PERSPECTIVE: Temperature-dependent density and thermal expansion of cryoprotective cocktails.

Density is a key thermophysical property, affecting the response of materials to temperature changes in different ways, consistent with the phase of state. In fluids, temperature variation across the domain leads to colder areas being heavier than warmer areas, where buoyancy effects drive fluid flow and thereby increase heat transfer. This phenomenon is known as natural heat convection, which in general is a more efficient heat transfer mechanism than heat conduction in the absence of flow. In solids, where the material is locked in place, colder areas tend to contract while warmer areas tend to expand, leading the material to deform. When this deformation is constrained by the geometry of the domain and/or its container, mechanical stresses develop. This phenomenon is known as thermomechanical stress (or thermal stress), which can lead to structural damage such as fractures. The picture becomes even more complex during vitrification (or glass formation), where the material gradually changes from liquid to an amorphous solid over a significant temperature range. There, due to temperature variation across the domain, fluid mechanics and solid mechanics effects may coexist. It follows that characterization of the density as a function of temperature is crucial for the analyses of thermal, fluid, and mechanical effects during cryopreservation, with the goals of protocol planning, optimization, and preserving structural integrity. For this purpose, the current study focuses on the density of the material and its companion property of thermal expansion. Specifically, this paper reviews literature data on thermal expansion of cryoprotective agents (CPAs), discusses the mathematical relationship between thermal expansion and density, and presents new calculated density data. This study focuses on the CPA cocktails DP6, VS55, M22, and their key ingredients at various concentrations, including DMSO, propylene glycol, and formamide. Data for DP6 combined with a selection of synthetic ice modulators (SIMs) are further presented.

Network Formation by Cross-Hybridization of Complementary Strands to Grafted ssDNA.

When a low density brush of single-stranded DNA (ssDNA) targets end-grafted to a surface is immersed in a solution of complementary ssDNA probes, a regular brush of DNA duplexes is formed by 1:1 hybridization between probe and target DNA. We suggest that in higher density brushes of ssDNA this process competes with cross-hybridization of a target strand to several neighboring probe strands resulting in the formation of a cross-linked DNA network. We analyze a simple 2D model of a dense DNA brush and use analytic methods and computer simulations to find how the conditions for network formation depend on system size and DNA length. We argue that in 3D brushes cross-hybridization will nearly always lead to network formation and suggest that this may explain some intriguing results on dense DNA brushes. Experiments on DNA monolayers and concentrated DNA solutions that could test our predictions are proposed.

Computerized training of cryosurgery - a system approach.

The objective of the current study is to provide the foundation for a computerized training platform for cryosurgery. Consistent with clinical practice, the training process targets the correlation of the frozen region contour with the target region shape, using medical imaging and accepted criteria for clinical success. The current study focuses on system design considerations, including a bioheat transfer model, simulation techniques, optimal cryoprobe layout strategy, and a simulation core framework. Two fundamentally different approaches were considered for the development of a cryosurgery simulator, based on a finite-elements (FE) commercial code (ANSYS) and a proprietary finite-difference (FD) code. Results of this study demonstrate that the FE simulator is superior in terms of geometric modeling, while the FD simulator is superior in terms of runtime. Benchmarking results further indicate that the FD simulator is superior in terms of usage of memory resources, pre-processing, parallel processing, and post-processing. It is envisioned that future integration of a human-interface module and clinical data into the proposed computer framework will make computerized training of cryosurgery a practical reality.

Model of DNA bending by cooperative binding of proteins.

We present a model of nonspecific cooperative binding of proteins to DNA in which the binding of isolated proteins generates local bends but binding of proteins at neighboring sites on DNA straightens the polymer. We solve the statistical mechanical problem and calculate the effective persistence length, site occupancy, and cooperativity. Cooperativity leads to nonmonotonic variation of the persistence length with protein concentration, and to an unusual shape of the binding isotherm. The results are in qualitative agreement with recent single molecule experiments on nucleoid protein HU-DNA complexes.

Cryopreservation of carotid artery segments via vitrification subject to marginal thermal conditions: correlation of freezing visualization with functional recovery.

