Mass transfer during freezing in rat prostate tumor tissue

Adult Stem Cells Freezing Processes and Cryopreservation Protocols

The development of simple but effective storage protocols for adult stem cells will greatly enhance their use and utility in tissue-engineering applications. Cryopreservation has shown the most promise but is a fairly complex process, necessitating the use of chemicals called cryoprotective agents (CPAs), freezing equipment, and obviously, storage in liquid nitrogen. The purpose of this chapter is to present a general overview of cryopreservation storage techniques and the optimal protocols/results obtained in our laboratory for long-term storage of adult stem cells using freezing storage.

Freezing of Solute-Laden Aqueous Solutions: Kinetics of Crystallization and Heat- and Mass-Transfer-Limited Model

Following an earlier study, we reexamined the latent heat of fusion during freezing at 5 K/min of twelve different pre-nucleated solute-laden aqueous solutions using a Differential Scanning Calorimeter (DSC) and correlated it with the amount of initially dissolved solids or solutes in the solution. In general, a decrease in DSC-measured heat release (in comparison to that of pure water, 335 mJ/mg) was observed with an increasing fraction of dissolved solids or solutes, as observed in the earlier study. In addition, the kinetics of ice crystallization was also obtained in three representative biological media by performing additional experiments at 1, 5 and 20 K/min. A model of ice crystallization based on the phase diagram of a water–NaCl binary solution and a modified Avrami-like model of kinetics was then developed and fit to the experimental data. Concurrently, a heat and mass transfer model of the freezing of a salt solution in a small container is also presented to account for the effect of the cooling rate as well as the solute concentration on the measured latent of freezing. This diffusion-based model of heat and mass transfer was non-dimensionalized, solved using a numerical scheme and compared with experimental results. The simulation results show that the heat and mass transfer model can predict (± 10%) the experimental results.

Mathematical Modeling and Optimization of Cryopreservation in Single Cells

Cryobiology is a multiscale and interdisciplinary field. The scope and scale of interactions limit the gains that can be made by one theory or experiment alone. Because of this, modeling has played a critical role in both explaining cryobiological phenomena and predicting improved protocols. Modeling facilitates understanding of the biophysical and some of the biochemical mechanisms of damage during all phases of cryopreservation including CPA equilibration and cooling and warming. Moreover, as a tool for optimization of cryopreservation protocols, modeling has yielded many successes. Modern cryobiological modeling includes very detailed descriptions of the physical phenomena that occur during freezing, including ice growth kinetics and spatial gradients that define heat and mass transport models. Here we reduce the complexity and approach only a small but classic subset of these problems. Namely, here we describe the process of building and using a mathematical model of a cell in suspension where spatial homogeneity is assumed for all quantities. We define the models that describe the critical cell quantities used to describe optimal and suboptimal protocols and then give an overview of classical methods of how to determine optimal protocols using these models. We include practical considerations of modeling in cryobiology, including fitting transport models to cell volume data, performing optimization with cell volume constraints, and a look at expanding cost functions to cooling regimes.

Modeling and optimization of cryopreservation

Modeling plays a critical role in understanding the biophysical processes behind cryopreservation. It facilitates understanding of the biophysical and some of the biochemical mechanisms of damage during all phases of cryopreservation including CPA equilibration, cooling, and warming. Modeling also provides a tool for optimization of cryopreservation protocols and has yielded a number of successes in this regard. While modern cryobiological modeling includes very detailed descriptions of the physical phenomena that occur during freezing, including ice growth kinetics and spatial gradients that define heat and mass transport models, here we reduce the complexity and approach only a small but classic subset of these problems. Namely, here we describe the process of building and using a mathematical model of a cell in suspension where spatial homogeneity is assumed for all quantities. We define the models that describe the critical cell quantities used to describe optimal and suboptimal protocols and then give an overview of classical methods of how to determine optimal protocols using these models.

Freezing-induced fluid-matrix interaction in poroelastic material

Freezing of biological tissue is emerging in various biomedical applications. The success of these applications requires precise control of the tissue functionality, which is closely associated with the microstructure of the extracellular matrix (ECM). In the present study, the spatiotemporal effects of freezing on the ECM were experimentally and theoretically investigated by approximating biological tissue as a poroelastic material saturated with interstitial fluid. The experiments with type I collagen gel showed that its matrix underwent two distinct levels of structural changes due to freezing: enlarged pore structure of the matrix and increased collagen fibril diameters. The extent of these changes was augmented as the freezing temperature was lowered. The theoretical model suggested that the interstitial fluid might be transported toward the unfrozen region from the phase change interface due to the volumetric expansion associated with the water-ice phase change, and the transported fluid could interact with the matrix and enlarge its pore structure. The model also illustrated the effects of matrix structural properties on this interaction including initial porosity, hydraulic conductivity, and elastic modulus. These results imply that an identical macroscopic freezing protocol may result in different microstructural alterations of poroelastic materials depending on the structural properties of the matrix. This may be relevant to understanding the tissue-type dependent outcomes of cryomedicine applications and be useful in designing cryomedicine applications for a wide variety of tissues.

