Review of biomaterial thermal property measurements in the cryogenic regime and their use for prediction of equilibrium and non-equilibrium freezing applications in cryobiology

It is well accepted in cryobiology that the temperature history and cooling rates experienced in biomaterials during freezing procedures correlate strongly with biological outcome. Therefore, heat transfer measurement and prediction in the cryogenic regime is central to the field. Although direct measurement of temperature history (i.e. heat transfer) can be performed, accuracy is usually achieved only for local measurements within a given system and cannot be readily generalized to another system without the aid of predictive models. The accuracy of these models rely upon thermal properties which are known to be highly dependent on temperature, and in the case of significant cryoprotectant loading, also on crystallized fraction. In this work, we review the available thermal properties of biomaterials in the cryogenic regime. The review shows a lack of properties for many biomaterials in the subzero temperature domain, and especially for systems with cryoprotective agents. Unfortunately, use of values from the limited data available (usually only down to −40 °C) lead to an underestimation of thermal property change (i.e. conductivity rise and specific heat drop due to ice crystallization) with lower temperatures. Conversely, use of surrogate values based solely on ice thermal properties lead to an overestimation of thermal property change for most biomaterials. Additionally, recent work extending the range of available thermal properties to −150 °C has shown that the thermal conductivity will drop in both PBS and tissue (liver) due to amorphous/glassy phases (versus crystalline) of biomaterials with the addition of cryoprotective additives such as glycerol. Thus, we investigated the implications of using approximated or constant property values versus measured temperature-dependent values for predicting temperature history during freezing in PBS (phosphate-buffered saline) and porcine liver with and without cryoprotectants (glycerol). Using measured property values (thermal conductivity, specific heat, and latent heat of phase change) of porcine liver, a standard was created which showed that values based on surrogate ice properties under-predicted cooling times, while constant properties (i.e. based on limited data reported near the freezing point) over-predicted cooling times. Additionally, a new iterative numerical method that accommodates non-equilibrium cooling effects as a function of time and position (i.e. crystallization versus amorphous phase) was used to predict temperature history during freezing in glycerol loaded systems. Results indicate that in addition to the increase in cooling times due to the lowering of thermal diffusivity with more glycerol, non-equilibrium effects such as the prevention of maximal crystallization (i.e. amorphous phases) will further increase required cooling times. It was also found that the amplified effect of non-equilibrium cooling and crystallization with system size prevents the thermal history to be described with non-dimensional lengths, such as was possible under equilibrium cooling. These results affirm the need to use accurate thermal properties that incorporate temperature dependence and crystallized fraction. Further studies are needed to extract thermal properties of other important biomaterials in the subzero temperature domain and to develop accurate numerical methods which take into account non-equilibrium cooling events encountered in cryobiology when partial or total vitrification occurs.     

Supercooling,ice nucleation and crystal growth: a systematic study in plant samples

This paper presents an innovative technological platform which is based on infrared video recording and is used for monitoring multiple ice nucleation events and their interactions, as they happen in 96 well microplates. Thousands of freezing curves were obtained during this study and the following freezing parameters were measured: cooling rate, nucleation point, freezing point, solidus point, degree of supercooling, duration of dendritic phase and duration of crystal growth. We demonstrate the use of this platform in the detection of ice nuclei in plant samples. Future applications of this platform may include breeding for frost tolerance, cryopreservation, frozen food technology and atmospheric sciences.     

Studies on Rapidly Frozen Suspensions of Yeast Cells by Differential Thermal Analysis and Conductometry

Few, if any, yeast cells survived rapid cooling to -196°C and subsequent slow warming. After rapid freezing, the suspensions absorbed latent heat of fusion between -15° and 0°C during warming, and the relation between the amount of heat absorbed and the concentration of cells was the same as that in equivalent KCl solutions, indicating that frozen suspensions behave thermally like frozen solutions. The amount of heat absorbed was such that more than 80 per cent of the intracellular solution had to be frozen. The conductometric behavior of frozen suspensions showed that cell solutes were still inside the cells and surrounded by an intact cell membrane at the time heat was being absorbed. Two models are consistent with these findings. The first assumes that intracellular freezing has taken place; the second that all freezable water has left the cells and frozen externally. The latter model is ruled out because rapidly cooled cells do not shrink by an amount equal to the volume of water that would have to be withdrawn to prevent internal freezing.     

