Towards a quantitative understanding of oxygen tension and cell density evolution in fibrin hydrogels.

The in vitro culture of hydrogel-based constructs above a critical size is accompanied by problems of unequal cell distribution when diffusion is the primary mode of oxygen transfer. In this study, an experimentally-informed mathematical model was developed to relate cell proliferation and death inside fibrin hydrogels to the local oxygen tension in a quantitative manner. The predictive capacity of the resulting model was tested by comparing its outcomes to the density, distribution and viability of human periosteum derived cells (hPDCs) that were cultured inside fibrin hydrogels in vitro. The model was able to reproduce important experimental findings, such as the formation of a multilayered cell sheet at the hydrogel periphery and the occurrence of a cell density gradient throughout the hydrogel. In addition, the model demonstrated that cell culture in fibrin hydrogels can lead to complete anoxia in the centre of the hydrogel for realistic values of oxygen diffusion and consumption. A sensitivity analysis also identified these two parameters, together with the proliferation parameters of the encapsulated cells, as the governing parameters for the occurrence of anoxia. In conclusion, this study indicates that mathematical models can help to better understand oxygen transport limitations and its influence on cell behaviour during the in vitro culture of cell-seeded hydrogels.