Modelling the Cryopreservation Process of a Suspension of Cells: The Effect of a Size-Distributed Cell Population - Computational Modeling in Tissue Engineering - page 158

Fig. 5 Comparison between
experimental and model
results in terms of PIIF when
CPA is absent at a cooling
rate of -400C/min
(adapted from [ 9 ])

1.0

0.8

0.6

0.4

Experimental data [40]
Model fitting ( n 0 (V) in Fig. 3)
Model simulation (n 0 (V) in Fig. 4)
Model simulation (n 0 (V) in Fig. 4)

0.2

0.0

-4 -6 -8 -10 -12 -14 -16

Temperature, T [°C]

Fig. 6 NaCl concentration
path of the smallest and the
largest classes of the cell
population on the phase
diagram when CPA is
absent at a cooling rate
of -400C/min (adapted
from [ 10 ]

0

Liquidus line
Smaller size class cells
Larger size class cells

-10

-20 Eutectic temperature

0.00

2.50x10 3 5.00x10 3 7.50x10 3 1.00x10 4 1.25x10 4 1.50x10 4

-3 ]

NaCl concentration, m NaCl [mol m water

n 0 (V) is depicted on the relevant phase diagram as a function of the system
temperature, during the cooling stage at -400C/min. It is worth noting that, the
occurrence of IIF may be recognised from the abrupt slope change of the path,
towards higher salt concentration values. It may be seen that, largest and smallest
size class cells follow different paths. Ice forms inside the largest size class cells at
about -5C, then the intra-cellular salt concentration rapidly increases, thus
reaching a final intra-cellular salt concentration higher than that one of the smallest
size class cells. Once IIF takes place, the computed sodium chloride concentration
profile significantly overlaps with the liquidus line. The smallest size class cells
undergo the same fate, but at quite lower temperature (& -17C).
Thus, differently sized cells in a population exhibit a different IIF temperature
under the same operative conditions. Specifically, the temperature of IIF is higher
for the larger cells and, correspondingly, the smaller cells are less prone to IIF.