Mathematical predictions of oxygen availability in micro- and macro-encapsulated human and porcine pancreatic islets

Optimal function of immunoisolated islets requires adequate supply of oxygen to metabolically active insulin producing beta-cells. Using mathematical modeling, we investigated the influence of the pO2 on islet insulin secretory capacity and evaluated conditions that could lead to the development of tissue anoxia, modeled for a 300 μm islet in a 500 μm microcapsule or a 500 μm planar, slab-shaped macrocapsule. The pO2 was used to assess the part of islets that contributed to insulin secretion. Assuming a 500 μm macrocapsule with a 300 μm islet, with oxygen consumption rate (OCR) of 100-300 nmol min-1 mg-1 DNA, islets did not develop any necrotic core. The nonfunctional zone (with no insulin secretion if pO2  < 0.1 mmHg) was 0.3% for human islets (OCR ~100 nmol/min/mg DNA) and 35% for porcine islets (OCR ~300 nmol/min/mg DNA). The OCR of the islet preparation is profoundly affected by islet size, with optimal size of <250 μm in diameter (human) or <150 μm (porcine). Our data suggest that microcapsules afford superior oxygen delivery to encapsulated islets than macrocapsules, and optimal islet function can be achieved by encapsulating multiple, small (<150 μm) islets with OCR of ~100 nmol min-1 mg-1 DNA (human islets) or ~200 nmol min-1 mg-1 DNA (porcine islets)

Oxygenation of the Intraportally Transplanted Pancreatic Islet

Intraportal islet transplantation (IT) is not widely utilized as a treatment for type 1 diabetes. Oxygenation of the intraportally transplanted islet has not been studied extensively. We present a diffusion-reaction model that predicts the presence of an anoxic core and a larger partly functional core within intraportally transplanted islets. Four variables were studied: islet diameter, islet fractional viability, external oxygen partial pressure (P) (in surrounding portal blood), and presence or absence of a thrombus on the islet surface. Results indicate that an islet with average size and fractional viability exhibits an anoxic volume fraction (AVF) of 14% and a function loss of 72% at a low external P. Thrombus formation increased AVF to 30% and function loss to 92%, suggesting that the effect of thrombosis may be substantial. External P and islet diameter accounted for the greatest overall impact on AVF and loss of function. At our institutions, large human alloislets (>200 μm diameter) account for ~20% of total islet number but ~70% of total islet volume; since most of the total transplanted islet volume is accounted for by large islets, most of the intraportal islet cells are likely to be anoxic and not fully functional

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

<p>Abstract</p> <p>Background</p> <p>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.</p> <p>Methods</p> <p>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.</p> <p>Results</p> <p>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 <it>μ</it>m 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.</p> <p>Conclusion</p> <p>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.</p

A local glucose-and oxygen concentration-based insulin secretion model for pancreatic islets

<p>Abstract</p> <p>Background</p> <p>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.</p> <p>Methods</p> <p>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.</p> <p>Results</p> <p>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.</p> <p>Conclusions</p> <p>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.</p

Cell Encapsulation in Sub-mm Sized Gel Modules Using Replica Molding

For many types of cells, behavior in two-dimensional (2D) culture differs from that in three-dimensional (3D) culture. Among biologists, 2D culture on treated plastic surfaces is currently the most popular method for cell culture. In 3D, no analogous standard method—one that is similarly convenient, flexible, and reproducible—exists. This paper describes a soft-lithographic method to encapsulate cells in 3D gel objects (modules) in a variety of simple shapes (cylinders, crosses, rectangular prisms) with lateral dimensions between 40 and 1000 μm, cell densities of 105 – 108 cells/cm3, and total volumes between 1×10−7 and 8×10−4 cm3. By varying (i) the initial density of cells at seeding, and (ii) the dimensions of the modules, the number of cells per module ranged from 1 to 2500 cells. Modules were formed from a range of standard biopolymers, including collagen, Matrigel™, and agarose, without the complex equipment often used in encapsulation. The small dimensions of the modules allowed rapid transport of nutrients by diffusion to cells at any location in the module, and therefore allowed generation of modules with cell densities near to those of dense tissues (108 – 109 cells/cm3). This modular method is based on soft lithography and requires little special equipment; the method is therefore accessible, flexible, and well suited to (i) understanding the behavior of cells in 3D environments at high densities of cells, as in dense tissues, and (ii) developing applications in tissue engineering

Islet Oxygen Consumption Rate (OCR) Dose Predicts Insulin Independence in Clinical Islet Autotransplantation

