Multiphase modelling of cell behaviour on artificial scaffolds: effects of nutrient depletion and spatially nonuniform porosity

This paper contains analysis of a recently formulated multiphase model for the growth of biological tissue that comprises motile cells and water inside a rigid scaffold material. The model is extended here to include a term describing cell proliferation which is mediated by the supply of a diffusible nutrient and to include the case where the scaffold porosity varies in space. Numerical solutions of the model equations are presented for different values of the parameters. Comparison is drawn between the different types of growth that arise when using static or dynamic methods for seeding the scaffold with cells. Analytical solutions are presented for the limiting cases in which the coefficient of drag between the cells and the scaffold is very large or zero. In the limit of large time, solutions reveal preferential tissue growth in the vicinity of the scaffold edge due to depletion of nutrient by the cells, consistent with experimental results. However, it is shown that reducing the coefficient of drag between the scaffold and the cells overcomes the effects of nutrient depletion by increasing cell mobility, thereby leading to improved uniformity of the cell distribution within the scaffold.