Biomedical Engineering Reference
In-Depth Information
cells are less prone to IIF injury. Correspondingly, the PIIF results to be dependent
on the initial size distribution of the cell population and should not be related to
statistical variations. On the basis of this successful two-step experimental vali-
dation we felt safe to carry out model investigations on system behaviour when
CPA is used and EIF dynamics is taken into account. More specifically, the effect
of the cell size distribution when varying cooling rate and CPA concentration
within practicable values for a standard cryopreservation protocol is investigated.
On the other hand, experimental data related to these specific cases and suitable for
a proper comparison with our novel modelling approach are not available in the
literature. Thus, even if only from a theoretical perspective, the effect of removing
the limiting assumption of thermodynamic equilibrium in the extra-cellular
compartment may be carefully analysed along with the sequence of CPA addition
and cooling stages experimentally adopted. In this regard, we bridged the gap
between the modelling of the two subsequent stages (i.e. CPA equilibration and
cooling) that were independently studied so far in the literature, thus reaching a more
comprehensive description of system behaviour. The possibility to predict the effect
of specific combinations of operating conditions (i.e. cooling rate and CPA content)
on cell survival confirmed that IIF may be lethal for a fraction of the cell population
(i.e. larger size classes) whilst it may not reach a dangerous level for the intermediate
size class cells and it will not even take place for the smaller ones. EIF dynamics may
play a role in this context, depending on the used cooling rate. In addition, an original
and physically sound explanation for several, well-known experimental evidences,
which appeared in a number of articles available in the literature of cell cryopres-
ervation in presence of CPA, was comprehensively reached.
Finally, in the concluding section, the general outputs of the novel modelling
approach are summarised and the future directions are outlined by addressing the
limitations still present in the proposed model and the corresponding potential
improvements.
2 Model Section
2.1 Cell Model
In the framework of the mathematical modelling of cell response to cryopreser-
vation, the behaviour of a single cell is usually described through the ''saltwater
sack'' model [
45
], whose schematic representation is given in Fig.
1
.
Basically, the cell is seen as a spherical drop of a salty (NaCl) aqueous solution
representing the cytoplasm, where proteins, organelles, and other macromolecules
are suspended. For cryopreservation all these materials suspended in the cytoplasm
are actually inactive. As such, they are lumped together in the inactive cell fraction
which remains constant during cryopreservation, depending only on the specific
level of maturation achieved by the cell along its mitotic life-cycle. In this regard,
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