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

Permeation kinetics of dimethyl sulfoxide in porcine corneoscleral discs

The cornea is the transparent tissue in front of the eye that bends light to help the eye focus. More than five million people's vision can be restored by a corneal transplant (keratoplasty), but there is a scarcity of suitable donor tissue. Cryopreservation could potentially increase the on-demand availability of corneas by reducing expiration and contamination during hypothermic storage, and allow equitable distribution. Understanding the transport of water and cryoprotectants across the tissue is important in developing effective cryopreservation protocols. Here, we first measured the shrinking and swelling kinetics at 22 °C and 0 °C of porcine corneoscleral discs when exposed to phosphate-buffered saline and to a cryoprotectant vehicle solution containing 2.5% chondroitin sulfate and 1% dextran. Other valuable measurements were made including the density and osmolality of the vehicle solution at 0 °C, and the water fraction of porcine cornea and sclera. Using the knowledge gained from this first part to minimize background swelling, we then examined permeation kinetics of dimethyl sulfoxide (Me2SO) in porcine corneoscleral discs at 0 °C, the temperature at which cryoprotectant loading typically occurs. The concentration data obtained as a function of time were fitted to a Fick's law model of one-dimensional diffusion to measure an effective diffusion coefficient of Me2SO, which was found to be 5.306×10-11 m2/s. We further quantified permeation kinetics of Me2SO in sclera alone at 0 °C to support our hypothesis that our measurements for corneoscleral discs will not be affected by the presence of the sclera. The obtained effective diffusion coefficient can be used in modelling aimed at developing cryopreservation protocols that minimize the exposure time of the corneas during the cryoprotectant loading step.

Modeling the Simultaneous Transport of Multiple Cryoprotectants into Articular Cartilage Using a Triphasic Model

Cryopreserving articular cartilage by vitrification can increase the availability of tissue for osteochondral allograft transplantation to treat cartilage defects. Developing well-optimized vitrification protocols can be supported by mathematical modeling to reduce the amount of trial-and-error experimentation needed. Fick's law has been used to model cryoprotectant diffusion, but it assumes ideal, dilute solution behavior, neglects water movement, and assumes diffusion of each cryoprotectant is independent of the presence of other cryoprotectants. The modified triphasic model addresses some of these shortcomings by accounting for water movement and the nonideal, nondilute nature of cryoprotectant vitrification solutions. However, it currently only exists for solutions containing a single cryoprotectant. As such, we extend the modified triphasic model to include two permeating cryoprotectants so that simultaneous diffusion occurring in vitrification protocols can be more accurately modeled. Using previously published experimental data, we determine suitable values for the fitting parameters of the new model. We then model a successful vitrification protocol for particulated cartilage cubes by calculating concentration, freezing point, vitrifiability, and strain profiles at the end of each loading step. We observe that Fick's law consistently underestimates cryoprotectant concentration throughout the cartilage compared to the modified triphasic model, leading to an underestimation of tissue vitrifiability. We additionally observe that simultaneous diffusion of cryoprotectants increases the permeation rate of each individual cryoprotectant, which Fick's law fails to consider. This suggests that using the two-cryoprotectant modified triphasic model to develop vitrification protocols could reduce excess exposure to cryoprotectants and improve preserved tissue outcomes.

General tissue mass transfer model for cryopreservation applications

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 because of 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 for cells. 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.

Vitrification of particulated articular cartilage via calculated protocols

Preserving viable articular cartilage is a promising approach to address the shortage of graft tissue and enable the clinical repair of articular cartilage defects in articulating joints, such as the knee, ankle, and hip. In this study, we developed two 2-step, dual-temperature, multicryoprotectant loading protocols to cryopreserve particulated articular cartilage (cubes ~1 mm3 in size) using a mathematical approach, and we experimentally measured chondrocyte viability, metabolic activity, cell migration, and matrix productivity after implementing the designed loading protocols, vitrification, and warming. We demonstrated that porcine and human articular cartilage cubes can be successfully vitrified and rewarmed, maintaining high cell viability and excellent cellular function. The vitrified particulated articular cartilage was stored for a period of 6 months with no significant deterioration in chondrocyte viability and functionality. Our approach enables high-quality long-term storage of viable articular cartilage that can alleviate the shortage of grafts for use in clinically repairing articular cartilage defects.

