Numerical Investigation of Blood Rheology and Phase Distribution in Micro-Arterial Networks

Abstract: Blood flow in micro-arterial networks exhibits complex non-Newtonian behavior due to the rheological properties of blood and the unequal distribution of red blood cells at vascular bifurcations. This study numerically investigates blood rheology and phase distribution using a Bingham plastic model combined with hematocrit-dependent viscosity and plasma-skimming effects. In this study, the equations describing the flow of blood through the network of blood vessels have been solved in order to determine how mass, momentum, and hematocrit (the ratio of red blood cells to total blood) will distribute during steady state laminar flow. Both analytical and numerical results show that a central “plug-flow” region is developed; that there are non-linear relationships between the velocity of blood flow and shear rates at various locations within the vessel; and that the amount of hematocrit present in each of the two daughter vessels differs significantly from one another. The larger daughter vessel has a high concentration of red blood cells relative to its size, which increases its overall viscosity as well as it's ability to resist flow. Conversely, the smaller daughter vessel contains a low concentration of red blood cells and therefore has a lower viscosity than the larger vessel. Overall, the model accurately describes plasma skimming and illustrates a direct relationship between hematocrit levels and the rheological properties of blood throughout the microvascular system thereby illustrating potential implications for tissue perfusion.

Keywords: Micro-arterial networks, Bingham plastic fluid, Blood rheology, Hematocrit transport, Plasma skimming, Phase separation, Non-Newtonian blood flow, Microcirculation