Estimation of hematocrit profile symmetry recovery length downstream from a bifurcation

Downstream from a microvascular bifurcation the distribution of blood cells in the vessel lumen is not symmetric. A diffusion process is used to model the rearrangement of red cells as blood flows between junctions in the microcirculation. A Fourier series approach is used to solve the model diffusion convection equation in slit geometry. Both flat and parabolic velocity profiles are considered. The eigenvalues, found using the Rayleigh-Ritz method, are used to find an upper bound on distance required for a symmetric red cell distribution to be obtained. The method has also been applied to cylindrical geometry and the computed symmetry recovery lengths are compared to distances between bifurcations measured in vivo. These estimates indicate that red cell distributions are frequently asymmetric in the microcirculation. Such asymmetries can have a strong effect on plasma skimming and material balance calculations.