Article

General tissue mass transfer model for cryopreservation applications

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Abstract

Successful cryopreservation of complex specimens, such as tissues and organs, would greatly benefit both the medical and scientific research fields. Vitrification is one of the most promising techniques for complex specimen cryopreservation, but toxicity remains a major challenge due to the high concentration of cryoprotectants (CPAs) needed to vitrify. Our group has approached this problem using mathematical optimization to design less toxic CPA equilibration methods. To extend this approach to tissues, an appropriate mass transfer model is required. Fick’s law is commonly used, but this simple modeling framework does not account for the complexity of mass transfer in tissues, such as the effects of fixed charges, tissue size changes, and the interplay between cell membrane transport and transport through the extracellular fluid. Here, we propose a general model for mass transfer in tissues that accounts for all of these phenomena. To create this model, we augmented a previously published acellular model of mass transfer in articular cartilage to account for the effects of cells. We show that the model can accurately predict changes in CPA concentration and tissue size for both articular cartilage and pancreatic islets, tissue types with vastly different properties.

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... As the CPA then permeates into the cell, the gradient is diminished and cell volume recovers to a significant extent [34]. In larger structures, exposure to the gradient, and the responses to it, will be delayed for those cells embedded deeper in the structure [44]. This generates a risk of insufficient CPA protection if cooling proceeds before CPA equilibration is reached in the central regions of the structure. ...
... However, an extended incubation time in the CPA to ensure deep equilibration can lead to damaging levels of toxicity for more peripheral cells. The larger and more complex the structure the more challenging this issue becomes, with both extracellular channels, cell membrane parameters, viscosity, temperature and physical distance all playing a role [19,24,44]. A similar issue, but reversed in direction, is encountered on warming and subsequent CPA removal [18]. ...
... As CPA diffusion is driven by concentration gradients, this higher concentration external to the biological sample will increase the CPA diffusion rate and thereby reduce the required incubation time. When the tissue is calculated to be sufficiently protected, the extracellular CPA concentration can be reduced to its equilibrium value [17,23,44]. Such methods are more often used with systems preserved through vitrification (ice-free cryopreservation) but are equally useful to overcome CPA loading issues in slow-cooling techniques. ...
Chapter
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This chapter covers the key physical, biological and practical challenges encountered when developing cryopreservation protocols for larger biological structures and examines areas where cryopreservation has been successful in scaling to larger structures. Results from techniques being used in attempts to overcome these challenges are reviewed together with the indicators for future development that arise from them. The scale-up of cryopreservation to tissues with diverse functions and cell types makes the control of freezing and thawing more challenging. Technology may—or may not—be available depending on the size of the material involved. To meet the challenge there must be innovation in technology, techniques and understanding of damage-limiting strategies. Diversity of cell structure, size, shape and expected function means a similarly diverse response to any imposed cryopreservation conditions and interaction with ice crystals. The increasing diffusion distances involved, and diversity of permeability properties, will affect solutes, solvents, heat and cryoprotectant (CPA) transfer and so add to the diversity of response. Constructing a single protocol for cryopreservation of a larger sample (organoids to whole organs) becomes a formidable challenge.
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The ability to replace organs and tissues on-demand could save or improve millions of lives each year globally and create public health benefits on par with curing cancer. Unmet needs for organ and tissue preservation place enormous logistical limitations on transplantation, regenerative medicine, drug discovery and a variety of rapidly advancing areas spanning biomedicine. A growing coalition of researchers, clinicians, advocacy organizations, academic institutions and other stakeholders has assembled to address the unmet need for preservation advances, outlining remaining challenges and identifying areas of underinvestment and untapped opportunities. Meanwhile, recent discoveries provide proofs of principle for breakthroughs in a family of research areas surrounding biopreservation. These developments indicate that a new paradigm, integrating multiple existing preservation approaches and new technologies that have flourished in the last 10 years, could transform preservation research. Capitalizing on these opportunities will require engagement across many research areas and stakeholder groups. A coordinated effort is needed to expedite preservation advances that can revolutionize a number of areas of medicine and medical science.
