Biomedical Engineering Reference
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class of the cell population. This generates the PIIF curve intersection reported in
Fig. 15 e. In this regard, it is worth noting that some experimental data reporting
this bizarre behaviour of intersecting PIIF curves are available in the literature
[ 12 , 34 ]. However, the corresponding theoretical interpretation based on the pre-
vious modelling approach addressing the sporadic nucleation of the single sized,
average cell was not provided. As such, these data were supposed to be the con-
sequence of scattered measurements. It is presumable that, the previous modelling
approach may be adopted to simulate this behaviour only by resorting to different
mechanisms of ice nucleation as it was done in order to justify the two-step profiles
reported in Fig. 9 d that are found also in Fig. 15 d-e. These different mechanisms of
ice nucleation should be assumed to act differently and eventually prevail each other
at different temperatures, as a function of the operating conditions due to unknown
(statistical) reasons. On the contrary, all these behaviours may now be compre-
hensively taken into account through our novel modelling approach, i.e. by
addressing the effect of the size distribution of the cell population with a single ice
nucleation mechanism. This way differently sized cells behave differently and their
fate during the cooling stage depends on the initial cells size distribution of the cell
population. Moreover, differently sized cells behave differently at the intermediate
cooling rates considered in our simulations -1to-100 C/min. This is noteworthy
from a practical perspective since only the intermediate cooling rates can actually be
attained nowadays for a suspension of cells inside a standard programmable cooling
chambers commercially available in the market.
As a representative example, the case of -50C/min is addressed in Fig. 16 .
Here, by keeping constant the cooling rate, the system behaviour at several,
increasing CPA contents (from 0 to 12 kosmol/m 3 water ) is shown in terms of g ice
and g water distributions at -60C reported as functions of the initial cell volume in
order to easily identify the classes of cells with different fates. It is apparent that,
the size distribution may affect the cooling stage of a cell population not only in
the absence (Fig. 16 a) but even in the presence of CPA (Fig. 16 b-e), respectively.
In general, the larger cells are more prone to form a lethal amount of intra-
cellular ice, whilst the smaller ones may even remain unfrozen and will eventually
vitrify. Depending on the specific CPA content and the adopted thresholds of g ice
and g water , it may also happen that only a small amount of ice is formed inside
medium sized cells (Fig. 16 a-b). On the other hand, all the differently sized cells
of the population may behave similarly, as it may be seen from Fig. 16 c and 16 f,
where
all
size
classes
result
to
be
lethally iced-up
at
-60C
or
unfrozen,
correspondingly.
Specifically, by progressively increasing the CPA content, the lethally frozen
portion of the cell population indicated by the dark shadowed area initially
increases and then decreases, till it completely vanishes, thus showing a maximum.
Correspondingly, the PIIF sigmoid first moves towards higher temperatures
reaching its maximum value equal to 1 whilst displaying a more abrupt, sharp
variation, and then returns back to the lower ones (not shown here for brevity).
Clearly, as already discussed previously, the CPA content of 12 kosmol/m 3 con-
sidered in Fig. 16 f may be too high so that cytotoxicity and excessive volumic
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