A simple filtering procedure for removing negative values from numerical solutions of the advection equation

General tissue mass transfer model for cryopreservation applications

Successful cryopreservation of complex specimens, such as tissues and organs, would greatly benefit both the medical and scientific research fields. Vitrification is one of the most promising techniques for complex specimen cryopreservation, but toxicity remains a major challenge because of the high concentration of cryoprotectants (CPAs) needed to vitrify. Our group has approached this problem using mathematical optimization to design less toxic CPA equilibration methods for cells. To extend this approach to tissues, an appropriate mass transfer model is required. Fick's law is commonly used, but this simple modeling framework does not account for the complexity of mass transfer in tissues, such as the effects of fixed charges, tissue size changes, and the interplay between cell membrane transport and transport through the extracellular fluid. Here, we propose a general model for mass transfer in tissues that accounts for all of these phenomena. To create this model, we augmented a previously published acellular model of mass transfer in articular cartilage to account for the effects of cells. We show that the model can accurately predict changes in CPA concentration and tissue size for both articular cartilage and pancreatic islets, tissue types with vastly different properties.