Question

Steady-state Diffusion with Chemical Reaction. One of the most studied bioarticificial organ systems is the encapsulation of islets of Langerhans cells to produce insulin in diabetic patients. They consist of islets encapsulated in a spherical gel bead. The spheres are kept at 310K, are 150 microns in diameter, and the islets consume oxygen at a rate of 25.9 mu M/s. The diffusivity of oxygen into the system is 1.67 Times 10-5 cm2/sec. The average partial pressure of oxygen at the capsule boundary is 68 mmHg. Henry's constant is 0.74 mmHg/mu M. Derive the equation that describes the concentration at a radial position r in the gel bead in the absence of bulk flow (analytical solution only). What is the oxygen flux at the surface of the spherical gel r = R? What is the oxygen concentration half the total radius from the center? If the Michaelis-Menton constant KM for the oxygen uptake is 1 mu M, does the zeroth order reaction still hold? What is the maximum consumption rate without the presence of necrotic region?

Answer 1