Numerical Simulation of Local Temperature Distortions During Ice Nucleation of Cells in Suspension

Knowledge of intercellular ice formation in cells embedded in an extra-cellular suspension is essential for effective design of freezing protocols. The presence of cell membrane causes super-cooling of the intra-cellular region, which nucleates at much lower temperatures than the surrounding extra-cellular space and is accompanied by the exothermic release of the latent heat. This is a dynamic process and causes thermal distortions in and around the cell where nucleation occurs. In the present study, an attempt has been made to numerically determine the magnitude of thermal distortion (ΔT) and the time (dt) it takes for this distortion to damp out to the local temperature. A two-dimensional computational model is presented in which the maximum thermal distortions (with an assumed cell diameter of 50 μm, nucleating at -5 °C while being cooled at 5 °C/min; denoted as Scenario 1) and the lowest-possible thermal distortions (with an assumed cell diameter of 5 μm, nucleating at -20 °C while being cooled at 100 °C/min; denoted as Scenario 2) are determined. Extensive computations have been performed assuming either the presence of a single, dual, or four cells in suspension. It is expected that these representative results would serve the purpose of estimating an effective sampling rate of microscale thermocouples currently being fabricated and of other biomedical devices used to measure intracellular ice formation.

Membrane Transport Properties of Equine and Macaque Ovarian Tissues Frozen in Mixtures of Dimethylsulfoxide and Ethylene Glycol

The rate at which equine and macaque ovarian tissue sections are first cooled from +25°Cto+4°C has a significant effect on the measured water transport when the tissues are subsequently frozen in 0.85M solutions of glycerol, dimethylsulfoxide (DMSO), or ethylene glycol (EG). To determine whether the response of ovarian tissues is altered if they are suspended in mixtures of cryoprotective agents (CPAs), rather than in solutions of a single CPA, we have now measured the subzero water transport from ovarian tissues that were suspended in mixtures of DMSO and EG. Sections of freshly collected equine and macaque ovaries were suspended either in a mixture of 0.9M EG plus 0.7M DMSO (equivalent to a mixture of ∼5%v∕v of EG and DMSO) or in a 1.6M solution of only DMSO or only EG. The tissue sections were cooled from +25°Cto+4°C and then frozen to subzero temperatures at 5°C∕min. As the tissues were being frozen, a shape-independent differential scanning calorimeter technique was used to measure water loss from the tissues and, consequently, the best fit membrane permeability parameters (Lpg and ELp) of ovarian tissues during freezing. In the mixture of DMSO+EG, the respective values of Lpg and ELp for equine tissue first cooled at 40°C∕min between +25°C and +4°C before being frozen were 0.15μm∕minatm and 7.6kcal∕mole. The corresponding Lpg and ELp values for equine tissue suspended in 1.6M DMSO were 0.12μm∕minatm and 27.2kcal∕mole; in 1.6M EG, the values were 0.06μm∕minatm and 21.9kcal∕mole, respectively. For macaque ovarian tissues suspended in the mixture of DMSO+EG, the respective values of Lpg and ELp were 0.26μm∕minatm and 26.2kcal∕mole. Similarly, the corresponding LLg and ELp values for macaque tissue suspended in 1.6M DMSO were 0.22μm∕minatm and 31.4kcal∕mole; in 1.6M EG, the values were 0.20μm∕minatm and 27.9kcal∕mole. The parameters for both equine and macaque tissue samples suspended in the DMSO+EG mixture and first cooled at 0.5°C∕min between +25°C and +4°C were very similar to the corresponding values for samples cooled at 40°C∕min. In contrast, the membrane parameters of equine and macaque samples first cooled at 0.5°C∕min in single-component solutions were significantly different from the corresponding values for samples cooled at 40°C∕min. These results show that the membrane properties of ovarian cells from two species are different, and that the membrane properties are significantly affected both by the solution in which the tissue is suspended and by the rate at which the tissue is cooled from +25°Cto+4°C before being frozen. These observations suggest that these variables ought to be considered in the derivation of methods to cryopreserve ovarian tissues.

Subzero water transport characteristics and optimal rates of freezing rhesus monkey (Macaca mulatta) ovarian tissue

The purpose of the present study was to examine the effect of two different suprazero (room temperature +25 degrees C to +4 degrees C) cooling conditions on the measured water transport response of primate (Macaca mulatta) ovarian tissue in the presence and absence of cryoprotective agents (CPAs). Freshly collected Macaca mulatta (rhesus monkey) ovarian tissue sections were cooled at either 0.5 degrees C/min or 40 degrees C/min from 25 to 4 degrees C. A shape independent differential scanning calorimeter (DSC) technique was then used to measure the volumetric shrinkage during freezing of ovarian tissue sections at a freezing rate of 5 degrees C/min in the presence and absence of three different CPAs (0.85 M glycerol, 0.85 M dimethylsulfoxide, and 0.85 M ethylene glycol). Thus, water transport during freezing of primate ovarian tissue was obtained at eight different conditions (i.e., at four different freezing media with two different suprazero cooling conditions). The water transport response of ovarian tissue cooled rapidly from 25 to 4 degrees C was significantly different (P < 0.01) than that of slow cooled tissue, in the freezing media without CPAs and with dimethylsulfoxide. However, the differences in the measured water transport response due to the imposed suprazero cooling conditions were reduced with the addition of glycerol and ethylene glycol (statistically different with P < 0.05). By fitting a model of water transport to the experimentally obtained volumetric shrinkage data the best-fit membrane permeability parameters (L(pg) and E(Lp)) were determined. The best-fit parameters of water transport in primate ovarian tissue sections ranged from: L(pg) = 0.7 to 0.15 microm/min-atm and E(Lp) = 22.1 to 32.1 kcal/mol (the goodness of fit parameter, R(2) > 0.96). These parameters suggest that the "optimal rates of cryopreservation" for ovarian tissue are significantly dependent upon suprazero cooling conditions and the choice of CPA.

