Measurement of grouped intracellular solute osmotic virial coefficients.

Models of cellular osmotic behaviour depend on thermodynamic solution theories to calculate chemical potentials in the solutions inside and outside the cell. These solutions are generally thermodynamically non-ideal under cryobiological conditions. The molality-based Elliott et al. form of the multi-solute osmotic virial equation is a solution theory which has been demonstrated to provide accurate predictions in cryobiological solutions, accounting for the non-ideality of these solutions using solute-specific thermodynamic parameters called osmotic virial coefficients. However, this solution theory requires as inputs the exact concentration of every solute in the solution being modeled, which poses a problem for the cytoplasm, where such detailed information is rarely available. This problem can be overcome by using a grouped solute approach for modeling the cytoplasm, where all the non-permeating intracellular solutes are treated as a single non-permeating "grouped" intracellular solute. We have recently shown (Zielinski et al., J Physical Chemistry B, 2017) that such a grouped solute approach is theoretically valid when used with the Elliott et al. model, and Ross-Rodriguez et al. (Biopreservation and Biobanking, 2012) have previously developed a method for measuring the cell type-specific osmotic virial coefficients of the grouped intracellular solute. However, the Ross-Rodriguez et al. method suffers from a lack of precision, which-as we demonstrate in this work-can severely impact the accuracy of osmotic model predictions under certain conditions. Thus, we herein develop a novel method for measuring grouped intracellular solute osmotic virial coefficients which yields more precise values than the existing method and then apply this new method to measure these coefficients for human umbilical vein endothelial cells.

Thermal expansion of substrate may affect adhesion of Chinese hamster fibroblasts to surfaces during freezing.

Despite success in cryopreservation of cells in suspension, cryopreservation of cells in monolayers is still challenging. One of the major problems is detachment of the cells from the substrate which occurs during cryopreservation. We hypothesized that this detachment may be due to a mismatch in the coefficient of linear thermal expansion αL between glass and the frozen cell layer which manifests as residual stress and stress relaxation. This mismatch results in a difference between the thermal expansion of ice and glass as they undergo temperature changes. Rinzl plastic coverslips were selected as a possible substitute for glass because Rinzl has an αL (60 × 10-6/K) similar to that of ice (51 × 10-6/K) whereas glass has a much lower αL (5 × 10-6/K). V79-4 Chinese hamster fibroblasts were cultured on both glass and Rinzl coverslips until confluent and the area of coverage was measured before and after freezing at -9 °C. The glass coverslips showed significant loss of cells (coverage = 77.9 ±â€¯8.0%) compared with Rinzl (coverage = 97.9 ±â€¯1.4%). We concluded that Rinzl coverslips may improve cell attachment in future monolayer cryopreservation experiments.

Cryopreservation of human umbilical vein and porcine corneal endothelial cell monolayers.

Cryopreservation of endothelium is one of the major challenges in the cryopreservation of complex tissues. Human umbilical vein endothelial cells (HUVECs) in suspension are available commercially and recently their post-thaw cell membrane integrity was significantly improved by cryopreservation in 5% dimethyl sulfoxide (Me2SO) and 6% hydroxyethyl starch (HES). However, cryopreservation of cells in monolayers has been elusive. The exact mechanisms of damage during cell monolayer cryopreservation are still under investigation. Here, we show that a combination of different factors contribute to significant progress in cryopreservation of endothelial monolayers. The addition of 2% chondroitin sulfate to 5% Me2SO and 6% HES and cooling at 0.2 or 1 °C/min led to high membrane integrity (97.3 ±â€¯3.2%) immediately after thaw when HUVECs were cultured on a substrate with a coefficient of thermal expansion similar to that of ice. The optimized cryopreservation protocol was applied to monolayers of primary porcine corneal endothelial cells, and resulted in high post-thaw viability (95.9 ±â€¯3.7% membrane integrity) with metabolic activity 12 h post-thaw comparable to unfrozen control.

Expansion and cryopreservation of porcine and human corneal endothelial cells.

