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

Abstract

Optimization of cryopreservation protocols for cells and tissues requires accurate models of heat and mass transport. Model selection often depends on the configuration of the tissue. Here, a mathematical and conceptual model of water and solute transport for whole hamster pancreatic islets has been developed and experimentally validated incorporating fundamental biophysical data from previous studies on individual hamster islet cells while retaining whole-islet structural information. It describes coupled transport of water and solutes through the islet by three methods: intracellularly, intercellularly, and in combination. In particular we use domain decomposition techniques to couple a transmembrane flux model with an interstitial mass transfer model. The only significant undetermined variable is the cellular surface area which is in contact with the intercellularly transported solutes, Ais. The model was validated and Ais determined using a 3 × 3 factorial experimental design blocked for experimental day. Whole islet physical experiments were compared with model predictions at three temperatures, three perfusing solutions, and three islet size groups. A mean of 4.4 islets were compared at each of the 27 experimental conditions and found to correlate with a coefficient of determination of 0.87 ± 0.06 (mean ± S.D.). Only the treatment variable of perfusing solution was found to be significant (p < 0.05). We have devised a model that retains much of the intrinsic geometric configuration of the system, and thus fewer laboratory experiments are needed to determine model parameters and thus to develop new optimized cryopreservation protocols. Additionally, extensions to ovarian follicles and other concentric tissue structures may be made.

Toxicity Minimized Cryoprotectant Addition and Removal Procedures for Adherent Endothelial Cells

“…First, tissues may have multiple cell types that have differential membrane transport kinetics, toxicity rates or osmotic tolerance characteristics. Additionally, these three dimensional structures require more complicated transport models and may require models that account for biomechanical effects [ 43 ] or cell-cell, cell-interstitium, and interstitial transport [ 44 ]. Once a suitable transport model is determined, a cost function must be defined that accounts for the chemical toxicity and osmotic damage experienced by each cell in the tissue, as well as the potential effects of tissue level mechanical stresses.…”

A Mathematical Framework for Developing Freezing Protocols in the Cryopreservation of Cells

“…In general, we expect all these parameters to decrease as the temperature decreases. Looking at activation energies [8,15], we note that the activation energies for diffusivities are smaller than those for membrane permeability. Hence, the distinct timescales in §3 will separate rather than coalesce as the temperature decreases, maintaining the asymptotic structure that we identified in the main text.…”

“…Universal gas constant σ 0.65 [8] CPA reflection coefficient at cell membranẽ X 0 1 × 10 3 mol m −3 [34] Initial CPA concentration (intra and extra) Y 0 1 × 10 2 mol m −3 [23] Initial ion concentration (intra and extra)…”

“…However, as noted previously [1], the spatial variation of important physical quantities, such as the location of the freezing front and the CPA concentration through the system, are not typically taken into account in the KK equations. Although there are some exceptions (see, for example, [8,16,24]), most currently available spatial models only consider some aspect of spatial dependence, and rely on numerical simulations to solve them. The aim of this paper is to provide a model that accounts for the spatial dependence of temperature and chemical concentration and to systematically deduce the conditions under which simpler ODE models are applicable.…”

Sensing and Sensibility: Single‐Islet‐based Quality Control Assay of Cryopreserved Pancreatic Islets with Functionalized Hydrogel Microcapsules

“…In the last two decades, numerous work has been performed to improve the islet viability and functionality with cryopreservation procedures by investigating fundamental cryobiological mechanisms, [31][32][33] exploring different cryoprotectants, [34][35][36] pre-and postculture with different cells, antioxidants or kinase inhibitor during the cryoprocedures, [37][38][39][40] developing novel technology and integrated devices for islet encapsulation with cryopreservation, [ 41 ] exploring alternative cryopreservation approaches by vitrifi cation. [42][43][44][45] Recently, a study of 20 year cryogenic banking of islets showed that the cryopreserved islets retained some functions, but the capability of reversing diabetes was limited due to reduced insulin content.…”