42 COMPARISON OF COOLING RATES IN OOCYTE VITRIFICATION SYSTEMS USING A NUMERICAL SIMULATION

Abstract

Interest in oocyte cryopreservation has increased due to the application of assisted reproductive technologies and the need for the establishment of ova/gene banks worldwide. In order to maintain cell viability, biological functions must be halted, inducing a suspended animation state by cooling it into a solid phase. Compared to cryopreservation of male gametes, oocytes represent a greater challenge due to their low surface area:volume. Vitrification, the solidification into an amorphous, glassy state while maintaining absence of intra- and extracellular ice crystals, requires high concentrations of cryoprotectants and extremely rapid cooling rates. Several vitrification devices such as open pulled straws (OPS), ultra fine pipette tips, nylon loops and polyethylene films have been introduced to manipulate minimal volumes and achieve high cooling rates. However, experimental comparison of cooling rates presents difficulties mainly because of the reduced size of these systems. To circumvent this limitation, a numerical simulation of cooling rates of various vitrification systems immersed in liquid nitrogen was conducted, solving the non-stationary heat transfer partial differential equation using the finite element method. Three external heat transfer coefficients (h = 200, 1000 and 2000 W m^–2 K) were considered. The Cryotip^® and OPS were approached as 2 concentric finite cylinders; differential equations representing heat transfer in cylindrical coordinates were described considering radial and axial coordinates and were numerically solved as a 1-dimensional heat conduction problem in an infinite cylinder. The Cryoloop^® was approximated as a 1-dimensional heat flow system in Cartesian coordinates and Cryotop^® was numerically described as an irregular bi-dimensional axial-symmetric problem. All differential equations were numerically solved using the finite element method in COMSOL Multiphysics 3.4. The domain was discretized in triangular (Cryotip^®, OPS and Cryotop^®) and linear elements (Cryoloop^®) in order to obtain accurate numerical approximations. In each case, the warmest point of the system was identified to determine the time-temperature curve that allows the evaluation of the slowest cooling rate (worst condition). Results indicate the nylon loop (Cryoloop^®) is the most efficient heat transfer system analysed, with a predicted cooling rate of 180 000°C min^–1 for an external heat transfer coefficient h = 1000 W m^–2 K when cooling from 20 to –130°C; in contrast, the pipette tips (Miniflex^® showed the lowest performance with a cooling rate of 6164°C min^–1 at same value of external heat transfer coefficient. Predicted cooling rates of OPS and Cryotop^® (polyethylene film) were 40 909 and 37 500°C min^–1, respectively for the same heat transfer coefficient. It can be concluded that in oocyte cryopreservation systems, in which experimental comparison of cooling rates presents difficulties due to the reduced size of the vitrification devices, the numerical simulations and the analysis of the predicted thermal histories could contribute to determine the performance of the different techniques.