Biorheology

The purpose of this study was to examine the theoretical impact of the local bifurcation geometry on the shear rate gradient in a divergent arteriolar‐type bifurcation. Newtonian flow through an arteriolar bifurcation was modeled using 3‐dimensional computational fluid dynamics (CFD). Branching angles of 30^○, 50^○, 70^○, 90^○, 110^○, 130^○, and 150^○ were studied at a Reynolds number (Re) of 0.01 in seven separate models. Both the flow split (30%) and the branch to main vessel diameter ratio (4/5) were held constant. Velocity profiles were predicted to deviate significantly from a parabolic form, both immediately before and after the branch. This deviation was shown to be a function of the local bifurcation geometry of each model, which consisted of a branching angle and associated feed‐branch intersection shape. Immediately before and after the branch, the shear rate along the lateral branching wall was predicted to exceed (5‐fold) that calculated for fully developed flow in the feed. In vivo data were from the anesthetized (pentobarbital, 70 mg/kg) hamster cremaster muscle preparation. Red blood cells were used as flow markers in arteriolar branch points (n=74) show that a significant gradient in shear rate occurs at the locations and branch shapes predicted by the computational model. Thus, for low Re divergent flow, the gradient in shear rate measured for non‐Newtonian conditions, is approximated by a finite element fluid dynamics model of Newtonian flow.

To evaluate the fluid forces acting on cells adhered to a microvessel wall, we numerically studied the flow field around adherent cells and the distribution of the stresses on their surfaces. For simplicity, the cells were modeled as rigid particles attached to a wall of a circular cylindrical tube regularly in the flow direction, in a row or two rows. It was found that not the detailed shape of the model cells but their height from the vessel wall is a key determinant of the fluid forces and torque acting on them. In both arrangements of one row and two rows, the axial spacing between neighboring adherent cells significantly affects the distributions of the stresses on them, which results in drastic variations of the fluid forces with the axial spacing and the relative positions with respect to their neighboring cells. The drag force acting on an adherent cell in the vessel was evaluated to be larger than the value in the 2D chamber flow at the same wall shear stress, mainly due to much larger variations of the pressure distribution on the cell surface in the vessel flow.

The state of leukocyte and erythrocyte adhesiveness/aggregation was determined in the peripheral blood of 382 patients with infection/inflammation as well as in 72 controls by using a simple slide test and image analysis. A highly significant correlation (r=0.4, n=455, p<0.001) was found between the state of leukocyte and erythrocyte adhesiveness/aggregation. The extent of both leukocyte and erythrocyte aggregation correlated with the concentration of fibrinogen. Significant aggregation of leukocytes with erythrocytes was noted as well. We conclude that both leukocyte and erythrocyte aggregation occur in the peripheral blood of patients with infection/inflammation. Such cell aggregation, which might have detrimental rheological consequences, can be detected by using our novel technique.

To substantiate the occurrence of flow‐dependent concentration or depletion of atherogenic lipoproteins, which has been theoretically predicted to take place at a blood/endothelium boundary, we have studied the effects of perfusion pressure and wall shear rate on the accumulation and uptake of microspheres by cultured vascular endothelial cells in a monolayer. The study was carried out by flowing a cell culture medium containing fetal calf serum and fluorescent microspheres through a parallel‐plate flow chamber having a cultured bovine aortic endothelial cell (BAEC) monolayer on one wall of the chamber. The microspheres had a nominal diameter of 19 nm, approximately the same as that of low‐density lipoproteins, and thus served as models and tracers of plasma proteins and lipoproteins. Experiments were carried out in steady flow in the physiological range of wall shear rate and water filtration velocity at the monolayer, while monitoring the intensity of fluorescence of the spheres accumulated at and taken up by the endothelial cells. It was found that in a perfusate containing only fluorescent microspheres, due to increased phagocytic activity of the endothelial cells, the intensity of fluorescence which reflected the number of the microspheres taken up by the endothelial cells, increased almost linearly with time and independently of wall shear rate. However, with perfusates containing fetal calf serum, this abnormal phenomenon did not occur, and the intensity of fluorescence increased with increasing perfusion pressure and decreasing wall shear rate. It was also found that the number of fluorescent microspheres accumulated at and taken up by the BAEC monolayer was shear‐dependent only at low wall shear rates, and increased sharply when the flow rate was reduced to zero. These results provided solid experimental evidence that flow‐dependent concentration or depletion of macromolecules occurs at the luminal surface of the endothelium at physiological wall shear rates and water filtration velocities, and strongly supports the hypothesis that flow‐dependent concentration polarization of lipoproteins plays an important role in the localization of atherosclerosis and intimal hyperplasia in man by facilitating the uptake of atherogenic lipoproteins by endothelial cells.

