Numerical analysis of the influence of RBCs on oxygen transport within a tissue with an embedded capillary network

Abstract

In this paper, the oxygen transport in a capillary network and the surrounding tissue was simulated by considering the influence of red blood cells (RBCs). To simplify this problem, the erythrocytes as the oxygen carriers were modelled as one-dimensional (1 D) spheres, and oxygen and haemoglobin diffusion took place only in the radial direction. The direction of movement of the RBCs at the network bifurcations was determined by a probability function related to the ratio of the flow rate in the mother vessel to that in a daughter vessel. The capillaries were reduced to a skeleton structure that included vessels with different radii, lengths, and three-dimensional (3 D) coordinates. The capillary network was embedded in a 3 D tissue, which was considered as a homogeneous porous medium. The interactions between the capillary network and the surrounding tissue were solved by the immersed boundary method. The influence of RBC rheological behaviours, such as deformation capacity and flux, on oxygen transport were analysed. The oxygen dissociation capacity of the RBCs was also investigated. The results showed that when the RBCs’ deformation capacity was weakened, the probability of RBCs choosing large-flow daughter vessel at the bifurcation increased considerably, leading to a highly non-uniform distribution of RBCs in the network. The non-uniformity of the RBCs further led to partial hypoxia in regions through which no RBCs passed. In contrast, a lower haematocrit and weakening of the oxygen release capability led to the overall decline of oxygen partial pressure in the whole region.