An analytical model has been developed for the prediction of the spatial and temporal distribution of the concentration of cryophylactic agent (CPA) in perfused tissues and organs. Perfusate concentration of the CPA is allowed to change according to a protocol in which the concentration increases linearly from zero during a time interval t0. Between time t0 and tf, the concentration is constant. The numerical results of this analysis show that the typical time required to reach an appropriate CPA concentration by simple diffusion alone is sufficiently long that the natural vascular network must be employed as a means of introducing the CPA. The results of this analysis also demonstrate the importance of careful protocol design with the aid of this model. There is evidence to show that protocols previously reported in the literature failed to achieve the appropriate CPA concentration. Further work in this area requires more detailed information concerning the diffusion coefficients of the various CPA's in biological tissues. With the aid of this information and the present model, optimum protocols can be designed so that the CPA concentration can be increased to the desired level without inducing osmotic shock. ?? 1979.
Rubinsky, B., & Cravalho, E. G. (1979). An analytical model for the prediction of the local concentration of cryophylactic agents in perfused organs. Cryobiology, 16(4), 362–371. https://doi.org/10.1016/0011-2240(79)90049-X