Chapter 5
Mathematical Modeling of Protectant Transport in Tissues
Ross M. Warner and Adam Z. Higgins
Abstract
Mass transfer of protectant chemicals is a fundamental aspect of cryopreservation and freeze-drying
protocols. As such, mass transfer modeling is useful for design of preservation methods. Cell membrane
transport modeling has been successfully used to guide design of preservation methods for isolated cells.
For tissues, though, there are several mass transfer modeling challenges that arise from phenomena
associated with cells being embedded in a tissue matrix. Both cells and the tissue matrix form a barrier to
the free diffusion of water and protective chemicals. Notably, the extracellular space becomes important to
model. The response of cells embedded in the tissue is dependent on the state of the extracellular space
which varies both spatially and temporally. Transport in the extracellular space can also lead to changes in
tissue size. In this chapter, we describe various mass transfer models that can be used to describe transport
phenomena occurring during loading of tissues with protective molecules for cryopreservation applications.
Assumptions and simplifications that limit the applicability of each of these models are discussed.
Key words Mass transfer, Diffusion, Cryoprotectant, Tissue, Fixed charges
1 Introduction
Cryopreservation and freeze-drying can be used to store biological
specimens, but freezing and drying can be very damaging. To
prepare a specimen to survive these processes, it is first necessary
to introduce protectants; these chemicals are referred to as either
lyoprotectants for freeze-drying or cryoprotectants (CPAs) for
cryopreservation. Transport phenomena play an important role in
preservation technology. Cryopreservation and freeze-drying both
subject biological samples to large temperature gradients leading to
transfer of heat, whereas loading cells or tissues with protective
agents results in mass transfer. In this chapter, we will focus on
delivery of CPAs into cells and tissues for cryopreservation applications, but many of the same principles apply to delivery of lyoprotectants as well.
There are two main cryopreservation approaches, slow cooling
and vitrification, and both of these approaches involve the use of
CPAs to help guard against the damage associated with ice
Willem F. Wolkers and Harrie ¨ tte Oldenhof (eds.), Cryopreservation and Freeze-Drying Protocols, Methods in Molecular Biology,
vol. 2180, https://doi.org/10.1007/978-1-0716-0783-1_5, © Springer Science+Business Media, LLC, part of Springer Nature 2021
173
Mathematical Modeling of Protectant Transport in Tissues
Ross M. Warner and Adam Z. Higgins
Abstract
Mass transfer of protectant chemicals is a fundamental aspect of cryopreservation and freeze-drying
protocols. As such, mass transfer modeling is useful for design of preservation methods. Cell membrane
transport modeling has been successfully used to guide design of preservation methods for isolated cells.
For tissues, though, there are several mass transfer modeling challenges that arise from phenomena
associated with cells being embedded in a tissue matrix. Both cells and the tissue matrix form a barrier to
the free diffusion of water and protective chemicals. Notably, the extracellular space becomes important to
model. The response of cells embedded in the tissue is dependent on the state of the extracellular space
which varies both spatially and temporally. Transport in the extracellular space can also lead to changes in
tissue size. In this chapter, we describe various mass transfer models that can be used to describe transport
phenomena occurring during loading of tissues with protective molecules for cryopreservation applications.
Assumptions and simplifications that limit the applicability of each of these models are discussed.
Key words Mass transfer, Diffusion, Cryoprotectant, Tissue, Fixed charges
1 Introduction
Cryopreservation and freeze-drying can be used to store biological
specimens, but freezing and drying can be very damaging. To
prepare a specimen to survive these processes, it is first necessary
to introduce protectants; these chemicals are referred to as either
lyoprotectants for freeze-drying or cryoprotectants (CPAs) for
cryopreservation. Transport phenomena play an important role in
preservation technology. Cryopreservation and freeze-drying both
subject biological samples to large temperature gradients leading to
transfer of heat, whereas loading cells or tissues with protective
agents results in mass transfer. In this chapter, we will focus on
delivery of CPAs into cells and tissues for cryopreservation applications, but many of the same principles apply to delivery of lyoprotectants as well.
There are two main cryopreservation approaches, slow cooling
and vitrification, and both of these approaches involve the use of
CPAs to help guard against the damage associated with ice
Willem F. Wolkers and Harrie ¨ tte Oldenhof (eds.), Cryopreservation and Freeze-Drying Protocols, Methods in Molecular Biology,
vol. 2180, https://doi.org/10.1007/978-1-0716-0783-1_5, © Springer Science+Business Media, LLC, part of Springer Nature 2021
173