Gibbsian Surface Thermodynamics

Gibbsian composite-system thermodynamics is the framework governing the equilibrium of composite systems, including systems that at equilibrium have more than one value of pressure because of the action of surface tension, semipermeable membranes, or fields, and thus cannot be treated as simple systems. J. W. Gibbs's paper that lays out composite-system thermodynamics, "On the Equilibrium of Heterogeneous Substances", communicated in two parts in 1876 and 1878, is widely regarded as one of the most important pieces of scientific literature of its century. Many scientists adopted and stressed the importance of Gibbsian thermodynamics. In 1960, H. B. Callen wrote a textbook that made Gibbsian composite-system thermodynamics more accessible to thermodynamicists. However, Callen's book left out Gibbs's work on curved fluid interfaces and did not treat the complicated nonideal systems of interest to today's thermodynamicists. In this Feature Article, I have attempted to convey in a comprehensive manner the framework of Gibbsian composite-system thermodynamics including in detail the treatment of systems with interface effects and with nonideal, multicomponent phases. This work lays out the relationships between important equilibrium equations including the following: the Gibbs-Duhem equation, the Gibbs adsorption equation, the Young-Laplace equation, the Young equation, the Cassie-Baxter equation, the Wenzel equation, the Kelvin equation, the Gibbs-Thompson equation, and the Ostwald-Freundlich equation, including nonideal and multicomponent forms. Equations of state that are often useful for Gibbsian composite-system thermodynamics are reviewed including adsorption isotherms and our own work on two semiempirical equations of state: the Elliott et al. form of the osmotic virial equation and the Shardt-Elliott-Connors-Wright equation for the temperature and composition dependence of surface tension. I summarize the work of our group developing Gibbisan composite-system thermodynamics including new equations for such things as the curvature-induced depression of the eutectic temperature or the removal of azeotropes by nanoscale fluid interface curvature. Gibbsian composite-system thermodynamics has broad applications in biotechnology, nanostructured materials, surface textures and coatings, microfluidics, nanoscience, atmospheric and environmental physics, among others.

Using engineering models to shorten cryoprotectant loading time for the vitrification of articular cartilage

Osteochondral allograft transplantation can treat full thickness cartilage and bone lesions in the knee and other joints, but the lack of widespread articular cartilage banking limits the quantity of cartilage available for size and contour matching. To address the limited availability of cartilage, vitrification can be used to store harvested joint tissues indefinitely. Our group's reported vitrification protocol [Biomaterials 33 (2012) 6061-6068] takes 9.5 h to load cryoprotectants into intact articular cartilage on bone and achieves high cell viability, but further optimization is needed to shorten this protocol for clinical use. Herein, we use engineering models to calculate the spatial and temporal distributions of cryoprotectant concentration, solution vitrifiability, and freezing point for each step of the 9.5-h protocol. We then incorporate the following major design choices for developing a new shorter protocol: (i) all cryoprotectant loading solution concentrations are reduced, (ii) glycerol is removed as a cryoprotectant, and (iii) an equilibration step is introduced to flatten the final cryoprotectant concentration profiles. We also use a new criterion-the spatially and temporally resolved prediction of solution vitrifiability-to assess whether a protocol will be successful instead of requiring that each cryoprotectant individually reaches a certain concentration. A total cryoprotectant loading time of 7 h is targeted, and our new 7-h protocol is predicted to achieve a level of vitrifiability comparable to the proven 9.5-h protocol throughout the cartilage thickness.

Foundations of modeling in cryobiology-II: Heat and mass transport in bulk and at cell membrane and ice-liquid interfaces

Modeling coupled heat and mass transport in biological systems is critical to the understanding of cryobiology. In Part I of this series we derived the transport equation and presented a general thermodynamic derivation of the critical components needed to use the transport equation in cryobiology. Here we refine to more cryobiologically relevant instances of a double free-boundary problem with multiple species. In particular, we present the derivation of appropriate mass and heat transport constitutive equations for a system consisting of a cell or tissue with a free external boundary, surrounded by liquid media with an encroaching free solidification front. This model consists of two parts-namely, transport in the "bulk phases" away from boundaries, and interfacial transport. Here we derive the bulk and interfacial mass, energy, and momentum balance equations and present a simplification of transport within membranes to jump conditions across them. We establish the governing equations for this cell/liquid/solid system whose solution in the case of a ternary mixture is explored in Part III of this series.