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Chapter
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In this paper, variable space grid and boundary Immobilisation Techniques based on the explicit finite difference are applied to the one-phase classical Stefan problem. It is shown that all the results obtained by the two methods are in good agreement with the exact solution, and exhibit the expected convergence as the mesh size is refined.
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Transport of a non-permeating CPA in liver tissue was studied by experimental and theoretical techniques. The system consisted of a 20 mm × 15 mm × 500 μm (thick) slab of liver tissue which was exposed to culture media and hyperosmotic sucrose (0.3 or 0.6 M) at the boundary. The volumetric changes of cell and vascular spaces within the tissue slab at 125μm from one of the symmetric boundaries was studied by slam freezing followed by freeze substitution microscopy. The experimental data was then theoretically investigated using two models; one based on an effective diffusion coefficient for sucrose, and another which incorporated the convective flux of water out of the cells (and the tissue) while sucrose diffuses in. We estimate the effective diffusion of sucrose as 16–33% of the actual diffusivity of sucrose in bulk water. The role of convection of water out of the tissue is against the flow of sucrose and appears to be important in reducing the effective diffusivity of the sucrose. The role of vascular compliance, porosity and tortuosity are also discussed with respect to our results.
Article
Human embryonic stem cells (hESC) hold tremendous potential in the emerging fields of gene and cell therapy as well as in basic scientific research. One of the major challenges regarding their application is the development of efficient cryopreservation protocols for hESC since current methods present poor recovery rates and/or technical difficulties which impair the development of effective processes that can handle bulk quantities of pluripotent cells. The main focus of this work was to compare different strategies for the cryopreservation of adherent hESC colonies. Slow-rate freezing protocols using intact hESC colonies was evaluated and compared with a surface-based vitrification approach. Entrapment within ultra-high viscous alginate was investigated as the main strategy to avoid the commonly observed loss of viability and colony fragmentation during slow-rate freezing. Our results indicate that entrapment beneath a layer of ultra-high viscous alginate does not provide further protection to hESC cryopreserved through slow-rate freezing, irrespectively of the cryomedium used. Vitrification of adherent hESC colonies on culture dishes yielded significantly higher recovery rates when compared to the slow-rate freezing approaches investigated. The pluripotency of hESC was not changed after a vitrification/thawing cycle and during further propagation in culture. In conclusion, from the cryopreservation methods investigated in this study, surface-based vitrification of hESC has proven to be the most efficient for the cryopreservation of intact hESC colonies, reducing the time required to amplify frozen stocks thus supporting the widespread use of these cells in research and clinical applications.
Article
A simple nonlinear filter which completely removes negative values from the multidimensional numerical fields is presented. This filter conserves total mass (sum of all elements in the field) with accuracy better than 0.0001%. Also, the maxima and shape of the filtered function are unaltered. Basically, the filter can be combined with an arbitrary method used for the numerical solution of the advection equation. Two-dimensional advective tests show that negative values are removed, and short waves are significantly damped with the pseudospectral method. The filtering algorithm is very simple. Additional computational time required by the filter is about 4% of that required by the pseudospectral method alone.
Article
Vitrification is a method of cryopreservation by which cells and tissues can be preserved at low temperatures using cryoprotective agents (CPAs) at high concentrations (typically ≥6.0 M) to limit the harmful effects of ice crystals that can form during cooling processes. However, at these concentrations CPAs are significantly cytotoxic and an understanding of their toxicity characteristics and interactions is important. Therefore, single-CPA and multiple-CPA solutions were evaluated for their direct and indirect toxicities on chondrocytes. Chondrocytes were isolated from human articular cartilage samples and exposed to various single-CPA and multiple-CPA solutions of five common CPAs (dimethyl sulfoxide (DMSO), ethylene glycol (EG), propylene glycol (PG), glycerol (Gy) and formamide (Fm)) at both 6.0 and 8.1 M concentrations at 0 °C for 30 min. Chondrocyte survival was determined using a fluorescent cell membrane integrity assay. The data obtained was statistically analyzed and regression coefficients were used to represent the indirect toxicity effect which a specific combination of CPAs exerted on the final solution's toxicity. Multiple-CPA solutions were significantly less toxic than single-CPA solutions (P<0.01). The indirect toxicity effects between CPAs were quantifiable using regression analysis. Cell survival rates of approximately 40% were obtained with the four-CPA combination solution DMSO-EG-Gy-Fm. In the multiple-CPA combinations, PG demonstrated the greatest degree of toxicity and its presence within a combination solution negated any benefits of using multiple lower concentration CPAs. Multiple-CPA solutions are less cytotoxic than single-CPA solutions of the same total concentration. PG was the most toxic CPA when used in combinations. The highest chondrocyte survival rates were obtained with the 6.0 M DMSO-EG-Gy-Fm combination solution.
