Modeling of cryopreservation of engineered tissues with one-dimensional geometry

Long-term storage of engineered bio-artificial tissues is required to ensure the off-the-shelf availability to clinicians due to their long production cycle. Cryopreservation is likely the choice for long-term preservation. Although the cryopreservation of cells is well established for many cell types, cryopreservation of tissues is far more complicated. Cells at different locations in the tissue could experience very different local environmental changes, i.e., the change of concentration of cryoprotecting chemicals (CPA) and temperature, during the addition/removal of CPA and cooling/warming, which leads to nonuniformity in cell survival in the tissue. This is due to the limitation of mass and heat transfer within the tissue. A specific aim of cryopreservation of tissue is to ensure a maximum recovery of cells and their functionality throughout a tissue. Cells at all locations should be protected adequately by the CPA and frozen at rates conducive to survival. It is hence highly desirable to know the cell transient and final states during cryopreservation within the whole tissue, which can be best studied by mathematical modeling. In this work, a model framework for cryopreservation of one-dimensional artificial tissues is developed on the basis of solving the coupled equations to describe the mass and heat transfer within the tissue and osmotic transport through the cell membrane. Using an artificial pancreas as an example, we carried out a simulation to examine the temperature history, cell volume, solute redistribution, and other state parameters during the freezing of the spherical heterogeneous construct (a single bead). It is found that the parameters affecting the mass transfer of CPA in tissue and through the cell membrane and the freezing rate play dominant roles in affecting the cell volume transient and extracellular ice formation. Thermal conductivity and extracellular ice formation kinetics, on the other hand, have little effect on cell transient and final states, as the heat transfer rate is much faster than mass diffusion. The outcome of such a model study can be used to evaluate the construct design on its survivability during cryopreservation and to select a cryopreservation protocol to achieve maximum cell survival.