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.

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.

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.

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.

Analysis of Thermal Stresses around a Cryosurgical Probe

Large thermal stresses easily exceeding the tissue yield strength may develop in the frozen region around a cryosurgical probe. A new integrodifferential solution for the heat transfer problem of biological tissues freezing around a cryosurgical probe is presented in this article. This solution is suitable for cases of high Stephan numbers and for a temperature-dependent forcing function at the cryoprobe. A new solution for the thermal stresses around a cryosurgical probe is also presented, based on an elastic-perfectly plastic model. It is proposed that thermal stresses beyond the elastic limit of the frozen region may sharply increase the mechanical damage to the cell membranes due to plastic deformation. It was found that plastic deformation always starts at the cryoprobe surface; however, plastic deformation may also be formed near the freezing front at high cooling rates and large cryoprobes. It is demonstrated that under some conditions plastic deformation may occur in the entire frozen region. A parametric study to identify the best cooling protocol for maximal plastic deformation is presented.

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.

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.

A compact cryosurgical apparatus for minimally invasive procedures.

A new liquid-nitrogen-based apparatus for minimally invasive cryosurgery is presented. The cryoprobe was designed for application to breast tumors; however, it can be used for the treatment of other tumors. The cryoprobe has three major components, a cryoneedle, a thermal insulation shell, and a protective tube, which may be assembled as part of the operation. This special assembly keeps destruction to surrounding tissues due to cryoprobe penetration minimal, and allows accurate localization of the cryoprobe tip by means of stereotactic or needle-localization techniques. An alternative cryoprobe consists of a cryoneedle and a thermal insulation shell, which are rigidly connected. The liquid nitrogen supply system has two major components, an air-pressure source and a liquid nitrogen container, which are physically separated. This special configuration allows placement of the liquid nitrogen container adjacent to the cryotreated tissue and decreases the length of the cryoprobe feeding tube. In turn, heat losses to the surroundings are reduced, and therefore coolant consumption is reduced. The short feeding tube allows safe operation at low pressures. The small size of the apparatus makes it attractive for cryosurgical operations. It has been evaluated in gelatin solutions and in porcine skeletal muscle and liver. In-vivo results do not differ significantly from those obtained in gelatin solutions with regard to the dimensions of frozen regions. Using a three cryoprobe configuration, a frozen region with an average diameter of 50 mm and a length of 75 mm was obtained within 11 minutes. The thermal efficiency of that procedure was found to be 43%.

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.

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.

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.

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.

Combined solution of the inverse Stefan problem for successive freezing/thawing in nonideal biological tissues.

A new combined solution of the one-dimensional inverse Stefan problem in biological tissues is presented. The tissue is assumed to be a nonideal material in which phase transition occurs over a temperature range. The solution includes the thermal effects of blood perfusion and metabolic heat generation. The analysis combines a heat balance integral solution in the frozen region and a numerical enthalpy-based solution approach in the unfrozen region. The subregion of phase transition is included in the unfrozen region. Thermal effects of blood perfusion and metabolic heat generation are assumed to be temperature dependent and present in the unfrozen region only. An arbitrary initial condition is assumed that renders the solution useful for cryosurgical applications employing repeated freezing/thawing cycles. Very good agreement is obtained between the combined and an exact solution of a similar problem with constant thermophysical properties and a uniform initial condition. The solution indicated that blood perfusion does not appreciably affect either the shape of the temperature forcing function on the cryoprobe or the location and depth of penetration of the freezing front in peripheral tissues. It does, however, have a major influence on the freezing/thawing cycle duration, which is most pronounced during the thawing stage. The cooling rate imposed at the freezing front also has a major inverse effect on the duration of the freezing/thawing.

A new cryosurgical device for controlled freezing.

A new cryosurgical device utilizing liquid nitrogen, which is a modification of an existing commercial system, was developed. In the new computer-controlled cryodevice the temperature of the cryoprobe is controlled by means of an electrical heating element. The desired temperature-forcing function is calculated to ensure a specified constant cooling rate at the freezing front. The new device facilitates real-time data processing, and, in particular, simulation of the heat transfer processes. A series of tests was performed to study the characteristics of the cryodevice and to validate the underlying assumptions. These tests were performed using organic tissue, i.e., potatoes, as an in vivo simulating medium of biological tissue. The differences between experimental data and computed results were found to be within +/-0.5 degrees C, which falls within the uncertainty range of the experimental temperature measurements. A typical control error of the new device is within +/-0.3 degrees C, prior to the formation of the freezing front, and +/-0.6 degrees C thereafter, which is of the same order of magnitude as the uncertainty range of the temperature measurements. The new device is capable of producing maximal cooling rates of 50 degrees C/min down to temperatures of -165 degrees C and a maximal heating rate of 300 degrees C/min. The maximal cooling power of the cryoprobe, due to LN2 boiling, is 80 W; the maximal electrical heating power of the cryoprobe is 160 W. Precooling of the device requires about 30 min, and it can be operated continuously for about 3 h. Initial results of experimental in vivo cryosurgery performed on rabbit hindlimbs, including histological observations and thermal analysis, are presented in the second part of this study.

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.