Effect of microscale phenomena on phase change in tissues

A numerical model for predicting 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 liberation of latent heat due to phase change in the medium is assumed to be rate-limited by the cellular-level biophysical processes of water transport and intracellular ice formation (IIF). Well-accepted models for the biophysical processes are adopted from the literature to calculate the amount of phase change occurring at each location (control volume) in the domain as a function of temperature and time. These biophysical models are used in an iterative source term matching algorithm to determine the proper latent heat source term value in the heat transfer model. In this way, the latent heat release for each control volume in the domain is determined by the cellular water transport and IIF processes (a coupled thermal/biophysical approach), instead of the commonly-adopted scheme of assuming a priori a temperature-dependence of latent heat release, Λ(T) (an uncoupled approach). The coupled model is applied to two freezing problems, analogous to cryopreservation and cryosurgery, using the thermal properties of water and the biophysical properties of rat liver tissue (taken from the literature). Thermal histories predicted by the model are compared to predictions of an enthalpy-method model in which 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 rat liver during freezing do little to limit the rate at which phase change can occur, and that the uncoupled approach to numerical solution would be adequate to accurately determine thermal history for this case.