A Monte Carlo simulation of nutrient diffusion and reaction in immobilized cell systems

In this study a Monte Carlo simulation was used to investigate the effect of cell reactivities and particle diffusivities in the cells and matrix on the diffusion and reaction rate constants in gel-immobilized cell systems with different spatial cell configurations. A variety of conditions were examined ranging from instantaneous to very slow reactions with reaction probabilities equal to or less than one, and diffusivity ratios bigger or smaller than one in a spherical domain. In the case of high reactivity (diffusion-limited), the simulation results indicated a decrease in the reaction rate constants when heterogeneity in the cell distribution was increased. In the case of low reactivity (reaction-limited), however, cell distribution did not significantly affect the reaction rate constants as both homogeneous and heterogeneous cell distributions resulted in similar rate constants. The simulation results also indicated an inverse dependence of the reaction rate constants on the diffusivity ratio in reaction-limited cases.