Modelling the Cryopreservation Process of a Suspension of Cells: The Effect of a Size-Distributed Cell Population - Computational Modeling in Tissue Engineering - page 140

at various operating conditions. This is done both in absence or presence of a
cryo-protectant agent, as well as when the extra-cellular ice is assumed to form
under thermodynamic equilibrium or its dynamics is taken into account consis-
tently by means of an additional population balance. More specifically, the effect
of the cell size distribution on system behaviour when varying cooling rate and
cryo-protectant content within practicable values for a standard cryopreservation
protocol is investigated. It is demonstrated that, cell survival due to intra-cellular ice
formation depends on the initial cell size distribution and its osmotic parameters.
At practicable operating conditions in terms of cooling rate and cryo-protectant
concentration, intra-cellular ice formation may be lethal for the fraction of larger size
classes of the cell population 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.
1 Introduction
In the tissue engineering field, preservation is a core technology to bring cell-based
products to market, as they have to be supplied on demand [ 18 ]. In general,
preservation can be defined as the process of reversibly arresting the biochemical
reactions, i.e. the metabolism of an organism, thus reaching the so-called state of
suspended animation.
The principal preservation method consists of freezing the bio-specimens to
cryogenic temperature in order to take advantage of the preservative power of the
cold. Indeed, compared to the other preservation methods like maintaining the bio
samples in continuous culture, cryopreservation has the benefits of affording
long shelf lives, genetic stability, reduced microbial contamination risks, and
cost effectiveness [ 18 ]. The other side of the coin is that cryopreserved bio-
logical material can be damaged by the cryopreservation process itself [ 25 ].
Cryopreservation consists of cooling to subzero temperatures with or without a
Cryo-Protectant Agent (CPA), storage, thawing and return to physiological envi-
ronment for specific usages. A part from the storage, all these stages are potentially
able to damage the cells due to the physical and/or chemical phenomena involved.
Limiting the analysis to the cryopreservation process of a cell suspension where
heat transfer phenomena are less restrictive than for 2-D and 3-D tissue samples, in
general during the cooling stage ice initially forms in the extra-cellular medium
surrounding the cells. As the extra-cellular ice phase grows, the extra-cellular
solute concentration increases, thus imposing a chemical potential difference
between the cytoplasm and the unfrozen external solution which acts as the driving
force for water diffusion out of the cell through the plasma membrane, i.e. the
osmotic transport. The rate of the osmotic water transport is limited by the per-
meability of the plasma membrane to water, and the osmotic equilibrium can be
maintained only if the rate of cooling is sufficiently slow. If the temperature is
lowered too fast, a significant dehydration cannot take place and the cytoplasm