Modelling the Cryopreservation Process of a Suspension of Cells: The Effect of a Size-Distributed Cell Population - Computational Modeling in Tissue Engineering - page 167

(a) (b)

1.2

4x10 16

n 0 (V) without CPA addition
n(V) with m ext
CPA,0 = 1000 osmol m -3 water

n(V) with m ext
CPA,0 = 2000 osmol m -3

water

1.1

n(V) with m ext
CPA,0 = 5000 osmol m -3

3x10 16

water

1.0

2x10 16

m ext

C PA,0 [osmol/m 3

water ]

0.9

1000
2000
5000

1x10 16

0.8

0

0.0

5.0x10 -15 1.0x10 -14 1.5x10 -14

0.00 0.01 0.02 0.03 0.04

Equilibration time, t eq [s]

Cell volume, V [m 3 ]

Fig. 13 Model results of the equilibration stage at different CPA concentrations: cell number
density distribution at start and end of equilibration (a), and average cell volume of the size-
distributed population as a function of time during equilibration (b) (adapted from [ 10 ])

Fig. 14 Histogram
representing the volume
composition of largest size
class cells after equilibration
with different CPA
concentrations
(adapted from [ 10 ])

1.50x10 -14

Cell volume
Water volume
CPA volume

-14

1.25x10

1.00x10 -14

7.50x10 -15

5.00x10 -15

2.50x10 -15

0.00

0 1000 2000 3000 4000 5000

ext
CPA,0 [mol m water

-3

CPA concentration, m ]

The start of the simulation for the cooling stage from the modelling results
obtained at the end of the equilibration stage represents a novelty that permits to
overcome the apparent limitation of previous IIF models. There, the modelling of
equilibration and cooling stages are not coupled, and at the beginning of cooling
stage it was assumed that intra-cellular water of the cells with isotonic volume is
simply replaced by a proper amount of CPA [ 19 ]. However, during the equili-
bration stage the CPA does not replace water, but it is basically added to the cell.
This is actually well known by all the investigators addressing the osmotic
response of cells and it may be clearly seen from Fig. 14 . Here, the behaviour of
the largest size class cells is considered as representative of the entire population.
Cell volume, as well as those ones of intracellular water and CPA, are respectively
shown after equilibration with different extra-cellular CPA concentration levels. It
is seen that whilst water volume remains constant, cell volume increases due to