Unloading oxygen in a capillary vessel under a pathological condition

In this work, we study theoretically the unloading of oxygen from a hemoglobin molecule to the wall of a typical capillary vessel, considering that the hemoglobin under pathological conditions, obeys the rheological Maxwell model. Based on recent experimental evidences in hypertension, we consider that the red blood cells (RBCs) are composed by a single continuous medium in contrast with the classical particulate or discrete RBC models, which are only valid under normal physiological conditions. The analysis considers the hemodynamic interactions between the plasma and the hemoglobin, both circulating in a long horizontal capillary. We apply numerical and analytical methods to obtain the main fluid-dynamic characteristics for both fluids in the limit of low Reynolds and Womersley numbers. A diffusion boundary layer formulation for the oxygen transport in the combined plasma-hemoglobin core region is presented. The main aspects derived are the time and spatial evolution of the membrane. The hemoglobin and plasma velocities and the pressure distributions are shown. For the oxygen unloading the results are the oxy-hemoglobin saturation, the oxygen flux and the oxygen concentration in the cell-free plasma layer. The volume fraction of red blood cells and the Strouhal number have a great influence on the hemodynamic interactions.