Cellular response of adipose derived passage-4 adult stem cells to freezing stress

A differential scanning calorimeter technique was used to generate experimental data for volumetric shrinkage during cooling at 20 degrees C/min in adipose derived adult stem cells (ASCs) in the presence and absence of cryoprotective agents (CPAs). By fitting a model of water transport to the experimentally determined volumetric shrinkage data, the membrane permeability parameters of ASCs were obtained. For passage-4 (P4) ASCs, the reference hydraulic conductivity Lpg and the value of the apparent activation energy ELP were determined to be 1.2 X 10(-13) m3/Ns and 177.8 kJ/mole, respectively. We found that the addition of either glycerol or dimethylsulfoxide (DMSO) significantly decreased the value of the reference hydraulic conductivity Lpg(cpa) and the value of the apparent activation energy ELp(cpa) in P4 ASCs. The values of Lpg(cpa) in the presence of glycerol and DMSO were determined as 0.39 x 10(-13) and 0.50 X 109-13) m3/Ns, respectively, while the corresponding values of ELp(cpa) were 51.0 and 61.5 kJ/mole. Numerical simulations of water transport were then performed under a variety of cooling rates (5-100 degreesC/min) using the experimentally determined membrane permeability parameters. And finally, the simulation results were analyzed to predict the optimal rates of freezing P4 adipose derived cells in the presence and absence of CPAs.

Suprazero cooling conditions significantly influence subzero permeability parameters of mammalian ovarian tissue

To model the cryobiological responses of cells and tissues, permeability characteristics are often measured at suprazero temperatures and the measured values are used to predict the responses at subzero temperatures. The purpose of the present study was to determine whether the rate of cooling from +25 to +4 degrees C influenced the measured water transport response of ovarian tissue at subzero temperatures in the presence or absence of cryoprotective agents (CPAs). Sections of freshly collected equine ovarian tissue were first cooled either at 40 degrees C/min or at 0.5 degrees C/min from 25 to 4 degrees C, and then cooled to subzero temperatures. A shape-independent differential scanning calorimeter (DSC) technique was used to measure the volumetric shrinkage during freezing of equine ovarian tissue sections. After ice was induced to form in the extracellular fluid within the specimen, the sample was frozen from the phase change temperature to -50 degrees C at 5 degrees C/min. Replicate samples were frozen in isotonic medium alone or in medium containing 0.85 M glycerol or 0.85 M dimethylsulfoxide. The water transport response of ovarian tissue samples cooled at 40 degrees C/min from 25 to 4 degrees C was significantly different (confidence level >95%) from that of tissue samples cooled at 0.5 degrees C/min, whether in the presence or absence of CPAs. We fitted a model of water transport to the experimentally-derived volumetric shrinkage data and determined the best-fit membrane permeability parameters (L(pg) and E(Lp)) of equine ovarian tissue during freezing. Subzero water transport parameters of ovarian tissue samples cooled at 0.5 degrees C/min from 25 to 4 degrees C ranged from: L(pg) = 0.06 to 0.73 microm/min.atm and E(Lp) = 6.1 to 20.5 kcal/mol. The corresponding parameters of samples cooled at 40 degrees C/min from 25 to 4 degrees C ranged from: L(pg) = 0.04 to 0.61 microm/min.atm and E(Lp) = 8.2 to 54.2 kcal/mol. Calculations made of the theoretical response of tissue at subzero temperatures suggest that the optimal cooling rates to cryopreserve ovarian tissue are significantly dependent upon suprazero cooling conditions.

A simplified procedure to determine the optimal rate of freezing biological systems

The effect of several cell-level parameters on the predicted optimal cooling rate B(opt) of an arbitrary biological system has been studied using a well-defined water transport model. An extensive investigation of the water transport model revealed three key cell level parameters: reference permeability of the membrane to water L(pg), apparent activation energy E(Lp), and the ratio of the available surface area for water transport to the initial volume of intracellular water (SA/WV). We defined B(opt) as the "highest" cooling rate at which a predefined percent of the initial water volume is trapped inside the cell (values ranging from 5% to 80%) at a predefined end temperature (values ranging from -5 degrees C to -40 degrees C). Irrespective of the choice of the percent of initial water volume trapped and the end temperature, an exact and linear relationship exists between L(pg), SA/WV, and B(opt0. However, a nonlinear and inverse relationship is found between E(Lp) and B(opt). Remarkably, for a variety of biological systems a comparison of the published experimentally determined values of B(opt) agreed quite closely with numerically predicted B(opt) values when the model assumed 5% of initial water is trapped inside the cell at a temperature of -15 degrees C. This close agreement between the experimental and model predicted optimal cooling rates is used to develop a generic optimal cooling rate chart and a generic optimal cooling rate equation that greatly simplifies the prediction of the optimal rate of freezing of biological systems.

