AN INVESTIGATION BY MATHEMATICAL-MODELING OF WHETHER MOUSE AND HUMAN PREIMPLANTATION EMBRYOS IN STATIC CULTURE CAN SATISFY THEIR DEMANDS FOR OXYGEN BY DIFFUSION

Mammalian preimplantation embryos are conventionally grown in small, static droplets of medium. By contrast, embryos within the oviduct are subject to mixing forces arising from the action of cilia and the contractions of the myosalpinx. Such forces will minimize the buildup of unstirred layers around the embryos and facilitate the exchange of gases and metabolites. We have devised a mathematical model to investigate whether preimplantation mouse and human embryos grown in static culture can satisfy their requirement for oxygen solely by diffusion i.e. in the absence of stirring. The model incorporates the diffusion coefficients for oxygen in the medium outside and within the embryo, the oxygen tension of the culture medium, the size of the embryo and its oxygen uptake. Solutions of the model are provided for mouse oocytes and 2-cell embryos, mouse blastocysts and human morulae. In each case, the model is solved for two different values of the diffusion coefficient of oxygen within the cell and of the oxygen content of the medium (5 and 20%). The conclusion is that mouse embryos in static culture are likely to be able to satisfy their demands for oxygen by diffusion alone, but that human embryos may become marginally hypoxic, especially at lower oxygen levels.