A mathematical model for cell proliferation in a tissue-engineering scaffold pore

In a tissue-engineering scaffold pore lined with cells, nutrient-rich culture medium flows through the scaffold and cells proliferate. In this process, both environmental factors such as flow rate, scaffold elasticity, as well as cell properties have significant effects on tissue growth. Recent studies focused on effects of scaffold pore geometry, elasticity and nutrient depletion on tissue growth seperatley, while in this work, we focus on all of these effects togetther. Our objectives are threefold: (i) design a mathematical model for the cell proliferation describing fluid dynamics, scaffold elasticity, nutrient concentration and tissue growth; (ii) solve the models and then simulate the tissue proliferation process; (iii) design a `reverse algorithm' to find the initial configuration of the scaffold with the knowledge of the desired property of the final tissue geometry. Our model reduces the numerical burdens and captures the experimental observations from the literature. In addition, it provides an efficient algorithm to simulate the cell proliferation and determine the design of a tissue engineering scaffold given a desired tissue profile outcome.