Morphometric and passive biomechanical properties were studied in isolated segments of the thoracic and abdominal aorta, left common carotid artery, left femoral artery and the left pulmonary artery in 20 non‐diabetic and 28 streptozotocin (STZ)‐induced diabetic rats. The diabetic and non‐diabetic rats were divided into groups living 1, 4, 8, and 12 weeks after the induction of diabetes (n=7 for each diabetic group) or sham injection (n=5 for each group). The mechanical test was performed as a distension experiment where the proximal end of the arterial segment was connected via a tube to the container used for applying pressures to the segment and the distal end was left free. The vessel diameter and length were obtained from digitized images of the arterial segments at pre‐selected pressures and at no‐load and zero‐stress states. Circumferential and longitudinal stresses (force per area) and strains (deformation) were computed from the length, diameter and pressure data and from the zero‐stress state data. The zero‐stress state was obtained by cutting vessel rings radially causing the rings to open up into a sector. Diabetes was associated with pronounced morphometric changes, e.g., wall thickness. With respect to the biomechanical data, the opening angle increased and reached a plateau in 4 weeks after which it decreased again (p<0.05). The opening angle was smallest in the thoracic aorta and largest in the pulmonary artery. Furthermore, it was found that the circumferential stiffness of the arteries studied increased with the duration of diabetes. In the longitudinal direction significant differences were found 8 weeks after injection of STZ in all arteries except the pulmonary artery. In the 12 weeks group, the femoral artery was stiffest in the circumferential direction whereas the thoracic aorta was stiffest in the longitudinal direction. The accumulated serum glucose level correlated with the arterial wall thickness and elastic modulus (correlation coefficient between 0.56 and 0.81).

It was found that solutions of calcium hyaluronate (CaHA) (0.1∼0.5 wt%) could form a gel by mixing with solutions of sodium type gellan (0.1∼0.5 wt%), although neither polymer by itself forms a gel at low concentrations (0.1∼0.5 wt% in this experiment). The rheological properties of CaHA–gellan mixtures were investigated by dynamic and steady shear measurements. Both storage shear modulus G′ and loss shear modulus G″ for CaHA–gellan mixtures increased with increasing time, and tended to an equilibrium value after 1 h. After reaching steady values of G′ and G″, the frequency dependence of G′ and G″ was observed. G′ was always larger than G″ in the accessible frequency range from 10⁻² to 10² rad/s. The effects of pH and calcium ions were examined. Gel formation of the mixtures was promoted by decreasing pH and adding from 0.01 to 0.1 M calcium ions, but excessive calcium ions weakened the gel.

The theoretical extinction of blood suspensions submitted to a slow dialysis is analyzed in terms of their NaCl concentration. The model involves two adjustable parameters, χ and K, related to swelling and hemolysis. During swelling, the erythrocyte volume is supposed to vary linearly with the saline concentration. During hemolysis, an exponential decay of the hemoglobin concentration in the erythrocyte is used. The theoretical transmittance curves are consistent with the measurements carried out at a wavelength of 0.808 μm on native and incubated blood samples. χ and K are relevant parameters to characterize quantitatively the fragility of the erythrocyte membrane. The effect of a non ideal character of the hemoglobin solutions and of normal distributions of χ and K is also discussed.

Differences of red blood cell (RBC) aggregation among various mammalian species has been previously reported for whole blood, for RBC in autologous plasma, and for washed RBC re‐suspended in polymer solutions. The latter observation implies the role of cellular factors, yet comparative studies of such factors are relatively limited. The present study thus investigated RBC aggregation and RBC electrophoretic mobility (EPM) for guinea pigs, rabbits, rats, humans and horses; RBC were re‐suspended in isotonic 500 kDa dextran solutions for the EPM and aggregation measurements, with aggregation studies also done in autologous plasma. Salient results included: (1) species‐specific RBC aggregation in both plasma and dextran (horse > human > rat > rabbit ≅ guinea pig) with a significant correlation between aggregation in the two media; (2) similar EPM values in PBS for rat, human and horse, a lower value for guinea pig, and a markedly reduced EPM for rabbit RBC; (3) EPM values in dextran with a rank order identical to that for cells in PBS; (4) relative EPM results indicating formation of a polymer‐poor, low viscosity depletion layer at the RBC surface (greatest depletion for horse RBC). EPM‐aggregation correlations were evident and generally consistent with the Depletion Model for aggregation, yet did not fully explain differences between species; additional studies at various ionic strengths and with various dextran fractions thus seem warranted.

A method based on dielectric properties of dispersed systems was applied to investigate the kinetics of RBC aggregation and the break‐up of the aggregates. Experimentally, this method consists of measuring the capacitance at a frequency in the beginning of the β‐dispersion. Two experimental protocols were used to investigate the aggregation process. In the first case, blood samples were fully dispersed and then the flow was decreased or stopped to promote RBC aggregation. It was found that the initial phases of RBC aggregation are not affected by the shear rate. This finding indicates that RBC aggregation is a slow coagulation process. In the second case, RBCs aggregated under flow conditions at different shear rates and after the capacitance reached plateau levels, the flow was ceased. The steady‐state capacitance of the quiescent blood and the kinetics of RBC aggregation after stoppage of shearing depend on the prior shear rate. To clarify the reasons for this effect, the kinetics of the disaggregation process was studied. In these experiments, time courses of the capacitance were recorded under different flow conditions and then a higher shear stress was applied to break up RBC aggregates. It was found that the kinetics of the disaggregation process depend on both the prior and current shear stresses. Results obtained in this study and their analysis show that the kinetics of RBC aggregation in stasis consists of two consecutive phases: At the onset, red blood cells interact face‐to‐face to form linear aggregates and then, after an accumulation of an appropriate concentration of these aggregates, branched rouleaux are formed via reactions of ends of the linear rouleaux with sides of other rouleaux (face‐to‐side interactions). Branching points are broken by low shear stresses whereas dispersion of the linear rouleaux requires significantly higher energy.