The flow of sickle blood in glass capillaries: Fundamentals and potential applications

We have characterized the imbibed horizontal flow of sickle blood into 100-μm-diameter glass capillaries. We find that blood containing sickled cells typically traverses the capillaries between three and four times as slowly as oxygenated cells from the same patient for all genotypes tested, including SS, AS, SC and Sβ⁺ thalassemia blood. Blood from SS patients treated with hydroxyurea has a viscosity intermediate between the SS and AA values. Blood containing cells that are not rigidified, such as normal red cells or oxygenated sickle cells, follows a simple Lucas-Washburn flow throughout the length of the 3-cm capillary. By fitting the flexible-cell data to the Lucas-Washburn model, a viscosity can be derived that is in good agreement with previous measurements over a range of volume fractions and is obtained using an apparatus that is far more complex. Deoxygenation sickles and thus rigidifies the cells, and their flow begins as Lucas-Washburn, albeit with higher viscosity than flexible cells. However, the flow further slows as a dense mass of cells forms behind the meniscus and increases in length as flow progresses. By assuming that the dense mass of cells exerts a frictional force proportional to its length, we derive an equation that is formally equivalent to vertical imbibition, even though the flow is horizontal, and this equation reproduces the observed behavior well. We present a simple theory using activity coefficients that accounts for this viscosity and its variation without adjustable parameters. In the course of control experiments, we have found that deoxygenation increases the flexibility of normal human red cells, an observation only recently published for mouse cells and previously unreported for human erythrocytes. Together, these studies form the foundation for an inexpensive and rapid point-of-care device to diagnose sickle cell disease or to determine blood viscosity in resource-challenged settings.     

Folding of red blood cells in capillaries and narrow pores.

The geometric features of red blood cells in narrow channels in vivo and in vitro were studied by electron microscopy. In rabbit myocardial capillaries about half of the red cells were folded. In polycarbonate filters with pore diameters of 2.2-4.5 microns approximately one third of the trapped red blood cells were folded. The frequency of folding did not depend on the applied pressure, which ranged from 0.1 to 8.0 cm H2O. The folding of the red blood cells in filter pores was used to estimate the bending stiffness of the membrane. An analysis based on the large deformation theory of bending of an elastic sheet was developed. Using pressures of 0.2 and 1.0 cm H2O, the bending stiffness of human red cell membranes was estimated to be approximately 2.4 - 11.6 x 10(-12) dyn-cm, which is in good agreement with other methods. A limiting radius of curvature of about 85 nm was found at higher pressures.     

The flow of sickle-cell blood in the capillaries.

Oxygen tension levels and red cell velocities for the flow of sickle-cell blood in the capillaries are determined by using the Krogh model for oxygen transport and lubrication theory for the cell motion. The coupling and interaction between these arises from the red cell compliance, which is assumed to vary with the oxygen concentration. Microsieving data is used to establish an upper bound for this relationship. Calculations are carried out for a range of capillary sizes, taking into account the rightward shift of the oxyhemoglobin dissociation curve and the reduced hematocrit of sickle-cell blood, and are compared to, as a base case, the flow of normal blood under normal pressure gradient. The results indicate that under normal pressure gradients the oxygen tensions and cell velocities for sickle blood are considerably higher than for normal blood, thus acting against the tendency for cells to sickle, or significantly change their rheological properties, in the capillaries. Under reduced pressure gradients, however, the concentrations and velocities drop dramatically, adding to the likelihood of such shape or flow property changes.     

Optimum kinetic energy dissipation in blood flow in glass capillaries by flow field determination: Analysis of curvature effect by axial tomographic and image velocimetry techniques

Based on the variation in the optical density due to erythrocyte concentration and movement, the axial tomographic and image velocimetry techniques are respectively applied to determine the flow field, i.e., the distribution of erythrocytes and axial and radial velocity components, in steady blood flow through a curved glass capillary with a diameter of 180 μm. The data at four positions (two straight and two curved segments of the capillary) are recorded by a video-microscopic system on a video cassette. The erythrocyte and velocity distribution profiles change from symmetric at the straight position to an asymmetric shape at the curved sections. These profiles become symmetric again at the straight section of the capillary. The increase in the radial velocity component at curved portions is attributed to the secondary flow. The tomograms obtained by concentration profiles show respective changes in the cellular population at various cross-sectional positions. The kinetic energy dissipation, as calculated based on a determination of the flow field, is the minimum for the observed profiles. Any deviation towards parabolic form leads to the dissipation of a higher amount of energy.     

Potential fields and barriers to diffusion in narrow cylindrical capillaries

In this paper, the wall potential along the center line of narrow solid capillaries has been derived. The potential barriers at the open end of such capillaries have been studied in detail. The influence of these potential barriers on the diffusion coefficients and their dependence on temperature and capillary radius have been evaluated. The implications of these energy barriers in the clarification of low pressure hysteresis phenomena have been pointed out.     