Impairment of the corneal endothelium causes blindness that afflicts millions worldwide and constitutes the most often cited indication for corneal transplants. The scarcity of donor corneas has prompted the alternative use of tissue-engineered grafts which requires the ex vivo expansion and cryopreservation of corneal endothelial cells. The aims of this study are to culture and identify the conditions that will yield viable and functional corneal endothelial cells after cryopreservation. Previously, using human umbilical vein endothelial cells (HUVECs), we employed a systematic approach to optimize the post-thaw recovery of cells with high membrane integrity and functionality. Here, we investigated whether improved protocols for HUVECs translate to the cryopreservation of corneal endothelial cells, despite the differences in function and embryonic origin of these cell types. First, we isolated endothelial cells from pig corneas and then applied an interrupted slow cooling protocol in the presence of dimethyl sulfoxide (Me2SO), with or without hydroxyethyl starch (HES). Next, we isolated and expanded endothelial cells from human corneas and applied the best protocol verified using porcine cells. We found that slow cooling at 1 °C/min in the presence of 5% Me2SO and 6% HES, followed by rapid thawing after liquid nitrogen storage, yields membrane-intact cells that could form monolayers expressing the tight junction marker ZO-1 and cytoskeleton F-actin, and could form tubes in reconstituted basement membrane matrix. Thus, we show that a cryopreservation protocol optimized for HUVECs can be applied successfully to corneal endothelial cells, and this could provide a means to address the need for off-the-shelf cryopreserved cells for corneal tissue engineering and regenerative medicine.

Beyond membrane integrity: Assessing the functionality of human umbilical vein endothelial cells after cryopreservation.

Assessment of cell membrane integrity is one of the most widely used methods to measure post-cryopreservation viability of cells such as human umbilical vein endothelial cells (HUVECs). However, an evaluation of cell function provides a better measure of cell quality following cryopreservation. The tube formation assay mimics angiogenesis in vitro and can be used to quantitate the ability of endothelial cells to form capillary-like tubular structures when cultured on reconstituted basement membrane (Matrigel). We compared the membrane integrity (measured by flow cytometry) and tube forming ability of HUVEC suspensions exposed to 10% dimethyl sulfoxide (Me2SO), cooled at 1 °C/min to various sub-zero temperatures, plunged directly into liquid nitrogen, stored for an hour, and thawed rapidly. We found that as membrane integrity increased so did the various parameters associated with the extent of in vitro angiogenesis; however, in comparison to fresh cells with a similar percentage of membrane-intact cells, the extent of tube formation, expressed as total tube length, is significantly lower in previously frozen cells for the lower range of post-thaw membrane integrities. Our findings underscore the value of an assay that quantifies a specific function that a cell is known to perform in vivo to measure the success of cryopreservation protocols.

Cryoprotectant kinetic analysis of a human articular cartilage vitrification protocol.

We recently published a protocol to vitrify human articular cartilage and a method of cryoprotectant removal in preparation for transplantation. The current study's goal was to perform a cryoprotectant kinetic analysis and theoretically shorten the procedure used to vitrify human articular cartilage. First, the loading of the cryoprotectants was modeled using Fick's law of diffusion, and this information was used to predict the kinetics of cryoprotectant efflux after the cartilage sample had been warmed. We hypothesized that diffusion coefficients obtained from the permeation of individual cryoprotectants into porcine articular cartilage could be used to provide a reasonable prediction of the cryoprotectant loading and of the combined cryoprotectant efflux from vitrified human articular cartilage. We tested this hypothesis with experimental efflux measurements. Osteochondral dowels from three patients were vitrified, and after warming, the articular cartilage was immersed in 3 mL X-VIVO at 4 °C in two consecutive solutions, each for 24 h, with the solution osmolality recorded at various times. Measured equilibrium values agreed with theoretical values within a maximum of 15% for all three samples. The results showed that diffusion coefficients for individual cryoprotectants determined from experiments with 2-mm thick porcine cartilage can be used to approximate the rate of efflux of the combined cryoprotectants from vitrified human articular cartilage of similar thickness. Finally, Fick's law of diffusion was used in a computational optimization to shorten the protocol with the constraint of maintaining the theoretical minimum cryoprotectant concentration needed to achieve vitrification. The learning provided by this study will enable future improvements in tissue vitrification.

Cryopreserved amniotic membrane as transplant allograft: viability and post-transplant outcome.

