Is isochoric vitrification feasible?

This study investigates the feasibility of ice-free isochoric vitrification for cryopreservation applications using mathematical modeling, computation tools, and the underlying principles of thermo-mechanics. This study is triggered by an increasing interest in the possibility of isochoric vitrification, following promising experimental results of isochoric cryopreservation. In general, isochoric cryopreservation is the preservation of biological materials in subzero temperatures in a rigid-sealed container, where some ice crystallization creates favorable pressure elevation due to the anomaly of water expansion upon ice Ih formation. Vitrification on the other hand is the transformation of liquid into an amorphous solid in the absence of any crystals, which is typically achieved by rapid cooling of a highly viscous solution. The current study presents a mathematical model for vitrification under variable pressure conditions, building upon a recently published thermo-mechanics modeling approach for isochoric cryopreservation. Using the physical properties of dimethyl sulfoxide (DMSO) as a representative cryoprotective agent (CPA), this study suggests that vitrification under isochoric conditions is not feasible, essentially since the CPA solution contracts more than the isochoric chamber by an order of magnitude. This differential contraction can lead to absolute zero pressure in the isochoric chamber, counteracting the premise of the isochoric cryopreservation process. It is concluded that the only alternative to prevent ice formation while benefiting from the potential advantages of higher pressures is to create the required pressures by external means, and not merely by passively enclosing the specimen in an isochoric chamber.

Large surface deformation due to thermo-mechanical effects during cryopreservation by vitrification - mathematical model and experimental validation.

This study presents a simplified thermal-fluids (TF) mathematical model to analyze large surface deformations in cryoprotective agents (CPA) during cryopreservation by vitrification. The CPA deforms during vitrification due to material flow caused by the combined effects of thermal gradients within the domain, thermal contraction due to temperature, and exponential increase in the viscosity of the CPA as it is cooled towards glass transition. While it is well understood that vitrification is associated with thermo-mechanical stress, which might lead to structural damage, those large deformations can lead to stress concentration, further intensifying the probability to structural failure. The results of the TF model are experimentally validated by means of cryomacroscopy on a cuvette containing 7.05M dimethyl sulfoxide (DMSO) as a representative CPA. The TF model presented in this study is a simplified version of a previously presented thermo-mechanics (TM) model, where the TM model is set to solve the coupled heat transfer, fluid mechanics and solid mechanics problems, while the TF model omits further deformations in the solid state. It is demonstrated in this study that the TF model alone is sufficient to capture large-body deformations during vitrification. However, the TF model alone cannot be used to estimate mechanical stresses, which become significant only when the deformation rates become so small that the deformed body practically behaves as an amorphous solid. This study demonstrates the high sensitivity of deformation predictions to variation in material properties, chief among which are the variations of density and viscosity with temperature. Finally, this study includes a discussion on the possibility of turning on and off the TF and TM models in respective parts of the domain, in order to solve the multiphysics problem in a computationally cost-effective manner.

Thermo-mechanics aspects of isochoric cryopreservation: A new modeling approach and comparison with experimental data.

A new mathematical model is proposed for the analysis of thermo-mechanics effects during isochoric cryopreservation. In that process, some ice crystallization in a fixed-volume container drives pressure elevation, which may be favorable to the preservation of biological material when it resides in the unfrozen portion of the same container. The proposed model is comprehensive, integrating for the first time concepts from the disparate fields of thermodynamics, heat transfer, fluid mechanics, and solid mechanics. The novelty in this study is in treating the cryopreserved material as having a pseudo-viscoelastic behavior over a very narrow temperature range, without affecting the mechanical behavior of the material in the rest of the domain. This unique approach permits treating the domain as a continuum, while avoiding the need to trace freezing fronts and sperate the analysis to liquid and solid subdomains. Consistent with the continuum approach, the heat transfer problem is solved using the enthalpy approach. The presented analysis focusses on isochoric cooling of pure water between standard atmospheric conditions and the triple point of liquid water, ice Ih, and ice III (-22°C and 207.4 MPa). The proposed model is also applicable to isochoric vitrification, by substituting the pseudo-viscoelastic material model with the real viscosity model of the vitrifying material. Results of this study display good agreement with phase-diagram data at steady state, and with experimental data from the literature. Furthermore, this study provides a venue to discussing experimentation aspects of isochoric cryopreservation. The proposed model is further demonstrated on a 3D problem, while discussing scale considerations, crystallization conditions, and transient effects. Notably, the new model can be used to bridge the gap between limited pressure and temperature measurements during cryopreservation and the analysis of the continuum. Arguably, this study presents the most advanced thermo-mechanics model to solve practical problems relating to isochoric cryopreservation.

Thermomechanical stress analysis of rabbit kidney and human kidney during cryopreservation by vitrification with the application of radiofrequency heating.

This study presents a computational framework for thermomechanical stress analysis in a specimen undergoing cryopreservation, with emphasis on radiofrequency (RF) heating for recovering from cryogenic storage. In particular, this study addresses cryopreservation by vitrification, where the specimen is stored in the amorphous phase (vitreous means glassy). In broad terms, the relatively high cooling and rewarming rates necessary for vitrification result in differential thermal expansion in the specimen, which is the driving force for thermomechanical stress. Thermomechanical stress can lead to structural damage, such as fractures or plastic deformation, rendering the specimen useless. Not without technical difficulties, those hazardous effects during the rewarming phase of the protocol can be mitigated by applying volumetric heating, with RF heating as an attractive means. The proposed computational framework in this study addresses the coupled electromagnetic, thermal and solid mechanics fields, using commercially available solvers. This study advances from a spherical-case benchmark to realistic models of the rabbit kidney and the human kidney. Results of this study suggest that structural damage to the brittle material can be prevented when stress relaxation is facilitated around the glass transition temperature. Furthermore, this study suggests that volumetric heating is necessary to surpass the critical rewarming rate, while benefiting from lowering the overall thermomechanical stress during recovery from cryogenic storage. More broadly, the computational framework presented here can be used for the optimization of the RF heating parameters, chamber specifics, specimen container shape, and the thermal protocol in order to preserve structural integrity in the specimen.

