Abstract
Damped wave diffusion effects during oxygen transport in islets of Langerhans is studied. Simultaneous reaction and diffusion models were developed. The asymptotic limits of first and zeroth order in Michaelis and Menten kinetics was used in the study. Parabolic Fick diffusion and hyperbolic damped wave diffusion were studied separately. Method of relativistic transformation was used in order to obtain the solution for the hyperbolic model. Model solutions was used to obtain mass inertial times. Convective boundary condition was used. Sharma number (mass) may be used in evaluating the importance of the damped wave diffusion process in relation to other processes such as convection, Fick steady diffusion in the given application. Four regimes can be identified in the solution of hyperbolic damped wave diffusion model. These are; 1) Zero Transfer Inertial Regime, 0 0≤τ≤τinertia ; 2) Rising Regime during times greater than inertial regime and less than at the wave front, Xp > τ, 3) at Wave front ， τ = Xp; 4) Falling Regime in open Interval, of times greater than at the wave front, τ > Xp. Method of superposition of steady state concentration and transient concentration used in both solutions of parabolic and hyperbolic models. Expression for steady state concentration developed. Closed form analytic model solutions developed in asymptotic limits of Michaelis and Menten kinetic at zeroth order and first order. Expression for Penetration Length Derived-Hypoxia Explained. Expression for Inertial Lag Time Derived. Solution was obtained by the method of separation of variables for transient for parabolic model and by the method of relativistic transformation for hyperbolic models. The concentration profile was expressed as a sum of steadty state and transient parts.
Highlights
Diffusion of oxygen in pancreatic islets in an important consideration during development of models of viability and function of the islets of Langerhans (Figure 1)
Four regimes can be identified in the solution of hyperbolic damped wave diffusion model
Closed form analytic model solutions developed in asymptotic limits of Michaelis and Menten kinetic at zeroth order and first order
Summary
Diffusion of oxygen in pancreatic islets in an important consideration during development of models of viability and function of the islets of Langerhans (Figure 1). Islets of Langerhans are spheroidal aggregate of cells located in pancreas They secrete harmones such as insulin during glucose metabolism. These islets are transplanted in order to effect cure for Type I diabetes and are often encapsulated in devices. Leads to core cel death during islet transplantation as cure for Type I diabetes They attempted to measure the diffusion barrier in intact human islets and deterimine its role in cessation of insulin secretion. They monitored impeded diffusion into iselts using fluorescent destran beads. The oxygen supply is a critical limiting factor for the functionality and feasibility of islets that are encapsulated, placed in devices for implantation, cultured, used in aneorobic conditions. The parameters of the model require knowledge of the consumption rate of oxygen, oxygen solubility, effective diffusion coefficient to oxygen in the tissue
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