Amniotic membrane (AM) transplantation is increasingly used in ophthalmological and dermatological surgeries to promote re-epithelialization and wound healing. Biologically active cells in the epithelial and stromal layers deliver growth factors and cytokines with anti-inflammatory, anti-bacterial, anti-immunogenic and anti-fibrotic properties. In this work, confocal microscopy was used to show that our cryopreservation protocol for AM yielded viable cells in both the stromal and epithelial layers with favorable post-transplant outcome. AM was obtained from Caesarean-section placenta, processed into allograft pieces of different sizes (3 cm × 3 cm, 5 cm × 5 cm, and 10 cm × 10 cm) and cryopreserved in 10 % dimethyl sulfoxide using non-linear controlled rate freezing. Post-thaw cell viability in the entire piece of AM and in the stromal and epithelial cell layers was assessed using a dual fluorescent nuclear dye and compared to hypothermically stored AM, while surveys from surgical end-users provided information on post-transplant patient outcomes. There was no significant statistical difference in the cell viability in the entire piece, epithelial and stromal layers regardless of the size of allograft piece (p = 0.092, 0.188 and 0.581, respectively), and in the entire piece and stromal layer of hypothermically stored versus cryopreserved AM (p = 0.054 and 0.646, respectively). Surgical end-user feedback (n = 49) indicated that 16.3 % of AM allografts were excellent and 61.2 % were satisfactory. These results support the expanded clinical use of different sizes of cryopreserved AM allografts and address the issue of orientation of the AM during transplant for the treatment of dermatological defects and ocular surface disorders.

Investigating membrane and mitochondrial cryobiological responses of HUVEC using interrupted cooling protocols.

The success of cryopreservation protocols is largely based on membrane integrity assessments after thawing, since membrane integrity can be considered to give an upper limit in assessment of cell viability and the plasma membrane is considered to be a primary site of cryoinjury. However, the exposure of cells to conditions associated with low temperatures can induce injury to cellular structure and function that may not be readily identified by membrane integrity alone. Interrupted cooling protocols (including interrupted slow cooling without a hold time (graded freezing), and interrupted rapid cooling with a hold time (two-step freezing)), can yield important information about cryoinjury by separating the damage that occurs upon cooling to (and possibly holding at) a critical intermediate temperature range from the damage that occurs upon plunging to the storage temperature (liquid nitrogen). In this study, we used interrupted cooling protocols in the absence of cryoprotectant to investigate the progression of damage to human umbilical vein endothelial cells (HUVEC), comparing an assessment of membrane integrity with a mitochondrial polarization assay. Additionally, the membrane integrity response of HUVEC to interrupted cooling was investigated as a function of cooling rate (for interrupted slow cooling) and hold time (for interrupted rapid cooling). A key finding of this work was that under slow cooling conditions which resulted in a large number of membrane intact cells immediately post thaw, mitochondria are predominantly in a non-functional depolarized state. This study, the first to look directly at mitochondrial polarization throughout interrupted cooling profiles and a detailed study of HUVEC response, highlights the complexity of the progression of cell damage, as the pattern and extent of cell injury throughout the preservation process differs by injury site.

Comment on "Determination of the quaternary phase diagram of the water-ethylene glycol-sucrose-NaCl system and a comparison between two theoretical methods for synthetic phase diagrams" Cryobiology 61 (2010) 52-57.

Recently, measurements of a considerable portion of the phase diagram for the quaternary system water-ethylene glycol-sucrose-NaCl were published (Han et al., 2010). In that article, the data were used to evaluate the accuracy of two non-ideal multi-solute solution theories: the Elliott et al. form of the multi-solute osmotic virial equation and the Kleinhans and Mazur freezing point summation model. Based on this evaluation, it was concluded that the freezing point summation model provides more accurate predictions for the water-ethylene glycol-sucrose-NaCl system than the multi-solute osmotic virial equation. However, this analysis suffered from a number of issues, notably including the use of inconsistent solute-specific coefficients for the multi-solute osmotic virial equation. Herein, we reanalyse the data using a recently-updated and consistent set of solute-specific coefficients (Zielinski et al., 2014). Our results indicate that the two models have very similar performance, and, in fact, the multi-solute osmotic virial equation can provide more accurate predictions than the freezing point summation model depending on the concentration units used.

Mesenchymal stromal cells derived from various tissues: Biological, clinical and cryopreservation aspects.

Originally isolated from bone marrow, mesenchymal stromal cells (MSCs) have since been obtained from various fetal and post-natal tissues and are the focus of an increasing number of clinical trials. Because of their tremendous potential for cellular therapy, regenerative medicine and tissue engineering, it is desirable to cryopreserve and bank MSCs to increase their access and availability. A remarkable amount of research and resources have been expended towards optimizing the protocols, freezing media composition, cooling devices and storage containers, as well as developing good manufacturing practices in order to ensure that MSCs retain their therapeutic characteristics following cryopreservation and that they are safe for clinical use. Here, we first present an overview of the identification of MSCs, their tissue sources and the properties that render them suitable as a cellular therapeutic. Next, we discuss the responses of cells during freezing and focus on the traditional and novel approaches used to cryopreserve MSCs. We conclude that viable MSCs from diverse tissues can be recovered after cryopreservation using a variety of freezing protocols, cryoprotectants, storage periods and temperatures. However, alterations in certain functions of MSCs following cryopreservation warrant future investigations on the recovery of cells post-thaw followed by expansion of functional cells in order to achieve their full therapeutic potential.

