Abstract
The current standard method for organ preservation is Static Cold Storage (SCS) which allows for preservation times of up to 12-16 hours for livers. This time constraint limits the availability of donor organs for transplantation which is the only cure for end-stage organ failure. Different techniques are being studied for their potential to improve preservation times, and the most promising is cryopreservation. This method involves freezing a biological material to subzero temperatures where metabolic functions are completely halted without significantly affecting its viability when thawed. Mathematical modeling of the thermal history during this procedure can provide better insight into the injury mechanisms that occur during this process and help to improve cryopreservation techniques. The goal of this work was to create a numerical model to predict the freezing and thawing profile of a liver perfused with a cryoprotective agent (CPA). A one-dimensional model of heat transfer and phase change was developed, where the finite-difference and enthalpy methods were used for numerical solution. The enthalpy method was extended to model freezing cases for binary solutions. This model was validated using the analytical solutions for the plane wall with convection and Stefan problem with phase change, then a grid refinement study was carried out to establish mesh convergence. The model was then used to predict the thermal profiles for freezing experiments of rat livers loaded with different solutions and the numerical results showed very good agreement with the experimental data. The results also showed that the rat livers perfused with the University of Wisconsin (UW) solution behaved differently compared to the ones loaded with the UW + 12% Propylene Glycol (PG) solution, as the UW + 12%PG solution has a lower freezing point and undergoes binary freezing. Parametric studies were done to examine the effects of varying some important parameters for the liver freezing process. The temperature profiles for rat liver thawing experiments were also modeled. The results showed that the numerical model was not able to successfully capture the temperature gradient within the liver shown by the experimental data, and further investigation needs to be carried out to incorporate the missing thermal resistance effect into the model. This work gives new insight into the freezing behavior of livers loaded with a binary solution, and there is potential to improve the modeling capabilities of this numerical scheme, including scaling up to multiple dimensions and incorporating mass transfer effects into the model.