Mathematical Modeling of the Heat Tranfer Process in Vitrification Devices Used for Oocyte Cryopreservation

Abstract

Oocyte cryopreservation is of key importance in the preservation and propagation of germplasm, however, the cryopreservation of the female gamete has been met with limited success. Several vitrification devices such as open pulled straws (OPS), fine and ultra fine pipette tips, nylon loops and polyethylene films have been introduced in order 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 overcome this limitation, the cooling rates of various vitrification systems immersed in liquid nitrogen, (Cryoloop®, Cryotop® ,Miniflex® and Open Pulled Straw) were mathematically modeled using the finite element method by numerically solving the unsteady-state heat conduction partial differential equations for the appropriate geometries of the devices. The thermo-physical properties, thermal conductivity, density and specific heat, which are involved in the partial differential equations, were considered constant since during vitrification there is no phase change of water into ice crystals. The Cryoloop® system (Hampton Research, USA) consists of a mounted nylon loop where the oocytes are loaded and plunged into liquid nitrogen. The Cryotop® (Kitazato Supply, Inc, JP) is a thin polyethylene film strip that holds an open drop with oocytes in a minimal volume before being plunged directly into liquid nitrogen. The Miniflex® polyethylene tips (Sorenson Bioscience, Inc., USA) used for vitrification have 360 μm inner diameter and 77 μm wall thickness. The Open Pulled Straw (OPS) is normally manufactured in the laboratory from 0.25 mL polyethylene French straws (I. M. V., Orsay, France). Results showed that at a constant heat transfer coefficient (h=1000 W/m2K )the highest cooling rate (180000 °C/min) was observed for the Cryoloop® system and the lowest rate (5521°C/min) corresponded to the OPS. The Cryotop® exhibited the second best cooling rate of 37500 °C/min, whereas the Miniflex® only achieved a cooling rate of 6164 °C/min. It can be concluded that in cryopreservation systems, the information obtained using the numerical model enables biotechnologist in reproductive areas to determine the performance of each oocyte vitrification device under different operating conditions.