Effect of supercooling and cell volume on intracellular ice formation.

Intracellular ice formation (IIF) has been linked to death of cells cryopreserved in suspension. It has been assumed that cells can be supercooled by 2 to 10°C before IIF occurs, but measurements of the degree of supercooling that cells can tolerate are often confounded by changing extracellular temperature and solutions of different osmolality (which affect the cell volume). The purpose of this study was to examine how the incidence of IIF in the absence of cryoprotectants is affected by the degree of supercooling and cell volume. Human umbilical vein endothelial cells were suspended in isotonic (300 mOsm) and hypertonic (∼600 to 700 mOsm) solutions and exposed to supercooling ranging from 2 to 10°C before extracellular ice was nucleated. The number of cells undergoing IIF was examined in a cryostage (based on the darkening of cells upon intracellular freezing ("flashing")) as a function of the degree of supercooling, and cell survival post-thaw was assessed using a membrane integrity assay. We found that while the incidence of IIF increased with supercooling in both isotonic and hypertonic solutions, it was higher in the isotonic solution at any given degree of supercooling. Since cells in hypertonic solution were shrunken due to water efflux, we hypothesized that the difference in IIF behavior could be attributed to the decreased volume of cells in the hypertonic solution. Our results confirm that cells with a smaller diameter before extracellular ice nucleation have a decreased probability of IIF and suggest that cell volume could play a more significant role in the incidence of IIF than the extracellular ice nucleation temperature.

Osmotic parameters of red blood cells from umbilical cord blood.

The transfusion of red blood cells from umbilical cord blood (cord RBCs) is gathering significant interest for the treatment of fetal and neonatal anemia, due to its high content of fetal hemoglobin as well as numerous other potential benefits to fetuses and neonates. However, in order to establish a stable supply of cord RBCs for clinical use, a cryopreservation method must be developed. This, in turn, requires knowledge of the osmotic parameters of cord RBCs. Thus, the objective of this study was to characterize the osmotic parameters of cord RBCs: osmotically inactive fraction (b), hydraulic conductivity (Lp), permeability to cryoprotectant glycerol (Pglycerol), and corresponding Arrhenius activation energies (Ea). For Lp and Pglycerol determination, RBCs were analyzed using a stopped-flow system to monitor osmotically-induced RBC volume changes via intrinsic RBC hemoglobin fluorescence. Lp and Pglycerol were characterized at 4°C, 20°C, and 35°C using Jacobs and Stewart equations with the Ea calculated from the Arrhenius plot. Results indicate that cord RBCs have a larger osmotically inactive fraction compared to adult RBCs. Hydraulic conductivity and osmotic permeability to glycerol of cord RBCs differed compared to those of adult RBCs with the differences dependent on experimental conditions, such as temperature and osmolality. Compared to adult RBCs, cord RBCs had a higher Ea for Lp and a lower Ea for Pglycerol. This information regarding osmotic parameters will be used in future work to develop a protocol for cryopreserving cord RBCs.

Fluorescence as an alternative to light-scatter gating strategies to identify frozen-thawed cells with flow cytometry.

Flow cytometry is a key instrument in biological studies, used to identify and analyze cells in suspension. The identification of cells from debris is commonly based on light scatter properties as it has been shown that there is a relationship between forward scattered light and cell volume and this has become common practice in flow cytometry. Cryobiological conditions induce changes in cells that alter their light scatter properties. Cells with membrane damage from freeze-thaw stress produce lower forward scatter signals and may fall below standard forward scatter thresholds. In contrast to light scatter properties that cannot identify damaged cells from debris, fluorescent dyes used in membrane integrity and mitochondrial polarization assays are capable of labeling and discriminating all cells in suspension. Under cryobiological conditions, isolating cell populations is more effectively accomplished by gating on fluorescence rather than light scatter properties. This study shows the limitations of using forward scatter thresholds in flow cytometry to identify and gate cells after exposure to a freeze-thaw protocol and demonstrates the use of fluorescence as an alternative means of identifying and analyzing cells.