The high viscosity encountered during freezing in glycerol solutions: effects on cryopreservation

The objective of this study was to determine the viscosity of the residual unfrozen solution that cells are exposed to during freezing in the presence of glycerol and use this to interpret some key aspects of cryopreservation. The viscosity of the glycerol-water binary system exceeded 1000 cP at -40 degrees C, whilst the viscosity of the ternary system, glycerol-water-NaCl, exceeded 100,000 cP at -55 degrees C. The effect of these high viscosities on the diffusion of water at a constant temperature during freezing and during cooling at different linear rates has been estimated. At rates of cooling faster than 100 degrees C min(-1) the diffusion distance during freezing was calculated to be less than 15 microm. Validation of the diffusion calculations was confirmed by examination of the ultrastructure of the freeze concentrated matrix in samples prepared at a range of cooling rates. At a critical rate of cooling, water diffusion becomes limited by the high viscosity and two phenomena, of relevance to cryobiology, occur: (1) the composition of the freeze concentrated matrix around cells deviates from that of the equilibrium phase diagram; and (2) the osmotic loss of water from cells is restricted. These factors are of particular relevance to an understanding of the response of cells such as spermatozoa, red blood cells, and bacteria cooled rapidly with glycerol as cryoprotectant.     

Induced Synthesis of Mitochondrial RNA in Sweet Potato Root after Wounding

Ice structure was photographically analyzed for frozen soy protein curd and egg albumin gel frozen under various conditions. Dendritic ice structure was observed growing from the cooling plate parallel to the direction of the heat flux. The change in the ice structure size was analyzed at different locations from the cooling plate in the plane perpendicular to the direction of heat flux. In accordance with the theoretical relationship proposed by us before, the mean ice structure size was inversely proportional to the moving speed of the freezing front and the proportionality constant was not very much different from the diffusion coefficient of water, showing the important role of the molcular diffusion mechanism in the process of ice crystal growth. For the freezing accompanied with supercooling, the ice structure became very small, reflecting the very rapid moving speed of the freezing front when supercooling ceased. The theoretical model by us had advantages over the models proposed in the literature for its simple theoretical basis and wider applicability.     

Equilibrium,quasi-equilibrium,and nonequilibrium freezing of mammalian embryos

The first successful freezing of early embryos to −196°C in 1972 required that they be cooled slowly at ∼1°C/min to about −70°C. Subsequent observations and physical/chemical analyses indicate that embryos cooled at that rate dehydrate sufficiently to maintain the chemical potential of their intracellular water close to that of the water in the partly frozen extracellular solution. Consequently, such slow freezing is referred to as equilibrium freezing. In 1972 and since, a number of investigators have studied the responses of embryos to departures from equilibrium freezing. When disequilibrium is achieved by the use of higher constant cooling rates to −70°C, the result is usually intracellular ice formation and embryo death. That result is quantitatively in accord with the predictions of the physical/chemical analysis of the kinetics of water loss as a function of cooling rate. However, other procedures involving rapid nonequilibrium cooling do not result in high mortality. One common element in these other nonequilibrium procedures is that, before the temperature has dropped to a level that permits intracellular ice formation, the embryo water content is reduced to the point at which the subsequent rapid nonequilibrium cooling results in either the formation of small innocuous intracellular ice crystals or the conversion of the intracellular solution into a glass. In both cases, high survival requires that subsequent warming be rapid, to prevent recrystallization or devitrification. The physical/ chemical analysis developed for initially nondehydrated cells appears generally applicable to these other nonequilibrium procedures as well.     

Equilibrium, quasi-equilibrium, and nonequilibrium freezing of mammalian embryos.

The first successful freezing of early embryos to -196 degrees C in 1972 required that they be cooled slowly at approximately 1 degree C/min to about -70 degrees C. Subsequent observations and physical/chemical analyses indicate that embryos cooled at that rate dehydrate sufficiently to maintain the chemical potential of their intracellular water close to that of the water in the partly frozen extracellular solution. Consequently, such slow freezing is referred to as equilibrium freezing. In 1972 and since, a number of investigators have studied the responses of embryos to departures from equilibrium freezing. When disequilibrium is achieved by the use of higher constant cooling rates to -70 degrees C, the results is usually intracellular ice formation and embryo death. That result is quantitatively in accord with the predictions of the physical/chemical analysis of the kinetics of water loss as a function of cooling rate. However, other procedures involving rapid nonequilibrium cooling do not result in high mortality. One common element in these other nonequilibrium procedures is that, before the temperature has dropped to a level that permits intracellular ice formation, the embryo water content is reduced to the point at which the subsequent rapid nonequilibrium cooling results in either the formation of small innocuous intracellular ice crystals or the conversion of the intracellular solution into a glass. In both cases, high survival requires that subsequent warming be rapid, to prevent recrystallization or devitrification. The physical/chemical analysis developed for initially nondehydrated cells appears generally applicable to these other nonequilibrium procedures as well.     