An inverse approach to determine solute and solvent permeability parameters in artificial tissues

This study presents a generic numerical model to simulate the coupled solute and solvent transport in tissue sections during addition and removal of chemical additives or cryoprotective agents (CPA; dimethylsulfoxide or DMSO). Osmotic responses of various tissue cells within the artificial tissue are predicted by the numerical model with three model parameters: Permeability of the tissue cell membrane to water (Lp), permeability of the tissue cell membrane to the solute or CPA (omega), and the diffusion coefficient of the solute or CPA in the extracellular space (D). By fitting the model results with published experimental data on solute/water concentrations at various locations within an artificial tissue, we were able to determine the permeability parameters of artificial tissue cells in the presence of 1.538 M DMSO. Lp and omega were determined at three different locations within the artificial tissue assuming a constant value of solute diffusivity (D = 1.0 x 10(-9) m2/s). The best fit values of Lp ranged from 0.59 x 10(-14) to 4.22 x 10(-14) m3/N-s while omega ranged from 0 to 6.6 x 10(-13) mol/N-s. Based on these values of Lp and omega, the solute reflection coefficient, sigma = 1 - omegav(-)CPA/Lp, ranged from 0.9923 to 1.0. The relative values of omega and sigma suggest that the artificial tissue cells are relatively impermeable to DMSO (or omega approximately 0 and sigma approximately 1.0). This observation was used to modify our model to predict the values of Lp and D assuming omega = 0 and sigma = 1.0. The best fit values of Lp ranged from 640 x 10(-14) to 2.1 x 10(-14) m3/N-s while D ranged from 0.63 x 10(-9) to 1.52 x 10(-9) m2/s. The permeability parameters obtained in the present study represent the first such effort for artificial tissues.

Variation in the Membrane Transport Properties and Predicted Optimal Rates of Freezing for Spermatozoa of Diploid and Tetraploid Pacific Oyster, Crassostrea gigas1

In the present study, a shape-independent differential scanning calorimeter (DSC) technique was used to measure the dehydration response during freezing of sperm cells from diploid and tetraploid Pacific oysters, Crassostrea gigas. This represents the first application of the DSC technique to sperm cells from nonmammalian species. Volumetric shrinkage during freezing of oyster sperm cell suspensions was obtained at cooling rates of 5 and 20 degrees C/min in the presence of extracellular ice and 8% (v/v) concentration of dimethyl sulfoxide (DMSO), a commonly used cryoprotective agent (CPA). Using previously published data, sperm cells from diploid oysters were modeled as a two-compartment "ball-on-stick" model with a "ball" 1.66 microm in diameter and a "stick" 41 microm in length and 0.14 microm wide. Similarly, sperm cells of tetraploid oysters were modeled with a "ball" 2.14 microm in diameter and a "stick" 53 microm in length and 0.17 microm wide. Sperm cells of both ploidy levels were assumed to have an osmotically inactive cell volume, Vb, of 0.6 Vo, where Vo is the isotonic (or initial) cell volume. By fitting a model of water transport to the experimentally obtained volumetric shrinkage data, the best-fit membrane permeability parameters (Lpg and ELp) were determined. The combined-best-fit membrane permeability parameters at 5 and 20 degrees C/min for haploid sperm cells (or cells from diploid Pacific oysters) in the absence of CPAs were: Lpg = 0.30 x 10(-15) m(3)/Ns (0.0017 microm/min-atm) and ELp = 41.0 kJ/mole (9.8 kcal/mole). The corresponding parameters in the presence of 8% DMSO were: Lpg[cpa] = 0.27 x 10(-15) m(3)/Ns (0.0015 microm/min-atm) and ELp[cpa] = 38.0 kJ/mole (9.1 kcal/mole). Similarly, the combined-best-fit membrane permeability parameters at 5 and 20 degrees C/min for diploid sperm cells (or cells from tetraploid Pacific oysters) in the absence of CPAs were: Lpg = 0.34 x 10(-15) m(3)/Ns (0.0019 microm/min-atm) and ELp = 29.7 kJ/mole (7.1 kcal/mole). The corresponding parameters in the presence of 8% DMSO were: Lpg[cpa] = 0.34 x 10(-15) m(3)/Ns (0.0019 microm/min-atm) and ELp[cpa] = 37.6 kJ/mole (9.0 kcal/mole). The parameters obtained in this study suggest that optimal rates of cooling for Pacific oyster sperm cells range from 40 to 70 degrees C/min. These theoretical cooling rates are in close conformity with empirically determined optimal rates of cooling sperm cells from Pacific oysters, C. gigas.

