Numerical analysis of oxygen uptake processes by red blood cells in stopped-flow measurements: Effects of cell shape, membrane permeability and unstirred layer.

The transport process of oxygen and other gas species across red blood cell (RBC) membrane is of great importance for better understanding the critical biological functions of RBCs, and the stopped-flow experiments have often been employed for such investigations. In previous stopped-flow analyses, the RBC had usually been represented by a spherical capsule based on the RBC volume, and an assumed unstirred layer (USL) thickness had been used to determine the membrane permeability. In this research, unlike these previous studies, we simulate the oxygen uptake process with different RBC shapes (shperical, ellipsoidal and biconcave) and examine the effects of USL thickness and membrane permeability over broad ranges based on literature values. Our results show that the excess membrane area can greatly improve the oxygen transport efficiency, and a same uptake half-time can be obtained using different combinations of USL thickness and membrane permeability. These findings raise concerns on the reliability and uncertainty for the results and conclusions in previous studies, and also call for more complete numerical models, for example, with the fluid flow and cell deformation considered, and more in-depth investigations on the oxygen transport processes.

Tissue Oxygenation Around Capillaries: Effects of Hematocrit and Arteriole Oxygen Condition.

Oxygen transfer in the microvasculature is a complex phenomenon that involves multiple physical and chemical processes and multiple media. Hematocrit, the volume fraction of red blood cells (RBCs) in blood, has direct influences on the blood flow as well as the oxygen supply in the microcirculation. On the one hand, a higher hematocrit means that more RBCs present in capillaries, and thus, more oxygen is available at the source end. On the other hand, the flow resistance increases with hematocrit, and therefore, the RBC motion becomes slower, which in turn reduces the influx of oxygen-rich RBCs entering capillaries. Such double roles of hematocrit have not been investigated adequately. Moreover, the oxygen-hemoglobin dissociation rate depends on the oxygen tension and hemoglobin saturation of the cytoplasm inside RBCs, and the dissociation kinetics exhibits a nonlinear fashion at different oxygen tensions. To understand how these factors and mechanisms interplay in the oxygen transport process, computational modeling and simulations are favorite since we have a good control of the system parameters and also we can access to the detailed information during the transport process. In this study, we conduct numerical simulations for the blood flow and RBC deformation along a capillary and the oxygen transfer from RBCs to the surrounding tissue. Different values for the hematocrit, arteriole oxygen tension, tissue metabolism rate and hemoglobin concentration and affinity are considered, and the simulated spatial and temporal variations of oxygen concentration are analyzed in conjunction with the nonlinear oxygen-hemoglobin reaction kinetics. Our results show that there are two competing mechanisms for the tissue oxygenation response to a hematocrit increases: the favorite effect of the higher RBC density and the negative effect of the slower RBC motion. Moreover, in the low oxygen situations with RBC oxygen tension less than 50 mmHg at capillary inlet, the reduced RBC velocity effect dominates, resulting in a decrease in tissue oxygenation at higher hematocrit. On the opposite, for RBC oxygen tension higher than 50 mmHg when entering the capillary, a higher hematocrit is beneficial to the tissue oxygenation. More interestingly, the pivoting arteriole oxygen tension at which the two competing mechanisms switch dominance on tissue oxygenation becomes lower for higher oxygen-hemoglobin affinity and lower hemoglobin concentration. This observation has also been analyzed based on the oxygen supply from RBCs and the oxygen-hemoglobin reaction kinetics. The results and discussions presented in this article could be helpful for a better understanding of oxygen transport in microcirculation.

Oxygen transport across tank-treading red blood cell: Individual and joint roles of flow convection and oxygen-hemoglobin reaction.

Gas, especially oxygen, transport in the microcirculation is a complex phenomenon, however, of critical importance for maintaining normal biological functions, and the cytoplasm fluid in red blood cells (RBCs) is the major vehicle for transporting oxygen from lungs to tissues via the circulatory system. Existing theoretical and numerical studies have neglected the cytoplasm convection effect by treating RBCs as rigid particles undergoing a constant translation velocity. As a consequence, the influence and mechanism of the cytoplasm flow on oxygen transport are still not clear in microcirculation research. In this study, we consider a tank-treading capsule in shear flow, which is generated with two parallel plates moving in opposite directions: the top plate of a higher oxygen pressure (PO2) representing the RBC core in the central region of a microvessel and the bottom plate of a lower PO2 representing the microvessel wall. Numerical simulations are conducted to investigate the individual and combined effects of cytoplasm convection and oxygen-hemoglobin (O2-Hb) reaction on the oxygen transport efficiency across the tank-treading capsule, and different PO2 situations and shear rates are also tested. Due to the lower oxygen diffusivity in cytoplasm, the presence of the capsule reduces the oxygen transfer flux across the gap by 7.34 % in the pure diffusion system where the flow convection and O2-Hb reaction are both neglected. Including the flow convection or the O2-Hb reaction has little influence on the oxygen flux; however, when they act together as in real microcirculation situations, the enhancement in oxygen transport could be significant, especially in the low PO2 and high shear rate situations. In particular, with the respective PO2 at 60 and 30 mmHg on the top and bottom plates and a 400 s-1 shear rate, the oxygen flux reduction is only 0.02 %, suggesting that the cytoplasm convection can improve the oxygen transport across RBCs considerably. The simulation results are scrutinized to explore the underlying mechanism for the enhancement, and a new nondimensional parameter is introduced to characterize the importance of cytoplasm convection in oxygen transport. These simulation results, discussion and analysis could be helpful for a better understanding of the complex oxygen transport process and therefor valuable for relevant studies.