Cryoprotectant kinetic analysis of a human articular cartilage vitrification protocol

Abstract

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.

Numerical Study of Heat and Mass Transfer during Cryopreservation Process with Application of Directed Interval Arithmetic

“…A multi-physical field weak coupling problem mainly consists of modelling the following processes: heat transfer, including the crystallization and moving boundary problem, as well as mass transport at the macroscale in the extracellular matrix and at the microscale—through the cell membrane [ 2 ]. Cryopreservation by slow freezing [ 9 ] and by vitrification [ 10 , 11 , 12 ] can both be analyzed. These models are considered not only for articular cartilage [ 12 , 13 , 14 , 15 , 16 ] but also for other biological tissues or cells, such as stem cells [ 9 , 17 , 18 ].…”

“…The microscale mass transfer model should be supplemented by the following analyses: mass transport in the extracellular matrix and thermal processing in the tissue. The model of mass transport at the macroscale is based on Fick’s second law, which provides for a concentration at a given time associated with diffusion [ 10 , 12 , 13 , 14 , 15 , 16 , 33 ]. The temperature distribution is determined from the Fourier equation [ 9 , 10 , 11 , 13 , 14 ].…”

Numerical Modeling of Heat and Mass Transfer during Cryopreservation Using Interval Analysis

“…Numerical modeling is an opportunity for the further development of cryopreservation. Models representing cryopreservation by slow freezing [23] and vitrification [12,24,25] have been created. Different biological tissues and cells such as stem cells [23,26,27] and articular cartilage [25,[28][29][30][31] have been analyzed.…”

“…The mass transport modeling during cryopreservation is divided into: (1) macroscale flow and (2) cell-level transfer. To model the mass transfer phenomenon on a macroscale, Fick's second law is used, which determines the local concentration over time caused by diffusion [12,25,[28][29][30][31]45]. Sometimes, Fick's second law is complemented by a velocity vector, which is defined by, e.g., the Navier-Stokes equation [11,17,34,46].…”

Nonideal Solute Chemical Potential Equation and the Validity of the Grouped Solute Approach for Intracellular Solution Thermodynamics

“…The modeling of aqueous solution thermodynamicsboth water and solute chemical potentialshas applications in a number of different fields, including biomolecule separation, microdrop concentrating processes, − the study of micelle formation, , and the primary focus of this work, that is, cryopreservation. − Recently, a form of the multisolute osmotic virial equation has been demonstrated to have wide-ranging success in predicting water chemical potential in aqueous solutions. ,,− In this work, we address two key theoretical aspects of this practically important model in the general context of its application to cellular cryopreservation: (i) we derive a novel and required equation for solute chemical potential that is thermodynamically consistent with the molality-based form of the osmotic virial equation, and (ii) we provide a proof that the “grouped solute” modeling approach, practically necessary to model the cellular cytoplasm, is mathematically rigorous.…”