Computational study of red cell distribution in simple networks

The distribution of red blood cells (RBC) across the vessel lumen is disturbed when blood flows through a junction. As the blood flows downstream from the junction, the RBC distribution corrects itself to regain its original symmetric character. A dispersion-type process has been used to model this rearrangement process in 3-dimensional branching tubes. In this study, the disturbance in the RBC profile is quantified by tracing streamlines through the junction. The tracing technique is based on scaled-up dye studies. The computation starts at a location where the velocity profile is fully developed. Both uniform and parabolic RBC profiles are examined as possible, final symmetric distributions for the computations. Three velocity profiles are used alternatively. The dispersion convective equation of continuity in cylindrical geometry is solved with the method of finite differences. The resulting RBC concentration profiles is then used to compute flux-flow curves which are frequently used to examine plasma skimming phenomena. The numerically computed flux-flow curves are compared to in vitro experimental data from 50 $\mu$m serial bifurcation replicas. The dispersion coefficient is used as an adjustable parameter to give the best match between computation and measurement. The averaged dispersion coefficients obtained agree with previous experimental data and show an enhanced dispersion. Simple vascular networks are generated and the dispersion model is further applied to the networks. By calculating the discharge hematocrit of each branch vessel in the network the network Fahraeus effect is observed. Influences of flow disturbance to the downstream hematocrit are examined. The effects of flow heterogeneity and the dispersion model on the hematocrit heterogeneity are presented