Effects of spatial variation of cells and nutrient and product concentrations coupled with product inhibition on cell growth in a polymer scaffold.

The effects of spatial variation of cells and nutrient and product concentration, in combination with product inhibition in cell growth kinetics on chondrocyte generation in a polymer scaffold, are analyzed. Experimental studies reported previously have demonstrated spatial dependence in the cultivation of chondrocytes. In the present study, the cell-polymer system is assumed to consist of two distinct phases. The cells, fluid, polymer matrix, and extracellular matrix comprise one phase, and the other phase consists of a fluid and polymer matrix. The only two species in the fluid considered to affect cell growth are the nutrient and product. The multiphase transport process of these two species in the cell-polymer system is described by the species continuity equations and corresponding boundary conditions for each individual phase. A volume-averaging approach is utilized for this system to derive averaged species continuity equations for the nutrient and product concentrations. The volume-averaging approach allows for a single species in a two-phase system to be represented by a single averaged continuity equation. Competitive product inhibition, saturation kinetics of substrate, and cell population control are assumed to affect the cell growth kinetics. A modified Contois growth kinetic model is used to represent the three factors that affect cell growth. A parameter analysis is performed and the results are compared qualitatively with experimental data found in the literature.