Network thermodynamic model of coupled transport in a multicellular tissue--the islet of Langerhans.

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'.