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FEM-based oxygen consumption and cell viability models for avascular pancreatic islets.

ABSTRACT: The function and viability of cultured, transplanted, or encapsulated pancreatic islets is often limited by hypoxia because these islets have lost their vasculature during the isolation process and have to rely on gradient-driven passive diffusion, which cannot provide adequate oxygen transport. Pancreatic islets (islets of Langerhans) are particularly susceptible due to their relatively large size, large metabolic demand, and increased sensitivity to hypoxia. Here, finite element method (FEM) based multiphysics models are explored to describe oxygen transport and cell viability in avascular islets both in static and in moving culture media.Two- and three-dimensional models were built in COMSOL Multiphysics using the convection and diffusion as well as the incompressible Navier-Stokes fluid dynamics application modes. Oxygen consumption was assumed to follow Michaelis-Menten-type kinetics and to cease when local concentrations fell below a critical threshold; in a dynamic model, it was also allowed to increase with increasing glucose concentration.Partial differential equation (PDE) based exploratory cellular-level oxygen consumption and cell viability models incorporating physiologically realistic assumptions have been implemented for fully scaled cell culture geometries with 100, 150, and 200 microm diameter islets as representative. Calculated oxygen concentrations and intra-islet regions likely to suffer from hypoxia-related necrosis obtained for traditional flask-type cultures, oxygen-permeable silicone-rubber membrane bottom cultures, and perifusion chambers with flowing media and varying incoming glucose levels are presented in detail illustrated with corresponding colour-coded figures and animations.Results of the computational models are, as a first estimate, in good quantitative agreement with existing experimental evidence, and they confirm that during culture, hypoxia is often a problem for non-vascularised islet and can lead to considerable cell death (necrosis), especially in the core region of larger islets. Such models are of considerable interest to improve the function and viability of cultured, transplanted, or encapsulated islets. The present implementation allows convenient extension to true multiphysics applications that solve coupled physics phenomena such as diffusion and consumption with convection due to flowing or moving media.

SUBMITTER: Buchwald P

PROVIDER: S-EPMC2678100 | biostudies-literature | 2009 Apr

REPOSITORIES: biostudies-literature

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FEM-based oxygen consumption and cell viability models for avascular pancreatic islets.

Buchwald Peter P

Theoretical biology & medical modelling 20090416

<h4>Background</h4>The function and viability of cultured, transplanted, or encapsulated pancreatic islets is often limited by hypoxia because these islets have lost their vasculature during the isolation process and have to rely on gradient-driven passive diffusion, which cannot provide adequate oxygen transport. Pancreatic islets (islets of Langerhans) are particularly susceptible due to their relatively large size, large metabolic demand, and increased sensitivity to hypoxia. Here, finite ele ...[more]

PMID: 19371422

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Project description:BACKGROUND: Because insulin is the main regulator of glucose homeostasis, quantitative models describing the dynamics of glucose-induced insulin secretion are of obvious interest. Here, a computational model is introduced that focuses not on organism-level concentrations, but on the quantitative modeling of local, cellular-level glucose-insulin dynamics by incorporating the detailed spatial distribution of the concentrations of interest within isolated avascular pancreatic islets. METHODS: All nutrient consumption and hormone release rates were assumed to follow Hill-type sigmoid dependences on local concentrations. Insulin secretion rates depend on both the glucose concentration and its time-gradient, resulting in second-and first-phase responses, respectively. Since hypoxia may also be an important limiting factor in avascular islets, oxygen and cell viability considerations were also built in by incorporating and extending our previous islet cell oxygen consumption model. A finite element method (FEM) framework is used to combine reactive rates with mass transport by convection and diffusion as well as fluid-mechanics. RESULTS: The model was calibrated using experimental results from dynamic glucose-stimulated insulin release (GSIR) perifusion studies with isolated islets. Further optimization is still needed, but calculated insulin responses to stepwise increments in the incoming glucose concentration are in good agreement with existing experimental insulin release data characterizing glucose and oxygen dependence. The model makes possible the detailed description of the intraislet spatial distributions of insulin, glucose, and oxygen levels. In agreement with recent observations, modeling also suggests that smaller islets perform better when transplanted and/or encapsulated. CONCLUSIONS: An insulin secretion model was implemented by coupling local consumption and release rates to calculations of the spatial distributions of all species of interest. The resulting glucose-insulin control system fits in the general framework of a sigmoid proportional-integral-derivative controller, a generalized PID controller, more suitable for biological systems, which are always nonlinear due to the maximum response being limited. Because of the general framework of the implementation, simulations can be carried out for arbitrary geometries including cultured, perifused, transplanted, and encapsulated islets.

