Motion, deformation, and aggregation of multiple red blood cells in three-dimensional microvessel bifurcations

A theoretical model has been developed to simulate blood flow through large microcirculatory networks. The model takes into account the dependence of apparent viscosity of blood on vessel diameter and hematocrit (the Fahraeus-Lindqvist effect), the reduction of intravascular hematocrit relative to the inflow hematocrit of a vessel (the Fahraeus effect), and the disproportionate distribution of red blood cells and plasma at arteriolar bifurcations (phase separation). The model was used to simulate flow in three microvascular networks in the rat mesentery with 436,583, and 913 vessel segments, respectively, using experimental data (length, diameter, and topological organization) obtained from the same networks. Measurements of hematocrit and flow direction in all vessel segments of these networks tested the validity of model results. These tests demonstrate that the prediction of parameters for individual vessel segments in large networks exhibits a high degree of uncertainty; for example, the squared coefficient of correlation between predicted and measured hematocrit of single vessel segments ranges only between 0.15 and 0.33. In contrast, the simulation of integrated characteristics of the network hemodynamics, such as the mean segment hematocrit or the distribution of blood flow velocities, is very precise. In addition, the following conclusions were derived from the comparison of predicted and measured values: 1) The low capillary hematocrits found in mesenteric microcirculatory networks as well as their heterogeneity can be explained on the basis of the Fahraeus effect and phase-separation phenomena. 2) The apparent viscosity of blood in vessels of the investigated tissue with diameters less than 15 microns is substantially higher than expected compared with measurements in glass tubes with the same diameter.

Since the original publications by Martini et al. (Dtsch. Arch. Klin. Med. 169: 212-222, 1930) and Fahraeus and Lindqvist (Am. J. Physiol. 96: 562-568, 1931), it has been known that the relative apparent viscosity of blood in tube flow depends on tube diameter. Quantitative descriptions of this effect and of the dependence of blood viscosity on hematocrit in the different diameter tubes are required for the development of hydrodynamic models of blood flow through the microcirculation. The present study provides a comprehensive data base for the description of relative apparent blood viscosity as a function of tube diameter and hematocrit. Data available from the literature are compiled, and new experimental data obtained in a capillary viscometer are presented. The combined data base comprises measurements at high shear rates (u > or = 50 s-1) in tubes with diameters ranging from 3.3 to 1,978 microns at hematocrits of up to 0.9. If corrected for differences in suspending medium viscosity and temperature, the data show remarkable agreement. Empirical fitting equations predicting relative apparent blood viscosity from tube diameter and hematocrit are presented. A pronounced change in the hematocrit dependence of relative viscosity is observed in a range of tube diameters in which viscosity is minimal. While a linear hematocrit-viscosity relationship is found in tubes of or = 9 microns. This is interpreted to reflect the hematocrit-dependent transition from single- to multifile arrangement of cells in flow.