Nonsteady state oxygen transport in engineered tissue: Implications for design

Engineered tissue constructs are limited in size, and thus clinical relevance, when diffusion is the primary mode of oxygen transport. Understanding the extent of oxygen diffusion and cellular consumption is necessary for the design of engineered tissues, particularly those intended for implantation into hypoxic wound sites. This study presents a combined experimental and computation model to predict design constraints for cellularized fibrin tissues subjected to a step change in the oxygen concentration to simulate transplantation. Nonsteady state analysis of oxygen diffusion and consumption was used to estimate the diffusion coefficient of oxygen (mean±SD, 1.7×10 ^-9±8.4×10^-11 m²/s) in fibrin hydrogels as well as the Michaelis-Menten parameters, V_max (1.3×10^-17±9.2×10^-19 mol·cell^-1·s^-1), and K_m (8.0×10^-3±3.5×0^-3 mol/m³), of normal human lung fibroblasts. Nondimensionalization of the governing diffusion-reaction equation enabled the creation of a single dimensionless parameter, the Thiele modulus (φ), which encompasses the combined effects of oxygen diffusion, consumption, and tissue dimensions. Tissue thickness is the design parameter with the most pronounced influence on the distribution of oxygen within the system. Additionally, tissues designed such that φ<1 achieve a near spatially uniform and adequate oxygen concentration following the step change. Understanding and optimizing the Thiele modulus will improve the design of engineered tissue implants.