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Platelet retention test: Accumulation of corpuscles at the advancing blood-air interface
MICROVASCULAR
RESEARCH
Platelet
HARRY
9, 304-309 (1975)
Retention Test: at the Advancing
Accumulation of Corpuscles Blood-Air Interface’
L. GOLDSMITH*, PAUL L. RIFKIN, AND MARJORIE B. ZUCKER
McGill University Medical Clinic, Montreal General Hospital, Montreal, Quebec H3G 1A4, and the Departments of Pathology and Medicine, New York University School of Medicine, New York, N. Y. 10016 Received August 12, 1974 The hematocrit of the first drops of EDTA human blood emerging from a column of glass beads was greater than that in the syringe reservoir. Relative to the reservoir concentration the increase was greater at lower hematocrits, similar results being obtained with ghost cells suspended in plasma. The number concentration of platelets in platelet-rich plasma was also appreciably greater in the first drops than in the reservoir, but in whole blood there was no significant accumulation of platelets in the first drops. The results may be explained by postulating an accumulation of blood cells at the advancing suspension-air interfaces in the channels of the column of beads, similar effects having been previously observed at the advancing meniscus of suspensions of rigid spherical particles flowing through glass tubes.
INTRODUCTION When native, heparinized or titrated blood is passed through a column of glass beads at an appropriate rate, platelets are retained (Hellem, 1960; Bowie et al., 1969; Coller and Zucker, 1971). The mechanism of platelet retention is poorly understood. It was originally thought that ADP released from erythrocytes was responsible. However, recent evidence suggests that the released ADP comes from platelets (McPherson et al., 1974) and that the role of the erythrocytes is to produce a marked lateral dispersion of plasma and platelets which greatly increases the frequency of collisions between platelets and the beads and with each other (Goldsmith, 1971; Zucker et al., 1972). Our interest in this test prompted us to study the changes in hematocrit and platelet count of the first drops of blood passingthrough the column of glass beads. This led to the finding that there was always a significant increase in red cell concentration in the first drop issuing from the column, an observation made earlier with longer columns by O’Brien and Heywood (1967). This and subsequent experiments with ghost cells and platelet-rich plasma form the subject of this paper. METHODS The method for passing blood through a column of beads was based on that of Bowie et al. (1969)asmodified by Coller and Zucker (1971). However, to avoid retention 1 This work was supported in part by USPHS Grant Nos. HL-12859 and S-TOl-AM-05283 from the National Heart and Lung Institute. 2 Research Associate of the Medical Research Ccuncil of Canada. 304 Copyright 0 1975 by Academic Press, Inc. All rights of reproduction Printed in GreatBritain
in any form reserved.
CELL ACCUMULATION
AT BLOOD-AIR
INTERFACE
305
of platelets in the column, blood was drawn into a plastic syringe containing 0.013 ~1 15 % K,HEDTA per ml blood instead of heparin. The contents were mixed by rolling the syringe between the palms 15 times in each of two planes. The syringe was placed on a Harvard pump and the blood forced at a rate of 5.7 ml/min through a column made of plastic tubing 41.3 cm long, 0.30 cm internal diameter containing 3.9 g glass beads (3M Co., 070-5005), 0.047 cm mean diameter. Other details of the method have been reported elsewhere (Coller and Zucker, 1971). In preliminary experiments it was noted that the first drop or two of EDTA-treated blood passing through a column of unwashed beads usually clotted presumably because of residual calcium on the unwashed beads. Therefore the beads were washed with 0.1% EDTA followed by distilled water, or with water alone and dried overnight at 100°C before filling the columns. Washing did not affect platelet retention as measured with heparinized blood. Drops emerging from the column fell serially onto Parafilm and were covered with a Petri dish containing moist paper; microhematocrits and duplicate platelet counts were carried out immediately on the drops and on the reservoir of blood remaining in the syringe after it was thoroughly mixed. The platelets in 1 square millimeter of a hematocytometer chamber were counted under phase contrast as described by Brecher and Cronkite (1950). Judging by their results, the reproducibility of duplicate counts was about &8 % (Brecher et al., 1953). The “plasma platelet count” was calculated by dividing the whole blood platelet count by (I-hematocrit). Experiments were also performed on platelet-rich plasma. In these, platelets were counted using a Coulter Counter Model B with a 70 pm orifice tube (Bull et al., 1965). The hematocrit was increased in some experiments by centrifuging the blood at about 300 g for 10 min, removing some platelet-rich plasma, and remixing. This avoided packing the erythrocytes or platelets tightly. In other experiments, the hematocrit was lowered by adding platelet-poor plasma to whole blood. Ghost cells were prepared by lysis in 20 mosmolar phosphate buffer (Dodge et al., 1963; Zucker et al., 1972). The number concentration of cells was determined under phase contrast using a hematocytometer. RESULTS The hematocrit cI of the first drop of blood emerging from the column was always considerably higher than that of the blood in the reservoir syringe, c,. A typical outflow curve of hematocrit against drop number is shown in Fig. 1. After the first drop, the hematocrit fell, usually reaching the reservoir concentration by the fourth or fifth drop, i.e., by the time 0.2-0.25 ml of blood had passed through the column. Sometimes, as illustrated in Fig. 1, the hematocrit of the fourth and fifth drops fell a little below that of the reservoir, although the mean concentration in drops 4-7 was statistically not significantly different from that in the reservoir. Table 1 gives mean values of the increase, c,-c,, and relative increase, (cl-c,)/cO, in red cell concentration of the first drop within various ranges of hematocrit, increasing from 13 to 57 %. Similar results were obtained with platelet-rich plasma, as shown by the second curve (open circles) in Fig. 1. In seven experiments in which the reservoir concentration n, varied from 4.1 x lo5 to 8.7 x lo5 cells/pi, the mean relative increase in platelet con-
306
GOLDSMITH,
RIFKIN,
AND
ZUCKER
centration of the first drop was 25.6% + 2.1 % (SD). In contrast, the platelet number concentration n, calculated for the plasma in the first drops of whole blood was not significantly different from that in the reservoir syringe over a range n, from 1.4 x lo5 to 5.6 x IO5 cells/PI (Table 1).
