Dependence of cartilage matrix composition on biosynthesis, diffusion, and reaction

The steady-state composition of articular cartilage has previously been described as a balance between the metabolism of matrix molecules and the loss of these components from the tissue. Single compartment kinetic models have previously been developed to describe the relationship between these processes and overall (spatially-averaged) concentration of matrix molecules. Here, we develop a continuum model to describe the relationship between spatially-varying matrix concentrations and the processes of matrix formation, binding, degradation, and molecular transport within and from the cartilage tissue. At steady-state, the resultant concentration profile, and also spatially-averaged concentration, are predicted to depend on the balance between diffusivity and binding rate, diffusivity and formation rate, and various rate processes, some of which depend on tissue thickness. The predicted concentration profile, for certain parameter values, exhibits similarities to that known to exist for the proteoglycan matrix component, suggesting that transport factors may play an important role in causing the spatial variation in this component. Under other conditions, the predicted concentration profile may have a large portion of bound components and be relatively constant, consistent with the known distribution of collagen in cartilage. Thus, the continuum model may provide insight into the biophysical mechanism underlying matrix distribution within different regions of articular cartilage.