Cryopreservation of Collagen-Based Tissue Equivalents. II. Improved Freezing in the Presence of Cryoprotective Agents

In Part I of this study we determined an optimal cooling rate for cryopreservation of collagen-based tissue equivalents (TEs) that preserves both the postthaw cell viability and mechanical properties, but results in tissue contraction and an overall loss of opacity. The empirically determined optimal cooling rate (5 degrees C/min) was obtained in a freezing medium consisting solely of phosphate-buffered saline (PBS) at physiological concentration (1x). In the present study we report the effect of freezing on TEs in the presence of PBS and two cryoprotective agents (CPAs) (glycerol and dimethyl sulfoxide [Me(2)SO]), at two different concentrations (0.5 and 1.0 M), to two different end temperatures (-80 and -160 degrees C), at a cooling rate of 5 degrees C/min. The controlled rate freezing experiments, postthaw cell viability, and mechanical property measurements were performed as described in Part I of this study. In addition to studying the effect of CPAs on the postthaw properties of TEs, we also investigated (1). the effect of freezing TEs attached to the substrate (as opposed to detached and floating in medium) to determine differences when freezing TEs subject to static mechanical stress via a mechanical constraint to contraction; (2). the effect of freezing glutaraldehyde-fixed TEs to determine differences in freezing-mediated damage to the microstructure; and (3). the effect of freezing more mature TEs that were incubated for 4 weeks in growth factor-supplemented medium as opposed to 2 weeks in basal medium. All TEs frozen at 5 degrees C/min to -80 degrees C in the presence of 0.5 M glycerol or Me(2)SO in PBS were found to be optimally cryopreserved in terms of maintaining opacity and structure as well as cell viability and mechanical properties as compared with unfrozen TEs. The postthaw mechanical properties were adversely affected by freezing to the lower end temperature of -160 degrees C in the presence of CPAs, with the samples frozen in the 1.0 M concentration of CPAs exhibiting a total loss of structural integrity on thawing. Furthermore, TEs frozen attached to the substrate showed decreased opacity and significant contraction as compared with TEs frozen detached from the substrate, as did cross-linked samples frozen without CPA.

Predicted permeability parameters of human ovarian tissue cells to various cryoprotectants and water

This study presents a generic numerical model to simulate the coupled solute and solvent transport in human ovarian tissue sections during addition and removal of chemical additives or cryoprotective agents (CPA). The model accounts for the axial and radial diffusion of the solute (CPA) as well as axial convection of the CPA, and a variable vascular surface area (A) during the transport process. In addition, the model also accounts for the radial movement of the solvent (water) into and out of the vascular spaces. Osmotic responses of various cells within an human ovarian tissue section are predicted by the numerical model with three model parameters: permeability of the tissue cell membrane to water (L(p)), permeability of the tissue cell membrane to the solute or CPA (omega) and the diffusion coefficient of the solute or CPA in the vascular space (D). By fitting the model results with published experimental data on solute/water concentrations within an human ovarian tissue section, I was able to determine the permeability parameters of ovarian tissue cells in the presence of 1.5M solutions of each of the following: dimethyl sulphoxide (DMSO), propylene glycol (PROH), ethylene glycol (EG), and glycerol (GLY), at two temperatures (4 degrees C and 27 degrees C). Modeling Approach 1: Assuming a constant value of solute diffusivity (D = 1.0 x 10(-9) m(2)/sec), the best fit values of L(p) ranged from 0.35 x 10(-14) to 1.43 x 10(-14) m(3)/N-sec while omega ranged from 2.57 x 10(-14) to 70.5 x 10(-14) mol/N-sec. Based on these values of L(p) and omega, the solute reflection coefficient, sigma defined as sigma = 1-omega v(CPA)/L(P) ranged from 0.9961 to 0.9996. Modeling Approach 2: The relative values of omega and sigma from our initial modeling suggest that the embedded ovarian tissue cells are relatively impermeable to all the CPAs investigated (or omega approximately 0 and sigma approximately 1.0). Consequently the model was modified and used to predict the values of L(p) and D assuming omega = 0 and sigma = 1.0. The best fit values of L(p) ranged from 0.44 x 10(-14) to 1.2 x 10(-14) m(3)/N-sec while D ranged from 0.85 x 10(-9) to 2.08 x 10(-9) m(2)/sec. Modeling Approach 3: Finally, the best fit values of D from modeling approach 2 were incorporated into model 1 to re-predict the values of L(p) and omega. It is hoped that the ovarian tissue cell parameters reported here will help to optimize chemical loading and unloading procedures for whole ovarian tissue sections and consequently, tissue cryopreservation procedures.