Article
Cryopreservation nearly universally depends on the equilibration of cells and tissues with high concentrations of permeating chemicals known as cryoprotective agents, or CPAs. Despite their protective properties, CPAs can cause damage as a result of osmotically-driven cell volume changes, as well as chemical toxicity. In this study, we have used previously published data to determine a toxicity cost function, a quantity that represents the cumulative damage caused by toxicity. We then used this cost function to define and numerically solve the optimal control problem for CPA equilibration, using human oocytes as representative cell type with high clinical relevance. The resulting toxicity-optimal procedures are predicted to yield significantly less toxicity than conventional stepwise procedures. In particular, our results show that toxicity is minimized during CPA addition by inducing the cell to swell to its maximum tolerable volume and then loading it with CPA while in the swollen state. This counterintuitive result is considerably different from the conventional stepwise strategy, which involves exposure to successively higher CPA concentrations in order to avoid excessive shrinkage. The procedures identified in the present study have the potential to significantly reduce damage due to toxicity and warrant further investigation.
Article
This review covers Verification, Validation, Confirmation and related subjects for computational fluid dynamics (CFD), including error taxonomies, error estimation and banding, convergence rates, surrogate estimators, nonlinear dynamics, and error estimation for grid adaptation vs Quantification of Uncertainty.
Article
Long-term storage of natural tissues or tissue-engineered constructs is critical to allow off-the-shelf availability. Vitrification is a method of cryopreservation that eliminates ice formation, as ice may be detrimental to the function of natural or bioartificial tissues. In order to achieve the vitreous state, high concentrations of CPAs must be added and later removed. The high concentrations may be deleterious to cells as the CPAs are cytotoxic and single-step addition or removal will result in excessive osmotic excursions and cell death. A previously described mathematical model accounting for the mass transfer of CPAs through the sample matrix and cell membrane was expanded to incorporate heat transfer and CPA cytotoxicity. Simulations were performed for two systems, an encapsulated system of insulin-secreting cells and articular cartilage, each with different transport properties, geometry and size. Cytotoxicity and mass transfer are dependent on temperature, with a higher temperature allowing more rapid mass transfer but also causing increased cytotoxicity. The effects of temperature are exacerbated for articular cartilage, which has larger dimensions and slower mass transport through the matrix. Simulations indicate that addition and removal at 4°C is preferable to 25°C, as cell death is higher at 25°C due to increased cytotoxicity in spite of the faster mass transport. Additionally, the model indicates that less cytotoxic CPAs, especially at high temperature, would significantly improve the cryopreservation outcome. Overall, the mathematical model allows the design of addition and removal protocols that insure CPA equilibration throughout the sample while still minimizing CPA exposure and maximizing cell survival.
Article
Large articular cartilage defects have proven difficult to treat and often result in osteoarthritis of the affected joint. Cryopreservation of articular cartilage can provide an increased supply of tissues for osteochondral allograft but cryoprotective agents are required; however, few studies have been performed on the toxicity of these agents. This study was designed to determine the order of toxicity of five commonly used cryoprotectant agents as well as interactions that occur between them. Isolated porcine articular chondrocytes were exposed to individual cryoprotectant agents and combinations of these agents at 1M and 3M concentrations for 5 min and 120 min. Cell viability was determined using membrane integrity dyes and a metabolic activity assay. Subsequently, a regression analysis based study was undertaken to extract the maximum amount of information from this data. Results of this study demonstrated that all 1M solutions were minimally toxic. The 3M solutions demonstrated varying toxicity after 120 min. Ethylene glycol and glycerol were less toxic than propylene glycol, dimethyl sulfoxide, and formamide. Combinations of cryoprotectant agents were less toxic than single cryoprotectant agents at the same concentration. This is the most comprehensive study investigating cryoprotectant agent toxicity in articular chondrocytes and has resulted in important information regarding the order of toxicity and interactions that occur between these agents.
