Mathematical modelling of human mesenchymal stem cell proliferation and differentiation inside artificial porous scaffolds.

We present a mathematical model for the proliferation and differentiation of human mesenchymal stem cells grown inside artificial porous scaffolds under different oxygen concentrations. The values of parameters in the model are determined by comparison of the model solutions to published experimental data, complemented with a sensitivity analysis of the fitted parameters. It is shown that a simple hypothesis whereby the secretion of extra-cellular matrix (ECM) is oxygen dependent and that ECM itself stimulates cell proliferation is sufficient to explain the experimental data, which under conditions of low oxygen reveals increased total cell proliferation, upregulation of the numbers of undifferentiated cells, and extended lag phase. These results may help further to understand how cells proliferate inside artificial materials and are of importance to the field of tissue engineering.