Quantitative measurement and prediction of biophysical response during freezing in tissues

Cryopreservation and cryosurgery are important biomedical applications used to selectively preserve or destroy cellular systems through freezing. Studies using cryomicroscopy techniques, which allow the visualization of the freezing process in single cells, have shown that a drop in viability correlates with the extent of two biophysical events during the freezing process: (a) intracellular ice formation and (b) cellular dehydration. These same biophysical events operate in tissue systems; however, the inability to visualize and quantify the dynamics of the freezing process in tissues has hampered direct correlation of these events with freezing-induced changes in viability. This review highlights two new techniques that use freeze substitution and differential scanning calorimetry to provide dynamic freezing data in tissue. Characteristic dimensions and parameters extracted from these new data are then used in a predictive model of biophysical freezing response in several tissues, including liver and tumor. This approach promises to help guide improved design of both cryopreservation and cryosurgical applications of tissue freezing.

Cryopreservation of equine sperm: optimal cooling rates in the presence and absence of cryoprotective agents determined using differential scanning calorimetry

Optimization of equine sperm cryopreservation protocols requires an understanding of the water permeability characteristics and volumetric shrinkage response during freezing. A cell-shape-independent differential scanning calorimeter (DSC) technique was used to measure the volumetric shrinkage during freezing of equine sperm suspensions at cooling rates of 5 degrees C/min and 20 degrees C/min in the presence and absence of cryoprotective agents (CPAs), i.e., in the Kenney extender and in the lactose-EDTA extender, respectively. The equine sperm was modeled as a cylinder of length 36.5 microm and a radius of 0.66 microm with an osmotically inactive cell volume (V(b)) of 0.6V(o), where V(o) is the isotonic cell volume. Sperm samples were collected using water-insoluble Vaseline in the artificial vagina and slow cooled at < or = 0.3 degrees C/min in an Equitainer-I from 37 degrees C to 4 degrees C. By fitting a model of water transport to the experimentally obtained DSC volumetric shrinkage data, the best-fit membrane permeability parameters (L(pg) and E(Lp)) were determined. The combined best-fit parameters of water transport (at both 5 degrees C/min and 20 degrees C/min) in Kenney extender (absence of CPAs) are L(pg) = 0.02 microm min(-1) atm(-1) and E(Lp) = 32.7 kcal/mol with a goodness-of-fit parameter R(2) = 0.96, and the best-fit parameters in the lactose-EDTA extender (the CPA medium) are L(pg)[cpa] = 0.008 microm min(-1) atm(-1) and E(Lp)[cpa] = 12.1 kcal/mol with R(2) = 0.97. These parameters suggest that the optimal cooling rate for equine sperm is approximately 29 degrees C/min and is approximately 60 degrees C/min in the Kenney extender and in the lactose-EDTA extender. These rates are predicted assuming no intracellular ice formation occurs and that the approximately 5% of initial osmotically active water volume trapped inside the cells at -30 degrees C will form innocuous ice on further cooling. Numerical simulations also showed that in the lactose-EDTA extender, equine sperm trap approximately 3.4% and approximately 7.1% of the intracellular water when cooled at 20 degrees C/min and 100 degrees C/min, respectively. As an independent test of this prediction, the percentage of viable equine sperm was obtained after freezing at 6 different cooling rates (2 degrees C/min, 20 degrees C/min, 50 degrees C/min, 70 degrees C/min, 130 degrees C/min, and 200 degrees C/min) to -80 degrees C in the CPA medium. Sperm viability was essentially constant between 20 degrees C/min and 130 degrees C/min.

Cryosurgery of normal and tumor tissue in the dorsal skin flap chamber: Part I--thermal response

Current research in cryosurgery is concerned with finding a thermal history that will definitively destroy tissue. In this study, we measured and predicted the thermal history obtained during freezing and thawing in a cryosurgical model. This thermal history was then compared to the injury observed in the tissue of the same cryosurgical model (reported in companion paper (Hoffmann and Bischof, 2001)). The dorsal skin flap chamber, implanted in the Copenhagen rat, was chosen as the cryosurgical model. Cryosurgery was performed in the chamber on either normal skin or tumor tissue propagatedfrom an AT-1 Dunning rat prostate tumor. The freezing was performed by placing a approximately 1 mm diameter liquid-nitrogen-cooled cryoprobe in the center of the chamber and activating it for approximately 1 minute, followed by a passive thaw. This created a 4.2 mm radius iceball. Thermocouples were placed in the tissue around the probe at three locations (r = 2, 3, and 3.8 mm from the center of the window) in order to monitor the thermal history produced in the tissue. The conduction error introduced by the presence of the thermocouples was investigated using an in vitro simulation of the in vivo case and found to be <10 degrees C for all cases. The corrected temperature measurements were used to investigate the validity of two models of freezing behavior within the iceball. The first model used to approximate the freezing and thawing behavior within the DSFC was a two-dimensional transient axisymmetric numerical solution using an enthalpy method and incorporating heating due to blood flow. The second model was a one-dimensional radial steady state analytical solution without blood flow. The models used constant thermal properties for the unfrozen region, and temperature-dependent thermal properties for the frozen region. The two-dimensional transient model presented here is one of the first attempts to model both the freezing and thawing of cryosurgery. The ability of the model to calculate freezing appeared to be superior to the ability to calculate thawing. After demonstrating that the two-dimensional model sufficiently captured the freezing and thawing parameters recorded by the thermocouples, it was used to estimate the thermal history throughout the iceball. This model was used as a basis to compare thermal history to injury assessment (reported in companion paper (Hoffmann and Bischof, 2001)).

