Biomedical Engineering Reference
In-Depth Information
Therefore it can be concluded that, depending on the particular system of
interest (cell lineage) and the employed cooling rates, the assumption of extra-
cellular thermodynamic equilibrium is not generally valid. A dynamic description
of the extra-cellular ice formation should be used to increase the predictive
capabilities of the model for realistic operating conditions.
3.3 The Effect of CPA
When CPA comes into play, system behaviour is more complex. For this reason,
our model investigations in presence of CPA have been performed only under the
classic assumption of thermodynamic equilibrium conditions for EIF. This way
only one factor at time with respect to our previous simulations have been
changed, thus helping the discussion and interpretation of the obtained theoretical
results.
Before beginning the analysis of the effect of CPA in our modelling approach, it
is necessary to recognise that the investigations performed have been limited to
practicable operating conditions. This is true from two different viewpoints. First,
in order to resemble the experimental procedure actually adopted in a standard
cryopreservation protocol, our model takes into account the simulation of the
initial equilibration stage as coupled to the subsequent cooling stage. This actually
represents a novelty in the field of cryopreservation modelling. As such, in our
investigations the simulation of the cooling stage always starts at the end of the
simulation of the preceding equilibration stage, especially in terms of the size
distribution of the cell population which we guess may play a role in our main
hypothesis. Secondly, the simulation of the two stages is always performed under
practicable conditions, i.e. cells initially under isotonic conditions are equilibrated
with CPA in a one-step addition at ambient temperature and then cooling starts
with a constant rate (''linear'' profile of system temperature). These represent
standard operations, even though different modalities have been proposed so far in
the literature especially for the equilibration stage (i.e. drop-by-drop or step-wise
addition and/or at low temperature). Moreover, only the region of relatively
slow cooling rates (i.e. 1-400C/min) and relatively low CPA concentrations
(i.e. 0-5000 osmol CPA = m water ) reported in the literature [ 19 ] is considered in our
investigations. Indeed, higher values of the cooling rates, i.e. 10 6 -10 13 C/min
investigated by Karlsson et al. [ 19 ], are not usually achieved, regardless the CPA
concentration levels. These extreme conditions do not resemble the standard
cryopreservation protocols adopted for biological samples of suspended cells, and
may not be obtained easily from a technological point of view. As a consequence,
the simulation of system behaviour under these relatively high cooling rates where
IIF is basically replaced by vitrification has not been performed. On the other hand,
due to its well known cytotoxic character, the cases of high CPA concentrations
are not considered either. This allows us to avoid drawing erroneous conclusions
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