Mathematical modeling of donor liver cooling during hypothermic perfusion

Proper cooling of donor liver is critical for transplantation, as it extends organ viability and minimizes tissue damage. Our mathematical model, although simplified, revealed that standard cooling methods do not provide uniformity: cooling rates of different liver regions vary significantly. This creates a risk of temperature gradient within the organ and uneven ischemic tissue damage. The results emphasize the need to improve cooling techniques to ensure more uniform temperature distribution in the donor organ. Objective. Development of a mathematical model to optimize donor liver cooling and minimize the risk of ischemia-reperfusion injury. Materials and methods. For modeling the liver cooling process, the Navier-Stokes equation system was used, accounting for porous media and heat transfer parameters. The calculations employed a standard cooling method with coolant delivery through the hepatic artery at constant pressure and temperature. The study was performed using the PHOENICS software package, which provided dynamic data on coolant flow velocity, pressure distribution, temperature, and temperature gradients within the liver over time. The model considers the anatomical features of the liver and the main characteristics of the vascular network. Results. Numerical modeling showed that liver cooling occurs unevenly. Segments located closer to the coolant inlet cool first, while distant segments reach optimal temperature significantly later. The temperature difference between various segments during cooling reaches critical values, which may lead to heterogeneous ischemic damage. Complete cooling of the organ in the proposed model occurs within 720 seconds, with significant temperature gradients observed between central and peripheral areas of the liver throughout most of the cooling process. Conclusions. Existing liver cooling methods require optimization to ensure uniform temperature distribution across all segments. A modification of the technique using variable coolant supply pressure and multipoint perfusion is proposed. The resulting mathematical model can be used to develop improved cooling methods for donor organs, which will enhance their preservation, reduce the risk of ischemiareperfusion injury, and improve transplantation outcomes. Further development of the model involves accounting for more detailed anatomical features and physiological parameters of the liver.