Background: Reliable in vitro islet quality assessment assays that can be performed routinely, prospectively, and are able to predict clinical transplant outcomes are needed. In this paper we present data on the utility of an assay based on cellular oxygen consumption rate (OCR) in predicting clinical islet autotransplant (IAT) insulin independence (II). IAT is an attractive model for evaluating characterization assays regarding their utility in predicting II due to an absence of confounding factors such as immune rejection and immunosuppressant toxicity. Methods: Membrane integrity staining (FDA/PI), OCR normalized to DNA (OCR/DNA), islet equivalent (IE) and OCR (viable IE) normalized to recipient body weight (IE dose and OCR dose), and OCR/DNA normalized to islet size index (ISI) were used to characterize autoislet preparations (n = 35). Correlation between pre-IAT islet product characteristics and II was determined using receiver operating characteristic analysis. Results: Preparations that resulted in II had significantly higher OCR dose and IE dose (p<0.001). These islet characterization methods were highly correlated with II at 6–12 months post-IAT (area-under-the-curve (AUC) = 0.94 for IE dose and 0.96 for OCR dose). FDA/PI (AUC = 0.49) and OCR/DNA (AUC = 0.58) did not correlate with II. OCR/DNA/ISI may have some utility in predicting outcome (AUC = 0.72). Conclusions: Commonly used assays to determine whether a clinical islet preparation is of high quality prior to transplantation are greatly lacking in sensitivity and specificity. While IE dose is highly predictive, it does not take into account islet cell quality. OCR dose, which takes into consideration both islet cell quality and quantity, may enable a more accurate and prospective evaluation of clinical islet preparations

Oxygen diffusion limitations in pancreatic islet culture and immunoisolation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2002.Includes bibliographical references.Data for oxygen consumption by rat islets of Langerhans in a batch microreactor were fitted using a numerical solution of the transient oxygen diffusion-reaction equation. Average best-fit values were 3.1 +/- 0.7 x 10-8 mol/cm3-s for the maximum oxygen consumption rate Vmax in aminoacid-free media and 1.2 +/- 0.4 x 10-14 mol/cm-mm Hg-s for the oxygen permeability in islet tissue. These parameter values, along with a 30-60% positive correction for the presence of aminoacids in Vmax, were used to predict oxygen profiles inside and around islets under perifusion, culture, and immunoisolation conditions. The difference between Michaelis-Menten and zero-order kinetics and the role of the necrosis process in modeling of oxygen profiles were found to increase with the severity of hypoxia. Internal and external diffusion limitations were characterized for homogeneously dispersed tissue. Oxygen profiles were determined with finite differences in perifused rat islets for which second-phase insulin secretion data were available. Data were fitted with ad hoc kinetic models describing the effect of local pO2 on insulin secretion. A two-step, one-parameter model that assumed that local insulin secretion rate as a function of local pO2 is first-order for pO2 P* resulted in the best data fit for P* values between 2 and 10 mm Hg, depending on the value of Vmax used. Oxygen profiles were estimated with finite elements for the axi-symmetric problem of single islet culture and the model did an excellent job in predicting loss of viability data, obtained using Trypan blue staining,(cont.) as a function of islet diameter both under normoxic (ambient pO2 = 142 mm Hg) and hypoxic (40 mm Hg) conditions. The model was extended to massive islet culture and the effects of islet surface density and medium depth on viability were characterized and suggestions were made for the improvement of porcine islet culture conditions. In bioartificial pancreas devices we found that there is an optimal islet surface density (NS)opt for which insulin secretion rate is maximized, while secretory efficiency decreases monotonically with tissue density above a critical value. The design tissue density must be chosen in the range between this critical value and (Ns)opt' and its value depends on whether minimization of the device size or the amount of loaded tissue is more important.by Efstathios Spyridon Avgoustiniatos.Ph.D

Oxygenation of the Intraportally Transplanted Pancreatic Islet

Intraportal islet transplantation (IT) is not widely utilized as a treatment for type 1 diabetes. Oxygenation of the intraportally transplanted islet has not been studied extensively. We present a diffusion-reaction model that predicts the presence of an anoxic core and a larger partly functional core within intraportally transplanted islets. Four variables were studied: islet diameter, islet fractional viability, external oxygen partial pressure (P) (in surrounding portal blood), and presence or absence of a thrombus on the islet surface. Results indicate that an islet with average size and fractional viability exhibits an anoxic volume fraction (AVF) of 14% and a function loss of 72% at a low external P. Thrombus formation increased AVF to 30% and function loss to 92%, suggesting that the effect of thrombosis may be substantial. External P and islet diameter accounted for the greatest overall impact on AVF and loss of function. At our institutions, large human alloislets (>200 μm diameter) account for ~20% of total islet number but ~70% of total islet volume; since most of the total transplanted islet volume is accounted for by large islets, most of the intraportal islet cells are likely to be anoxic and not fully functional