Network Thermodynamic Model of Coupled Transport in a Multicellular Tissue ‐ The Islet of Langerhans^a

Abstract

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'.

Mathematical model formulation and validation of water and solute transport in whole hamster pancreatic islets

“…Moreover, the network thermodynamic models described first by Schreuders et al [9] and used to model whole pancreatic islets by de Freitas et al [10, 45] are considerably simplified in the sense that they use compartmentalized flux models to reduce the spatial dependence to a system of coupled ordinary differential equations where spatial scales are ignored. This approach has the benefit of being considerably easier to solve numerically, but loses generality in the application of diffusion models, such as the simple porous media model used here.…”

“…Subsequently Schreuders et al [9] again used pseudo bond graph and network thermodynamics to model diffusion through a tissue and show that the effects of coupling on the multiple species present in the model is significant. Later, de Frietas et al expanded a network thermodynamics model of transport in islet cells to model solute and solvent transport in islets of Langerhans [10]. …”

Intracellular Ice Formation in Three-Dimensional Tissues: Pancreatic Islets

“…1 Independent experiments on a perfusion cryomicroscope have demonstrated a well-defined osmotic behavior during exposure of islets to a solution having an elevated solute concentration, and in the absence of freezing, in which there is significant net volume loss integrated over the entire islet, as shown in Figure 1. 2 This behavior implies that mass transport occurs through the entire volume as a partitioned continuum. A discrete model has been developed to describe islet osmotic behavior as a combination of extracellular diffusion and cell membrane transport in a three-dimensional space, 2 and it has been applied via inverse solution methods for analysis of controlled experimental data to determine the values of relevant transport properties for both water and CPAs.…”

“…2 This behavior implies that mass transport occurs through the entire volume as a partitioned continuum. A discrete model has been developed to describe islet osmotic behavior as a combination of extracellular diffusion and cell membrane transport in a three-dimensional space, 2 and it has been applied via inverse solution methods for analysis of controlled experimental data to determine the values of relevant transport properties for both water and CPAs.…”

“…The occurrence of IIF is a function in part of the osmotic history of the system, and we have previously developed a model for this phenomenon based on the principles of network thermodynamics. 2 The present challenge is to incorporate ice nucleation theory into a comprehensive description of tissue behavior in the sequence of physical states encountered during freezing. Cryopreservation has been applied…”