Cryopreservation is a well-established technique for long-term storage of viable cells and tissues. However, in recent years, application of established cryobiological principles to the preservation of multicellular tissues and organs has demanded considerable attention to ways of circumventing the deleterious effects of ice and thermal stresses in bulky tissues. As part of a multidisciplinary research program designed to study the interactions of thermo-physical events with tissue preservation, we report here on the implementation of a slow cooling (3 degrees C/min) and slow warming (62 degrees C/min) regimen towards scale-up of vitreous preservation of large tissue samples. Specifically, the correlation of thermo-physical events during vitrification of carotid artery segments with function recovery is reported using marginal thermal conditions for achieving vitrification in bulky samples. Moreover, the outcome is compared with a similar study reported previously using a 3-fold higher rate of rewarming (186+/-13 degrees C/min). Tissue vitrification using an 8.4M cryoprotectant cocktail solution (VS55) was achieved in 1 ml samples by imposing a low (2.6+/-0.1 degrees C/min) cooling rate, between -40 degrees C and -100 degrees C, and a low rewarming rate (62+/-4 degrees C/min) between -100 degrees C and -40 degrees C. Following cryoprotectant removal, the artery segments were cut into 3-4mm rings for function testing on a contractility apparatus by measuring isometric responses to four agonist and antagonists (norepinephrine, phenylepinephrine, calcium ionophore and sodium nitroprusside). In addition, non-specific metabolic function of the vessel rings was determined using the REDOX indicator alamarBlue. Contractile function, normalized to untreated control samples, in response to the agonists norepinephrine and phenylepinephrine was significantly better in the slowly rewarmed group of carotid segments (74+/-9% and 62+/-11%, respectively) than for the more rapidly warmed group 31+/-7% and 45+/-15%, respectively). However, EC(50) sensitivities were not significantly different between the groups. Thermo-physical events such as ice formation and fractures were monitored throughout the cooling and warming phases using cryomacroscopy with the aid of a purpose-built borescope device. This technique allowed a direct observation of the visual impact of ice formation on specific zones along the blood vessel segment where, in most cases, no ice formation or fractures were observed in the vicinity of the artery segments. However, in specific instances when some ice crystallization was observed to impact the artery segment, the subsequent testing of function revealed a total loss of contractility. The successful vitrification of blood vessel segments using marginal conditions of slow cooling and rewarming, provide essential information for the development of scale-up protocols that is necessary when clinically relevant size samples need to be cryopreserved in an essentially ice-free state. This information can further be integrated into computer simulations of heat transfer and thermo-mechanical stress, where the slowest cooling rate anywhere in the simulated domain must exceed the critical values identified in the current study.

Vitrification of Carotid Artery Segments: An Integrated Study of Thermophysical Events and Functional Recovery Toward Scale-Up for Clinical Applications.

In recent years, ice-free cryopreservation by vitrification has been demonstrated to provide superior preservation of tissues compared with conventional freezing methods. To date, this has been accomplished almost exclusively for small model systems, whereas cryopreservation of large tissue samples-of a clinically useful size-continues to be hampered by thermomechanical effects that compromise the structure and function of the tissue. Reduction of mechanical stress is an integral condition of successful cryopreservation of large specimens. The current study focuses on the impact of sample size on both the physical events, observed by cryomacroscopy, and on the outcome on tissue function. To this end, the current study sought to address the question of functional recovery of vitrified carotid artery segments, processed as either artery rings (3-4 mm long) or segments (25 mm long) as selected models; the latter model represents a significant increase in sample size for evaluating the effects of vitrification. Tissue vitrification using an 8.4 M cryoprotectant cocktail solution (VS55) was achieved in 1-ml samples by imposing either a high (50-70 °C/min) or a low (2-3 °C/min) cooling rate, between -40°C and -100°C, and a high rewarming rate between -100°C and -40°C. Following cryoprotectant removal, the artery segments were cut into 3 to 4-mm rings for function testing on a contractility apparatus by measuring isometric responses to four agonist and antagonists (norepinephrine, phenylepinephrine, calcium ionophore, and sodium nitroprusside). In addition, nonspecific metabolic function of the vessel rings was determined using the REDOX indicator alamarBlue. Contractile function in response to the agonists norepinephrine and phenylepinephrine was maintained at the same level (350%) for the segments as for the rings, when compared with noncryopreserved control samples. Relaxation in response to the antagonists calcium ionophore and sodium nitroprusside was maintained at between 75% and 100% of control levels, irrespective of cooling rate or sample size. No evidence of macroscopic crystallization or fractures was observed by cryomacroscopy at the above rates in any of the samples. In conclusion, this study verifies that the rate of cooling and warming can be reduced from our baseline vitrification technique such that the function of larger tissue samples is not significantly different from that of smaller blood vessel rings. This represents a step toward the goal of achieving vitreous cryopreservation of large tissue samples without the destructive effect of thermal stresses.

