ANALYSIS OF CELL-GROWTH IN A POLYMER SCAFFOLD USING A MOVING BOUNDARYAPPROACH

Two mathematical models of chondrocyte generation and nutrient consump tion are developed to analyze the behavior of cell growth in a biodegr adable polymer matrix. Substrate reaction and diffusion are analyzed i n two regions: one consisting of cells and nutrients and the other con sisting of only nutrients. A pseudo-steady state approximation for the transport of nutrients in these two regions is utilized. The rate of growth is determined by a moving boundary equation that equates the ra te at which the interfacial region between the cells and the void spac e moves to a substrate dependent growth reaction. The change in the lo cation of this interfacial region with time therefore depicts the rate at which the cells propagate. The two limiting cases discussed in thi s article represent extremes in how the cells will grow in the polymer matrix; one case assumes that cells grow inward from the external bou ndary, and the other case assumes that cells grow parallel to the exte rnal boundary. The results of both models are compared to experimental data found in the literature. it is found through these comparisons t hat the model parameters, including the unit cell spacing parameter L, the metabolic rate constant k, the growth rate constant k(G), and ext ernal mass transfer coefficient, K, may vary as the thickness of the p olymer matrix is changed, however, unrealistic and large changes in th e diffusion coefficients were required to account for the full range o f-experimental data. Furthermore, these results suggest modification o f the functional form of the growth kinetics to include substrate or p roduct inhibition, or death terms. Based upon diffusion/ reaction conc epts, these models for cell growth in a biodegradable polymer give bou nds for the upper and lower limits of the cellular growth rate and nut rient consumption in a polymer matrix and will aid in the development of more extensive models. (C) 1997 John Wiley & Sons, Inc.