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

• Abstract
• Introduction
• Materials and methods
• Results
• Discussion
• Conclusion
• References
• Figures
• Tables

Biology Articles » Cryobiology » Cryobiology of Rat Embryos II: A Theoretical Model for the Development of Interrupted Slow Freezing Procedures » Discussion

Discussion

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

In one form or another, ISF methods have been used and have provided varying levels of success for a diverse group of cell and tissue types, including red blood cells [19], pancreatic islets [20], and embryos [21]. Historically, mammalian embryo ISF procedures have further been divided into two categories on the basis of optimal plunging temperature and warming conditions [22]. One category (slow warming method) utilizes slow cooling ( by transfer into LN₂ (-196°C) and subsequent slow warming at rates of 25°C/min or less [23, 24]. The second procedure (rapid warming method) utilizes slow cooling to an intermediate temperature, usually between -25 and -40°C, followed by transfer into LN₂ and subsequent rapid warming at rates above 300°C/min [25, 26].

The current study proposes a new method by which rapid warming ISF procedures may be enhanced through modeling, taking into account typical cryobiological practices (i.e., the use of 0.25-ml plastic straws, 0 to 4 molal DMSO concentrations, and cooling rates between 0 to 2.5°C/min). To apply this approach, specific fundamental biophysical and physical-chemical parameters must be known, including cell membrane permeability coefficients and their activation energies, ternary solution (NaCl/CPA/H₂O) phase diagram information, and the solution's vitrification properties. This study presents a model designed to develop ISF procedures on the basis of two criteria: 1) the [S]ⁱ must reach a , at which the intracellular solution can be readily vitrified during plunging, and 2) lethal IIF must be avoided. The model was applied to the rat zygote using DMSO as the permeating CPA, and from the predicted optimal [CPA]⁰ range, B₁ range, and associated T_p values, a protocol consisting of a [CPA]⁰ of 1.2 M DMSO, a B₁ of 0.95°C/min, and a T_p of -35°C was predicted by calculating which set of conditions resulted in the minimum duration of slow cooling.

Several other models have been developed to attempt to quantitatively examine the biophysical events that occur during these procedures, the most recent being those developed by Karlsson et al. [7, 10, 17], who proposed a theoretical model of optimization and applied it to the mouse oocyte considering glycerol as the permeating CPA. In contrast to Karlsson's study, in the model described here, the changes of intracellular water volume and [S]ⁱ during cooling and warming were predicted as described by Liu et al. [6] considering that the cell remains permeable to CPA at low temperatures. In addition, a fixed initial CPA concentration was not a necessary constraint in the current model. This allows more flexibility in determining the set of conditions for optimum ISF protocols without needing to repeat the simulations for other fixed CPA concentrations. It also allows the possibility of considering other biological concerns that are equally crucial in cryopreservation. For example, the potential toxic effects of CPAs on cells usually become severe when CPA concentrations are high and the exposure time is long. In this regard, when the duration of slow cooling does not change greatly over a wide range of CPA concentrations, a lower CPA concentration should be chosen. This is possible using the current model, and from this point of view, the upper-right corner of Figure 5B (high [CPA]⁰, low B₁) on the initial concentration/cooling rate plane could be readily eliminated.

Another issue involved in ISF procedure development is IIF estimation. Lacking the necessary parameters for the rat zygote, the most current IIF models could not be used (i.e., Karlsson et al. [7, 10, 17]); however, Mazur's model [11] agreed closely with experimental data (Fig. 3) and was therefore considered adequate. The use of different IIF models will affect the shape of zones II and III. However, the use of different IIF models would not fundamentally change our results because 1) the boundary between zones I and II (Fig. 4) is independent of the choice of slow cooling IIF model (it is based on the [CPA]_c required for vitrification during the rapid cooling step), with the boundary between zones II and III (Fig. 4) constrained to stay within zone I; and 2) IIF curves from the experimental data agree closely with predictions made using Mazur's model [11] as well as those from Karlsson's predictions for mouse oocytes [7] (Fig. 3).

The current model could also be used to optimize a situation in which the cell type is biologically sensitive to supercooling and not to CPA exposure time. The high [CPA]⁰, low B₁ region of Figure 5 indicates that the T_p values are much higher in this section (approximately 10 degrees higher). Although the cells are exposed to relatively high CPA concentrations and subzero temperatures much longer (due to lower B₁ values), the absolute temperature values are much higher and supercooling is much lower. According to Pitt et al. [15], two effects dominate IIF: 1) supercooling and 2) exposure time. Therefore, it would be predicted that these cells should be cooled at a lower B₁ value with a higher [CPA]⁰ value.

