Solution of a population balance equation for mouse ESCs (mESCs) cultured as aggregates in a 100 mL-spinner flask. Approximately 2 × 10
4 mESCs/mL were seeded and cultured for 4 days at 60 rpm as described.
17 Equation 12 was recast in terms of the logarithm of the mESC aggregate diameter
d (i.e.,

) instead of mass, assuming a spherical shape for single cells and aggregates. The von Smoluchowski kernel,

, was used and the equation was solved as described before.
170 
is an average shear rate (Eq. 3) in the culture vessel. The collision efficiency

was estimated in 12-h intervals based on distributions of mESC aggregate sizes determined by image analysis of micrographs. (
A) The first moment

of the density function

normalized to the total biomass (i.e.,

, where

is the diameter of a single mESC) is shown for mESC aggregates. (
B) Temporal profile of the total biomass. (
C) Values for the average diameter of mESC aggregates at different times. Gray bars: simulation; black bars: experimental data. Color images available online at www.liebertonline.com/ten.