Mathematical Modelling of Oxygen and Glucose Conditions for Mesenchymal Stem Cells in Culture and Bone Marrow

Abstract

The prevalence of 3D tissue culture systems is increasing in order to overcome the perceived limitations of 2D culture in terms of providing a biomimetic niche for cells. However, the move to 3D systems requires that the availability of nutrients and oxygen within a 3D system is understood. The aim of this project was to develop mathematical models which would allow conditions in 2D and 3D culture and in vivo to be better understood. A mass transfer model was developed using physical data from experiments, the conservation of mass and Fick’s law of diffusion, using the 2D and 3D culture of mesenchymal stromal cells as an exemplar system. The model was then used to create oxygen and glucose profiles in 2D and 3D (spheroids and suspension) culture to provide a basis for comparison between the different systems. Predicted mass transfer of oxygen was found not to be affected by spheroid culture when compared to 2D culture, however mass transfer of glucose was restricted creating significant glucose concentration gradients through the spheroids. The predicted profiles in spheroid culture were applied to other culture systems with the aim of inducing the changes observed in the mesenchymal stromal cells in spheroid culture Altered glucose concentrations were not sufficient to induce dedifferentiation in 2D adherent mesenchymal stromal cells nor result in the same cell size decrease as seen in 3D spheroid culture. Using suspension cultures, a comparable size decrease to 3D spheroid culture was observed. Mass transfer modelling of the in vivo mesenchymal stromal cells environment in bone marrow was also developed to compare the in vitro culture conditions to the natural environment. It is concluded that oxygen concentrations within cell culture are lower than in bone marrow but relatively stable in the culture systems modelled. Glucose concentrations are significantly reduced within spheroid culture.