Modelling the Cryopreservation Process of a Suspension of Cells: The Effect of a Size-Distributed Cell Population - Computational Modeling in Tissue Engineering - page 168

CPA permeation through the membrane. As a consequence, at the end of equili-
bration stage (i.e. at the beginning of the cooling one) the actual intracellular water
volumic content is almost similar to the initial, isotonic one, so that it remarkably
affects IIF kinetics (i.e. Eqs. 1 and 11 ) and its interplay with osmosis rate. This
result is in contrast with the typical consideration that IIF inhibition by CPA is
partially related to the reduction of intra-cellular water volume through CPA
entrapment during equilibration [ 16 , 19 ].
Turning our attention to the cooling stage of the modelled cryopreservation
process, it is noteworthy that when using an increasing CPA content two main
effects may generally result: the osmosis phenomenon is hindered and the viscosity
of the intracellular liquid solution (cytoplasm) increases. These have contrasting
effects on IIF and may prevail each other depending on the adopted cooling rate
and the volume class of cells. More specifically, according to the phase diagram as
CPA increases the thermodynamic temperature for phase change from liquid
solution to ice is lowered, so that EIF may take place only at lower temperatures.
As a consequence, during cooling at a given cooling rate the cells start to loose
their internal water through osmosis later, at lower temperatures. Then, more water
eventually remains entrapped inside the cells, thus favoring IIF. In conclusion, if
CPA increases IIF is thermodynamically favored, because exo-osmosis is ther-
modynamically limited. On the other hand, if CPA increases the intra-cellular
solution viscosity increases as well. This represents a kinetic limitation for IIF,
since the liquid diffusion that limits the nucleation and growth of ice crystals is
reduced, accordingly.
These are the general considerations that help to understand and rationalise the
results of the simulations performed in presence of CPA as grouped in Fig. 15 .
Here the PIIF is reported as a function of temperature for different cooling rates, at
various CPA concentrations. It is shown that, the sigmoidal plot of PIIF as a
function of temperature dramatically changes when varying the cooling rate.
If CPA is absent, the PIIF sigmoid moves towards higher temperatures when
increasing the cooling rate (the solid lines of Fig. 15 a-f).
This is expected and it is a well-known behaviour of the system, i.e. cells are
iced up at higher temperatures (IIF is favoured) when increasing the cooling rate, if
CPA is absent.
On the other hand, IIF may be favored even in presence of CPA, which is not
consistent with the common thought that the antifreeze should always decrease the
IIF temperature [ 2 , 17 ]. This is shown in Fig. 15 a-b where at the lowest cooling
rates considered (i.e. -1C/min and -10C/min) the paradox of increasing IIF
temperature when increasing CPA concentration is now obtained. Actually, also
this undesired effect is well known in the literature [ 17 , 19 ]. It is due to the
thermodynamic limitation of water exo-osmosis that enhances IIF, if CPA content
increases at low cooling rates. On the contrary, at relatively higher cooling rates
(i.e. -400C/min, in Fig. 15 f) IIF is inhibited and it occurs at lower temperatures
when increasing CPA content, as commonly expected. This is due to the kinetic
limitations resulting from an higher viscosity and lower diffusivity of the cyto-
plasmic solution that, at these operating conditions, overcomes the thermodynamic