Effects of elasticity on tissue growth in a tissue-engineering scaffold pore

Scaffolds engineered for use in tissue regeneration consist of multiple pores which are lined with cells, through which nutrient-rich culture medium flows. Nutrient solution circulates throughout the scaffold pores, promoting cellular proliferation. The proliferation process depends on several factors such as; scaffold geometry, the nutrient solution flow rate, the shear stress, and the elastic properties of the scaffold material. These factors greatly affect tissue growth rate. Recent studies focus on the first three factors, while in this work, we focus on the cellular growth rate in elastic scaffolds under constant flux of nutrients. As cells grow, the pore radius decreases, therefore, in order to sustain the nutrient flux, the inlet applied pressure at the top of the scaffold pore should be increased. This results in expansion of the elastic scaffold pore, which in turn influences the growth rate of cells. Under elastic conditions, the pore deformation allows further tissue growth beyond that of inelastic conditions. In this paper, our objectives are as follows: (i) develop a mathematical model for cell proliferation describing fluid dynamics, scaffold elasticity, and tissue growth; (ii) solve the models and then simulate the tissue proliferation process. The simulation can emulate real-life cell growth in a tissue engineering pore and offer a solution that reduces the numerical burdens. Our algorithm is demonstrated to be in agreement with experimental observations from literature.