Metastable network model of protein transport through nuclear pores.

To reconcile the observed selectivity and the high rate of translocation of cargo-importin complexes through nuclear pores, we propose that the core of the nuclear pore complex is blocked by a metastable network of phenylalanine and glycine nucleoporins. Although the network arrests the unfacilitated passage of objects larger than its mesh size, cargo-importin complexes act as catalysts that reduce the free energy barrier between the cross-linked and the dissociated states of the Nups, and open the network. Using Brownian dynamics simulations we calculate the distribution of passage times through the network for inert particles and cargo-importin complexes of different sizes and discuss the implications of our results for experiments on translocation of proteins through the nuclear pore complex.

Is intracellular hyperthermia superior to extracellular hyperthermia in the thermal sense?

More than 20 years ago, it was hypothesized that intracellular hyperthermia is superior to extracellular hyperthermia. It was further hypothesized that even a single biological cell containing magnetic nanoparticles can be treated for hyperthermia by an AC magnetic field, independent of its surrounding cells. Since experimental investigation of the thermal effects of intracellular hyperthermia is not feasible, these hypotheses have been studied theoretically. The current report shows that nano-scale heating effects are negligible. This study further shows that intracellular heat generation is sufficient to create the necessary conditions for hyperthermia only in a large group of cells loaded with nanoparticles, having an overall diameter of at least 1mm. It is argued in this report that there is no reason to believe that intracellular hyperthermia is superior to extracellular hyperthermia in the thermal sense.

Fluctuating elastic rings: statics and dynamics.

We study the effects of thermal fluctuations on elastic rings. Analytical expressions are derived for correlation functions of Euler angles, mean-square distance between points on the ring contour, radius of gyration, and probability distribution of writhe fluctuations. Since fluctuation amplitudes diverge in the limit of vanishing twist rigidity, twist elasticity is essential for the description of fluctuating rings. We discover a crossover from a small scale regime in which the filament behaves as a straight rod, to a large scale regime in which spontaneous curvature is important and twist rigidity affects the spatial configurations of the ring. The fluctuation-dissipation relation between correlation functions of Euler angles and response functions, is used to study the deformation of the ring by external forces. The effects of inertia and dissipation on the relaxation of temporal correlations of writhe fluctuations, are analyzed using Langevin dynamics.

Kinetics and mechanism of DNA uptake into the cell nucleus.

Gene transfer to eukaryotic cells requires the uptake of exogenous DNA into the cell nucleus. Except during mitosis, molecular access to the nuclear interior is limited to passage through the nuclear pores. Here we demonstrate the nuclear uptake of extended linear DNA molecules by a combination of fluorescence microscopy and single-molecule manipulation techniques, using the latter to follow uptake kinetics of individual molecules in real time. The assays were carried out on nuclei reconstituted in vitro from extracts of Xenopus eggs, which provide both a complete complement of biochemical factors involved in nuclear protein import, and unobstructed access to the nuclear pores. We find that uptake of DNA is independent of ATP or GTP hydrolysis, but is blocked by wheat germ agglutinin. The kinetics are much slower than would be expected from hydrodynamic considerations. A fit of the data to a simple model suggests femto-Newton forces and a large friction relevant to the uptake process.

Fluctuating filaments: statistical mechanics of helices

We examine the effects of thermal fluctuations on thin elastic filaments with noncircular cross section and arbitrary spontaneous curvature and torsion. Analytical expressions for orientational correlation functions and for the persistence length of helices are derived, and it is found that this length varies nonmonotonically with the strength of thermal fluctuations. In the weak fluctuation regime, the local helical structure is preserved and the statistical properties are dominated by long-wavelength bending and torsion modes. As the amplitude of fluctuations is increased, the helix "melts" and all memory of intrinsic helical structure is lost. Spontaneous twist of the cross section leads to resonant dependence of the persistence length on the twist rate.

