Dynamic matrix composition in engineered cartilage with stochastic supplementation of growth factors

Dynamic extracellular matrix (ECM) synthesis is explored in a hypothesized engineered cartilage construct. Growth (α) and decay (β) rate parameters are developed from a previous engineered cartilage model. The presented mathematical model was constructed from the parameterized experimental data using a deterministic and stochastic examination of ECM synthesis based on a negative feedback control mechanism. A growth factor supplementation is incorporated in a probabilistic mathematical approach. The growth factor component modified an initial deterministic model through a Gaussian white noise fluctuation. As the primary constituents of ECM, the mathematical tool is intended to characterize the probable steady state distribution of glycosaminoglycan (GAG) and collagen molecules as well as mean mass accumulation at homeostasis. Computer simulation of the models is applied to reported data from four similar chondrocyte-polymer construct culture systems. The range in rate ratios reflect the differing nature of GAG and collagen synthesis (α_GAG/β_GAG = 4.2 to 148.6; α_collagen/β_collagen = 8.1 to 2590.4). This technique reduced the influencing synthesis factors to a few key descriptive parameters. Additional anabolic and catabolic factors may further be built into the models.