Mathematical Modeling of Protectant Transport in Tissues

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.