Comparison of non-ideal solution theories for multi-solute solutions in cryobiology and tabulation of required coefficients.

Thermodynamic solution theories allow the prediction of chemical potentials in solutions of known composition. In cryobiology, such models are a critical component of many mathematical models that are used to simulate the biophysical processes occurring in cells and tissues during cryopreservation. A number of solution theories, both thermodynamically ideal and non-ideal, have been proposed for use with cryobiological solutions. In this work, we have evaluated two non-ideal solution theories for predicting water chemical potential (i.e. osmolality) in multi-solute solutions relevant to cryobiology: the Elliott et al. form of the multi-solute osmotic virial equation, and the Kleinhans and Mazur freezing point summation model. These two solution theories require fitting to only single-solute data, although they can make predictions in multi-solute solutions. The predictions of these non-ideal solution theories were compared to predictions made using ideal dilute assumptions and to available literature multi-solute experimental osmometric data. A single, consistent set of literature single-solute solution data was used to fit for the required solute-specific coefficients for each of the non-ideal models. Our results indicate that the two non-ideal solution theories have similar overall performance, and both give more accurate predictions than ideal models. These results can be used to select between the non-ideal models for a specific multi-solute solution, and the updated coefficients provided in this work can be used to make the desired predictions.

Cryopreservation of articular cartilage.

Cryopreservation has numerous practical applications in medicine, biotechnology, agriculture, forestry, aquaculture and biodiversity conservation, with huge potentials for biological cell and tissue banking. A specific tissue of interest for cryopreservation is the articular cartilage of the human knee joint for two major reasons: (1) clinically, there exists an untapped potential for cryopreserved cartilage to be used in surgical repair/reconstruction/replacement of injured joints because of the limited availability of fresh donor tissue and, (2) scientifically, successful cryopreservation of cartilage, an avascular tissue with only one cell type, is considered a stepping stone for transition from biobanking cell suspensions and small tissue slices to larger and more complicated tissues. For more than 50years, a great deal of effort has been directed toward understanding and overcoming the challenges of cartilage preservation. In this article, we focus mainly on studies that led to the finding that vitrification is an appropriate approach toward successful preservation of cartilage. This is followed by a review of the studies on the main challenges of vitrification, i.e. toxicity and diffusion, and the novel approaches to overcome these challenges such as liquidus tracking, diffusion modeling, and cryoprotective agent cocktails, which have resulted in the recent advancements in the field.

Clinical efflux of cryoprotective agents from vitrified human articular cartilage.

In previous research, we successfully cryopreserved intact human articular cartilage on its bone base with high chondrocyte viability using a vitrification protocol that entailed sequential exposure to several cryopreserving agents (CPAs) at lowering temperatures resulting in a high final concentration of CPA. The CPA must be removed from the cartilage at warming due to its toxicity to cells in the cryopreserved tissue and the post-transplant adjacent tissues. The current experiment explores the relationship between removal solution volume and time required for complete removal of CPA from bone-cartilage samples. Osteochondral dowels of 10mm diameter from five patients undergoing total knee arthroplasty were vitrified using our protocol resulting in 6.5M CPA within the matrix. In the primary experiment, the warmed dowels were immersed in 10 mL of X-VIVO for 30 min and this was repeated 5 times (the last wash being 5 min only). Removal solution osmolality was recorded at various times and compared to controls of pure X-VIVO. Changes in removal solution osmolality over time were normalized to tissue volume. In a secondary experiment, the procedure was repeated using double the volume of removal solution (20 mL X-VIVO). Results showed a rapid change in the osmolality of the removal solution indicating a rapid efflux of CPA from cartilage. The efflux rate decreased with time and during subsequent immersions until equilibrium was reached during the 4th immersion indicating effectively complete removal of CPA. Doubling the amount of removal solution demonstrated the effective removal of CPAs by the third immersion. The results of this study yield a practical relationship between the amount of removal solution and the time and number of immersions required to remove CPA from the transplantable tissue.

Transport phenomena in articular cartilage cryopreservation as predicted by the modified triphasic model and the effect of natural inhomogeneities.

