formation. For slow cooling approaches, formation of ice in the
extracellular space concentrates extracellular solutes, providing a
driving force for water to flow out of the cell. CPAs protect cells
by reducing the extent of this cell dehydration and by mitigating
damage caused by the increasingly freeze-concentrated extracellular
solution. The goal of vitrification, on the other hand, is to
completely avoid ice crystallization and instead achieve a glassy
state throughout the sample by adding large amounts of CPA and
cooling and warming rapidly. The question of ice formation and the
amount that can be tolerated depends on the specimen. For tissues
and organs, extracellular ice formation can disrupt the spatial organization of the cells and extracellular matrix and compromise
mechanical integrity. As a result, vitrification is typically considered
to be the preferred approach for cryopreservation of complex samples such as tissues and organs.
Mass transfer modeling has been used for decades to guide the
design of cryopreservation methods for isolated cells. The backbone of these approaches is a mathematical model that describes the
flow of water and CPA across the cell membrane, which allows
prediction of changes in cell volume and intracellular CPA content.
Membrane transport models have classically been used to design
multistep CPA equilibration methods that avoid excessive cell volume changes [1, 2]. More recently membrane transport modeling
has been used to design CPA equilibration methods that not only
avoid excessive cell volume changes but also minimize protocol
duration or CPA toxicity [3–8]. In particular, our group has presented an approach for designing minimally toxic CPA equilibration methods for isolated cells [5–7]. This approach is based on the
minimization of a toxicity cost function using predictions of cell
membrane transport during CPA addition and removal. The resulting CPA addition methods involve exposure to CPA in hypotonic
buffer solution, which causes cell swelling. In contrast, conventional CPA addition methods utilize isotonic buffer and focus on
avoiding excessive cell shrinkage. This counterintuitive result highlights the potential for mathematical modeling and optimization to
open up promising new avenues of investigation.
Application of such mathematical modeling approaches to
three-dimensional tissues will require an appropriate mass transfer
model for predicting the evolution of CPA concentration in the
tissue with time, as well as potentially damaging changes in cell and
tissue volume. The mass transfer process in tissues is more complex
than that of isolated cells and requires consideration of the coupled
effects of cell membrane transport and mass transfer in the extracellular space, mechanical properties of the tissue and how they
relate to tissue volume changes, and fixed electrical charges in the
extracellular space. In the following, we briefly discuss some of
these mass transfer phenomena and provide an overview of tissue
mass transfer models that have been presented in the literature.
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Ross M. Warner and Adam Z. Higgins
extracellular space concentrates extracellular solutes, providing a
driving force for water to flow out of the cell. CPAs protect cells
by reducing the extent of this cell dehydration and by mitigating
damage caused by the increasingly freeze-concentrated extracellular
solution. The goal of vitrification, on the other hand, is to
completely avoid ice crystallization and instead achieve a glassy
state throughout the sample by adding large amounts of CPA and
cooling and warming rapidly. The question of ice formation and the
amount that can be tolerated depends on the specimen. For tissues
and organs, extracellular ice formation can disrupt the spatial organization of the cells and extracellular matrix and compromise
mechanical integrity. As a result, vitrification is typically considered
to be the preferred approach for cryopreservation of complex samples such as tissues and organs.
Mass transfer modeling has been used for decades to guide the
design of cryopreservation methods for isolated cells. The backbone of these approaches is a mathematical model that describes the
flow of water and CPA across the cell membrane, which allows
prediction of changes in cell volume and intracellular CPA content.
Membrane transport models have classically been used to design
multistep CPA equilibration methods that avoid excessive cell volume changes [1, 2]. More recently membrane transport modeling
has been used to design CPA equilibration methods that not only
avoid excessive cell volume changes but also minimize protocol
duration or CPA toxicity [3–8]. In particular, our group has presented an approach for designing minimally toxic CPA equilibration methods for isolated cells [5–7]. This approach is based on the
minimization of a toxicity cost function using predictions of cell
membrane transport during CPA addition and removal. The resulting CPA addition methods involve exposure to CPA in hypotonic
buffer solution, which causes cell swelling. In contrast, conventional CPA addition methods utilize isotonic buffer and focus on
avoiding excessive cell shrinkage. This counterintuitive result highlights the potential for mathematical modeling and optimization to
open up promising new avenues of investigation.
Application of such mathematical modeling approaches to
three-dimensional tissues will require an appropriate mass transfer
model for predicting the evolution of CPA concentration in the
tissue with time, as well as potentially damaging changes in cell and
tissue volume. The mass transfer process in tissues is more complex
than that of isolated cells and requires consideration of the coupled
effects of cell membrane transport and mass transfer in the extracellular space, mechanical properties of the tissue and how they
relate to tissue volume changes, and fixed electrical charges in the
extracellular space. In the following, we briefly discuss some of
these mass transfer phenomena and provide an overview of tissue
mass transfer models that have been presented in the literature.
174
Ross M. Warner and Adam Z. Higgins