Asymmetric cell flow in narrow tubes: Experimental analysis of cellular interactions

MICROVASCULAR

RESEARCH

39, 240-245

(1990)

BRIEF COMMUNICATIONS Asymmetric

Cell Flow in Narrow Tubes: Experimental of Cellular Interactions

Analysis

P. GAEHTGENS AND A. R. PRIES Institut

fir

Physiologic,

Freie

Universitiit Received

Berlin, June

D-1000

Berlin,

Federal

Republic

of Germany

14. 1989

INTRODUCTION In an attempt to gain insight into the rheological characteristics of blood flow in narrow vessels, Sugihara-Seki and Skalak (1988, 1989) have recently modeled the flow behavior of blood cells in single- and two-file arrangement typically seen under such conditions. In a first approximation of red cell flow behavior these authors have used a two-dimensional model of rigid circular cylinders moving down a channel in a zipper-like configuration, with eccentric radial particle positions alternating between the two sides of the channel axis. The model describes the motion of the suspending fluid between the particles which rotate about an axis perpendicular to the flow direction. The results suggest that particle arrangement in the channel exerts a pronounced influence on the velocity ratio between the particles and the bulk fluid, thus affecting the Fahraeus and Fahraeus-Lindqvist effects. The present report describes an experimental correlate of the above theoretical analysis which is observed as a result of interactions between red and white blood cells within cell trains. During flow of blood exhibiting an extremely high leukocyte count, the accumulation of white cells which results from the formation of cell trains in narrow tubes leads to a situation which is very similar to that analyzed by the above authors. MATERIALS

AND METHODS

Flow behavior of blood cells was studied during blood perfusion through straight glass capillaries (I.D. 12 pm, length 5 cm) at constant hydrostatic driving pressure. The capillaries were mounted onto the stage of a microscope and observed with an oil immersion objective. The microscope stage was moved by a motor in a direction parallel to the tube axis and at a speed which could be adjusted to match the velocity of the flowing cells. The cells or groups of cells moving through the tube appeared to be stationary within the microscope field 240 0026-2862/W $3.00 Copyright Q 1990 by Academic Press, Inc. All rights of reproduction in any form reserved Printed in U.S.A.

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of view. The resulting image was recorded on videotape together with the output of a video timer and analyzed off-line. For this purpose, the recordings were replayed through a video position analyzer in order to quantify the relative motion of flowing particles within the tube during slow motion or single-frame analysis. The absolute velocity of the traveling capillary was obtained from the displacement, within the field of view, of visible marker particles on the outside tube wall. The blood sample used in the experiment described here was obtained from a patient who exhibited an extraordinarily high lymphocyte count (180 X lo3 ~1~~). The sample was drawn by venipuncture and anticoagulated with EDTA (2.5 III/ml). RESULTS

AND DISCUSSION

Extensive formation of blood cell trains was observed during the perfusion of the traveling tube. In most instances, polymorphonuclear granulocytes (PMN) represented the leading cells of the train. As a result of cell size and shape, the PMN occupied more than 50% of the tube cross-section and therefore exhibited a flow velocity which was lower than that of all other cell species. Consequently, red blood cells (RBC) tended to accumulate upstream of the PMN at a substantially elevated concentration. This phenomenon of train formation has previously been investigated in tubes of various sizes (Gaehtgens et al., 1984; Secomb et al., 1987). Within the blood cell train, the different species of blood cells are seen in distinct groups which are axially separated (Fig. l), presumably according to their relative velocity in free flow. Thus, the cells immediately following the leading PMN (mostly RBC) do so because they are relatively the fastest until they are forced, within the train, to assume the velocity of the PMN. In the study described here, the lymphocytes were observed as a group usually at the end of a train, trailed only by a cloud of platelets. Within this group, the lymphocytes were arranged in the interlocking zipper formation assumed for the model calculations of Sugihara-Seki and Skalak (1988). This arrangement is unique for the blood samples exhibiting very high lymphocyte concentration, while in normal blood only one lymphocyte per train may, on average, be expected. An average cell/tube diameter ratio of approximately 0.42 was obtained from several lymphocytes of different zipper configurations; the cells were positioned FLOW

DIRECTION

LYMPHOCYTE ZIPPER

v

RED

BLOOD CELLS

PMN

FIG. 1. Blood cell train in the 12+m traveling tube (photograph taken from video monitor).

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asymmetrically with their centers located at a radial position of r/R = 0.309 + 0.075 (mean + SD, 17 cells in five trains). In the typical zipper formation, the lymphocytes as well as occasional PMN were seen to rotate with a speed which in some cases could be determined by slow motion analysis. As shown in Fig. 2, rotational speed increases with decreasing cell/tube diameter ratio. In this analysis, the differences in the eccentric radial position of the cells are not taken into consideration because the cells assumed preferred radial positions within the tube, and not much variation in eccentric radial position was observed. In order to normalize the angular velocity of the rotating white cells with respect to their translational velocity down the tube (zipper velocity), the former was multiplied with the circumference of the cell. The resulting “relative rotational

0

I 0.L

I

I

I

I 0.6

FIG. 2. Top panel: Frequency of white cell rotation as a function of the cell/tube diameter ratio (d/D). Data are from PMN and lymphocytes observed in the typical “zipper” arrangement. Bottom panel: Rotational velocity, normalized with respect to zipper velocity, as a function of cell/tube diameter ratio. Data are calculated from rotational frequency and cell circumference for the same cells shown in the top panel.

