Mathematical modeling of cell proliferation in a scaffold with elastic branching channels

Tissue engineering scaffolds consist of pores lined with cells through which a nutrient-filled fluid passes. Over time, cells consume the nutrients and proliferate, causing the pores to shrink until they fill with tissue. Existing literature has investigated the effects of nutrient flow rate, nutrient concentration, cell hunger rate, scaffold elasticity, and shear stress on cell proliferation within cylindrically shaped pores. In this work, we model tissue growth considering all factors except nutrient concentration simultaneously while utilizing a branching structure; a scaffold which begins as a single pore that repeatedly bifurcates over the depth of the scaffold. Our objectives are the following: (i) develop a model of cell proliferation which includes nutrient flow dynamics and concentration, cell hunger, and scaffold elasticity; (ii) solve the model and then simulate the cell proliferation process; and (iii) optimize the initial configuration of the scaffold channels to maximize cell growth. We find that elasticity enhances overall tissue yields at the cost of time. Inelastic scaffolds yield tissue faster than elastic scaffolds, however their maximum yield is marginally lower. The results of this study are key to adapting the equations governing cell proliferation to more complex geometries, ones which can more accurately represent scaffolds used in experimental tissue engineering.