44
L ,-c Reservoir
A2
;
40
0
. I
2
3
5
4
Drop
6
7
a
9
’ 500
IO
w
Number
FIG. 1. Hematocrit in the first drops of whole blood (filled circles) and platelet concentration m the first drops of platelet-rich plasma (open circles) emerging from a column of glass beads. TABLE 1 RED CELL AND PLATELETCONCENTRATION CHANGESIN FIRST DROPOF BLEND
Red cells Hematacrit, %
Platelets No. of cells/p1 plasma x low3 (calculated)’
Mean increase in first drop Reservoir, No. of c, range runs 13-19 20-29 33-39 4G44 45-49 50-57
11 8 10 8 11 5
Cl-CO 4.4 + 0.2” 6.7 + 0.4 9.3 rf: 0.6 9.9 ?I 0.6 10.3 k 0.6 9.2 + 0.7
(cl-3/to,
%
29.1 + 1.1” 28.4 _+1.4 25.5 + 1.6 23.9 f 1.6 22.3 + 1.4 17.5 * 1.1
Mean increase in first drop Reservoir, No. of runs n, range 140-380 390-560
9 9
nt-% -1.4 + 10.8” -3.2+ 3.2
h-no)/&,
%
-1.8 + 4.2” -2.9 -t 2.6
ROne standard deviation. b In 18 experiments in which the hematocrit varied from 17 to 57; obtained by dividing whole blood platelet count by (1-hematocrit).
The data on red cells, summarized in Table 1, are plotted in Fig. 2 and it is evident that there is a considerable scatter in the values of the relative increase in red cell concentration in each hematocrit range. Nevertheless, as indicated by the mean values in Table 1, there was a significant increase in the relative accumulation of cells with decreasing hematocrit until reservoir concentrations below 20% were reached. As
CELL ACCUMULATION
AT BLOOD-AIR
INTERFACE
307
shown in Table 2, a similar effect of concentration was seenin experiments carried out with suspensionsof red cell ghosts in plasma. With platelet-rich plasma, however, no such trend could be discerned, but it should be remembered that the particle volume concentration in these runs only ranged from 0.36 to 0.69% (assuming a mean corpuscular volume 8 pm3).
. i---L1
I,.
40
20 Reservoir
60
Hemotocrit,
CO, %
FIG. 2. Relative increase in hematocrit of the first drop of blood as a functionrof the reservoir concentration.
