Modelling the Cryopreservation Process of a Suspension of Cells: The Effect of a Size-Distributed Cell Population - Computational Modeling in Tissue Engineering - page 163

light shadowed area, i.e. g ice C 0.5 and g water \ 0.1), or iced-up with a large, lethal
amount of water (i.e. large size class cells represented by the dark shadowed area,
i.e. g ice C 0.5 and g water C 0.1).
The results of the simulations related to -400C/min are reported in Fig. 9 e-f.
At this relatively high cooling rate, ice forms inside cells of any size class at
temperatures above the eutectic one, in the range [-15 Cto-5C] (see Fig. 9 f).
Therefore, in Fig. 9 it is shown at a glance that, the different size classes of cells
behave similarly at the lowest and the highest cooling rates, albeit for different
reasons. Specifically, at low cooling rates a significant osmosis takes place thus
limiting IIF for all the different size classes of cells. On the contrary, at high
cooling rates osmosis is very limited, IIF is favoured and takes place rapidly and
lethally for all the different size classes of cells. Different fates among the size
classes of cells are obtained only at intermediate cooling rates, when osmosis and
IIF do not dominate each other and their interplay leads to completely unfrozen
small cells, lethally iced-up larger cells, and iced-up for intermediate class cells
but with an innocuous amount of ice (see Fig. 10 ).
On passing, it is worth noting that the two-step profile of PIIF versus
temperature shown in Fig. 9 d as obtained at the intermediate cooling rate of
-50C/min is qualitatively similar to the experimental behaviour reported by
Toner et al. [ 39 ] and Berrada et al. [ 4 ] even if with different cell lineages and
operating conditions. The corresponding interpretation was performed by
invoking two different ice nucleation mechanisms (namely surface and volumic
catalysed heterogeneous nucleation), acting at different temperatures on the
averaged size cells, in the framework of the sporadic nucleation modelling
approach. Instead, in this work such behaviour is simulated by considering only
one heterogeneous nucleation mechanism of ice formation taking place in a
population of differently sized cells.
When the assumption of thermodynamic equilibrium conditions is removed
thus accounting for a dynamic EIF, very similar results are obtained for the
extreme cooling rates (not reported for the sake of brevity). Indeed, at relatively
low and high cooling rates osmosis or IIF dominates each other, independently to
what occurs in the extra-cellular environment. More specifically, at a low cooling
rate of -1C/min osmosis is so slow that a dynamic EIF results to be as rapid as
the instantaneous ice formation obtained under the assumption of thermodynamic
equilibrium conditions. As such no difference is obtained between the two cases.
On the other hand, at relatively high cooling rates as -400C/min, osmosis is so
slow with respect to IIF that there is no interplay between any size class of cells
and the surrounding environment: cells of any size are basically isolated from
the surrounding medium. As such, considering a dynamic modelling of EIF or
thermodynamic equilibrium conditions is not relevant either.
It is then apparent that, at intermediate cooling rates, even when a dynamic EIF
is accounted for, the interplay between osmosis and IIF generates different fates
among the differently sized classes of cells just like it was obtained assuming
thermodynamic equilibrium conditions in the suspending medium. This is shown
in Fig. 11 , where the comparison between the simulation results obtained for the