Mathematical prediction of freezing times of bovine semen in straws placed in static vapor over liquid nitrogen.

A widespread practice in cryopreservation is to freeze spermatozoa by suspending the straws in stagnant nitrogen vapor over liquid nitrogen (N(2)V/LN(2)) for variable periods of time before plunging into liquid nitrogen (-196°C) for indefinite storage. A mathematical heat transfer model was developed to predict freezing times (phase change was considered) required for bull semen and extender packaged in 0.5ml plastic straws and suspended in static liquid nitrogen vapor. Thermophysical properties (i.e. thermal conductivity, specific heat, density, initial freezing temperature) of bovine semen and extender as a function of temperature were determined considering the water change of phase. The non-stationary heat transfer partial differential equations with variable properties (nonlinear mathematical problem) were numerically solved considering in series thermal resistances (semen suspension-straw) and the temperature profiles were obtained for both semen suspension and plastic straw. It was observed both the external heat transfer coefficient in stagnant nitrogen vapor and its temperature (controlled by the distance from the surface of liquid nitrogen to the straw) affected freezing times. The accuracy of the model to estimate freezing times of the straws was further confirmed by comparing with experimental literature data. Results of this study will be useful to select "safe" holding times of bull semen in plastic straws placed N(2)V/LN(2) to ensure that complete freezing of the sample has occurred in the nitrogen vapor and avoid cryodamage when plunging in LN(2). Freezing times predicted by the numerical model can be applied to optimize freezing protocols of bull semen in straws.