Effect of Microscale Mass Transport and Phase Change on Numerical Prediction of Freezing in Biological Tissues

Abstract

A numerical model incorporating the microscale heat and mass transport in biological tissue during freezing is developed. The heat transfer problem is formulated in a general one-dimensional coordinate system (cartesian, cylindrical or spherical), and a finite control volume discretization is used. The latent heat release for each control volume in the domain is determined by the cellular water transport and intracellular ice formation processes occurring there (a coupled thermal/biophysical approach). The coupled model is applied to two cryobiological freezing problems, with different geometry and boundary conditions. The temperature dependent thermal properties of water and the biophysical properties of two biological tissues, normal rat liver and Dunning AT-1 rat prostate tumor tissue are used to simulate both the micro and macroscale freezing processes. A major advantage of the coupled thermal/biophysical model is its unique ability to predict both the macroscale thermal response and the microscale biophysical response at various locations within the tissue domain during a freezing process, simultaneously. Thermal histories predicted by the coupled model are compared to predictions of a standard enthalpy-method model in which the temperature dependence of the latent heat release, Λ(T) is an explicit function adapted from the water-NaCl phase diagram, and phase change is not rate-limited by microscale biophysical processes (i.e., an uncoupled approach). The results for both models are very similar; this suggests that the microscale biophysical processes which occur in the chosen biological tissues during freezing do little to limit the rate at which phase change occurs. Additional simulations suggest that the predicted macroscale thermal history results are not significantly affected (<2 percent variation) even with significantly altered biophysical parameters (i.e., a factor of 100 times lower or higher), as long as the magnitude of the latent heat is constant.