Nutrient gradients in engineered cartilage: metabolic kinetics measurement and mass transfer modeling

Since tissue-engineered cartilage is avascular, both nutrient supply and metabolic waste removal rely on diffusion. As a result, gradients of nutrients and wastes exist through the construct. Previous models usually calculate gradients of oxygen, glucose, and lactic acid separately, without taking into account the complex interdependence between concentrations of these substrates and rates of metabolism. In this study, these interactions were experimentally examined and incorporated into diffusion models. One-dimensional diffusion-reaction models were developed for three typical culture conditions, that is, static culture, perfusion culture, and suspended culture. The profiles of oxygen, glucose, lactic acid, and pH in the cultured constructs were calculated simultaneously using measured metabolic rates. The maximum construct size and cell density which could be supported before nutrients were depleted in the construct center was identified; a function predicting the relationship between construct dimension and the maximum viable cell density was developed. For constructs incubated under static culture the model demonstrated that the gradients which developed through the medium could not be neglected. Perfusion cultures could support a considerably higher cell density than static cultures, while for batch cultures in a rotating bioreactor, the volume of medium also influences the maximum cell density that could be supported. This study provides useful guidance for design of engineered cartilage constructs.