A differential scanning calorimeter for ice nucleation distribution studies--application to bacterial nucleators

A differential scanning calorimeter has been developed for the automatic detection and measurement of dropwise freezing within a sample of 100-200 water drops. A typical drop size of 1 microliter is employed. The sample is distributed on flat, square (4-cm) thermoelectric sensors and the temperature is scanned downward by conductive cooling to a liquid nitrogen bath. The rate of cooling, typically 1 degree C/min, is set by the choice of a heat conduction rod between the calorimeter and the liquid nitrogen bath. The voltages from the thermopiles along with a system temperature-measuring thermocouple are continuously monitored by digital voltmeters and recorded every half-second in a computer memory. A freezing event in a drop is detected by a characteristic voltage signal whose integral with time is proportional to the size of the drop and its heat of fusion. The half-life of a freezing event signal is 10 s for a 1-microliter drop. The integrated signal produced from multiple freezing events is shown to provide a direct measure of the number of drops frozen at a given temperature. A distribution curve and its smoothed derivative can be constructed directly from these measurements. The instrument, which is termed an "ice nucleometer," is illustrated in determining the ice nucleation distribution in a population of Escherichia coli harboring cloned ice nucleation genes.     

女贞和冬青卫矛叶片低温下胞外结冰模式的热力学新证据

低温条件下植物组织的结冰模式, 即胞外或胞内结冰, 直接决定着细胞的生死。目前胞外结冰的直接证据很少, 尤其缺乏热力学证据。用高分辨率差热扫描结合显微观察分析了女贞(Ligustrum lucidum)和冬青卫矛(Euonymus japonicus)叶片在降温过程中的结冰放热现象, 发现2种植物胞外结冰的热力学和组织结构变化的新证据。2种植物的活叶片在冷却过程中均呈现双放热峰, 即双相结冰的特征; 而预先冰冻杀死的叶片和叶片组织提取液浸润的滤纸片在同样冷却过程中仅有1个快速的大单放热峰, 即单相结冰的特征。显微观察也显示, 结冰过程中活组织细胞间隙中形成大量的白色冰晶, 且细胞虽然脱水收缩但细胞内的有色溶液没有流失, 表现出胞外结冰的特征。实验结果为深入揭示植物的冰冻伤害机制提供了新证据和研究方法。     

Influence of cooling rate on Saccharomyces cerevisiae destruction during freezing: unexpected viability at ultra-rapid cooling rates

The purpose of this work was to study cell viability as a function of cooling rate during freezing. Cooling rate strongly influences the viability of cells during cold thermal stress. One of the particularities of this study was to investigate a large range of cooling rates and particularly very rapid cooling rates (i.e., faster than 20000 degrees C min (-1)). Four distinct ranges of cooling rates were identified. The first range (A(')) corresponds to very slow cooling rates (less than 5 degrees C min (-1)), and results in high cell mortality. The second range (A) corresponds to low cooling rates (5-100 degrees C min (-1)), at which cell water outflow occurs slowly and does not damage the cells. The third range (B) corresponds to rapid cooling rates (100-2000 degrees C min (-1)), at which there is competition between heat flow and water flow. In this case, massive water outflow, which is related to the increase in extracellular osmotic pressure and the membrane-lipid phase transition, can cause cell death. The fourth range (C) corresponds to very high cooling rates (more than 5000 degrees C min (-1)), at which the heat flow is very rapid and partially prevents water exit, which seems to preserve cell viability.     

Thermally defined cryomicroscopy and thermodynamic analysis in lymphocyte freezing

A cryomicroscope is described which provides the possibility of quantifying the volume loss of cells during freezing, detection of intracellular ice formation during cooling and warming, as well as the determination of viability as function of (constant) cooling rates. The basic mechanisms occurring in cryopreservation have been studied with this system using the human lymphocyte suspended in pure saline as a biological model system; experimentally observed exosmosis during freezing is compared to predictions from a thermodynamic model. Cell volume loss during freezing has been determined experimentally for cooling rates of 2.4, 12, 48, and 120 degrees K/min. Exosmosis also was calculated corresponding to various assumptions regarding the concentration dependence of the hydraulic permeability of the cells. Further calculations of exosmosis are performed for determining the effects of the initial cell volume. The temperatures and transition cooling rate ranges of intracellular ice formation have been determined. On the basis of exosmosis and a lethal level of intracellular salt concentration, a hypothetical relative optimum of the cooling rate is theoretically predicted and compared to the experiments.     

