title: Mathematically optimized cryoprotectant equilibration procedures for cryopreservation of human oocytes.
abstract: BACKGROUND
  Simple and effective cryopreservation of human oocytes would have an enormous impact on the financial and ethical constraints of human assisted reproduction. Recently, studies have demonstrated the potential for cryopreservation in an ice-free glassy state by equilibrating oocytes with high concentrations of cryoprotectants (CPAs) and rapidly cooling to liquid nitrogen temperatures. A major difficulty with this approach is that the high concentrations required for the avoidance of crystal formation (vitrification) also increase the risk of osmotic and toxic damage. We recently described a mathematical optimization approach for designing CPA equilibration procedures that avoid osmotic damage and minimize toxicity, and we presented optimized procedures for human oocytes involving continuous changes in solution composition.
  
  
  METHODS
  Here we adapt and refine our previous algorithm to predict piecewise-constant changes in extracellular solution concentrations in order to make the predicted procedures easier to implement. Importantly, we investigate the effects of using alternate equilibration endpoints on predicted protocol toxicity. Finally, we compare the resulting procedures to previously described experimental methods, as well as mathematically optimized procedures involving continuous changes in solution composition.
  
  
  RESULTS
  For equilibration with CPA, our algorithm predicts an optimal first step consisting of exposure to a solution containing only water and CPA. This is predicted to cause the cells to initially shrink and then swell to the maximum cell volume limit. To reach the target intracellular CPA concentration, the cells are then induced to shrink to the minimum cell volume limit by exposure to a high CPA concentration. For post-thaw equilibration to remove CPA, the optimal procedures involve exposure to CPA-free solutions that are predicted to cause swelling to the maximum volume limit. The toxicity associated with these procedures is predicted to be much less than that of conventional procedures and comparable to that of the corresponding procedures with continuous changes in solution composition.
  
  
  CONCLUSIONS
  The piecewise-constant procedures described in this study are experimentally facile and are predicted to be less toxic than conventional procedures for human oocyte cryopreservation. Moreover, the mathematical optimization approach described here will facilitate the design of cryopreservation procedures for other cell types.
authors.forename: Allyson Fry
authors.initials: AF
authors.lastname: Davidson
authors.forename: James D
authors.initials: JD
authors.lastname: Benson
authors.affiliation: School of Chemical, Biological and Environmental Engineering, Oregon State University, 102 Gleeson Hall, Corvallis, Oregon 97331-2702, USA. adam.higgins@oregonstate.edu.
authors.forename: Adam Z
authors.initials: AZ
authors.lastname: Higgins
mesh_terms: D000465:Algorithms; D015925:Cryopreservation; D003451:Cryoprotective Agents / Q000494:pharmacology*; D005260:Female; D006801:Humans; D015233:Models, Statistical; D009865:Oocytes / Q000166:cytology / Q000187:drug effects*; D058989:Vitrification
chemical_list: D003451:Cryoprotective Agents