In this paper, we present a growth mixture model for cartilage. The main features of this model are illustrated in a simple equilibrium boundary-value problem that is chosen to illustrate how a mechanical theory of cartilage growth may be applied to growth-related experiments on cartilage explants. The cartilage growth mixture model describes the independent growth of the proteoglycan and collagen constituents due to volumetric mass deposition, which leads to the remodeling of the composition and the mechanical properties of the solid matrix. The model developed here also describes how the material constants of the collagen constituent depend on a scalar parameter that may change over time (e.g., crosslink density); this leads to a remodeling of the structural and mechanical properties of the collagen constituent. The equilibrium boundary-value problem that describes the changes observed in cartilage explants harvested at different stages of a growth or a degenerative process is formulated. This boundary-value problem is solved using existing experimental data for developing bovine cartilage explants harvested at three developmental stages. The solution of the boundary-value problem in conjunction with existing experimental data suggest the types of experimental studies that need to be conducted in the future to determine model parameters and to further refine the model.

Transtibial amputees may experience decreased quality of life due to increased risk of knee joint osteoarthritis (OA). No prior studies have compared knee joint biomechanics for the same group of transtibial amputees in gait, cycling, and elliptical training. Thus, the goal of this study was to identify preferred exercises for transtibial amputees in the context of reducing risk of knee OA. The hypotheses were: 1) knee biomechanics would differ due to participant status (amputee, control), exercise, and leg type (intact, residual) and 2) gait kinematic parameters would differ due to participant status and leg type. Ten unilateral transtibial amputee and ten control participants performed exercises while kinematic and kinetic data were collected. Two-factor repeated measures analysis of variance with post-hoc Tukey tests and non-parametric equivalents were performed to determine significance. Maximum knee compressive force, extension torque, and abduction torque were lowest in cycling and highest in gait regardless of participant type. Amputee maximum knee extension torque was higher in the intact vs. residual knee in gait. Amputee maximum knee flexion angle was higher in the residual vs. intact knee in gait and elliptical. Gait midstance knee flexion angle timing was asymmetrical for amputees and knee angle was lower in the amputee residual vs. control non-dominant knees. The results suggest that cycling, and likely other non-weight bearing exercises, may be preferred exercises for amputees due to significant reductions in biomechanical asymmetries and joint loads.

A constituent based nonlinear viscoelastic (VE) model was modified from a previous study (Vena, , 2006, “A Constituent-Based Model for the Nonlinear Viscoelastic Behavior of Ligaments ,” J. Biomech. Eng., 128, pp. 449–457) to incorporate a glycosaminoglycan (GAG)-collagen (COL) stress balance using compressible elastic stress constitutive equations specific to articular cartilage (AC). For uniaxial loading of a mixture of quasilinear VE constituents, time constant and relaxation ratio equations are derived to highlight how a mixture of constituents with distinct quasilinear VE properties is one mechanism that produces a nonlinear VE tissue. Uniaxial tension experiments were performed with newborn bovine AC specimens before and after $∼55%$ and $∼85%$ GAG depletion treatment with guanidine. Experimental tissue VE parameters were calculated directly from stress relaxation data, while intrinsic COL VE parameters were calculated by curve fitting the data with the nonlinear VE model with intrinsic GAG viscoelasticity neglected. Select tissue and intrinsic COL VE parameters were significantly different from control and experimental groups and correlated with GAG content, suggesting that GAG-COL interactions exist to modulate tissue and COL mechanical properties. Comparison of the results from this and other studies that subjected more mature AC tissue to GAG depletion treatment suggests that the GAGs interact with the COL network in a manner that may be beneficial for rapid volumetric expansion during developmental growth while protecting cells from excessive matrix strains. Furthermore, the underlying GAG-COL interactions appear to diminish as the tissue matures, indicating a distinctive remodeling response during developmental growth.

A cartilage growth mixture (CGM) model is proposed to address limitations of a model used in a previous study. New stress constitutive equations for the solid matrix are derived and collagen (COL) remodeling is incorporated into the CGM model by allowing the intrinsic COL material constants to evolve during growth. An analytical validation protocol based on experimental data from a recent in vitro growth study is developed. Available data included measurements of tissue volume, biochemical composition, and tensile modulus for bovine calf articular cartilage (AC) explants harvested at three depths and incubated for $13days$ in 20% fetal borine serum (FBS) and 20% $FBS+β$-aminopropionitrile. The proposed CGM model can match tissue biochemical content and volume exactly while predicting theoretical values of tensile moduli that do not significantly differ from experimental values. Also, theoretical values of a scalar COL remodeling factor are positively correlated with COL cross-link content, and mass growth functions are positively correlated with cell density. The results suggest that the CGM model may help us to guide in vitro growth protocols for AC tissue via the a priori prediction of geometric and biomechanical properties.