Mathematical modeling of cell growth in tissue engineering scaffold with complex internal morphology.*

This study introduces a network model aimed at optimizing scaffold designs in tissue engineering. Utilizing a variant of the Random Geometric Graph (RGG) method for network generation, the model simulates nutrient flow, mechanical stress distribution, and cellular migration within scaffold pores. It integrates fluid dynamics and elasticity principles to capture laminar flow and scaffold deformation. The governing equations for nutrient flow, nutrient concentration, scaffold elasticity, and cell growth are outlined, and scaling and non-dimensionalization techniques are applied to analyze the scaffold's microenvironment. The physical quantities of interest throughout the network are coupled via flux conservation at network junctions. The results underscore the significant impact of nutrient concentration and scaffold elasticity on tissue growth, providing actionable insights for designing scaffolds that enhance tissue regeneration.