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This study presents a theoretical model to develop efficient ISF procedures, on …

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- Cryobiology of Rat Embryos II: A Theoretical Model for the Development of Interrupted Slow Freezing Procedures

Cooling/Warming Rates in 0.25-ml Plastic Straws

Experimental measurements of temperature during plunging of four straws (0.25 ml) are presented in Figure 2A and during warming in Figure 2B. During plunging, the cooling rate changed from 0 to a maximum of approximately 1 x 104°C/min, then decreased to 0 as the sample temperature equilibrated with LN2 at -196°C. During warming (in a 37°C water bath), the warming rate changed from 0 to a maximum of approximately 2 x 104°C /min, then decreased to 0 when the sample temperature equilibrated with the water bath.

Estimation of Critical Concentration

To precisely calculate the from measured B2 and B3 is beyond the scope of the current study. The B2 for 40% (w/w) DMSO and NaCl concentration was calculated using Sutton's formula [8] and was determined to be 3.5 x 102°C/min, which is much lower than the actual cooling rate inside the straw during plunging. The B3 for 45% and 47.5% (w/w) binary solutions of DMSO (e.g., DMSO without NaCl) have been determined to be 2.38 x 103°C/min and 1.86 x 103°C/min, respectively [3], which is also much less than the actual warming rate. Considering both the cooling and warming rate requirements, the critical concentration was estimated as 40% w/w for the experimental conditions.

Experimental Determination of Intracellular Nucleation Temperature

Images captured from the recorded cryomicroscopy experiments were examined to determine the intracellular nucleation temperature. When rat zygotes were cooled at a rate of 10°C/min in 1.5 M DMSO, IIF reached 5% when the temperature reached -36°C and all zygotes had IIF at -46°C (no zygotes had IIF at -34°C; Fig. 3). Based upon these measurements, the onset of nucleation was estimated to be -35°C for rat zygotes.

Estimation of Optimal Plunging Temperature

A hypothetical rat zygote was considered suspended in 50 equally spaced [CPA]0 values ranging from 0.08 to 4 molal and cooled from Tseed to Tend at 1 of 50 equally spaced B1 values ranging from 0.05 to 2.5°C/min. For each of the 2500 combinations of [CPA]0 and B1 values, the model calculated [S]i, water volume, and supercooling at each temperature point (100 equally spaced points from Tseed to Tend). The criteria of exceeding 40% (w/w) and no predicted IIF were used to divide the plane of [CPA]0 vs. B1 into three regions (Fig. 4) as follows:

Region I. In this region, no combination of [CPA]0 and B1 allows the intracellular solute concentration to reach the at any temperature point. This region contains the high cooling rate zone and low initial CPA concentration zone. The high cooling rates in this region (bottom of Fig. 4) would not allow the cell to dehydrate sufficiently, and the low concentrations (left part of Fig. 4) are simply not high enough for the intracellular solute concentration (CPA and NaCl) to reach the . The cooling rates and concentrations in this region were rejected in the developing optimized ISF procedure.

Region II. The combinations of [CPA]0 and B1 allow the [S]i to reach at certain temperature points, but under these conditions there is a high probability of IIF during slow cooling. If a cell is cooled under these conditions, the cell would be supercooled more than 2°C when the temperature reaches the nucleation zone (-35°C in this case) and intracellular water content would be greater than 10% of its isotonic volume. These conditions were also rejected in developing the ISF procedure.

Region III. The combinations of [CPA]0 and B1 allow the [S]i to reach the , and no IIF is predicted during slow cooling. Figure 5 shows the Tp for each [CPA]0 and B1, indicated by the points in a three-dimensional plot (panel A) and a two-dimensional plot (panel B). These points range from approximately -25°C (for points around the high concentration/low cooling rate corner) to approximately -35°C (for points around the low concentration/high cooling rate corner).

There is a minimum [CPA]0 boundary below which no B1 (in the range of 0.05 to 2.5°C/min) allows the [S]i to reach the . There is also a maximum B1, above which any B1 causes the same effect. Roughly, these two limits construct a box of [CPA]0 and B1 values that are candidates for the optimized protocol. The optimum set of conditions was selected by minimizing {tau}i from equation 6 and determined to be a [CPA]0 of 1.2 M DMSO, a B1 of 0.95°C/min, and Tp of -35°C.

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