Spectroscopic monitoring of transport processes during loading of ovarian tissue with cryoprotective solutions

There is an increasing demand for female fertility preservation. Cryopreservation of ovarian cortex tissue by means of vitrification can be done ad-hoc and for pre-pubertal individuals. Obtaining a homogeneous distribution of protective agents in tissues is one of the major hurdles for successful preservation. Therefore, to rationally design vitrification strategies for tissues, it is needed to determine permeation kinetics of cryoprotective agents; to ensure homogeneous distribution while minimizing exposure time and toxicity effects. In this study, Fourier transform infrared spectroscopy (FTIR) was used to monitor diffusion of different components into porcine ovarian cortex tissue. Water fluxes and permeation kinetics of dimethyl sulfoxide (DMSO), glycerol (GLY), ethylene glycol (EG), and propylene glycol (PG) were investigated. Diffusion coefficients derived from FTIR data, were corroborated with differential scanning calorimetry and osmometer measurements. FTIR allowed real-time spectral fingerprinting of tissue during loading with mixtures of protective agents, while discriminating between different components and water. Exposure to vitrification solutions was found to cause drastic initial weight losses, which could be correlated with spectral features. Use of heavy water allowed distinguishing water fluxes associated with dehydration and permeation, both of which were found to precede permeation of cryoprotective agents. Overall, DMSO and EG were found to permeate faster than GLY and PG. In mixtures, however, solutes behave differently. The non-invasive spectroscopic method described here to study permeation of vitrification solution components into ovarian tissue can be applied to many other types of engineered constructs, tissues, and possibly organs.

The effect of additive compounds on glycerol-induced damage to human chondrocytes

High concentrations of cryoprotective agents are required for cryopreservation techniques such as vitrification. Glycerol is a common cryoprotective agent used in cryopreservation protocols but this agent is toxic at high concentrations. This work is an attempt to mitigate the toxic effects of high concentrations of glycerol on intact chondrocytes in human knee articular cartilage from total knee arthroplasty patients by simultaneous exposure to glycerol and a variety of additive compounds. The resulting cell viability in the cartilage samples as measured by membrane integrity staining showed that, in at least one concentration or in combination, all of the tested additive compounds (tetramethylpyrazine, ascorbic acid, chondroitin sulphate, glucosamine sulphate) were able to reduce the deleterious effects of glycerol exposure when examination of membrane integrity took place on a delayed time frame. The use of additive compounds to reduce cryoprotectant toxicity in articular cartilage may help improve cell recovery after cryopreservation.

Anatomical study: comparing the human, sheep and pig knee meniscus

BACKGROUND

Animal models are commonly used in investigating new treatment options for knee joint injuries including injuries to the meniscus. The reliability and applicability of these models to replicate findings in humans depends on determining the most suitable animal proxy. Therefore, this study was designed to compare the wet weight, volume and dimensions of the human meniscus with two commonly used animal models: sheep and pig.

METHODS

Human menisci (n = 6 pairs) were obtained from the knee joints of cadaveric male donors. Sheep menisci (n = 6 pairs) and pig menisci (n = 22 pairs) were obtained from the stifle joints of adult sheep and pigs. Meniscal wet weight, volume and dimensions of the body were measured and compared among the species. Anatomical dimensions included circumference, width, peripheral height, articular height and superior articular length.

RESULTS

The circumference of human menisci (lateral: 84.0 mm, medial: 88.7 mm) was significantly longer than that of sheep (lateral: 50.0 mm, medial: 55.5 mm) and pig (lateral: 66.8 mm, medial: 64.9 mm). The majority of the remaining dimensions of the medial and all of the remaining dimensions of the lateral menisci in sheep showed no statistical difference in comparison to the human menisci. The meniscal weight in pig was significantly larger (lateral: 6.4 g, medial: 5.0 g) than the human (lateral: 4.9 g, medial: 4.4 g) and sheep (lateral: 2.5 g, medial: 2.2 g). Porcine meniscal volume (lateral: 6.5 ml, medial: 5.1 ml) was also larger than the human (lateral: 5.0 ml, medial: 4.5 ml) and sheep (lateral: 2.3 ml, medial: 2.2 ml) menisci. The dimensions measured in the pig meniscus were generally larger than human menisci with statistically significant differences in most categories.

CONCLUSION

Sheep meniscal dimensions more closely matched human meniscal dimensions than the pig meniscal dimensions. This information may help guide the choice of an animal proxy in meniscal research.