Article
The fundamental physical mechanisms of water and solute transport across cell membranes have long been studied in the field of cell membrane biophysics. Cryobiology is a discipline that requires an understanding of osmotic transport across cell membranes under nondilute solution conditions, yet many of the currently-used transport formalisms make limiting dilute solution assumptions. While dilute solution assumptions are often appropriate under physiological conditions, they are rarely appropriate in cryobiology. The first objective of this article is to review commonly-used transport equations, and the explicit and implicit assumptions made when using the two-parameter and the Kedem-Katchalsky formalisms. The second objective of this article is to describe a set of transport equations that do not make the previous dilute solution or near-equilibrium assumptions. Specifically, a new nondilute solute transport equation is presented. Such nondilute equations are applicable to many fields including cryobiology where dilute solution conditions are not often met. An illustrative example is provided. Utilizing suitable transport equations that fit for two permeability coefficients, fits were as good as with the previous three-parameter model (which includes the reflection coefficient, sigma). There is less unexpected concentration dependence with the nondilute transport equations, suggesting that some of the unexpected concentration dependence of permeability is due to the use of inappropriate transport equations.
Article
Osteochondral allografting is an effective method to treat large osteochondral defects but difficulties in tissue preservation have significantly limited the application of this technique. Successful cryopreservation of articular cartilage (AC) could improve the clinical availability of osteochondral tissue and enhance clinical outcomes but cryopreservation of large tissues is hampered by a lack of knowledge of permeation kinetics within these tissues. This study describes the refinement and extension of a recently published technique to measure the permeation kinetics of cryoprotectant agents (CPAs) within porcine AC. Dowels of porcine AC (10mm diameter) were immersed in solutions containing 6.5 M concentrations of four commonly used CPAs [dimethyl sulfoxide (DMSO), propylene glycol (PG), ethylene glycol (EG) and glycerol] for different times (1s, 1, 2, 5, 10, 15, 30, 60, 120, 180 min , 24h) at three different temperatures (4, 22, and 37 degrees C). The cartilage was isolated and the amount of CPA within the matrix was determined. Diffusion coefficients (DMSO=2.4-6.2x10(-6)cm2/s; PG=0.8-2.7x10(-6)cm2/s; EG=1.7-4.2x10(-6)cm2/s; and glycerol=0.8-2.4x10(-6)cm2/s) and activation energies (DMSO=4.33 kcal/mol, PG=6.29 kcal/mol, EG=3.77 kcal/mol, and glycerol=5.56 kcal/mol) were determined for each CPA. The results of this experiment provide accurate permeation kinetics of four commonly used CPAs in porcine articular cartilage. This information will be useful for developing effective vitrification protocols for cryopreservation of AC.
Article
A micromethod was employed to estimate quantitatively and reproducibly the deoxyribonucleic acid (DNA) content of isolated rat islets of Langerhans. The DNA content per islet varied linearly with the mean diameter or the dry weight of the islets isolated. The DNA in the freeze-dried islets of male Sprague-Dawley or Wistar rats was about 21.0 mug/mug islet dry weight. Three to four weeks after hypophysectomy, with or without short term bovine growth hormone replacement, the DNA content per unit dry weight of islets was not significantly altered. Islet DNA content and islet dry weight are proposed as an interconvertible and reliable basis of reference for measurements of different islet functions.
