Mathematical Optimization of Cryoprotectant Addition and Removal Procedures for the Purpose of Adherent Cell Vitrification

Long-term storage of adherent cells is necessary for off-the-shelf availability of tissue engineered constructs, cell-based biosensors, and pharmaceutical testing materials.  Cryopreservation in an ice-free glassy state (i.e., vitrification) is a promising approach for the preservation of adherent cells and tissue because formation of ice crystals is known to be damaging.  To achieve vitrification, high concentrations of cryoprotectant additives (CPAs) are required. However, the addition and removal of CPAs can lead to cell damage due to osmotically induced cell volume changes and chemical toxicity, effects that becomes more prominent with increasing CPA concentration.  Preventing toxicity is a significant challenge when designing vitrification procedures, yet toxicity minimization is not addressed in traditional multi-step CPA addition and removal procedures.  We report a new mathematical optimization strategy for CPA addition and removal procedures which involves minimization of a toxicity cost functional.  Membrane permeability parameters, osmotic tolerance limits and a toxicity cost functional are required as inputs to our optimization algorithm.  Permeability parameters for endothelial monolayers were determined previously using a fluorescence quenching technique.  Osmotic tolerance limits were determined by exposing cell to a range of anisotonic solutions and assessing viability with a resazurin based fluorescence assay.  The 95% viability window corresponded to 20-200% of the isotonic cell water volume. To determine toxicity rates, cells were exposed to 1, 3, 5 and 7 molal CPA solutions for various time intervals, followed by estimation of viability as described above.  To ensure that decreased viability was due to toxicity and not osmotic damage, multi-step addition and removal procedures were used.  As expected, damage due to toxicity increased with exposure time and with CPA concentration.  Toxicity rates were determined by fitting the viability data using a first order rate model.  The concentration-dependence of the toxicity rates was approximated using a power law model, which was then used to define the toxicity cost functional.  Two step procedures for addition and removal of glycerol at 37°C were predicted using our iterative optimization strategy.  The resulting toxicity-minimized addition procedure included an initial step in which cells were induced to swell during exposure to a relatively low glycerol concentration (less than 1 molal), followed by shrinkage in the second step when the cells were exposed to the goal concentration of 17 molal glycerol.  Using endothelial cell monlayers, we compared the toxicity minimized procedure to single-step and traditional multi-step procedures.  In all cases, carrying out addition and removal of glycerol at 37°C resulted in low cell yields, with the highest yield attained using the toxicity-minimized procedure (<40%).  In an attempt to improve viability, we performed the 17 molal addition step on ice.  Cells were essentially nonviable for single-step (<1% viability) and multi-step procedures (3.9±0.5%), however the toxicity-minimized procedure exhibited significantly higher viability (80±15%).  Our results demonstrate that the toxicity minimization strategy yields improved viability after exposure to vitrifiable glycerol solutions compared with conventional multistep CPA addition and removal methods.