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243

velocity” would have a value of unity, if there was no relative motion between the tube wall and the cell surface facing it, such as in a rolling motion. The values obtained (Fig. 2, bottom panel) clearly demonstrate that the cells were in free flow and not rolling on the tube wall because of adhesion. Due to the experimental procedure chosen, the true mean blood velocity in the tube was unknown. It was therefore not possible to determine the ratio of lymphocyte velocity to mean blood velocity which is a relevant parameter characterizing the rheological flow conditions. The flow velocity of the lymphocyte zipper in the train at the applied driving pressure averaged 0.26 mm/set. However, the speed of a free lymphocyte zipper must be greater than single PMN velocity; this is evidenced by lymphocyte accumulation in the cell train. On the other hand, the zipper velocity is lower than the velocity of free flowing single RBC. This follows from the fact that lymphocyte zippers were always found toward the end of the cell trains, while RBC accumulated immediately upstream of the PMN. Moreover, single RBC were occasionally seen to overtake the lymphocyte zipper by penetrating along a meandering course through the interlocking cell arrangement. The velocity of single RBC unimpeded by white cells may be estimated from the known tube and cell diameters to exceed mean blood velocity by approx 80% (Skalak er al., 1972), while single PMN velocity may exceed by approx 35%. These values must therefore represent the upper and lower limits for the ratio between zipper and mean blood velocity. An example of RBC penetrating through the lymphocyte zipper is demonstrated in Fig. 3. On average, the axial velocity of the penetrating RBC exceeded that of the zipper by approximately 13%. This confirms the model prediction by demonstrating the existence of a faster flow stream between and around the rotating lymphocytes. Some further details of Fig. 3 may be worth mentioning. It is apparent that the passage of the single RBC through the zipper causes each of the lymphocytes passed to be slightly retarded, thus opening up the gap through which the RBC eventually moves. This retardation may be a consequence of a slight displacement of the lymphocyte toward the tube wall. As a result, the passage of the RBC through the entire lymphocyte zipper causes some disturbance of the relative axial positions which disappears only after RBC passage is completed. It can also be seen that at the end of this process the length of the lymphocyte zipper is reduced. While these findings demonstrate that the presence of the passing RBC in the rather narrow gap between two neighboring lymphocytes causes some disturbance of the local flow profile, this effect appears to be transitory. This confirms, in principle, the overall stability of the interlocking two-file arrangement predicted by the model calculation (Sugihara-Seki and Skalak, 1989). These calculations also describe periodic oscillations of the spheres in a lateral and longitudinal motion. The present experiments could not be used to study such motions in detail, since the time periods during which zippers were seen without interference by penetrating RBC were usually too short. However, oscillatory longitudinal motions may explain occasional observations of local “compression or expansion” of the zipper. During its passage through the lymphocyte zipper the red cell is forced into a meandering pathway (Fig. 4). This causes its velocity in the axial direction to be slightly (by approx 2.8%) lower than the actual velocity. All lymphocytes appear to remain in a rather constant eccentric radial position with their centers

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AXIAL 20

POSITION,

pm LO

f50

1

1.2

FIG. 3. Variation with time of axial cell position along the traveling tube of several lymphocytes (small dots) and two RBC (large dots). Data are taken from a video sequence in which the RBC were observed to penetrate the interlocking lymphocyte arrangement (photograph below taken from the video monitor at 0.6 set, arrowheads).

approx halfway between the tube center and the marginal exclusion zone. A narrow marginal gap between lymphocytes and tube wall exists in which flow is backward relative to the cells; this is made evident by occasional observation of platelets or even single red cells in this region of the tube cross-section showing relative backward movement. The flow path of RBC shown in Fig. 4 appears to exhibit some degree of asymmetry; this may indicate that the passing red cells analyzed here were not perfectly centered in the vertical midplane of the tube. The study presented describes a flow situation which is somewhat unique due to the unusually high lymphocyte concentration, which is not normally expected in microvessels. In the case of increased interaction between leukocytes and microvascular endothelium, with large numbers of cells rolling on the endothelial surface, seemingly similar situations may exist. However, in such cases the velocity of the rolling cells is strongly determined by the adhesive interaction. If similar arrangements (“zipper”) are seen under such circumstances, they are brought about by the geometrical conditions rather than by hydrodynamic interaction during free flow. As a consequence, the motion of the rolling cells relative to the vessel wall is much slower than in the present case, and the values

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-1 0

0.2

0.4

0.6 TIME.s

0.8

1

1.2

FIG. 4. Variation with time of relative radial cell position of eight lymphocytes forming a zipper and one RBC passing through. r/R = distance from tube axis, normalized with respect to tube radius. Dashed lines indicate exclusion zone (minimum distance from the tube wall of the center of a spherical lymphocyte).

of “relative rotational velocity” case described here (Fig. 2).

would be much closer to unity than found in the

REFERENCES P., PRIES, A. R., AND NOBIS, U. (1984). Flow behaviour of white cells in capillaries. In “White Cell Mechanics: Basic Science and Clinical Aspects” (H. J. Meiselman, M. A. Lichtman, and P. L. LaCelle, Eds.), pp. 147-157. A. R. Liss, New York. SECOMB, T. W., PRIES, A. R., AND GAEHTGENS, P. (1987). Hematocrit fluctuations within capillary tubes and estimation of Fahraeus effect. Int. J. Microcirc.: Clin. Exp. 5, 335-345. SKALAK, R., CHEN, P. H., AND CHIEN, S. (1972). Effect of hematocrit and rouleaux on apparent viscosity in capillaries. Biorheology 9, 67-82. SUGIHARA-SEKI, M., AND SKALAK, R. (1988). Numerical study of asymmetric flows of red blood cells in capillaries. Microvasc. Res. 36, 64-74. SUGIHARA-SEKI, M., AND SKALAK, R. (1980). Stability of particle motions in a narrow channel flow. Biorheology 26, 261-27. GAEHTGENS,