Microscopic and calorimetric assessment of freezing processes in uterine fibroid tumor tissue

The use of cryosurgery in the treatment of uterine fibroids is emerging as a possible treatment modality. The two known mechanisms of direct cell injury during the tissue freezing process are linked to intracellular ice formation and cellular dehydration. These processes have not been quantified within uterine fibroid tumor tissue. This study reports the use of a combination of freeze-substitution microscopy and differential scanning calorimetry (DSC) to quantify freeze-induced dehydration within uterine fibroid tumor tissue. Stereological analysis of histological tumor sections was used to obtain the initial cellular volume (V(o)) or the Krogh model dimensions (deltaX, the distance between the microvascular channels = 15.5 microm, r(vo), the initial radius of the extracellular space = 4.8 micro m, and L, the axial length of the Krogh cylinder = 19.1 microm), the interstitial volume ( approximately 23%), and the vascular volume ( approximately 7%) of the fibroid tumor tissue. A Boyle-van't Hoff plot was then constructed by examining freeze-substituted micrographs of "equilibrium"-cooled tissue slices to obtain the osmotically inactive cell volume, V(b) = 0.47V(o). The high interstitial volume precludes the use of freeze-substitution microscopy data to quantify freeze-induced dehydration. Therefore, a DSC technique, which does not suffer from this artifact, was used to obtain the water transport data. A model of water transport was fit to the calorimetric data at 5 and 20 degrees C/min to obtain the "combined best fit" membrane permeability parameters of the embedded fibroid tumor cells, assuming either a Krogh cylinder geometry, L(pg) = 0.92 x 10(-13) m(3)/Ns (0.55 microm/min atm) and E(Lp) = 129.3 kJ/mol (30.9 kcal/mol), or a spherical cell geometry (cell diameter = 18.3 microm), L(pg) = 0.45 x 10(-13) m(3)/Ns (0.27 microm/min atm) and E(Lp) = 110.5 kJ/mol (26.4 kcal/mol). In addition, numerical simulations were performed to generate conservative estimates, in the absence of ice nucleation between -5 and -30 degrees C, of intracellular ice volume in the tumor tissue at various cooling rates typical of those experienced during cryosurgery (< or =100 degrees C/min). With this assumption, the Krogh model simulations showed that the fibroid tumor tissue cells cooled at rates < or = 50 degrees C/min are essentially dehydrated; however, at rates >50 degrees C/min the amount of water trapped within the tissue cells increases rapidly with increasing cooling rate, suggesting the formation of intracellular ice.

Subzero water permeability parameters of mouse spermatozoa in the presence of extracellular ice and cryoprotective agents

Optimization of techniques for cryopreservation of mammalian sperm is limited by a lack of knowledge regarding water permeability characteristics during freezing in the presence of extracellular ice and cryoprotective agents (CPAs). Cryomicroscopy cannot be used to measure dehydration during freezing in mammalian sperm because they are highly nonspherical and their small dimensions are at the limits of light microscopic resolution. Using a new shape-independent differential scanning calorimeter (DSC) technique, volumetric shrinkage during freezing of ICR mouse epididymal sperm cell suspensions was obtained at cooling rates of 5 and 20 degrees C/min in the presence of extracellular ice and CPAs. Using previously published data, the mouse sperm cell was modeled as a cylinder (122-microm long, radius 0.46 microm) with an osmotically inactive cell volume (V(b)) of 0.61V(o), where V(o) is the isotonic cell volume. By fitting a model of water transport to the experimentally obtained volumetric shrinkage data, the best-fit membrane permeability parameters (L(pg) and E(Lp)) were determined. The "combined best-fit" membrane permeability parameters at 5 and 20 degrees C/min for mouse sperm cells in solution are as follows: in D-PBS: L(pg) = 1.7 x 10(-15) m(3)/Ns (0.01 microm/min-atm) and E(Lp) = 94.1 kJ/mole (22.5 kcal/mole) (R(2) = 0.94); in "low" CPA media (consisting of 1% glycerol, 6% raffinose, and 15% egg yolk in D-PBS): L(pg)[cpa] = 1.7 x 10(-15) m(3)/Ns (0.01 microm/min-atm) and E(Lp)[cpa] = 122.2 kJ/mole (29.2 kcal/mole) (R(2) = 0.98); and in "high" CPA media (consisting of 4% glycerol, 16% raffinose, and 15% egg yolk in D-PBS): L(pg)[cpa] = 0.68 x 10(-15) m(3)/Ns (0.004 microm/min-atm) and E(Lp)[cpa] = 63.6 kJ/mole (15.2 kcal/mole) (R(2) = 0.99). These parameters are significantly different than previously published parameters for mammalian sperm obtained at suprazero temperatures and at subzero temperatures in the absence of extracellular ice. The parameters obtained in this study also suggest that damaging intracellular ice formation (IIF) could occur in mouse sperm cells at cooling rates as low as 25-45 degrees C/min, depending on the concentrations of the CPAs. This may help to explain the discrepancy between the empirically determined optimal cryopreservation cooling rates, 10-40 degrees C/min, and the numerically predicted optimal cooling rates, greater than 5000 degrees C/min, obtained using suprazero mouse sperm permeability parameters that do not account for the presence of extracellular ice. As an independent test of this prediction, the percentages of viable and motile sperm cells were obtained after freezing at two different cooling rates ("slow" or 5 degrees C/min; "fast," or 20 degrees C/min) in both the low and high CPA media. The greatest sperm motility and viability was found with the low CPA media under fast (20 degrees C/min) cooling conditions.