Article
Swelling of articular cartilage depends on its fixed charge density and distribution, the stiffness of its collagen-proteoglycan matrix, and the ion concentrations in the interstitium. A theory for a tertiary mixture has been developed, including the two fluid-solid phases (biphasic), and an ion phase, representing cation and anion of a single salt, to describe the deformation and stress fields for cartilage under chemical and/or mechanical loads. This triphasic theory combines the physico-chemical theory for ionic and polyionic (proteoglycan) solutions with the biphasic theory for cartilage. The present model assumes the fixed charge groups to remain unchanged, and that the counter-ions are the cations of a single salt of the bathing solution. The momentum equation for the neutral salt and for the intersitial water are expressed in terms of their chemical potentials whose gradients are the driving forces for their movements. These chemical potentials depend on fluid pressure p, salt concentration c, solid matrix dilatation e and fixed charge density cF. For a uni-uni valent salt such as NaCl, they are given by μi = μoi + (RT/Mi)ln[γ±2c(c + cF)] and μw = μow + [p - RTφ(2c + cF) + Bwe]/ρTw, where R, T, Mi, γ±, φ, ρTw and Bw are universal gas constant, absolute temperature, molecular weight, mean activity coefficient of salt, osmotic coefficient, true density of water, and a coupling material coefficient, respectively. For infinitesimal strains and material isotropy, the stress-strain relationship for the total mixture stress is σ = - pI - TcI + λs(trE)I + 2μsE, where E is the strain tensor and (λs, μs) are the Lame constants of the elastic solid matrix. The chemical-expansion stress (- Tc) derives from the charge-to-charge repulsive forces within the solid matrix. This theory can be applied to both equilibrium and non-equilibrium problems.
Article
The ability of chondrocytes to survive conditions encountered during cryopreservation depends on the responses of the cells to the physiochemical changes that result when water is removed from the environment of the cells in the form of ice. Cellular responses are therefore closely related to the osmotic permeability properties of the plasma membrane. In order to optimize the conditions for cryopreservation of chondrocytes, osmotic properties of the chondrocyte membrane were determined from the kinetics of volume change in hypertonic solutions at different temperatures. The hydraulic conductivity of the plasma membrane was 0.305 +/- 0.025 micron3/micron2/min/atmosphere at 24 degrees C, with an Arrhenius activation energy of 8.06 kcal/mol. These values are similar to those reported for other cell types, but the osmotically inactive volume of the chondrocytes (0.41 +/- 0.04) was significantly higher than for other cells, implying that chondrocytes have a higher dry weight ratio or that they contain a higher proportion of osmotically inactive or bound water. These results were used to calculate the osmotic responses of chondrocytes at low temperatures and to predict that the least damaging cooling rate for isolated chondrocytes in the absence of cryoprotective compounds is 10 degrees C/min. The ultimate goal of this study is the development of an analytical model applicable to the optimization of techniques for cryopreservation of intact cartilage and other tissues.
Article
The ability to store pancreatic islets using cryopreservation methodology would greatly assist the application of clinical islet transplantation to Type 1 (insulin-dependent) diabetics. It is our working thesis that the illumination of fundamental biophysical characteristics of these cells will lead to increased cryosurvival rates through theoretically predicted and experimental testing of optimal freezing protocol; as has been found for cells and tissues such as mammalian and Drosophila embryos. Pancreatic islets were isolated from Golden hamsters and their osmometric behavior, including inactive cell volume (Vb), was determined for either whole islets or isolated individual islet cells. When islets or islet cells were exposed to various concentrations of NaCl, they were found to exhibit a "classic" "Boyle-Van't Hoff" osmometric response. The Boyle-Van't Hoff representation of the volume curve (relative cell volume vs. 1/osmolality) yields a linear response with r values of .99 for each curve. Extrapolations to the normalized osmotically inactive volumes (Vb) were .43 and .22 for whole islets and individual islet cells, respectively. These data regarding the fundamental cryobiological characteristics of islets and islet cells should provide the foundation upon which to further the investigation of osmotic parameters of these cells and eventually lead to the determination of optimal freezing protocols.