Kinetics of Water Loss from Cells at Subzero Temperatures and the Likelihood of Intracellular Freezing

The survival of various cells subjected to low temperature exposure is higher when they are cooled slowly. This increase is consistent with the view that slow cooling decreases the probability of intracellular freezing by permitting water to leave the cell rapidly enough to keep the protoplasm at its freezing point. The present study derives a quantitative relation between the amount of water in a cell and temperature. The relation is a differential equation involving cooling rate, surface-volume ratio, membrane permeability to water, and the temperature coefficient of the permeability constant. Numerical solutions to this equation give calculated water contents which permit predictions as to the likelihood of intracellular ice formation. Both the calculated water contents and the predictions on internal freezing are consistent with the experimental observations of several investigators.     

Correlated x-ray diffraction and freeze-fracture studies on membrane model systems. Perturbations induced by freeze-fracture preparative procedures.

Lipid-water and protein-lipid-water phases have been examined by X-ray methods before and after freezing. Frozen samples have been subsequently fractured and replicated, thus permitting an evaluation of the nature of structural perturbations in samples examined by freeze-fracture electron microscopy. Important results are summarized: (1) Freezing low water content (approx. less than 25%) phases causes perturbations in the packing of hydrocarbon chains. The results suggest that freezing liquied paraffin chains produces a condensed "glass-like" packing. (2) Additional perturbations occur in high water content samples. After freezing, much smaller lamellar repeat distances, intense ice reflections, and extensive perturbation of fracture faces are consistant with the expulsion of water from between lamellae. Presence of glycerol generally relieves these perturbations but in some cases introduces additional lattice disorder. (3) Surprisingly, cooling by a stream of cold N2 gas (-140 degrees C) produces qualitatively the same results as rapid cooling in liquid Freon-22 (-160 degrees C). (4) Complex perturbations occur in phases containing integral membrane proteins. Interesting results have been obtained with cytochrome b5-lecithin lamellar associations which display both smooth and rough fracture faces without clearly defined particles.     

Quantitative study of the importance of water permeability in plant cold hardiness

The rate of ice formation was measured for Hedera helix L. cv. Thorndale (English ivy) bark exposed to -10 C. The cooling rate of bark exposed to -10 C was 31 C per minute. The water efflux rate required for ice formation to occur extracellularly was calculated from the rate of ice formation and the average cell diameter. The water potential difference driving the efflux of water to sites of extracellular ice was calculated from the sample temperature, osmotic water potential, and fraction of water frozen at a given freezing temperature. From the water efflux rate and water potential difference, the resistance of the barrier controlling movement of intracellular water to sites of extracellular ice was calculated. Comparison of the resistance of this barrier to water movement with the resistance of the cell membrane revealed that the membrane represented only 0.5% of the barrier resistance. Thus, membrane resistance can have little influence on the rate of water efflux and ice formation when bark is cooled at a rate of 31 C per minute. If ice formation occurred at the same rate in ivy bark as it occurred in a 10 mm MnCl(2) solution, the membrane resistance would still have represented only 1% of the resistance of the barrier to ice formation. Therefore, at a cooling rate of 31 C/minute, heat removal plays a large part in determining the rate of ice formation. At slower cooling rates experienced under natural freezing conditions the ability to remove heat would play an even larger role. It is concluded that under natural freezing conditions membrane resistance does not limit water efflux.     

Cell size and water permeability as determining factors for cell viability after freezing at different cooling rates

This work studied the viabilities of five types of cells (two yeast cells, Saccharomyces cerevisiae CBS 1171 and Candida utilis; two bacterial strains, Escherichia coli and Lactobacillus plantarum; and one human leukemia K562 cell) as a function of cooling rate during freezing. The range of investigated cooling rates extended from 5 to 30,000 degrees C/min. Cell viability was classified into three ranges: (i) high viability for low cooling rates (5 to 180 degrees C/min), which allow cell water outflow to occur completely and do not allow any intracellular crystallization; (ii) low viability for rapid cooling rates (180 to 5,000 degrees C/min), which allow the heat flow to prevail over water outflow (in this case, cell water crystallization would occur as water was flowing out of the cell); (iii) high viability for very high cooling rates (>5,000 degrees C/min), which allow the heat flow to be very rapid and induce intracellular crystallization and/or vitrification before any water outflow from the cell. Finally, an assumption relating cell death to the cell water crystallization as water is flowing out of the cell is made. In addition, this general cell behavior is different for each type of cell and seems to be moderated by the cell size, the water permeability properties, and the presence of a cell wall.     

