Oxygen transport in hemoglobin solutions: applications in the microcirculation
Sheth, Bhupendrakumar V.
Hellums, Jesse D.
Master of Science
Numerical solutions are obtained for the unsteady-state oxygen release process from hemoglobin layers of thicknesses and concentrations typical of the microcirculation. A modification of the CrankNicolson scheme is used to solve the coupled, non-linear, parabolic partial differential equations in layers of thicknesses 1.6 u, and 6. u. Two types of boundary conditions on oxygen are employed: 1) constant concentration, and 2) constant flux. Analytical solutions are presented for two cases: 1) oxyhemoglobin dissociating irreversibly to give oxygen and hemoglobin, and 2) oxygen and oxyhemoglobin assumed always in chemical equilibrium, the saturation curve being a straight line. The numerical results are presented as Nusseltt number versus time required for deoxygenation. Oxyhemoglobin diffusion accelerates the oxygen release process. The facilitation increases with decreasing oxygen concentration. It is shown that the assumption of oxyhemoglobin-oxygen equilibrium leads to significant error for conditions of the microcirculation. Thus the chemical reaction rate constants must be taken into account. Furthermore, it is shown that the reaction rate constants must be taken into account in a way compatible with the known equilibrium relationship. The analytical solutions are shown to differ significantly from the numerical results, but are useful for simple order of magnitude estimates.