Biomedical Engineering Reference
In-Depth Information
represented by the phase diagram adopted to evaluate the driving forces of nucle-
ation and diffusion-limited growth of ice crystals (i.e. a binary phase diagram for the
water/NaCl system, and a ternary phase diagram for the water/NaCl/CPA system).
2.5 Extra-Cellular Ice Formation
In analogy to the intra-cellular compartment, even for the extra-cellular one an
independent equation is required to determine the extra-cellular volume of ice
V
ext
ice
ðÞ
when evaluating V
ext
water
ðÞ
from Eq.
2
. This task is accomplished by mod-
elling EIF.
In contrast with the intra-cellular compartment, EIF was traditionally described
by assuming that liquid solution and ice are constantly in thermodynamic equi-
librium conditions, thus neglecting the dynamics of EIF. The different assumptions
between intra- and extra-cellular compartments to describe the same physico-
chemical phenomenon of ice formation may be ascribed to the difference in the
volume capacities of the two compartments used in a standard cryopreservation
protocol. This reasoning has been already adopted above to justify that water
osmosis and CPA permeation cannot significantly change the extra-cellular
solution composition and volume. Thus, the relatively higher capacity of the
extra-cellular solution is also responsible for a faster ice formation with respect to
the intra-cellular one [
5
,
43
]. In fact, according to the classical nucleation theory,
ice nucleation rate increases if water volume increases (see Eq.
11
, due to the
statistically more frequent nucleation impact between water molecules. Therefore,
for the sake of model simplicity, traditionally in cryopreservation it was implicitly
assumed that the time scale of nucleation is much smaller in the extra-cellular
solution than inside the cells, and, accordingly, the corresponding ice formation
dynamics is so fast to practically reach equilibrium condition instantaneously.
In this case, Eq.
2
may not be used since all the variables necessary to describe
water osmosis and CPA permeation through Eqs.
5
and
7
(i.e. NaCl and/or CPA
concentrations in the extra-cellular compartment) may be directly obtained from
the corresponding phase diagram.
Actually, the assumption of thermodynamic equilibrium conditions should be
regarded as a model simplification, since any natural phenomenon is characterised
by a dynamics. If the time scales of the different phenomena involved in a process
are relatively different, this model simplification is reasonable. However, this is
not always the case, since the operating conditions may be changed, and the time
scales change accordingly. Thus, the assumption of equilibrium conditions needs
to be verified on a case by case basis.
On the other hand, there is experimental evidence that the temperature of EIF
plays an important role in optimising post-thaw viability of the cells [
30
]. For
example, different kinetics of IIF at slow cooling rates was found depending on
whether or not ice-crystals were seeded in the external solution [
42
]. Moreover, the
kinetics of IIF was found to strongly depend on the specific temperature at which
Search WWH ::
Custom Search