optimize and understand cryobiological protocols. This was followed by a biochemical argument for the damage from too-low
cooling rates [2]. The combination of these two creates a prototype
of optimization of cooling rates in (quasi) equilibrium cryopreservation protocols. In fact, modern cooling rate optimization still
combines a mass transport model (to estimate intracellular water
concentration), the phase diagram, and an ice kinetics model (see,
e.g. [3] or [4]).
A more recent development in cryobiological modeling is its
use to understand CPA equilibration processes. Addressed in more
detail below, note that the step-change exposure of cells to high
concentrations of permeating cryoprotectants causes the cells to
experience a rapid loss of water volume due to the temporary large
osmotic transmembrane gradient coupled with the differential permeability to water and CPA in the cell membrane. This exosmosis
can cause the cell to shrink below a critical volume, called a “lower
osmotic tolerance limit,” associated with irreversible cell damage,
oftentimes after swelling back to isosmotic volume, suggesting
possible membrane fusion or membrane resorption at low volumes
as the mechanism of damage [5, 6]. Modeling has played a significant role both in demonstrating that some cryopreservation practices are likely unsuccessful due to these damaging effects [7], and
in suggesting “safe” CPA equilibration strategies that end with an
equivalent final concentration but through step-wise or other gradual approaches [8–14].
Modeling has matured since the 1960s, both from a biophysical model point of view, and from a computational point of view.
Most of this chapter will address some of the changes in biophysical
models. Regarding the computational aspect, note that one can
now easily solve nonlinear differential equations with minimal forethought, numerical optimization of protocols can be done using off
the shelf packages, and numerical visualization and graphics production is trivial. These are distinct advantages to all modern cryobiologists, but one of the additional benefits is that the
computational modeling of cryobiological processes is considerably
more accessible to non-mathematician scientists. In fact, one of the
aims of this chapter is to convince the non-mathematician scientist
that modeling provides a valuable tool for optimization of cryopreservation protocols.
While considerable modeling advances in cryopreservation
have been made, there is still much work at the forefront of the
field, including attempts to understand the relationship between
cooling rate, concentration, viscosity, and the likelihood of crystallization or recrystallization events. Moreover, there are new questions about the necessity of optimal cooling rates if ultrarapid
warming rates are available [15] (see Note 1), and there are open
questions about model selection, model temperature dependence,
appropriate solution theories, among many others. We recently
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James D. Benson
cooling rates [2]. The combination of these two creates a prototype
of optimization of cooling rates in (quasi) equilibrium cryopreservation protocols. In fact, modern cooling rate optimization still
combines a mass transport model (to estimate intracellular water
concentration), the phase diagram, and an ice kinetics model (see,
e.g. [3] or [4]).
A more recent development in cryobiological modeling is its
use to understand CPA equilibration processes. Addressed in more
detail below, note that the step-change exposure of cells to high
concentrations of permeating cryoprotectants causes the cells to
experience a rapid loss of water volume due to the temporary large
osmotic transmembrane gradient coupled with the differential permeability to water and CPA in the cell membrane. This exosmosis
can cause the cell to shrink below a critical volume, called a “lower
osmotic tolerance limit,” associated with irreversible cell damage,
oftentimes after swelling back to isosmotic volume, suggesting
possible membrane fusion or membrane resorption at low volumes
as the mechanism of damage [5, 6]. Modeling has played a significant role both in demonstrating that some cryopreservation practices are likely unsuccessful due to these damaging effects [7], and
in suggesting “safe” CPA equilibration strategies that end with an
equivalent final concentration but through step-wise or other gradual approaches [8–14].
Modeling has matured since the 1960s, both from a biophysical model point of view, and from a computational point of view.
Most of this chapter will address some of the changes in biophysical
models. Regarding the computational aspect, note that one can
now easily solve nonlinear differential equations with minimal forethought, numerical optimization of protocols can be done using off
the shelf packages, and numerical visualization and graphics production is trivial. These are distinct advantages to all modern cryobiologists, but one of the additional benefits is that the
computational modeling of cryobiological processes is considerably
more accessible to non-mathematician scientists. In fact, one of the
aims of this chapter is to convince the non-mathematician scientist
that modeling provides a valuable tool for optimization of cryopreservation protocols.
While considerable modeling advances in cryopreservation
have been made, there is still much work at the forefront of the
field, including attempts to understand the relationship between
cooling rate, concentration, viscosity, and the likelihood of crystallization or recrystallization events. Moreover, there are new questions about the necessity of optimal cooling rates if ultrarapid
warming rates are available [15] (see Note 1), and there are open
questions about model selection, model temperature dependence,
appropriate solution theories, among many others. We recently
130
James D. Benson