Modelling the Cryopreservation Process of a Suspension of Cells: The Effect of a Size-Distributed Cell Population - Computational Modeling in Tissue Engineering - page 162

Fig. 10 Partitioning of the
initial cell size distribution
at -60C based on the
thresholds of internal ice
volume percentage g ice and
total water content g water
when cooling at -50C/min
in absence of CPA (adapted
from [ 10 ])

4x10 16

1.0

η ice
η water

0.8

3x10 16

0.6

2x10 16

0.4

1x10 16

0.2

0 0.0

0.0

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

Cell volume, V [m 3 ]

The picture changes dramatically when the cooling rate is increased to
-50C/min. Now, the fate of the cells, as a consequence of the different interplay
between osmosis and IIF, strongly depends on their initial size. Indeed, the small
size class cells dehydrate significantly (see Fig. 9 c), so that IIF does not take place
(see Fig. 9 d, where PIIF \ 0.81). On the other hand, for the largest size class cells,
osmosis is relatively slower, so that undercooling and the consequent IIF takes
place above the eutectic temperature. In particular, these cells are responsible of
the first step of PIIF reported in Fig. 9 d, where it is seen that a certain portion of
the cell population ices up at about -4C.
At this relatively high temperature, ice growth is rapid (see Fig. 9 d, where PIIF
and PIIF init overlap significantly around -4C) and the entrapped and iced-up
intra-cellular water volume represents a relevant portion of these cells (see Fig. 9 d,
where PIIF and PIIF detect overlap significantly around -4C).
For the medium size class cells, an intermediate behaviour between these two
extremes occurs. The latter ones, similarly to the small size class cells, dehydrate
significantly without forming internal ice until the eutectic temperature is reached
when osmosis phenomenon stops, and IIF inevitably occurs. These cells are
responsible of the second step of PIIF reported in Fig. 9 d, where it is seen that a
portion of the cell population ices up at about -35C. However, at this low
temperature and high saline concentration ice growth is a relatively slow process
(in Fig. 9 d, PIIF very different from PIIF init at intermediate temperatures).
Moreover, due to the significant osmosis, the entrapped and iced-up intra-cellular
water volume does not represent a relevant portion of these cells (see Fig. 9 d
where an additional, second step for PIIF detect at -35C is absent).
In summary, at a cooling rate of -50C/min the behaviour of the cells strongly
depends on their initial size, as reported in Fig. 10 . Here the initial cell size
distribution is shown along with the g ice and g water distributions in order to
distinguish the fractions of cells that result to be unfrozen (i.e. small size class
cells represented by the white area, i.e. g ice \ 0.5), iced-up with a small,
innocuous amount of water (i.e. intermediate size class cells represented by the