Several aspects are involved in the oxygen transport in capillaries, such as the red blood cell (RBC) membrane mechanics, the cytoplasm/plasma flow fields, and the mass transport across the semipermeable deformable membrane. The transport process is also influenced by association and dissociation kinetics, which considers the interaction between oxygen and hemoglobin molecules within the RBCs. Therefore, a model of oxygen transport must include these factors to accurately represent the process.

In chapter 1, the microcirculation system, human RBC structure and properties, and oxygenhemoglobin kinetics have been briefly introduced to provide basic background information for oxygen transport process in microcirculation. Then, the effects of several important factors (RBC shape, plasma/cytoplasm convective effect, RBC membrane treatment) on gas transport in microcirculation have been reviewed. The literature review has shown that an efficient and robust numerical scheme for simulating oxygen transport in capillaries is missing and the effects of RBC properties and behaviors have not been well addressed. The motivation of this Ph.D. research is to develop a transport model to study the effects of various RBC flows on oxygen transport in capillaries. Several specific research objectives have been outlined in Section 1.5.

In Chapter 2, we propose a new method called the immersed membrane method for mass transfer across flexible semipermeable membranes. This method is based on the classical immersed boundary method used for interaction between structures and flow, and it replaces the sharp interface of the membrane with an artificial fluid layer. This layer does not affect the fluid flow or the membrane deformation, but it does add resistance to mass transiii fer, based on the membrane’s original permeability. By using this approach, we can solve the mass transfer problem using a single numerical scheme on the same Eulerian mesh, and we can avoid the complicated interface treatment required for the membrane interface condition. We also validated this method by comparing numerical results with theoretical solutions, and satisfactory agreement has been observed.

In Chapter 3, we consider a tank-treading capsule in shear flow, which is generated with two parallel plates moving in opposite directions:​ the top plate represents the core of RBCs in a microvessel with a high oxygen pressure (PO2 ), while the bottom plate represents the microvessel wall with a lower PO2 . 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.

In Chapter 4, we conduct numerical simulations for the blood flow and RBC deformation along a capillary and the oxygen transfer from RBCs to the surrounding tissue. We look at different values of capillary hematocrit, the oxygen tension in the arterioles, and metabolic rate of oxygen consumption. Our results show that there are two competing factors that affect the tissue oxygenation while the capillary hematocrit increases:​ the positive effect of higher RBC density and the negative effect of the slower RBC movement;​ and the relevant strength of these two mechanisms is related to the oxygen-hemoglobin reaction and hemoglobin concentration and affinity in cytoplasm.

In Chapter 5, we simulate the oxygen uptake processes in stopped-flow experiments with different cell shapes, membrane permeability and unstirred layer thickness considered. Our results show that the uptake process from the spherical model is much slower than those from the ellipsoidal and biconcave shapers, meaning that results form previous studies using spherical cell models may need to be revisited. Also we find that it is difficult to distinguish the individual influences from the membrane permeability and unstirred layer, and more comprehensive models will be required for future studies.

At last, in Chapter 6, concluding statements and future work based on the research results are presented.