Prediction of Growth Factor Effects on Engineered Cartilage Composition Using Deterministic and Stochastic Modeling

In the design of engineered tissues, guided balance of biomaterial degeneration with tissue synthesis offers refined control of construct development. The objective of this study was to develop a mathematical model that describes the steady state metabolism of extracellular matrix molecules (ECM: glycosaminoglycan and collagen) in an engineered cartilage construct taking into account localized environmental changes that may arise because of the application of growth factors. The variable effects of growth factors were incorporated in the form of random noise rather than the difference in rates of synthesis and catabolism. Thus, the frequency of ECM accumulation for each matrix molecule in the steady state under the random influence of growth factor was produced relative to the matrix carrying capacity. Published synthesis-rate time constants and steady state ECM conditions from chondrocyte-polymer scaffold composites provided both input and validation for the model. Although the presence of growth factors in the presented system dynamics were considered randomized, the results described a positive feedback or promotional ECM synthesis at low levels of growth factors. While a negative feedback or inhibition of ECM synthesis was characterized at higher levels of growth factors. This transition phenomenon is based on a comparison with the results of a steady state condition in the form of a deterministic model and supports previous reports of guided accumulation in musculoskeletal, connective, and neuronal tissues.