The Cardiovascular Control of Heat Exchange: Consequences of Body Size

For blood flow to be an effective agent for the control of heatexchange, it must occur in a region of the body where conductionresistance in the tissues is relatively high, and in an environmentwhere external resistance to heat exchange is relatively low.If either of these conditions is not met, control of heat exchangeby blood flow is not possible. Very small reptiles should notbe able to control heat exchange by blood flow in any environment,unless they control blood flow specifically to appendages. Verylarge reptiles should be able to control heat exchange by bloodflow only under certain conditions, such as in water, very highwinds, or intense radiative heating. Otherwise, they shouldhave little control. An optimum body size should exist for areptile's ability to control heat exchange using blood flow.In air, this optimum body size for alligators appears to beabout 5 kg. Theoretically, the optimum size should be substantiallylarger than 5 kg for reptiles heating and cooling in water.     

小牛胸腺脱氧核糖核酸内水的量热研究——Ⅱ.非平衡态下水的恒温冻结动力学

用差示扫描量热法研究了DNA内水的冻结行为和在218K下的恒温冻结动力学.实验表明了低温下水-DNA体系及其冻结的非平衡性.冻结是个复杂的一级串联反应,其速率与初始水含量R及实验条件密切相关.在不同R及不同恒温时间t_k下冻结的微观过程不同.不同含水量样品在相同t_k下具有不同的不冻水量R_(nf)然而只要过程的自由能降低,在不同t_k下却可达到相同的R_(nf).“不冻水”是个纯动力学现象,其量与R、冻结温度及t_k等实验条件密切相关.所谓“不冻水”并非由于水同大分子的特殊相互作用所致.     

The Imine‐Based COF TpPa‐1 as an Efficient Cooling Adsorbent That Can Be Regenerated by Heat or Light

Adsorption‐based cooling systems, which can be driven by waste heat and solar energy, are promising alternatives to conventional, compression‐based cooling systems, as they demand less energy and emit less CO₂. The performance of adsorption‐based cooling systems relates directly to the performance of the working pairs (sorbent–water). Accordingly, improvement of these systems relies on the continual discovery of new sorbents that enable greater mass exchange while requiring less energy for regeneration. Here, it is proposed that covalent‐organic frameworks (COFs) can replace traditional sorbents for adsorption‐based cooling. In tests mimicking standard operating conditions for industry, the imine‐based COF TpPa‐1 exhibits a regeneration temperature below 65 °C and a cooling coefficient of performance of 0.77 – values which are comparable to those reported for the best metal–organic framework sorbents described to date. Moreover, TpPa‐1 exhibits a photothermal effect and can be regenerated by visible light, thereby opening the possibility for its use in solar‐driven cooling.     

The mechanism of freezing injury in xylem of winter apple twigs

In acclimated winter twigs of Haralson apple (Pyrus Malus L.), a lag in temperature during cooling at a constant rate was observed at about −41 C by differential thermal analysis. The temperature at which this low temperature exotherm occurred was essentially unaffected by the cooling rate. During thawing there was no lag in temperature (endotherm) near the temperature at which the low temperature exotherm occurred, but upon subsequent refreezing the exotherm reappeared at a somewhat higher temperature when twigs were rewarmed to at least −5 C before refreezing. These observations indicate that a small fraction of water may remain unfrozen to as low as −42 C after freezing of the bulk water in stems. The low temperature exotherm was not present in twigs freeze-dried to a water content below 8.5% (per unit fresh weight), but it reappeared when twigs were rehydrated to 20% water. When freeze-dried twigs were ground to a fine powder prior to rehydration, no exotherm was observed. Previous work has shown that the low temperature exotherm arises from xylem and pith tissues, and that injury to living cells in these tissues invariably occurs only when twigs are cooled below, but not above the temperature of the low temperature exotherm. This study revealed that the low temperature exotherm resulted from the freezing of a water fraction, that the freezing of this water was independent of the freezing of the bulk water, that the exotherm was associated with some gross structural feature but not the viability of the tissue, and that injury to living cells in the xylem and pith was closely and perhaps causally related to the initial freezing of this water.