Modelling the Cryopreservation Process of a Suspension of Cells: The Effect of a Size-Distributed Cell Population - Computational Modeling in Tissue Engineering - page 159

Fig. 7 Comparison between
experimental data and model
results in terms of temporal
behaviour of the normalised
average cell volume of
isolated rat hepatocytes kept
at -1.1C when CPA is
absent (adapted from [ 9 ])

1.0

0.8

0.6

0.4

0.2

Experimental data [40]
Model prediction ( n 0 (V) in Fig. 3)

0.0

0 4 8 12 16

Time, t [s]

Although model output reasonably matches with the experimental data shown
in Fig. 5 (the average percentage error is about 10%), this result has been obtained
through a non-ideal fitting procedure involving five adjustable parameters. Since
this represents a relatively large set of parameters, the experimental validation of
the new approach needs to be completed by testing model reliability also through
prediction runs. More specifically, system behaviour measured at operating con-
ditions different from those adopted during the experimental runs used for the
regression analysis is predicted by keeping constant the values of the adjustable
model parameters as tuned in the fitting procedure. For example, the temporal
behaviour of the normalised average cell volume of rat hepatocytes measured at a
constant holding temperature of -1.1C in absence of CPA is reported in Fig. 7
along with model predictions ( R V n V; ðÞ dV R

þ1 þ1

V n 0

ðÞ dV).

0 0

Actually, due to the relatively high value of system temperature, IIF does not
really take place during this experimental run. Accordingly, the proposed model
does not predict IIF in any size class of the cell population (not shown). Thus
the good matching shown in Fig. 7 demonstrates the prediction capability of the
proposed PBM to describe the osmosis induced by the external ice formation when
IIF does not take place. In other words, in Fig. 7 only the reliability of the values
assigned to osmotic parameters during the fitting procedure may be evaluated.
Then, model reliability has been further tested by predicting system behaviour
when IIF occurs, in order to weigh up also the values fitted for the parameters
related to ice nucleation rate. In Fig. 8 , experimental data are compared to model
results in terms of PIIF measured at -40C as a function of the cooling rate.
As can be seen, the cumulative fractional number of cells that underwent IIF is
predicted with a reasonable accuracy when the cell size distribution reported in Fig. 3
is adopted. The matching is definitely better than the one obtained by means of the
sporadic nucleation model as reported by Toner et al. [ 40 ]. In particular, an abrupt
increment of PIIF j 40 C at about -100C/min is predicted by Toner et al. [ 40 ].