Article
Long-term cryopreservation of islets of Langerhans would be advantageous to a clinical islet transplantation program. Fundamental cryobiology utilizes knowledge of basic biophysical characteristics to increase the understanding of the preservation process and possibly increase survival rate. In this study several of these previously unreported characteristics have been determined for individual islet cells isolated from Golden hamster islets. Using an electronic particle counting device and a temperature control apparatus, dynamic volumetric response of individual islet cells to anisosmotic challenges of 1.5 M dimethyl sulfoxide (DMSO) and 1.5 M ethylene glycol (EG) were recorded at four temperatures (8, 22, 28, and 37 degreesC). The resulting curves were fitted using Kedem and Katchalsky equations which describe water flux and cryoprotectant agent (CPA) flux based on hydraulic conductivity (Lp), CPA permeability (Ps), and reflection coefficient (final sigma) for the membrane. For Golden hamster islet cells, Lp, Ps, and final sigma for DMSO at 22 degreesC were found to be 0.23 +/- 0.06 microm/min/atm, 0.79 +/- 0.32 x 10(-3) cm/min, and 0.55 +/- 0.37 (n = 11) (mean +/- SD), respectively. For EG at 22 degreesC, Lp equaled 0.23 +/- 0.06 microm/min/atm, Ps equaled 0.63 +/- 0.20 x 10(-3) cm/min, and final sigma was 0.75 +/- 0.17 (n = 9). Arrhenius plots (ln Lp or ln Ps versus 1/temperature (K)) were created by adding the data from the other three temperatures and the resulting linear regression yielded correlation coefficients (r) of 0.99 for all four plots (Lp and Ps for both CPAs). Activation energies (Ea) of Lp and Ps were calculated from the slopes of the regressions. The values for DMSO were found to be 12.43 and 18.34 kcal/mol for Lp and Ps (four temperatures, total n = 52), respectively. For EG, Ea of Lp was 11.69 kcal/mol and Ea of Ps was 20.35 kcal/mol (four temperatures, total n = 58).
Article
The analysis of experiments for the purpose of determining cell membrane permeability parameters is often done using the Kedem-Katchalsky (KK) formalism (1958). In this formalism, three parameters, the hydraulic conductivity (Lp), the solute permeability (Ps), and a reflection coefficient (final sigma), are used to characterize the membrane. Sigma was introduced to characterize flux interactions when water and solute (cryoprotectant) cross the membrane through a common channel. However, the recent discovery and characterization of water channels (aquaporins) in biological membranes reveals that aquaporins are highly selective for water and do not typically cotransport cryoprotectants. In this circumstance, sigma is a superfluous parameter, as pointed out by Kedem and Katchalsky. When sigma is unneeded, a two-parameter model (2P) utilizing only Lp and Ps is sufficient, simpler to implement, and less prone to spurious results. In this paper we demonstrate that the 2P and KK formalism yield essentially the same result (Lp and Ps) when cotransporting channels are absent. This demonstration is accomplished using simulation techniques to compare the transport response of a model cell using a KK or 2P formalism. Sigma is often misunderstood, even when its use is appropriate. It is discussed extensively here and several simulations are used to illustrate and clarify its meaning. We also discuss the phenomenological nature of transport parameters in many experiments, especially when both bilayer and channel transport are present.
Article
Network thermodynamic modeling via bond graphs was used to describe the water and cryoprotectant additive (CPA) transport in a multicellular tissue. The model is presented as a tool to understand the osmotic behavior of the islets of Langerhans when exposed to ternary aqueous solutions containing an electrolyte and a CPA. It accounts for the effects of the location of cells within the tissue and an interstitial matrix, plus differential permeabilities to water and CPA. The interstitial matrix was assumed to be a porous medium able to store the chemical species being transported. Controlled osmotic stress experiments were conducted on isolated rat pancreas islets to measure the transient volumetric response to step-wise changes in dimethyl sulfoxide, Me2SO, concentration. The model provides a tool for predicting the transient volumetric response of peripheral and interior cells and of interstitial tissue, as well as the build up of solute concentration, during addition and removal of CPAs and freezing and thawing protocols. Inverse solution methods were applied to determine values for standard cell membrane permeability parameters Lp, omega and sigma as well as for the interstitial flow conductivities Kw and Kp'.
