On Damped Wave Diffusion of Oxygen In Iselts of Langergahns: Part-VI Comparison of Parabolic and Hyperbolic Models In a Finite Sphere for Pulse Boundary Condition

Oxygen availability becomes limited in some regions of the tissue.  The metabolic rate in the cells and demand for oxygen is greater than the oxygen that has diffused to that region. It becomes a diffusion limited process.  Due to this phenomena growth of multicellular systems over 100 μm does not happen.  A condition called hypoxia has been observed in Brockman bodies in fish.  Oxygen supply in addition to diffusion also comes about by the circulatory system and by hemoglobin molecule.  Oxygen is carried in the blood by convection to capillaries by the circulatory system. Islets of Langerhans (Figure 1.0) are spheroidal aggregates of cells that are located in the pancreas (2).  They secrete harmones that are involved in glucose metabolism particulary insulin. Transplantation of isolated cells is a promising treatment for some forms of Type I diabetes.  Islets removed from the pancreas are devoid of their internal vacularization. The metabolic requirement of the cells require oxygen to diffuse from the external envirnonment and through the oxygen-consuming islet tissue.  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.  Theoretical models are needed to describe the oxygen diffusion. The parameters of the model require knowledge of the consumption rate of oxygen,  oxygen solubility,  effective diffusion coefficient to oxygen in the tissue. Simultaneous diffusion and reaction model was developed by Colton (3).  This study is a continuation in the series of studies undertaken.  A finite sphere is considered. The transient concentration profile is obtained in both the asymptotic limits of zeroth order and first order limits of the Michaelis and Menten kinetics. The pulse boundary condition is studied. Both parabolic Fick diffusion and hyperbolic damped wave diffusion and relaxation are considered. The mass transfer coefficients are calculated. Sharma number effects in artificial pancreas is discussed.