A mathematical model for tissue growth in a tissue-engineering scaffold pore

A tissue engineering scaffold is composed of pores lined with cells that allow nutrient-rich culture medium to pass through, thereby encouraging the proliferation of cells. Growth of the tissue is affected by a number of factors, including the flow rate and concentration of nutrients in the feed, the elasticity of the scaffold, and the properties of the cells. Many studies have examined these factors separately, but in this project, we aim to examine all of them together. In this work, we (i) develop a mathematical model that describes the dynamics and concentration of nutrients, scaffold elasticity, and cell proliferation; (ii) solve the model and simulate the cell proliferation process; (iii) develop a reverse algorithm that determines the initial scaffold pore configuration based on the desired geometry of the final tissue.