Application of multiphysics models to efficient design of experiments of solute transport across articular cartilage

Transport of solutes helps to regulate normal physiology and proper function of cartilage in diarthrodial joints. Multiple studies have shown the effects of characteristic parameters such as concentration of proteoglycans and collagens and the orientation of collagen fibrils on the diffusion process. However, not much quantitative information and accurate models are available to help understand how the characteristics of the fluid surrounding articular cartilage influence the diffusion process. In this study, we used a combination of micro-computed tomography experiments and biphasic-solute finite element models to study the effects of three parameters of the overlying bath on the diffusion of neutral solutes across cartilage zones. Those parameters include bath size, degree of stirring of the bath, and the size and concentration of the stagnant layer that forms at the interface of cartilage and bath. Parametric studies determined the minimum of the finite bath size for which the diffusion behavior reduces to that of an infinite bath. Stirring of the bath proved to remarkably influence neutral solute transport across cartilage zones. The well-stirred condition was achieved only when the ratio of the diffusivity of bath to that of cartilage was greater than ≈1000. While the thickness of the stagnant layer at the cartilage-bath interface did not significantly influence the diffusion behavior, increase in its concentration substantially elevated solute concentration in cartilage. Sufficient stirring attenuated the effects of the stagnant layer. Our findings could be used for efficient design of experimental protocols aimed at understanding the transport of molecules across articular cartilage.

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.

Toxicity Minimized Cryoprotectant Addition and Removal Procedures for Adherent Endothelial Cells

Ice-free cryopreservation, known as vitrification, is an appealing approach for banking of adherent cells and tissues because it prevents dissociation and morphological damage that may result from ice crystal formation. However, current vitrification methods are often limited by the cytotoxicity of the concentrated cryoprotective agent (CPA) solutions that are required to suppress ice formation. Recently, we described a mathematical strategy for identifying minimally toxic CPA equilibration procedures based on the minimization of a toxicity cost function. Here we provide direct experimental support for the feasibility of these methods when applied to adherent endothelial cells. We first developed a concentration- and temperature-dependent toxicity cost function by exposing the cells to a range of glycerol concentrations at 21°C and 37°C, and fitting the resulting viability data to a first order cell death model. This cost function was then numerically minimized in our state constrained optimization routine to determine addition and removal procedures for 17 molal (mol/kg water) glycerol solutions. Using these predicted optimal procedures, we obtained 81% recovery after exposure to vitrification solutions, as well as successful vitrification with the relatively slow cooling and warming rates of 50°C/min and 130°C/min. In comparison, conventional multistep CPA equilibration procedures resulted in much lower cell yields of about 10%. Our results demonstrate the potential for rational design of minimally toxic vitrification procedures and pave the way for extension of our optimization approach to other adherent cell types as well as more complex systems such as tissues and organs.

Transport of Neutral Solute Across Articular Cartilage: The Role of Zonal Diffusivities

Transport of solutes through diffusion is an important metabolic mechanism for the avascular cartilage tissue. Three types of interconnected physical phenomena, namely mechanical, electrical, and chemical, are all involved in the physics of transport in cartilage. In this study, we use a carefully designed experimental-computational setup to separate the effects of mechanical and chemical factors from those of electrical charges. Axial diffusion of a neutral solute (Iodixanol) into cartilage was monitored using calibrated microcomputed tomography (micro-CT) images for up to 48 hr. A biphasic-solute computational model was fitted to the experimental data to determine the diffusion coefficients of cartilage. Cartilage was modeled either using one single diffusion coefficient (single-zone model) or using three diffusion coefficients corresponding to superficial, middle, and deep cartilage zones (multizone model). It was observed that the single-zone model cannot capture the entire concentration-time curve and under-predicts the near-equilibrium concentration values, whereas the multizone model could very well match the experimental data. The diffusion coefficient of the superficial zone was found to be at least one order of magnitude larger than that of the middle zone. Since neutral solutes were used, glycosaminoglycan (GAG) content cannot be the primary reason behind such large differences between the diffusion coefficients of the different cartilage zones. It is therefore concluded that other features of the different cartilage zones such as water content and the organization (orientation) of collagen fibers may be enough to cause large differences in diffusion coefficients through the cartilage thickness.

Non-ideal solution thermodynamics of cytoplasm

Quantitative description of the non-ideal solution thermodynamics of the cytoplasm of a living mammalian cell is critically necessary in mathematical modeling of cryobiology and desiccation and other fields where the passive osmotic response of a cell plays a role. In the solution thermodynamics osmotic virial equation, the quadratic correction to the linear ideal, dilute solution theory is described by the second osmotic virial coefficient. Herein we report, for the first time, intracellular solution second osmotic virial coefficients for four cell types [TF-1 hematopoietic stem cells, human umbilical vein endothelial cells (HUVEC), porcine hepatocytes, and porcine chondrocytes] and further report second osmotic virial coefficients indistinguishable from zero (for the concentration range studied) for human hepatocytes and mouse oocytes.

