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