  A contemporary procedure to grow artificial tissue is to seed cells onto a
porous biomaterial scaffold and culture it within a perfusion bioreactor to
facilitate the transport of nutrients to growing cells. Typical models of cell
growth for tissue engineering applications make use of spatially homogeneous or
spatially continuous equations to model cell growth, flow of culture medium,
nutrient transport, and their interactions. The network structure of the
physical porous scaffold is often incorporated through parameters in these
models, either phenomenologically or through techniques like mathematical
homogenization. We derive a model on a square grid lattice to demonstrate the
importance of explicitly modelling the network structure of the porous
scaffold, and compare results from this model with those from a modified
continuum model from the literature. We capture two-way coupling between cell
growth and fluid flow by allowing cells to block pores, and by allowing the
shear stress of the fluid to affect cell growth and death. We explore a range
of parameters for both models, and demonstrate quantitative and qualitative
differences between predictions from each of these approaches, including
spatial pattern formation and local oscillations in cell density present only
in the lattice model. These differences suggest that for some parameter
regimes, corresponding to specific cell types and scaffold geometries, the
lattice model gives qualitatively different model predictions than typical
continuum models. Our results inform model selection for bioactive porous
tissue scaffolds, aiding in the development of successful tissue engineering
experiments and eventually clinically successful technologies.