Liver freezing response of the freeze-tolerant wood frog, Rana sylvatica, in the presence and absence of glucose. I. Experimental measures

In this study, two methods are used to assess the equilibrium and dynamic cell volumes in Rana sylvatica liver tissue during freezing in the presence and absence of a cryoprotectant (glucose). The first is a "two-step" low-temperature microscopy (equilibrium and dynamic) freezing method and the second is a differential scanning calorimeter (DSC) technique. These two techniques were used to study (i) the in vitro architecture of R. sylvatica frog liver tissue and to measure its characteristic Krogh cylinder dimensions; (ii) the "equilibrium" (infinitely slow) cooling behavior and the osmotically inactive cell volume (V(b)) of R. sylvatica liver cells; and (iii) the dynamic water transport response of R. sylvatica liver cells in the presence and absence of the CPA (glucose) at a cooling rate of 5 degrees C/min. Stereological analysis of the slam frozen (>1000 degrees C/min) micrographs led to the determination that 74% of the liver tissue in control frogs was cellular versus 26% that was extracellular (vascular or interstitial). Mapping the stereological measurements onto a standard Krogh cylinder geometry (Model 1) yielded distance between adjacent sinusoid centers, DeltaX = 64 microm; original sinusoid (vascular) radius, r(vo) = 18.4 microm; and length of the Krogh cylinder, L = 0.71 microm (based on an isolated frog hepatocyte cell diameter of 16 microm). A significant observation was that approximately 24% of the frog hepatocyte cells are not in direct contact with the vasculature. To account for the cell-cell contact in the frog liver architecture a modified Krogh cylinder geometry (Model 2) was constructed. In this model (Model 2) a second radius, r(2) = 28.7 microm, was defined (in addition to the original sinusoid radius, r(vo) = 18.4 microm, defined above) as the radius of the membrane between the adjacent cells (directly adjacent to vascular spaces) and embedded cells (removed from vascular spaces). By plotting the two-step equilibrium cooling results on a Boyle-van't Hoff plot, the osmotically inactive cell volume, V(b) was obtained as 0.4. V(o) (where V(o) is the isotonic cell volume). The two-step dynamic micrographs and the heat release measurements from the DSC were used to obtain water transport data during freezing. The DSC technique confirmed that R. sylvatica cells in control liver tissue do not dehydrate completely when cooled at 5 degrees C/min but do so when cooled at 2 degrees C/min.

Liver freezing response of the freeze-tolerant wood frog, Rana sylvatica, in the presence and absence of glucose. II. Mathematical modeling

The "two-step" low-temperature microscopy (equilibrium and dynamic) freezing methods and a differential scanning calorimetry (DSC) technique were used to assess the equilibrium and dynamic cell volumes in Rana sylvatica liver tissue during freezing, in Part I of this study. In this study, the experimentally determined dynamic water transport data are curve fit to a model of water transport using a standard Krogh cylinder geometry (Model 1) to predict the biophysical parameters of water transport: L(pg) = 1.76 microm/min-atm and E(L(p)) = 75.5 kcal/mol for control liver cells and L(pg)[cpa] = 1.18 microm/min-atm and E(L(p))[cpa] = 69.0 kcal/mol for liver cells equilibrated with 0.4 M glucose. The DSC technique confirmed that R. sylvatica cells in control liver tissue do not dehydrate completely when cooled at 5 degrees C/min but do so when cooled at 2 degrees C/min. Cells also retained twice as much intracellular fluid in the presence of 0.4 M glucose than in control tissue when cooled at 5 degrees C/min. The ability of R. sylvatica liver cells to retain water during fast cooling (>/=5 degrees C/min) appears to be primarily due to its liver tissue architecture and not to a dramatically lower permeability to water, in comparison to mammalian (rat) liver cells which do dehydrate completely when cooled at 5 degrees C/min. A modified Krogh model (Model 2) was constructed to account for the cell-cell contact in frog liver architecture. Using the same biophysical permeability parameters obtained with Model 1, the modified Krogh model (Model 2) is used in this study to qualitatively explain the experimentally measured water retention in some cells during freezing on the basis of different volumetric responses by cells directly adjacent to vascular space versus cells at least one cell removed from the vascular space. However, at much slower cooling rates (1-2 degrees C/h) experienced by the frog in nature, the deciding factor in water retention is the presence of glucose and the maintenance of a sufficiently high subzero temperature (>/=-8 degrees C).