Modelling the Cryopreservation Process of a Suspension of Cells: The Effect of a Size-Distributed Cell Population - Computational Modeling in Tissue Engineering - page 141

becomes super-cooled when low temperatures are reached, indeed. In such a case,
a driving force for Intra-cellular Ice Formation (IIF) is established and a severe
damage of cells results that may even lead to lethality as a consequence of
membrane rupture and mechanical deformation. Actually, during freezing cell
injury occurs due not only to IIF taking place at high cooling rates, but also to the
''solution effects'' taking place at low cooling rates, when excessive, intolerable
cell dehydration and electrolyte concentrations may be reached [ 27 ]. As a result,
post thaw-viability of cryopreserved cell suspensions may be relatively low both at
high and low cooling rates, depending on the specific operating conditions adopted
and sample geometry and size [ 28 ].
In principle, an optimum cooling rate exists where the two mechanisms of
damage (i.e. IIF and solution injuries) are balanced and the probability of cell
survival reaches a maximum. The optimum cooling rate differs from cell to cell
lineage, as the result of different bio-physical properties such as water and CPA
permeabilities through plasma membrane which affect the dehydration rate and the
Probability of IIF (PIIF). In this context, the advent of CPAs represents a sort of
panacea in the field of cryopreservation technology, so much so that they are
routinely used in any standard cryopreservation protocol experimentally adopted
in a bio lab. This widespread use of CPAs is due to the fact that they allow one to
significantly prevent cell damage from both the two major sources of risk. When
CPA is added, on one hand the thermodynamic temperature of ice formation is
naturally reduced according to the corresponding phase diagram (i.e. protection
against IIF injury in favour of the eventual vitrification of water). On the other
hand, a lower intra-cellular concentration of electrolytes which otherwise would
increase due to water exo-osmosis during cooling may be obtained (i.e. protection
against solution injury). Unfortunately, CPAs are known to be cytotoxic. This
cytotoxic effect varies from cell to cell lineage and it is more dangerous at higher
temperatures, depending on the contact time with the cells. Thus, in order to
minimise cell damage one has to select not only the proper type of CPA but, also
the best way to put a CPA in contact with the cells: the CPA concentration levels,
the temperatures for pre-freezing addition and post-thawing removal of CPA
(i.e. washing). Even the choice between one step or continuous modality when
adding/removing CPA from the cell suspension has to be made [ 13 , 14 , 31 ].
It is apparent that, every cell lineage requires its own cryopreservation protocol
to be developed and optimised through a rational design method. However, since
the number of experiments required for a rigorous optimisation of a cryopreser-
vation procedure is prohibitively large due to the high number of operating con-
ditions to be set, shortcomings of experimental protocol optimisation are
necessarily adopted. In this context, a sequential optimisation of individual
operating conditions is typically performed, thus reaching only a pseudo-optimal
solution, strongly dependent on the initial values used in the search. As a result, the
empirical development of cryopreservation procedures has been limited to systems
that are relatively robust, or those in which damage can be tolerated [ 28 ].
On the basis of these considerations, it is clear that modelling may represent a
helpful tool. Indeed, a successful design of cryopreservation procedures may be