Application of interval arithmetic in numerical modeling of cryopreservation process during cryoprotectant loading to microchamber

This article presents numerical modeling of the heat and mass exchange occurring in a two-dimensional axially symmetric articular cartilage sample submerged in a microchamber into CPTes2 bathing solution undergoing cryopreservation. In the considered mathematical model, the parameters defined as interval numbers were assumed. The heat transfer process was described by the interval Fourier equation, the transport of cryoprotectant (CPA) through the cell membrane was given by a two-parameter model including the simulation of H₂O volume in chondrocytes and the change of DMSO concentration in time. In addition, the transport of CPA via microchannels to the sample in the microchamber was descripted by the Navier-Stokes equation. The model uses the liquidus tracking (LT) protocol introduced by Pegg et al. and refined by Yu et al. This approach regulates both the temperature and the concentration of CPA in the bathing solution. The protocol protects chondrocytes from ice crystal, osmotic stress, and electrolyte damage. The entire cryopreservation process considered is divided into 7 periods in the cooling and CPA supply phase and 6 periods in the heating and CPA removal phase, which allows precise regulation of the temperature and cryoprotectant (CPA) concentration in the bath solutions. In the final part of the article the results of numerical simulations are presented.