For instance, the hypoxic cell fractions are larger in the plots from dishes compared to spinner flask cultures for the same size aggregates. This is most likely due to the faster transfer of O 2 from the medium bulk to each (+)-JQ1 aggregate in agitated vessels compared to static cultures. Practically however, we rarely observed aggregates with a radius over 300 mm and only in static cultures. The higher hindrance for O2 transport to large clusters possibly impacts ESC viability and reduces proliferation by stimulating differentiation. This and the agitation-induced shear in spinner flask cultures may limit further growth of bigger aggregates. However, stirred-suspension cultures accommodate high cell densities resulting in fluctuating O2 levels in the bioreactor. Agitation and proliferation also drive the formation and growth of aggregates over time with concomitant changes in the intra- and inter-aggregate concentrations of O2. Given the multitude of effects of O2 on stem cell physiology, predicting the time-variant distribution of O2 in scalable ESC aggregate cultures is highly desirable. To that end, a PBE model was developed for the temporal evolution of the ESC cluster size distribution in an SSB. The growth rate of ESC aggregates due to cell proliferation was described by the Gompertz equation. For this purpose, the growth of sparsely cultured mESC aggregates in dishes was monitored and the Gompertz parameters were evaluated based on the recorded size changes. The Gompertz model accurately described the growth of mESC aggregates. The maximum attainable size for mESC aggregates was calculated at 1600 mm. Parameters for the aggregation kernel were determined from size data of mESC aggregates cultured in spinner flasks. It should be noted that the kernel parameters were calculated from data of cell cultures at 0–72 hours. At longer times, aggregation was negligible and cell proliferation drove the increase in cluster size. With increasing agitation rate, the parameter value trends are such that the coalescence frequencies become lower. At 60 rpm, the mean aggregate radius increased to,105 mm on day 2 in line with the model predictions. Subsequent increase in aggregate size was less pronounced as the mean radius was approximately 150 mm. The corresponding average size at higher agitation rates was lower. The simulation results were corroborated by observations that a lower agitation rate generally promotes formation of larger aggregates. It should also be noted that the cell viability was not affected significantly by agitation. Taken together, the PBE model developed here allowed the prediction of the temporal evolution of the ESC aggregate size distribution. Simulation results were in good agreement with the experimental observations from stirred-suspension ESC culture at different agitation rates. The transport of factors among cells within 3D structures such as aggregates is an important aspect of the performance of cultivation systems. The importance becomes even more pronounced for stem.