Modeling of blood flow as the result of filtration-reabsorption processes in capillaries

In our previous article (Am J Physiol Adv Physiol Educ 272: S26-S30, 1997) we proposed a model that permits analysis for the change of hemodynamics in vessels with local stenosis. This problem is connected with the blood-tissue metabolism. This article continues the classroom research on concepts related to blood flow physiology. We take into consideration the problem of the blood-tissue fluid exchange. A model based on basic principles of hydrodynamics and mathematics is proposed for analysis of "filtration-reabsorption equilibrium" and its disturbances under different external influences. It permits medical students to develop a scientific analytic approach to the solution of physiological and pathophysiological hemodynamics problems.     

Respiratory effect on the blood volume of pulmonary capillaries

We measured the density variations of aortic blood from rabbits ventilated by a positive end inspiratory pressure of 6 mmHg or a negative box pressure of the same magnitude. When calculated from the density variations, the fluctuations in blood volume of the pulmonary capillaries within one cycle as induced by an intermittent positive pressure ventilation were found to be similar to the ones induced by an intermittent negative pressure ventilation. Using these volumetric fluctuations as a means to assess the transpulmonary pressure and the transmural pressure across the pulmonary capillaries, we conclude that the switching of the ventilation method did not alter the cyclic fluctuations of these pressures.     

Quantifying the cleanliness of glass capillaries

I used capillary rise methods to investigate the lumenal surface properties of quartz (fused silica, Amersil T-08), borosilicate (Corning 7800), and high-lead glass (Corning 0010) capillaries commonly used to make patch pipets. I calculated the capillary rise and contact angle for water and methanol from weight measurements. The capillary rise was compared with the theoretical maximum value calculated by assuming each fluid perfectly wetted the lumenal surface of the glass (i.e., zero contact angle, which reflects the absence of surface contamination). For borosilicate, high-lead, and quartz capillaries, the rise for water was substantially less than the theoretical maximum rise. Exposure of the borosilicate, lead, and quartz capillaries to several cleaning methods resulted in substantially better—but not perfect—agreement between the theoretical maximum rise and calculated capillary rise. By contrast, the capillary rise for methanol was almost identical in untreated and cleaned capillaries, but less than its theoretical maximum rise. The residual discrepancy between the observed and theoretical rise for water could not be improved on by trying a variety of cleaning procedures, but some cleaning methods were superior to others. The water solubility of the surface contaminants, deduced from the effectiveness of repeated rinsing, was different for each of the three types of capillaries examined: Corning 7800>quartz>Corning 0010. A surface film was also detected in quartz tubing with an internal filament. I conclude that these borosilicate, quartz, and high-lead glass capillaries have a film on the lumenal surface, which can be removed using appropriate cleaning methods. The surface contaminants may be unique to each type of capillary and may also be hydrophobic. Two simple methods are presented to quantitate the cleanliness of glass capillary tubing commonly used to make pipets for studies of biological membranes. It is not known if the surface film is of importance in electrophysiological studies of biological membranes.     

A model of blood flow distribution during filtration-reabsorption processes in capillaries

A model of blood flow in a capillary was constructed, which takes into account the movement of plasma through its porous wall. The functions of changes in pressure and the rate of blood flow along the capillary were calculated. It was shown that, in the general case, the distribution of hemodynamic parameters as a result of filtration-reabsorption processes is nonlinear. Possible mechanism of tissue edema resulting from the disturbance of the filtration-reabsorption equilibrium were analyzed.     

Radial dispersion of red blood cells in blood flowing through glass capillaries: the role of hematocrit and geometry

The flow properties of blood in the microcirculation depend strongly on the hematocrit (Hct), microvessel geometry, and cell properties. Previous in vitro studies have measured the radial displacement of red blood cells (RBCs) at concentrated suspensions using conventional microscopes. However, to measure the RBCs motion they used transparent suspensions of ghost red cells, which may have different physical properties than normal RBCs. The present study introduces a new approach (confocal micro-PTV) to measure the motion of labeled RBCs flowing in concentrated suspensions of normal RBCs. The ability of confocal systems to obtain thin in-focus planes allowed us to measure the radial position of individual RBCs accurately and to consequently measure the interaction between multiple labeled RBCs. All the measurements were performed in the center plane of both 50 and 100 microm glass capillaries at Reynolds numbers (Re) from 0.003 to 0.005 using Hcts from 2% to 35%. To quantify the motion and interaction of multiple RBCs, we used the RBC radial dispersion (D(yy)). Our results clearly demonstrate that D(yy) strongly depends on the Hct. The RBCs exhibited higher D(yy) at radial positions between 0.4 and 0.8R and lower D(yy) at locations adjacent to the wall (0.8-1R) and around the middle of the capillary (0-0.2R). The present work also demonstrates that D(yy) tends to decrease with a decrease in the diameter. The information provided by this study not only complements previous investigations on microhemorheology of both dilute and concentrated suspensions of RBCs, but also shows the influence of both Hct and geometry on the radial dispersion of RBCs. This information is important for a better understanding of blood mass transport mechanisms under both physiological and pathological conditions.