Modelling and experimental studies on mass transport of multiple cryoprotective agents in articular cartilage

Cartilage transplantation is an effective way to repair, reconstruct, and replace damaged articular cartilage (AC) but its use is limited by the inability to preserve AC for long periods of time. Vitrification is an ideal choice for long-term storage of AC, and multiple cryoprotective agents (CPAs) with high concentration are usually used. To obtain high cell viability, chondrocytes at all locations inside AC should be protected properly by the CPAs during cooling and rewarming. Hence, it is important to know the mass transport properties of multiple CPAs as they synergistically infiltrate AC. In this study, a mathematical model to describe the mass transport behavior of multiple CPAs in AC was developed based on the mixture-averaged diffusion model. In addition, a methodology for the simultaneous determination of dimethyl sulfoxide, glycerol, ethylene glycol, and propylene glycol by carbon-13 nuclear magnetic resonance was established. The model is applicable for predicting single- and multiple-CPA permeation into AC, and its accuracy was verified by a massive experimental dataset. Simulation results showed reverse diffusion in the multiple-CPA permeation process, which was not found in the single-CPA permeation process. This curious phenomenon shows the sharp contrast between the diffusion behavior of a binary mixture and a multicomponent mixture.