Network thermodynamic modeling via bond graphs was used to describe the water and cryoprotectant additive (CPA) transport in a multicellular tissue. The model is presented as a tool to understand the osmotic behavior of the islets of Langerhans when exposed to ternary aqueous solutions containing an electrolyte and a CPA. It accounts for the effects of the location of cells within the tissue and an interstitial matrix, plus differential permeabilities to water and CPA. The interstitial matrix was assumed to be a porous medium able to store the chemical species being transported. Controlled osmotic stress experiments were conducted on isolated rat pancreas islets to measure the transient volumetric response to step-wise changes in dimethyl sulfoxide, Me2SO, concentration. The model provides a tool for predicting the transient volumetric response of peripheral and interior cells and of interstitial tissue, as well as the build up of solute concentration, during addition and removal of CPAs and freezing and thawing protocols. Inverse solution methods were applied to determine values for standard cell membrane permeability parameters Lp, omega and sigma as well as for the interstitial flow conductivities Kw and Kp'.

The introduction and removal of cryoprotective agents (CPA) to a kidney via vascular perfusion may induce changes in cell volume that are destructive to the tubular epithelial or capillary endothelial cells as well as causing significant increases in vascular resistance that compromise the perfusion process. A network thermodynamic model of the coupled osmotic, hydrodynamic and elastic properties of the kidney was applied to evaluate the sensitivity of these critical outputs to a set of physiological and perfusion variables. Simulation results suggest that in the design of perfusion protocols for CPAs such as glycerol, it may be advantageous to: (a) select a CPA with as high a cell membrane permeability as possible; (b) increase the concentration of mannitol in the perfusate to about 200 mos/kg, beyond which there is no discernible benefit; (c) when glycerol is the CPA, limit the rate of reduction in the perfusate during removal to 30 mM/min or less; (d) limit the perfusion pressure to 20-30 mm Hg, within the practical constraints of the perfusion system; (e) increase the concentration of impermeant in the perfusate to as high as 400 mos/kg, although it is recognized that this departure from plasma-like composition might impose other problems that are not considered in this model. Further, it was observed that the vascular membrane permeability plays a relatively minor role in controlling cellular osmotic injury and vascular perfusion resistance and is therefore not a critical parameter in the perfusion design process.

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A network thermodynamic model has been devised to describe the coupled movement of water and a permeable additive within a kidney during perfusion under the combined action of diffusive, hydrodynamic, and mechanical processes. The model has been validated by simulating perfusions with Me2SO, glycerol, and sucrose and comparing predicted weight and vascular resistance with experimental results obtained by Pegg (1993). The flows of CPA, water, colloid, and cellular impermeants are governed by a combination of the individual osmotic potential and pressure differences between compartments of the kidney, the viscoelastic behavior of the tissue, and the momentum transferred between the flows. The model developed in this study presents an analytical tool for understanding the dynamics of the perfused kidney system and for modifying perfusion protocols to minimize the changes in cell volume, internal pressure build-up, and increases in vascular resistance that currently present barriers to the successful perfusion of organs.