The Effect of Scaffold Morphology on Tissue Growth

Cell proliferation within a porous tissue-engineering scaffold depends on a sensitive choice of pore geometry and flow rates: regions of high curvature encourage cell proliferation while a critical flow rate is required to promote growth for certain cell types. When the flow rate is too slow the nutrient supply is limited; too fast and cells may be damaged by the high shear. As a result, determining appropriate tissue engineering construct geometries and operating regimes poses a significant challenge that cannot be addressed by experimentation alone. In this work, we present a mathematical theory for the fluid flow within a pore of a tissue-engineering scaffold, which is coupled to the growth of cells on the pore walls. We exploit the slenderness of a pore that is typical in such a scenario, to derive a reduced model that enables a comprehensive analysis of the system to be performed. We derive analytical solutions in a particular case and compare this with numerical solutions of the reduced model. We demonstrate how the simplified system may be used to make predictions on the design of a tissue-engineering scaffold and the appropriate operating regime, and present an example in which such a prediction can be made.