An elastic analysis of Listeria monocytogenes propulsion.

The bacterium Listeria monocytogenes uses the energy of the actin polymerization to propel itself through infected tissues. In steady state, it continuously adds new polymerized filaments to its surface, pushing on its tail, which is made from previously cross-linked actin filaments. In this paper we introduce an elastic model to describe how the addition of actin filaments to the tail results in the propulsive force on the bacterium. Filament growth on the bacterial surface produces stresses that are relieved at the back of the bacterium as it moves forward. The model leads to a natural competition between growth from the sides and growth from the back of the bacterium, with different velocities and strengths for each. This competition can lead to the periodic motion observed in a Listeria mutant.

Temperature-controlled microscopy for imaging living cells: apparatus, thermal analysis and temperature dependency of embryonic elongation in Caenorhabditis elegans.

A new experimental apparatus for temperature-controlled microscopy has been developed for the study of the temperature dependency of developmental processes in the nematode Caenorhabditis elegans. However, the application of this apparatus is rather general and can be used for a wide range of temperatures between - 10 and 90 degrees C. The new apparatus is easy to use, inexpensive, simple to construct, and is designed for precise temperature control of oil-immersion microscopy using epifluorescence. Thermal analysis of the experimental apparatus shows the effects of each of its components, as well as the effects of uncertainty in temperature measurements. Finally, results of this study indicate that: (i) embryos incubated and imaged at temperatures of 8 degrees C and below do not elongate; (ii) the initial elongation rate is strongly temperature-dependent between 9 and 25 degrees C.

Thermal fluctuations of elastic filaments with spontaneous curvature and torsion.

We study the effects of thermal fluctuations on thin elastic filaments with spontaneous curvature and torsion. We derive analytical expressions for the orientational correlation functions and for the persistence length of helices and find that this length varies nonmonotonically with the strength of thermal fluctuations. In the weak fluctuation regime, the persistence length of a spontaneously twisted helix has three resonance peaks as a function of the twist rate. In the limit of strong fluctuations, all memory of the helical shape is lost.

Is it reasonable to assume a uniformly distributed cooling-rate along the microslide of a directional solidification stage?

It is commonly assumed that the cooling-rate along the microslide of a directional solidification stage is uniformly distributed, an assumption which is typically applied in low cooling-rates studies. A new directional solidification stage has recently been presented, which is specified to achieve high cooling-rates of up to 1.8 x 104 degrees C min-1, where cooling-rates are still assumed to be uniformly distributed. The current study presents a closed-form solution to the temperature distribution and to the cooling-rate in the microslide. Thermal analysis shows that the cooling-rate is by no means uniformly distributed and can vary by several hundred percent along the microslide in some cases. Therefore, the mathematical solution presented in this study is essential for experimental planning of high cooling-rate experiments.

The effect of temperature-dependent thermal conductivity in heat transfer simulations of frozen biomaterials.

The thermal conductivity value of pure water ice is inversely proportional to the temperature and decreases about 5-fold as the temperature increases from the liquid nitrogen boiling temperature (77 K to the freezing point of pure water. The temperature dependency of the thermal conductivity is typically overlooked in bioheat transfer simulations. A closed-form solution of the one-dimensional temperature distribution in frozen water and blood is presented in this study, based on a new thermal conductivity model. Results indicate that temperatures are overestimated up to 38K, and heat fluxes through the frozen region boundaries are underestimated by a factor of 2, when the temperature dependency of the thermal conductivity is neglected.

Long-term follow-up post-cryosurgery in a sheep breast model.