Project description:Oxygen levels in cancerous tissue can have a significant effect on treatment response: hypoxic tissue is both more radioresistant and more chemoresistant than well-oxygenated tissue. While recent advances in medical imaging have facilitated real-time observation of macroscopic oxygenation, the underlying physics limits the resolution to the millimetre domain, whereas oxygen tension varies over a micrometre scale. If the distribution of oxygen in the tumour micro-environment can be accurately estimated, then the effect of potential dose escalation to these hypoxic regions could be better modelled, allowing more realistic simulation of biologically adaptive treatments. Reaction-diffusion models are commonly used for modelling oxygen dynamics, with a variety of functional forms assumed for the dependence of oxygen consumption rate (OCR) on cellular status and local oxygen availability. In this work, we examine reaction-diffusion models of oxygen consumption in spherically and cylindrically symmetric geometries. We consider two different descriptions of oxygen consumption: one in which the rate of consumption is constant and one in which it varies with oxygen tension in a hyperbolic manner. In each case, we derive analytic approximations to the steady-state oxygen distribution, which are shown to closely match the numerical solutions of the equations and accurately predict the extent to which oxygen can diffuse. The derived expressions relate the limit to which oxygen can diffuse into a tissue to the OCR of that tissue. We also demonstrate that differences between these functional forms are likely to be negligible within the range of literature estimates of the hyperbolic oxygen constant, suggesting that the constant consumption rate approximation suffices for modelling oxygen dynamics for most values of OCR. These approximations also allow the rapid identification of situations where hyperbolic consumption forms can result in significant differences from constant consumption rate models, and so can reduce the computational workload associated with numerical solutions, by estimating both the oxygen diffusion distances and resultant oxygen profile. Such analysis may be useful for parameter fitting in large imaging datasets and histological sections, and allows easy quantification of projected differences between functional forms of OCR.

Project description:BACKGROUND:Oxygen consumption reflects multiple processes in pancreatic islets including mechanisms contributing to insulin secretion, oxidative stress and viability, providing an important readout in studies of islet function, islet viability and drug testing. Due to the scarcity, heterogeneity, and intrinsic kinetic properties of individual islets, it would be of great benefit to detect oxygen consumption by single islets. We present a novel method we have developed to image oxygen in single islets. METHODOLOGY/PRINCIPAL FINDINGS:Using a microfluidics system, individual islets and a fluorescent oxygen-sensitive dye were encased within a thin alginate polymer layer. Insulin secretion by the encapsulated islets was normal. Fluorescent signal from the encased dye, detected using a standard inverted fluorescence microscope and digital camera, was stable and proportional to the amount of oxygen in the media. When integrated into a perifusion system, the sensing system detected changes in response to metabolic substrates, mitochondrial poisons, and induced-oscillations. Glucose responses averaged 30.1±7.1% of the response to a metabolic inhibitor (cyanide), increases were observed in all cases (n = 6), and the system was able to resolve changes in oxygen consumption that had a period greater than 0.5 minutes. The sensing system operated similarly from 2-48 hours following encapsulation, and viability and function of the islets were not significantly affected by the encapsulation process. CONCLUSIONS/SIGNIFICANCE:An oxygen-dependent dye situated around and within a pancreatic islet encapsulated by a thin layer of alginate was sensitive to changes in oxygen consumption, and was not harmful to the function or viability of islets over the course of two days. The microcapsule-based sensing method is particularly suited to assessing the effects of compounds (dose responses and time courses) and chronic changes occurring over the course of days. The approach should be applicable to other cell types and dyes sensitive to other biologically important molecules.

Dataset Information

FEM-based oxygen consumption and cell viability models for avascular pancreatic islets.

Publications

FEM-based oxygen consumption and cell viability models for avascular pancreatic islets.

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