Knowledge of the spatial and temporal distribution of cryoprotective agent (CPA) is necessary for the cryopreservation of articular cartilage. Cartilage dehydration and shrinkage, as well as the change in extracellular osmolality, may have a significant impact on chondrocyte survival during and after CPA loading, freezing, and thawing, and during CPA unloading. In the literature, Fick's law of diffusion is commonly used to predict the spatial distribution and overall concentration of the CPA in the cartilage matrix, and the shrinkage and stress-strain in the cartilage matrix during CPA loading are neglected. In this study, we used a previously described biomechanical model to predict the spatial and temporal distributions of CPA during loading. We measured the intrinsic inhomogeneities in initial water and fixed charge densities in the cartilage using magnetic resonance imaging and introduced them into the model as initial conditions. We then compared the prediction results with the results obtained using uniform initial conditions. The simulation results in this study demonstrate the presence of a significant mechanical strain in the matrix of the cartilage, within all layers, during CPA loading. The osmotic response of the chondrocytes to the cartilage dehydration during CPA loading was also simulated. The results reveal that a transient shrinking occurs to different levels, and the chondrocytes experience a significant decrease in volume, particularly in the middle and deep zones of articular cartilage, during CPA loading.

A Bayesian adjustment for multiplicative measurement errors for a calibration problem with application to a stem cell study.

We develop a Bayesian approach to a calibration problem with one interested covariate subject to multiplicative measurement errors. Our work is motivated by a stem cell study with the objective of establishing the recommended minimum doses for stem cell engraftment after a blood transplant. When determining a safe stem cell dose based on the prefreeze samples, the postcryopreservation recovery rate enters in the model as a multiplicative measurement error term, as shown in the model. We examine the impact of ignoring measurement errors in terms of asymptotic bias in the regression coefficient. According to the general structure of data available in practice, we propose a two-stage Bayesian method to perform model estimation via R2WinBUGS (Sturtz, Ligges, and Gelman, 2005, Journal of Statistical Software 12, 1-16). We illustrate this method by the aforementioned motivating example. The results of this study allow routine peripheral blood stem cell processing laboratories to establish recommended minimum stem cell doses for transplant and develop a systematic approach for further deciding whether the postthaw analysis is warranted.

Cryopreservation and post-thaw characterization of dissociated human islet cells.

The objective of this study is to optimize the cryopreservation of dissociated islet cells and obtain functional cells that can be used in single-cell transcriptome studies on the pathology and treatment of diabetes. Using an iterative graded freezing approach we obtained viable cells after cooling in 10% dimethyl sulfoxide and 6% hydroxyethyl starch at 1°C/min to -40°C, storage in liquid nitrogen, rapid thaw, and removal of cryoprotectants by serial dilution. The expression of epithelial cell adhesion molecule declined immediately after thaw, but recovered after overnight incubation, while that of an endocrine cell marker (HPi2) remained high after cryopreservation. Patch-clamp electrophysiology revealed differences in channel activities and exocytosis of various islet cell types; however, exocytotic responses, and the biophysical properties of voltage-gated Na+ and Ca2+ channels, are sustained after cryopreservation. Single-cell RNA sequencing indicates that overall transcriptome and crucial exocytosis genes are comparable between fresh and cryopreserved dispersed human islet cells. Thus, we report an optimized procedure for cryopreserving dispersed islet cells that maintained their membrane integrity, along with their molecular and functional phenotypes. Our findings will not only provide a ready source of cells for investigating cellular mechanisms in diabetes but also for bio-engineering pseudo-islets and islet sheets for modeling studies and potential transplant applications.

Permeability and Osmotic Parameters of Human Umbilical Vein Endothelial Cells and H9C2 Cells under Non-ideal Thermodynamic Assumptions: A Novel Iterative Fitting Method.

Cryopreservation is the use of very low subzero temperatures to preserve cells and tissues for later use. This is achieved by controlled cooling in the presence of cryoprotectants that moderate the amount of ice formed. Mathematical modeling of the cryopreservation process is a useful tool to investigate the different variables that affect the results of this process. The changing cell volume during cryopreservation can be modeled using cell membrane water and cryoprotectant permeabilities and the osmotically inactive fraction of the intracellular contents. These three cell-specific parameters have been found previously for different cell types under ideal and dilute assumptions, but biological solutions at subzero temperatures are far from ideal and dilute, especially when cryoprotectants are included. In this work, the osmotic virial equation is used to model the changing cell volume under non-ideal assumptions, and the intracellular environment is described using the grouped solute, which consists of all impermeant intracellular solutes grouped together, leading to two additional cell-specific parameters, the second and third osmotic virial coefficients of the grouped solute. Herein, we present a novel fitting method to efficiently determine these five cell-specific parameters by fitting kinetic cell volume data under non-ideal assumptions and report the results of applying this method to obtain the parameters for two cell types: human umbilical vein endothelial cells and H9C2 rat myoblasts.