This study constitutes the advanced stage of an ongoing project for the development of cryosurgical devices and techniques for breast cryosurgery. The current study focuses on the long-term follow-up post-cryosurgery in a sheep breast model. Results of this study indicate that the cryotreatment site in a sheep breast model cannot be identified up to 5 months post-cryosurgery by means of ultrasound, mammography, or MRI. Histology findings of this study further indicate that there is no gross or microscopic difference between lesions that have been subject to one versus three freeze/thaw cycles. Under either cryosurgical protocol, there is a main cryoinjured region that has uniform destruction of epithelium and healing scar formation and a transition zone of damaged lobules without acini, surrounded by healthy tissues. The cryoinjured region at 5 months post-cryosurgery was found to be about half the diameter of the ultrasound-imaged frozen region during the cryoprocedure. This study shows that, in terms of recovery and regeneration, surgical excision appears to have an advantage over cryosurgery, which results in a more rapid healing process. Based on observations that the cryoinjured region is no smaller than the ultrasound-imaged ice-ball and that the typical thickness of the transition zone is up to 5 mm, a conservative use of the cryosurgical device developed for the current study in an ultrasound-monitored cryoprocedure requires at least 5 mm safety margins of the frozen region radius around the target region.

Numerical solution of the multidimensional freezing problem during cryosurgery.

A multidimensional, finite difference numerical scheme for the freezing process of biological tissues during cryosurgery is presented, which is a modification of an earlier numerical solution for inanimate materials. The tissues are treated as nonideal materials, freezing over a temperature range and possessing temperature-dependent thermophysical properties, blood perfusion, and metabolic heat generation. The numerical scheme is based on the application of an effective specific heat, substituting the intrinsic property, to include the latent heat effect within the phase transition temperature range. Results of the numerical solution were verified against an existing exact solution of a one-dimensional inverse Stefan problem in Cartesian coordinates. Results were further validated against experimental data available from the literature. The utility of the numerical solution for the design and application of cryodevices is demonstrated by parametric studies of the freezing processes around spherical and cylindrical cryoprobes. The parameters studied are the cryoprobe cooling power and the dimensions of the frozen region. Results are calculated for typical thermophysical properties of soft biological tissues, for angioma and for water.

Thermal expansion measurements of frozen biological tissues at cryogenic temperatures.

Thermal expansion data are essential for analyses of cryodestruction associated with thermal stresses during cryopreservation protocols as well as during cryosurgery. The present study tests a commonly used hypothesis that the thermal expansion of frozen tissues is similar to that of pure water ice crystals. This study further provides insight into the potential effect of the presence of cryoprotectants on thermal expansion. A new apparatus for thermal strain measurements of frozen biological tissues within a cryogenic temperature range is presented. Results are presented for fresh tissue samples taken from beef muscle, chicken muscle, rabbit muscle, rabbit bone, and pig liver. Pilot studies of the effect of cryoprotectants on thermal expansion are further presented for rabbit muscle immersed in dimethyl sulphoxide (2 mols/l) and glycerol (2 mols/l), and for pig liver perfused with dimethyl sulphoxide (2 mols/l). Thermal expansion of frozen soft biological tissues was found to be similar to that of water ice crystals in the absence of cryoprotectant. Thermal expansion of the rabbit bone was found to be about one half of that of frozen soft tissues. A significant reduction in the thermal expansion at higher temperatures was observed in the presence of cryoprotectants. A rapid change of thermal strain near -100 degrees C was also observed, which is likely to be associated with the glass transition process of the cryoprotectant solutions.

Gross damage accumulation on frozen rabbit liver due to mechanical stress at cryogenic temperatures.

The second phase of a pilot study dealing with the mechanical response of frozen biological tissues to external compressive load is presented. This stage deals with histological observations of the damage accompanying mechanically induced permanent deformation in frozen rabbit liver. no significant gross histological damage was observed in the liver samples due to either processing the tissue in the frozen state, due to slow cooling of the liver tissues down to -20 degrees C, or due to rapid cooling of the samples down to -196 degrees C. No histological changes were observed in tissue samples that were loaded within the elastic regime, that is, below the yield strength of the material. Therefore, it is concluded that histological changes due to mechanical stresses are associated with plastic (permanent) deformations. Histological observations indicate that linear cracks which appear to have no preferred orientation develop due to mechanical stress beyond the yield strength of the frozen tissue. These cracks accumulate until final failure of the frozen tissue, when the tissue sample collapses to rubble. Based on histological observations and concepts from solid mechanics, an interaction between crack formation and irregularities in the frozen medium is suggested. Significant sources for such irregularities, in an homogeneous tissue such as the liver, are blood vessels and bile ducts. These irregularities may either initiate crack formation or, on the other hand, may also arrest propagating cracks.