Abstract
ABSTRACT
Devireddy et al. [1] previously showed that an enthalpy-based, macroscale model simulated tissue freezing histories are in close agreement with a coupled model incorporating cellular water transport and intracellular ice formation (IIF). That comparison, however, was performed for a limited set of tissue geometries, cooling conditions, and biophysical parameters. Here, we revisit that conclusion by reimplementing the published model from its governing equations and systematically expanding the parameter space to determine when microscale processes alter the predicted macroscale freezing response. We incorporate both surface-catalyzed nucleation (SCN) and volume-catalyzed nucleation (VCN) of intracellular ice with cellular osmotic dehydration and examine a broad range of tissue dimensions, cooling rates, convective boundary conditions, membrane permeabilities, cell sizes, activation energies, intracellular water fractions, and nucleation rates. Linearization of the cellular water-transport equation about osmotic equilibrium yields an osmotic relaxation time (
τ
osm
) that can be compared with the local residence time of tissue undergoing phase change (
τ
res
). Their ratio defines a dimensionless group, ∏, that organizes the transition between regimes in which the uncoupled enthalpy formulation and the coupled micro–macroscale formulation produce similar or substantially different results. Across the one-dimensional parameter space examined here, the two models remain within a prescribed thermal-error bound for ∏ below approximately 0.1, whereas the discrepancy increases systematically above this threshold. Model divergence also depends on intracellular ice nucleation, i.e., when nucleation is sufficiently slow, cellular water transport can become rate-limiting for latent-heat release. Conversely, sufficiently rapid intracellular ice formation reduces the macroscopic discrepancy by providing an additional pathway for latent-heat release. Multidimensional simulations further show that geometry alone can move a nominally conventional freezing protocol into the coupled regime. In particular, multidirectional cooling can reduce the local residence time sufficiently to produce substantial differences in predicted frozen volume even when the corresponding thermal histories appear similar. Finally, we formulate an inverse approach for estimating IIF parameters from tissue-scale thermal histories. Synthetic simulations indicate that parameter recovery is feasible within a finite range of cooling conditions, providing a testable strategy for future experimental measurements. Together, these results provide a mechanistic criterion for deciding when microscale biophysical processes must be retained in macroscale tissue-freezing models.
Abstract Figure
Graphical Abstract
The design space for tissue freezing is illustrated as a function of a non-dimensional grouping parameter, distinguishing between the uncoupled (equilibrium) model and the coupled micro–macro-scale model. Cooling conditions corresponding to grouping values below 0.1 can be adequately described using the uncoupled model, whereas values above 0.1 require the coupled micro–macro-scale tissue-freezing model. The critical value of 0.1 is established based on a maximum acceptable temperature difference of 3 K between the two models. The operating point reported in the 2002 study lies approximately two orders of magnitude within the uncoupled regime and is indicated by a star. In contrast, an 8 mm cube cooled on all six faces falls within the coupled regime and is represented by a red dot.
Nomenclature
1