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 finite element method model to simulate laser interstitial thermo therapy in anatomical inhomogeneous regions

BACKGROUND: Laser Interstitial ThermoTherapy (LITT) is a well established surgical method. The use of LITT is so far limited to homogeneous tissues, e.g. the liver. One of the reasons is the limited capability of existing treatment planning models to calculate accurately the damage zone. The treatment planning in inhomogeneous tissues, especially of regions near main vessels, poses still a challenge. In order to extend the application of LITT to a wider range of anatomical regions new simulation methods are needed. The model described with this article enables efficient simulation for predicting damaged tissue as a basis for a future laser-surgical planning system. Previously we described the dependency of the model on geometry. With the presented paper including two video files we focus on the methodological, physical and mathematical background of the model. METHODS: In contrast to previous simulation attempts, our model is based on finite element method (FEM). We propose the use of LITT, in sensitive areas such as the neck region to treat tumours in lymph node with dimensions of 0.5 cm – 2 cm in diameter near the carotid artery. Our model is based on calculations describing the light distribution using the diffusion approximation of the transport theory; the temperature rise using the bioheat equation, including the effect of microperfusion in tissue to determine the extent of thermal damage; and the dependency of thermal and optical properties on the temperature and the injury. Injury is estimated using a damage integral. To check our model we performed a first in vitro experiment on porcine muscle tissue. RESULTS: We performed the derivation of the geometry from 3D ultrasound data and show for this proposed geometry the energy distribution, the heat elevation, and the damage zone. Further on, we perform a comparison with the in-vitro experiment. The calculation shows an error of 5% in the x-axis parallel to the blood vessel. CONCLUSIONS: The FEM technique proposed can overcome limitations of other methods and enables an efficient simulation for predicting the damage zone induced using LITT. Our calculations show clearly that major vessels would not be damaged. The area/volume of the damaged zone calculated from both simulation and in-vitro experiment fits well and the deviation is small. One of the main reasons for the deviation is the lack of accurate values of the tissue optical properties. In further experiments this needs to be validated

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