The model's prediction, indicated by Figure 5, that a higher [CPA]⁰ allows for a lower B₁ value is entirely consistent with previous theory [27] and experimental data as well [28]. A contour map of maximum [S]ⁱ plotted for different [CPA]⁰ and B₁ values is presented in Figure 6. For discussion purposes, the section "AZ " of the line "40%" was used as the trace of optimal combinations of [CPA]⁰ and B₁ values. It is clear that the optimal B₁ decreases as the [CPA]⁰ increases. Two distinguishing aspects are important to note. First, as explained previously by Mazur [28], the introduction of CPA makes the cells susceptible to IIF at even lower cooling rates. This statement supports the current prediction because the IIF region in Figure 4 has the same trend as the line of "40%" in Figure 6. The cause of this phenomenon is most likely that the higher [CPA]⁰ values tend to trap more water inside the cell and thereby increase the probability of IIF [17, 29]. For a situation of the same cooling rate but different [CPA]ⁱ, a cell with lower [CPA]ⁱ has to dehydrate more than a cell with higher [CPA]ⁱ to make its intracellular concentration equilibrate with extracellular concentration, which increases during slow cooling in the first step. For this scenario, the IIF occurring during slow cooling could be avoided by using a lower B₁. Second, as illustrated in Figure 6, for a given B₁, higher [CPA]⁰ values tend to have a lower C_max during slow cooling (again, most likely due to the higher intracellular CPA concentration tending to trap more water inside the cell) [17, 29]. For this scenario, the issue is the [CPA], and a lower [CPA]⁰ must be chosen to ensure that the [S]ⁱ can become greater than the [CPA].

The calculation results for , and predicted IIF zone for mouse oocytes first presented by Karlsson et al. [17] in 1994 are in close agreement with the results predicted in the current study for rat zygotes using DMSO. Their plot is reconstructed along with the current predictions (Fig. 7), and the results indicate close agreement until low [CPA]⁰ values (less than 0.6 molal) are considered. The discrepancy in this range may be attributed to the current model's prediction that the C_max in this situation could not reach the required [CPA] if these [CPA]⁰ values were used.

In the most recent study by Karlsson et al. [7], a cost function was used to optimize the duration time of the freezing protocol, and this may be accomplished in a simplified manner in the current model by calculating the duration of slow cooling using equation 6. From Figure 8A it is obvious that higher B₁ values decrease _i dramatically, even though the corresponding T_p values are lower than those using the lower B₁ values. Figure 8B indicates that there is an optimal [CPA]⁰ for a given B₁, which minimizes the duration of the slow cooling step. For the rat zygote, this optimal [CPA]⁰ changes slightly for different B₁ values. When the B₁ increases from 0.1°C/min to 0.95°C/min, the optimal [CPA]⁰ decreases from 1.7 molal to 1.2 molal. Similar to the predictions made by Karlsson's model [7], these optimal conditions occur right on the border of regions at which unacceptable cell damage is predicted. Therefore, although theoretically optimal, this set of conditions may actually be risky in practice because any procedural error (e.g., fluctuation in cooling rate, error in solution preparation) or error in solution properties (e.g., error in [CPA] estimation) could result in unexpected negative consequences. Indeed, the determination of zone III is very sensitive to the value of [CPA]. The estimated [CPA] values used in the model were based on published data for binary solutions (e.g., CPA and H₂O only). If this approximation resulted in an underestimation of [CPA], it could be detrimental because, in practice, the [S]ⁱ would not be high enough at T_p to ensure vitrification during plunging. By selecting a point more toward the center of zone III (e.g., a [CPA]⁰ of 1.5 molal DMSO, a B₁ of 0.5°C/min, and a T_p of -30°C) a more conservative estimation can be achieved.

Consistent with the current model, Hirabayashi [30] recently reported cryopreservation of 2-cell rat embryos using an ISF method consisting of a 0.5°C/min B₁, a [CPA]⁰ of 10%(v/v) DMSO (1.4 5M), and a T_p of -30°C. Using late morula or early blastocysts obtained from naturally ovulated and mated Wistar female rats, Utsumi et al. [31] investigated the effects of [CPA]⁰ on percent survival (at a fixed B₁) and found a 0% and 20% survival rate for 0.15 M and 0.3 M DMSO, respectively. Survival increased to 60% and 59% for 1.0 M and 1.5 M. This same study also reported the effects of B₁ and T_p (at a fixed [CPA]⁰) on embryo survival. Utsumi et al. [31] concluded that survival decreased dramatically when a 5°C/min B₁ was used; while, for the same T_p, the percent survival tended to be higher if a lower B₁ was used. All of these experimental results correspond well with the current model predictions (region III in Fig. 4). However, it is important to note that direct comparisons cannot be made because embryo developmental stages and specific experimental conditions were different from those used to develop the model in the current study.

Figure 6 suggests an alternative way to optimize ISF procedures. If a discrete isoconcentration line is roughly used as the guideline for selecting [CPA]⁰ and B₁, the turning point (e.g., A and B in Fig. 6 at which the curve has the smallest radius) could be considered as the optimal point for corresponding isoconcentrations because B₁ has the maximum value while [CPA]⁰ is close to the minimum value. If a comparison is made between the turning points of 40% and 45% isoconcentration lines, we can conclude that the optimal B₁ is much higher for 40% than 45% and the [CPA]⁰ is relatively lower. The former condition, higher B₁ and lower [CPA]⁰, would appear to be optimal because the higher B₁ shortens the duration of slow cooling (therefore potentially reducing solution effects injury), and the lower [CPA]⁰ lowers the osmotic stress and lessens the potential CPA toxicity.

The is constrained by the B₂ during plunging and B₃ during thawing for a given solution. It is important to note that if these rates could be increased by using a thinner container, or material with higher heat transfer properties, then may be reduced. This would result in situations in which equilibrium cooling could be performed much more efficiently because higher B₂ values and lower [CPA]⁰ values could be applied. The positive results reported by investigators who use thermal-pulled, thin straws may be due to these reasons [32].