Application of a cell-dense triphasic model to cryoprotectant equilibration

The loading of cryoprotectants (CPAs) into tissue remains challenging due to the risk of both mechanical strain on the tissue and the risk of toxicity damage from the cryoprotectants flooding into the tissue. Many models have been developed to describe the loading of CPAs into either individual cells, or continuously into a thin slab of tissue, however there is little evidence of the two models being combined. To that end, we propose a model that builds upon the triphasic model for articular cartilage introduced in Abazari et. al. 2009, using a system of partial differential equations to describe the mass transport of each component, namely, water, CPA, salt, and the solid matrix. Within this system we incorporate the well-known two-parameter model (Kleinhans, 1998) to describe the cell membrane transport of both water and CPA within individual cells. Combining these two systems allows us to investigate the stress placed on the tissue by considering the interactions at both an extracellular and intracellular fluid level. In addition, this general model allows us to specify properties of a tissue, ranging from their structure and composition, i.e., their percentage of tissue solids and cells, to their hydraulic conductivity and CPA permeability rates. Using all of this information, and by defining a bath solution containing a CPA concentration, our model is able to predict the amount of stress that will be placed on the tissue during CPA loading. We will use our results to create optimised loading protocols to reduce the overall strain on the tissue during CPA loading.