Article
The amount and the types of glycosaminoglycans (GAGs) present in human pancreatic carcinoma were examined and compared with those in normal pancreas. Human pancreatic carcinoma contained increased levels (4-fold) of total GAGs. Particularly, this carcinoma is characterized by a 12-fold increase of hyaluronan (HA) and a 22-fold increase in chondroitin sulfate (CS) content. CS in pancreatic carcinoma exhibited an altered disaccharide composition which is associated with marked increase of non-sulfated and 6-sulfated disaccharides. Dermatan sulfate (DS) was also increased (1.5-fold) in carcinoma, whereas heparan sulfate (HS), the major GAG of normal pancreas, becomes the minor GAG in pancreatic carcinoma without significant changes in the content and in molecular size. In all cases, the galactosaminoglycans (GalGAGs, i.e. CS and DS) derived from pancreatic carcinomas were of lower molecular size compared to those from normal pancreas. The results in this study indicate, for the first time, that human pancreatic carcinoma is characterized by highly increased amounts of HA and of a structurally altered CS.
Article
Long-term storage of engineered bio-artificial tissues is required to ensure the off-the-shelf availability to clinicians due to their long production cycle. Cryopreservation is likely the choice for long-term preservation. Although the cryopreservation of cells is well established for many cell types, cryopreservation of tissues is far more complicated. Cells at different locations in the tissue could experience very different local environmental changes, i.e., the change of concentration of cryoprotecting chemicals (CPA) and temperature, during the addition/removal of CPA and cooling/warming, which leads to nonuniformity in cell survival in the tissue. This is due to the limitation of mass and heat transfer within the tissue. A specific aim of cryopreservation of tissue is to ensure a maximum recovery of cells and their functionality throughout a tissue. Cells at all locations should be protected adequately by the CPA and frozen at rates conducive to survival. It is hence highly desirable to know the cell transient and final states during cryopreservation within the whole tissue, which can be best studied by mathematical modeling. In this work, a model framework for cryopreservation of one-dimensional artificial tissues is developed on the basis of solving the coupled equations to describe the mass and heat transfer within the tissue and osmotic transport through the cell membrane. Using an artificial pancreas as an example, we carried out a simulation to examine the temperature history, cell volume, solute redistribution, and other state parameters during the freezing of the spherical heterogeneous construct (a single bead). It is found that the parameters affecting the mass transfer of CPA in tissue and through the cell membrane and the freezing rate play dominant roles in affecting the cell volume transient and extracellular ice formation. Thermal conductivity and extracellular ice formation kinetics, on the other hand, have little effect on cell transient and final states, as the heat transfer rate is much faster than mass diffusion. The outcome of such a model study can be used to evaluate the construct design on its survivability during cryopreservation and to select a cryopreservation protocol to achieve maximum cell survival.
Article
Cryopreservation is likely the choice for long-term preservation of natural and engineered tissues, and high concentration multiple cryoprotective agents (CPAs) are usually used in such a process. To achieve high cell viability after cryopreservation, cells at all locations within the tissue must be protected properly by the CPAs during freezing. It is hence essential to know the distribution and concentration of CPAs within the tissue during multiple-CPA addition, to maximize cell survival and minimize tissue damage. In this work, a model to describe the CPA transport during multiple-CPA addition in a one-dimensional porous medium, as a simplified model of living tissue, was developed on the basis of the Maxwell-Stefan (M-S) equations. The UNIFAC and UNIQUAC models were used to evaluate the activity coefficients, and the Siddiqi-Lucas correlation was used for estimation of Maxwell-Stefan diffusivities. Simulations were carried out to examine the effect of temperature, tissue property, CPA type and the interactions between solutes on the CPA transport within construct during the CPA addition. It was found that these parameters, especially the interactions between the different CPA molecules, which was neglected before, significantly affect the transport of each individual CPA component. It is hence concluded that the traditional single-component analysis on the CPA diffusion is not adequate to quantify the multiple-CPA distribution in the tissue, particularly when the CPA concentrations are relatively high.
