Evaluation of Diffusive Transport and Cellular Uptake of Nutrients in Tissue Engineered Constructs Using a Hybrid Discrete Mathematical Model

Tissue engineering systems for orthopedic tissues, such as articular cartilage, are often based on the use of biomaterial scaffolds that are seeded with cells and supplied with nutrients or growth factors. In such systems, relationships between the functional outcomes of the engineered tissue construct and aspects of the initial system design are not well known, suggesting the use of mathematical models as an additional tool for optimal system design. This study develops a reaction-diffusion model that quantitatively describes the competing effects of nutrient diffusion and the cellular uptake of nutrients in a closed bioreactor system consisting of a cell-seeded scaffold adjacent to a nutrient-rich bath. An off-lattice hybrid discrete modeling framework is employed in which the diffusion equation incorporates a loss term that accounts for absorption due to nutrient uptake by cells that are modeled individually. Numerical solutions are developed based on a discontinuous Galerkin finite element method with high order quadrature to accurately resolve fine-scale cellular effects. The resulting model is applied to demonstrate that the ability of cells to absorb nutrients over time is highly dependent on both the normal distance to the nutrient bath, as well as the nutrient uptake rate for individual cells.