The parameter conversion from the Kedem-Katchalsky model into the two-parameter model

Cryopreservation is an important process for preserving cells and tissues. The process itself can, however, cause damage to cells and tissues. During addition and removal of a cryoprotective agent (CPA), cells are subjected to imbalanced osmotic pressures between the intracellular and extracellular solutions. Cells can be injured if these shrinkage and swelling events are beyond their tolerable limits. The characteristics of the cell volume changes during these processes depend on the types of CPA, the methods of adding and removing of the CPA and the permeability of cells to CPA and water. The typical models of this transportation are the two-parameter (2-p) model and the Kedem-Katchalsky (K-K) model. The K-K model is more general than the 2-p model. However, there is evidence that in many cases water and CPAs do not permeate through common pathways, hence the use of the reflection coefficient in the K-K model may be unnecessary and in some cases it may create conceptual errors. Therefore, the 2-p model is more suitable for use as a transport model than the K-K model. The aim of this study is to use the values of the K-K model parameters from data in the literature to calculate the corresponding parameters for the 2-p model. The results from these simulations demonstrate that the cell volume changes during CPA addition and removal from the K-K model can be closely estimated by the 2-p model.