Article
The addition of cryopreservative agents (CPAs) to chondrocytes and natural and engineered cartilage is critical to protect the cells and tissues from freezing damage during cryopreservation, but this may cause cell damage, e.g. by osmotic shock. The damage could be minimized by the control of the cell volume excursion with the knowledge of cell membrane permeability. In this study, the cell volume responses of chondrocytes to three commonly used CPAs were evaluated using a perfusion microscope stage. The osmotic response of chondrocytes was measured to the perfusion with 1.4 M dimethyl sulfoxide (Me2SO), 1,2-propanediol and glycerol at 21 degrees C. Cell volumes and their transients were determined with image analysis. The cell membrane permeability parameters, including the hydraulic conductivity (Lp), the CPA permeability (omega) and the reflection coefficients (sigma) in the Kedem-Katchalsky (K-K) model, and the Lp and omega in the two-parameter model were determined. The correlated K-K parameters at 21 degrees C were Lp=0.166 +/- 0.035, 0.149 +/- 0.061, 0.212 +/- 0.041 microm/min atm, omega=(7.630 +/- 0.174) x 10(-2), (1.428 +/- 0.627) x 10(-2), (2.744 +/- 0.775) x 10(-2) microm/s and sigma=0.91 +/- 0.09, 0.82 +/- 0.11, 0.88 +/- 0.10 for Me(2)SO, glycerol and 1,2-propanediol, respectively. For the two-parameter model, the parameter values were Lp=0.163 +/- 0.040, 0.128 +/- 0.031, 0.169 +/- 0.025 microm/min atm, omega=(7.881 +/- 0.178) x 10(-2), (1.529 +/- 0.525) x 10(-2), (3.716 +/- 0.493) x 10(-2) microm/s for Me2SO, glycerol and 1,2-propanediol, respectively. No significant difference in the predictions of cell volume excursion during CPA addition was observed when using either the K-K model or the two-parameter model and it was hence advised to adopt the simple two-parameter model in the evaluation. The measured parameters can be used to optimise the CPA addition and removal protocols to maximize the cell survival during cryopreservation.
Article
The cryopreservation of organs became an active area of research in the 1950s as a result of the rediscovery of the cryoprotective properties of glycerol by Polge, Smith, and Parkes in 1949. Over the ensuing four decades of research in this area, the advantages of vitrification, or ice-free cryopreservation, have become apparent. To date, experimental attempts to apply vitrification methods to vascularized whole organs have been confined almost entirely to the rabbit kidney. Using techniques available as of 1997, it was possible to vitrify blood vessels and smaller systems with reasonable success, but not whole organs. Beginning in 1998, a series of novel advances involving the control of cryoprotectant toxicity, nucleation, crystal growth, and chilling injury began to provide the tools needed to achieve success. Based on these new findings, we were first able to show that an 8.4M solution (VMP) designed to prevent chilling injury at -22 degrees C was entirely non-toxic to rabbit kidneys when perfused at -3 degrees C and permitted perfusion-cooling to -22 degrees C with only mild additional damage. We next investigated the ability of the kidney to tolerate a 9.3M solution known as M22, which does not devitrify when warmed from below -150 degrees C at 1 degrees C/min. When M22 was added and removed at -22 degrees C, it was sometimes [corrected] fatal, but when it was perfused for 25min at -22 degrees C and washed out simultaneously with warming, postoperative renal function recovered fully. When kidneys loaded with M22 at -22 degrees C were further cooled to an average intrarenal temperature of about -45 degrees C (about halfway through the putative temperature zone of increasing vulnerability to chilling injury), all kidneys supported life after transplantation and returned creatinine values to baseline, though after a higher transient creatinine peak. However, medullary, papillary, and pelvic biopsies taken from kidneys perfused with M22 for 25min at -22 degrees C were found to devitrify when vitrified and rewarmed at 20 degrees C/min in a differential scanning calorimeter. It remains to be determined whether this devitrification is seriously damaging and whether it can be suppressed by improving cryoprotectant distribution to more weakly perfused regions of the kidney or by rewarming at higher rates. In conclusion, although the goal of organ vitrification remains elusive, the prospects for success have never been more promising.