Transport Phenomena in Articular Cartilage Cryopreservation as Predicted by the Modified Triphasic Model and the Effect of Natural Inhomogeneities

Abstract

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.

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

“…Many of the mathematical models that are used to simulate cryopreservation protocols [1,2,15,25,26,31,34,35,44,54,59,60,68] rely on the ability to accurately predict thermodynamic solution behavior, since important processes such as water and solute transport and ice formation are ultimately dictated by differences in chemical potential. As a consequence, it is important to give some thought to the choice of the solution theories that are used to calculate these chemical potentials.…”

“…Freezing point depression and osmotic pressure are physically measurable solution properties, and the relationships between them and osmolality (described below in Eqs. (2) and (3) and in Eq. (4), respectively) allow one to experimentally obtain values for the osmolality of a solution.…”

Foundations of modeling in cryobiology—I: Concentration, Gibbs energy, and chemical potential relationships

“…[71,72,112] and others), defined cryobiology as a science where much could be gained even by relatively simple models making broadly unrealistic assumptions. In fact as cryobiology has progressed as a discipline, various researchers have made use of models to determine optimal cooling and/or warming profiles [16,51,81,102,103,117,122], optimal pre-and post-cooling processing protocols [11,12,37,39,69,93,108], intracellular ice formation kinetics [3,45,46,119,125], ice damage in and optimal cryopreservation of tissues [1,2,23,31,99,111,114,126,127], among others. While Mazur's work laid the foundation for modeling success in cryobiology, another foundation of cryosuccess is a chemical one: cryopreservation nearly universally requires the presence of cryoprotective chemicals, known as cryoprotective agents or CPAs.…”

Non-ideal Solution Thermodynamics of Cytoplasm

“…Herein, we use the osmotic virial equation, a non-ideal solution thermodynamics model, being applied with success in cryobiological modeling of the extracellular solution. [23][24][25][26][27][28][29] While the solution properties are known for some individual components (e.g., hemoglobin 3,30 ) and combinations of known single-solute components using, for example, the osmotic virial equation, 3,26 the cytoplasm is too complex to make general use of the individual solute solution properties feasible. It is precisely because of the requirement to incorporate thermodynamics of a wide variety of molecules that we have chosen the osmotic virial approach.…”

“…The osmotic virial equation has been shown by many researchers over decades to apply to a vast number of types of solutes in aqueous systems, including sugars, electrolytes, cryoprotectants, macromolecules, proteins, alcohols, and starches. 3,24,26,27,[31][32][33][34][35][36][37][38][39][40][41][42][43][44] Osmolality describes the concentration dependence of the chemical potential of water in a solution and is the solution thermodynamics quantity that appears directly in equations describing freezing point depression of a solution (see Eq. 12) or the driving force for passive osmotic transport.…”