Droplet based vitrification for cell aggregates: Numerical analysis

Crystallisation Degree Analysis during Cryopreservation of Biological Tissue Applying Interval Arithmetic

This paper presents the numerical modelling of heat transfer and changes proceeding in the homogeneous sample, caused by the crystallisation phenomenon during cryopreservation by vitrification. Heat transfer was simulated in a microfluidic system in which the working fluid flowed in micro-channels. The analysed process included single-phase flow during warming, and two-phase flow during cooling. In the model under consideration, interval parameters were assumed. The base of the mathematical model is given by the Fourier equation, with a heat source including the degree of ice crystallisation. The formulated problem has been solved using the interval version of the finite difference method, with the rules of the directed interval arithmetic. The fourth order Runge-Kutta algorithm has been applied to determine the degree of crystallisation. In the final part of this paper, examples of numerical computations are presented.

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

In the present paper, numerical modelling of heat and mass transfer proceeding in a two-dimensional axially symmetrical articular cartilage sample subjected to a cryopreservation process is presented. In the model under consideration, interval parameters were assumed. The heat transfer process is described using the Fourier interval equation, while the cryoprotectant transport (DMSO) across the cell membrane is analyzed using a two-parameter model taking into account the simulation of the water volume in the chondrocytes and the change in DMSO concentration over time. The liquidus tracking (LT) protocol introduced by Pegg et al. was used to model the cryopreservation process. This procedure divides the heating and cooling phases into eight and seven steps, respectively, allowing precise regulation of temperature and cryoprotectant (CPA) concentration of bathing solutions. This protocol protects chondrocytes from ice crystal, osmotic stress, and electrolyte damage. The obtained interval concentrations of cryoprotectant in chondrocytes were compared with previous simulations obtained using the deterministic model and they are mostly in agreement with the simulation data.

high-throughput droplet vitrification of stallion sperm using permeating cryoprotective agents

Stallion sperm is typically cryopreserved using low cooling rates and low concentrations of cryoprotective agents (CPAs). The inevitable water-to-ice phase transition during cryopreservation is damaging and can be prevented using vitrification. Vitrification requires high cooling rates and high CPA concentrations. In this study, the feasibility of stallion sperm vitrification was investigated. A dual-syringe pump system was used to mix sperm equilibrated in a solution with a low concentration of CPAs, with a solution containing a high CPA concentration, and to generate droplets of a defined size (i.e., ~20 μL) that were subsequently cooled by depositing on an aluminum alloy block placed in liquid nitrogen. Mathematical modeling was performed to compute the heat transfer and rate of cooling. The minimum CPA concentration needed for vitrification was determined for various CPAs (glycerol, ethylene glycol, propylene glycol, dimethyl sulfoxide) and combinations thereof, while effects of droplet size and carrier solution were also identified. Sperm vitrification was eventually done using a glycerol/propylene glycol (1/1) mixture at a final concentration of 45% in buffered saline supplemented with 3% albumin and polyvinylpyrrolidon, while warming was done in standard diluent supplemented with 100 mM sucrose. The sperm concentration was found to greatly affect sperm membrane integrity after vitrification-and-warming, i.e., was found to be 21 ± 12% for 10 × 10⁶ sperm mL^-1 and 54 ± 8% for 1 × 10⁶ sperm mL^-1. However, an almost complete loss of sperm motility was observed. In conclusion, successful sperm vitrification requires establishing the narrow balance between droplet size, sperm concentration, CPA type and concentration, and exposure time.

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

In the paper, the numerical analysis of heat and mass transfer proceeding in an axially symmetrical articular cartilage sample subjected to the cryopreservation process is presented. In particular, a two-dimensional (axially symmetrical) model with imprecisely defined parameters is considered. The base of the heat transfer model is given by the interval Fourier equation and supplemented by initial boundary conditions. The phenomenon of cryoprotectant transport (Me2SO) through the extracellular matrix is described by the interval mass transfer equation. The liquidus-tracking (LT) method is used to control the temperature, which avoids the formation of ice regardless of the cooling and warming rates. In the LT process, the temperature decreases/increases gradually during addition/removal of the cryoprotectant, and the articular cartilage remains on or above the liquidus line so that no ice forms, independent of the cooling/warming rate. The discussed problem is solved using the interval finite difference method with the rules of directed interval arithmetic. Examples of numerical computations are presented in the final part of the paper. The obtained results of the numerical simulation are compared with the experimental results, realized for deterministically defined parameters.