-diffusion equation was used to predict the viscoelastic properties. Subsequently, finite element (FE) models were created using identical geometry, properties and test conditions as used for the in-vitro tests. Two constitutively different underlying mathematical formulations were applied to the FE models to reveal possible differences in their predictions for the relaxation response. While the first FE model mimicked the analytical model (FE1), the second FE model used a different biphasic, non-linear approach (FE2). Regression analyses showed promising coefficients of determination (R(2)>0.73) between the experimental data and the predictions obtained from the diffusion equation and the two FE models. Mean aggregate modulus, predicted with the diffusion equation (HA=64.0 kPa) was lower than those obtained with the two FE analyses (HA,FE1=91.9 kPa; HA,FE2=81.5 kPa). Mean hydraulic permeability (kFE2=1.5×10(-15)m(4)/Ns) of the second FE2 approach was statistically lower (p<0.01) than the other permeability values (k=3.9×10(-15)m(4)/Ns; kFE1=3.4×10(-15)m(4)/Ns). These differences are mainly due to the different underlying mathematical models used. However, when compared with corresponding literature, the results of the present study indicated good agreement. The results of the present study contribute to a better understanding of the complex nature of meniscal tissue and might also have an impact on the design of future meniscal substitutes.

Keywords: 1-D; AH; Aggregate modulus; Al(2)O(3); Aluminum oxide; Anterior (meniscal) horn; BC; BW; Biphasic model; Body weight; Boundary condition; Coefficient of determination; DNA; Deoxyribonucleic acid; E(eq); Equilibrium modulus; Equilibrium stress; FE; FE1; FE2; Finite element; First and second invariants of the right Cauchy-Green tensor; First, linear finite element approach; GAGs; Glycosaminoglycans; H(A); Hydraulic permeability; I(1), I(2); In vitro; Initial height of the sample; Initial porosity; J; Jacobian of the deformation gradient tensor; Kilopascal; Lamè parameters of the nonlinear, poroelastic solid structure; M; Meniscus; OA; One-dimension(al); Osteoarthritis; PH; PI; Pars intermedia; Posterior (meniscal) horn; R(2); SEM; Scanning electron microscope; Second, nonlinear finite element approach; Stiffening coefficient; Strain level (0.1, 0.15, 0.2); Strain-dependence exponential coefficient; Time; Viscoelastic properties; h(0); k; kPa; t; β; ε(i); λ, μ; σ(t→∞); φ(0).