Scaling Effects on the Residual Thermomechanical Stress During Ice-Free Cooling to Storage Temperature.

Cryopreservation via vitrification (glass formation) is a promising approach for long-term preservation of large-size tissues and organs. Unfortunately, thermomechanical stress, which is driven by the tendency of materials to change size with temperature, may lead to structural failure. This study focuses on analysis of thermomechanical stress in a realistic, pillow-like shape cryobag as it is cooled to cryogenic storage, subject to sufficiently high cooling rates to facilitate vitrification. Contrary to common perception, it is demonstrated in this study that the maximum stress in the specimen does not necessarily increase with increasing size of the specimen. In fact, the maximum stress is affected by the combination of two competing effects, associated with the extent of the temperature gradients within the specimen and its overall volume. On one hand, the increase in specimen size gives rise to more prominent temperature gradients, which can intensify the thermomechanical stress. On the other hand, the temperature distribution at the core of larger specimens is more uniform, which leads to a larger portion of the specimen transitioning from fluid to a glassy material almost instantaneously, which carries a moderating effect on the overall mechanical stress at the glassy state (i.e., lower residual stress). In conclusion, this study demonstrates the role of container shape optimization in reducing the thermomechanical stress during cooling.

Analysis of polarized-light effects in glass-promoting solutions with applications to cryopreservation and organ banking.

This study presents experimental results and an analysis approach for polarized light effects associated with thermomechanical stress during cooling of glass promoting solutions, with applications to cryopreservation and tissue banking in a process known as vitrification. Polarized light means have been previously integrated into the cryomacroscope-a visualization device to detect physical effects associated with cryopreservation success, such as crystallization, fracture formation, and contamination. The experimental study concerns vitrification in a cuvette, which is a rectangular container. Polarized light modeling in the cuvette is based on subdividing the tridimensional (3D) domain into a series of planar (2D) problems, for which a mathematical solution is available in the literature. The current analysis is based on tracking the accumulated changes in light polarization and magnitude, as it passes through the sequence of planar problems. Results of this study show qualitative agreement in light intensity history and distribution between experimental data and simulated results. The simulated results help explaining differences between 2D and 3D effects in photoelasticity, most notably, the counterintuitive observation that high stress areas may correlate with low light intensity regions based on the particular experimental conditions. Finally, it is suggested that polarized-light analysis must always be accompanied by thermomechanical stress modeling in order to explain 3D effects.

Thermo-mechanical stress analysis of cryopreservation in cryobags and the potential benefit of nanowarming.

Cryopreservation by vitrification is the only promising solution for long-term organ preservation which can save tens of thousands of lives across the world every year. One of the challenges in cryopreservation of large-size tissues and organs is to prevent fracture formation due to the tendency of the material to contract with temperature. The current study focuses on a pillow-like shape of a cryobag, while exploring various strategies to reduce thermo-mechanical stress during the rewarming phase of the cryopreservation protocol, where maximum stresses are typically found. It is demonstrated in this study that while the level of stress may generally increase with the increasing amount of CPA filled in the cryobag, the ratio between width and length of the cryobag play a significant role. Counterintuitively, the overall maximum stress is not found when the bag is filled to its maximum capacity (when the filled cryobag resembles a sphere). Parametric investigation suggests that reducing the initial rewarming rate between the storage temperature and the glass transition temperature may dramatically decrease the thermo-mechanical stress. Adding a temperature hold during rewarming at the glass transition temperature may reduce the thermo-mechanical stress in some cases, but may have an adverse effect in other cases. Finally, it is demonstrated that careful incorporation of volumetric heating by means on nanoparticles in an alternating magnetic field, or nanowarming, can dramatically reduce the resulting thermo-mechanical stress. These observations display the potential benefit of a thermo-mechanical design of the cryopreservation protocols in order to prevent structural damage.

Polarized light scanning cryomacroscopy, part II: Thermal modeling and analysis of experimental observations.

This study aims at developing thermal analysis tools and explaining experimental observations made by means of polarized-light cryomacroscopy (Part I). Thermal modeling is based on finite elements analysis (FEA), where two model parameters are extracted from thermal measurements: (i) the overall heat transfer coefficient between the cuvette and the cooling chamber, and (ii) the effective thermal conductivity within the cryoprotective agent (CPA) at the upper part of the cryogenic temperature range. The effective thermal conductivity takes into account enhanced heat transfer due to convection currents within the CPA, creating the so-called Bénard cells. Comparison of experimental results with simulation data indicates that the uncertainty in simulations due to the propagation of uncertainty in measured physical properties exceeds the uncertainty in experimental measurements, which validates the modeling approach. It is shown in this study that while a cavity may form in the upper-center portion of the vitrified CPA, it has very little effect on estimating the temperature distribution within the domain. This cavity is driven by thermal contraction of the CPA, with the upper-center of the domain transitioning to glass last. Finally, it is demonstrated in this study that additional stresses may develop within the glass transition temperature range due to nonlinear behavior of the thermal expansion coefficient. This effect is reported here for the first time in the context of cryobiology, using the capabilities of polarized-light cryomacroscopy.