Stirred-suspension bioreactors are an attractive modality for the large-scale manufacturing of stem cell products. Key to the stirred-suspension cultivation of cells is their agglomeration which influences viability, proliferation and the stem cell differentiation trajectory . A mathematical framework based on population balance equations (PBE) was applied to describe the temporal evolution of the size distribution of embryonic stem cell (ESC) aggregates cultured in a stirred-suspension bioreactor. Both cell proliferation and collision-induced aggregation were taken into account. Experiments were run at different agitation rates (60-100 rpm) and data on transient size distributions were collected. Coupling this information with the solution of the inverse problem  allowed for the extraction of aggregation kernels of ESCs cultivated in stirred suspension at different stirring speeds. The results obtained by forward simulation were in agreement with the experimental data supporting the validity of the computed kernels. The rate of change of the average aggregate size was greater at the intermediate stirring speed tested suggesting a trade-off between increased collisions and agitation-induced shear. More importantly, our study revealed that conditions at approximately the first 12 hours rather than the later stage (days 1-4) of cultivation determine the outcome of ESC culture. We conclude that the inverse problem framework can be applied to further our understanding of the dynamics of agglomeration processes transpiring in stem cell populations. Such frameworks are essential for the design and control of bioprocesses for the production of stem cell therapeutics.
 J. Wu, M.R. Rostami, D.P. O. Cadavid, E.S. Tzanakakis. Oxygen transport and stem cell aggregation in stirred-suspension bioreactor cultures. PLoS One 9(7):e102486, 2014.
 H. Wright et al. Solutions of inverse problems in population balances. – I. Aggregation kinetics. Comput. Chem. Eng. 16(12):1019-1038.