Foundations of modeling in cryobiology-I: concentration, Gibbs energy, and chemical potential relationships

Mathematical modeling plays an enormously important role in understanding the behavior of cells, tissues, and organs undergoing cryopreservation. Uses of these models range from explanation of phenomena, exploration of potential theories of damage or success, development of equipment, and refinement of optimal cryopreservation/cryoablation strategies. Over the last half century there has been a considerable amount of work in bio-heat and mass-transport, and these models and theories have been readily and repeatedly applied to cryobiology with much success. However, there are significant gaps between experimental and theoretical results that suggest missing links in models. One source for these potential gaps is that cryobiology is at the intersection of several very challenging aspects of transport theory: it couples multi-component, moving boundary, multiphase solutions that interact through a semipermeable elastic membrane with multicomponent solutions in a second time-varying domain, during a two-hundred Kelvin temperature change with multi-molar concentration gradients and multi-atmosphere pressure changes. In order to better identify potential sources of error, and to point to future directions in modeling and experimental research, we present a three part series to build from first principles a theory of coupled heat and mass transport in cryobiological systems accounting for all of these effects. The hope of this series is that by presenting and justifying all steps, conclusions may be made about the importance of key assumptions, perhaps pointing to areas of future research or model development, but importantly, lending weight to standard simplification arguments that are often made in heat and mass transport. In this first part, we review concentration variable relationships, their impact on choices for Gibbs energy models, and their impact on chemical potentials.

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.

A model for predicting the permeation of dimethyl sulfoxide into articular cartilage, and its application to the liquidus-tracking method

Long-term storage of articular cartilage (AC) has excited great interest due to the practical surgical significance of this tissue. The liquidus-tracking (LT) method developed by Pegg et al. (2006) [29] for vitreous preservation of AC achieved reasonable survival of post-warming chondrocytes in situ, but the design of the entire procedure was more dependent on trial and error. Mathematical modeling would help to better understand the LT process, and thereby make possible improvements to attain higher cell survival. Mass transfer plays a dominant role in the LT process. In the present study, a diffusion model based on the free-volume theory and the Flory-Huggins thermodynamics theory was developed to predict the permeation of dimethyl sulfoxide (Me2SO) into AC. A comparison between the predicted mean concentration of Me2SO in the AC disc and the experimental data over wide temperature and concentration ranges [-30 to 37 °C, 10 to 64.5% (w/w)] shows that the developed model can accurately describe the permeation of Me2SO into AC [coefficient of determination (R(2)): 0.951-1.000, mean relative error (MRE): 0.8-12.8%]. With this model, the spatial and temporal distribution of Me2SO in the AC disc during a loading/unloading process can be obtained. Application of the model to Pegg et al.'s LT procedure revealed that the liquidus line is virtually not followed for the center part of the AC disc. The presently developed model will be a useful tool in the analysis and design of the LT method for vitreous preservation of AC.

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.

MR spectroscopy measurement of the diffusion of dimethyl sulfoxide in articular cartilage and comparison to theoretical predictions

Cartilage cryopreservation requires optimal loading of protective solutes, most commonly dimethyl sulfoxide (DMSO), to maximize chondrocyte survival. Previously, diffusion models have been used to predict the distribution of solutes in tissue samples, but the accuracy of spatiotemporal predictions of these models have not been validated with empirical studies and remains unknown.

OBJECTIVE

In this study, magnetic resonance spectroscopic imaging was used to measure the spatial and temporal changes in DMSO and water concentrations in porcine articular cartilage plugs, throughout 1 h of solute loading.

DESIGN

A custom NMR spectroscopic imaging pulse sequence provided water and DMSO concentration images with an in-plane spatial resolution of 135 μm and a temporal resolution of 150 s, repeated for 60 min throughout DMSO loading. Delayed gadolinium-enhanced magnetic resonance of cartilage (d-GEMRIC) imaging provided fixed charge density and spin-density imaging provided water density images prior to DMSO loading.

RESULTS

The measured spatial and temporal distribution of DMSO in three different samples was compared to independent predictions of Fick's law and the modified triphasic biomechanical model by Abazari et al. (2011) with the empirical data more closely agreeing with the triphasic model.

CONCLUSION

Dynamic NMR spectroscopic imaging can measure spatial and temporal changes in water and cryoprotectant concentrations in articular cartilage. The modified triphasic model predictions for the interstitial distribution of DMSO were confirmed and its advantage over the predictions by Fick's law model, which is commonly used in the literature of cryobiology, was demonstrated.