Stem cell cryopreservation in three-dimensional (3D) scaffolds may offer better protection to cells leading to higher survival rates. However, it introduces heterogeneity in cryoprotective agent (CPA) concentrations, durations of exposure to CPA, and freezing and thawing rate within constructs. This paper applies a mathematical model which couples the mass transport of dimethyl sulphoxide (DMSO) in a cell-seeded spherical construct and cell membrane transport into mouse embryonic stem cells (mESCs) to predict overall cell survival rate (CSR) based on CPA equilibrium exposure times (t(E)) and concentrations. The effect of freeze-concentration is also considered. To enable such a prediction, a contour plot was constructed using experimental data obtained in cryopreservation of cell suspensions with DMSO at a cooling rate of 1 degrees C/min. Thereafter, the diffusion in the alginate bead and the membrane transport of CPA was numerically simulated. Results were mapped onto the survival rate contours yielding 'predicted' CSR. The effects of loading time, hindrance, construct radius, and CPA concentration on predicted CSR were examined. From these results, an operation window with upper and lower t(E) of 12-19 min (for 0.6 mm radius beads and 1.4 M DMSO) yielded an overall viability of 60 per cent. The model predictions and the best experimental cryopreservation results with encapsulated mESCs were in agreement. Hence, optimization based on post-thaw CSR can accelerate the identification of cryopreservation protocols and parameters for maximizing cell survival.
