Our approach relied on measurement
Our approach relied on measurement of bulk solute diffusivity in the three tissue types of interest. Our diffusivity values (Table 3) are on the order of 10−6 cm2/s and are comparable to the PG diffusion coefficient in water at infinite dilution, which is about 10−5 cm2/s at room temperature, as well as the diffusivity at a PG mole fraction of 0.2, which is about 5 × 10−6 cm2/s . We also note that the skin tissue has a diffusivity value that is half that of the other tissues. This might be related to the dense packing of the epidermis layer in skin when compared with myometrial and fibroid tissues. While our desorption curves were well-fit by our simple linear diffusion model, we note that, at the very least, diffusivity is typically considered a function of concentration  and that we do not model the interaction among the CPA and the apoptosis pathway media nonpermeating solutes. It would be more appropriate to use a transport model that accounts for the salt, water, and CPA concentrations throughout. In fact, our approach neglecting the movement of salt and water is limiting in some ways because our previous work on CPA equilibration optimization , , ,  relied on media containing only CPA, instead of including standard nonpermeating solutes. By omitting the nonpermeating solute in these studies, an additional 300 mOsm of permeating solute could be used at each step, increasing the speed at which equilibration occurred. This more complete model is a subject of our future work. In the present study we demonstrate that a clear choice exists between minimal time and minimal toxicity protocols. Minimal time protocols are simply constrained by the osmotic tolerance limit constraint: in their absence a minimal time optimal equilibration protocol would be to place the tissue in a media of concentration Cmax until the mass transfer model predicts that the center of the tissue has concentration CD. In fact, because of this, minimal time protocols can be predicted using the much simpler single cell dynamics. One could then use the minimal time optimal protocols that use continuous concentration controls instead of multistep protocols (see e.g. Benson et al. ). Considerable gains in time-saving could be made in this case. On the other hand, we have defined a concentration and time dependent tissue equilibration cost function dependent on a parameter . In fact, in our previous work on endothelial cells , we showed that there is a clear delineation between protocols where and. Optimal equilibration protocols based on this cost function are much different from those of time-optimal () protocols. In particular, the time optimal approaches drive the exterior cells to their minimal volume at each step, and in so doing achieve the maximum extratissue concentration in minimal time. In contrast, the toxicity optimal approaches achieve a high extratissue concentration in a longer time, followed by backing off to the desired concentration near the end of the protocol. This approach reduces the exposure of the exterior cells to unnecessarily high concentrations. This is seen most clearly in Fig. 2, where the predicted toxicity accumulated is focused and considerably higher on the exterior of the tissue for the time-optimal method, whereas there is less localized damage in the toxicity optimal protocol. Additionally, our results provide a rational explanation for the successful approach to cartilage cryopreservation developed by Jomha et al., who equilibrate the CPA in a “wave”, where successively increasing concentration steps are followed by a final lower step that allows the CPA to distribute throughout the tissue . In future publications we will explore the effects of the value of on the resultant optimal protocols. Moreover, considerable improvements in post-equilibration recovery were made in our previous work with plated endothelial cells when the use of more than one temperature was made available. Therefore, considerable work is needed to explore the temperature dependence of these parameters, as well as the effects of the relative magnitude of these parameters.