Mathematical optimization of procedures for cryoprotectant equilibration using a toxicity cost function

Cryopreservation nearly universally depends on the equilibration of cells and tissues with high concentrations of permeating chemicals known as cryoprotective agents, or CPAs. Despite their protective properties, CPAs can cause damage as a result of osmotically-driven cell volume changes, as well as chemical toxicity. In this study, we have used previously published data to determine a toxicity cost function, a quantity that represents the cumulative damage caused by toxicity. We then used this cost function to define and numerically solve the optimal control problem for CPA equilibration, using human oocytes as representative cell type with high clinical relevance. The resulting toxicity-optimal procedures are predicted to yield significantly less toxicity than conventional stepwise procedures. In particular, our results show that toxicity is minimized during CPA addition by inducing the cell to swell to its maximum tolerable volume and then loading it with CPA while in the swollen state. This counterintuitive result is considerably different from the conventional stepwise strategy, which involves exposure to successively higher CPA concentrations in order to avoid excessive shrinkage. The procedures identified in the present study have the potential to significantly reduce damage due to toxicity and warrant further investigation.