TABLE 2 ACCUMULATION
OF GHOST CELLS IN FIRST SUSPENSION
DROP
OF
Ghost cells, PI-’ x 10m3 Reservoir no
First drop n1
nl-no
3350
5250 6750 6350 7200
1900 1750 1320 680
8000
1000
5ooo 5030 6520 7000
n,-no no % 57 35 26
10 14
DISCUSSION When the blood first enters the column of dry beads, it advancesin a seriesof small channels eachhaving an air-blood interface. It has beenknown for sometime that when dilute suspensionsof neutrally buoyant spheresflow through narrow, empty circular tubes there is an accumulation of particles at the advancing liquid-air meniscus, the contrary being true at the receding meniscus when the tube empties (Whitmore, 1959; Bhattacharji and Savic, 1965; Karnis and Mason, 1967). A theoretical analysis of the streamlines followed by particles in the region at, and immediately behind the meniscus (Bhattacharji and Savic, 1965), showed that the particles arriving at the interface on centrally located streamlines at velocities faster than the meniscus move radially
308
GOLDSMITH, RIFKIN, AND ZUCKER
outward and return on slower moving paths nearer the tube walls. As a result, there is a net gain of particles at the meniscus and for some distance behind it. The particle paths were measuredexperimentally (Karnis and Mason, 1967)in dilute suspensionsof rigid spheres(c, < 2%) and found to be in substantial agreement with the theory. The observations were extended to concentrations as high as 40% and it was found that the rate of accumulation of spheresat the interface increased with increasing reservoir concentration, although the relative increase in meniscusconcentration at a given time was greater at lower reservoir concentrations. It was also noted that the rate of accumulation was greater the larger the ratio of sphere to tube diameter. The above phenomenon was earlier qualitatively observed in whole blood flowing through glass tubes by Fahraeus (1928) and Vejlens (1938). It appears reasonable then to suppose that the observed increase in hematocrit in the first drops of blood issuing from the column is due to the accumulation of red blood cells at the air interfaces of the numerous little channels as the blood percolates through the tube. A gross estimate of the mean channel thickness within the column can be made assuming an interstitial volume of 42 %, as experimentally found by Cronberg (1967), and dividing the total bead surface area (199 cm”) into the total interstitial volume (1.23 cm3). This yields an average channel thickness of 61 pm, only eight times the diameter of the erythrocyte and -20 times that of the platelet. From the results of model experiments (Karnis and Mason, 1967), one would have expected a much more rapid accumulation of red cells and ghost cells than that of platelets; however no runs with platelets were possible at comparable volume concentrations. Nevertheless, the results do show some of the effects expected: thus the relative increasein red cell and ghost cell concentrations in the first drop was somewhat greater at lower reservoir concentrations. No such effect was observed in the plateletrich plasma, presumably becausethe volume concentrations were very low and covered too small a range. At a given hematocrit, the relative increase in red cell concentration in the first drop exhibited considerable scatter (Fig. 2). This is likely due to the fact that one is dealing with a multitude of small, noncylindrical and nonuniform channels in which separate streams of blood flowing at locally varying rates continually meet and diverge again. Nor can the conditions in the column be expected to be exactly reproduced from one run to the next. The result that platelets did not accumulate in the first drops of whole blood is of interest. Presumably, this is evidence of the much faster arrival of the larger red cells at the menisci. In addition, there is the effect of red cells on platelets during flow; as shown by model studies in tubes (Goldsmith, 1971), continual interactions between red cells result in marked lateral displacements of the platelets and one would expect numerous collisions with the beads.The resultant mixing of platelets within the blood will tend to offset their accumulation at the advancing meniscus, such as occurred in the absenceof red cells. ACKNOWLEDGMENTS The authors are indebted to the members of the Columbia University Seminar on Biomaterials for useful discussions, Sook-Ja Kim and Larry Marcus for their technical assistance and Hedi Podbere for typing the manuscript.
CELL ACCUMULATION
AT BLOOD-AIR
INTERFACE
309
REFERENCES BHATTACHARII, S., AND SAVIC, P. (1965). Real and apparent non-Newtonian behaviour in viscous pipe
flow of suspensions driven by a fluid piston. In “Proc. Heat Transfer Fluid Mech. Inst.” (A. F. Charwat et al., eds.), pp. 248-262. Stanford University Press, Stanford, CA. BOWIE, E. J. W., OWEN, C. A., JR., THOMPSON, J. H., JR., AND DIDISHEIM, P. (1969). Platelet adhesiveness in von Willebrand’s disease. Amer. J. Clin. Pathol. 52,69-77. BRECHER, G., AND CRONKITE, E. P. (1950). Morphology and enumeration of human blood platelets. J. Appl. Physiol. 3, 365-377. BRECHER, G., SCHNEIDERMAN, M., AND CRONKITE, E. P. (1953). The reproducibility and constancy of the platelet count. Amer. J. Clin. Pathol. 23, 15-26. BULL, B. S., SCHNEIDERMAN, M. A., AND BRECHER, G. (1965). Platelet counts with the Coulter Counter. Amer. J. Clin. Pathol. 44,678-688. COLLER, B. S., AND ZUCKER, M. B. (1971). Reversible decrease in platelet retention by glass bead columns (adhesiveness) induced by disturbing the blood. Proc. SOC. Exp. Biol. Med. 136, 769-771. CRONBERG, S. (1967). Methodological problems in testing of platelet adhesiveness. &and. J. Haematol. 4,385-400. DODGE, J. T., MITCHELL, C., AND HANAHAN, D. J. (1963). The preparation and chemical characteristics of hemoglobin-free ghosts of human erythrocytes. Arch. Biochem. Biophys. 100,119-130. FAHRAEUS, R. (1928). Die Stromungsverhalten und die Verteilung der Blutzellen im Gefassystem. Zur Frage der Bedeutung der intravascularen Erythrocyten Aggregation. Klin. Wochenschr.7,100-106. FRIEDBERG, N. M., AND ZUCKER, M. B. (1972). ADP as the cause of reversible inhibition of platelet retention in glass-bead columns. J. Lab. Chin. Med. 80,603-612. GOLDSMITH, H. L. (1971). Red cell motions and wall interactions in tube flow. Fed. Proc. 30,1578-1588. HELLEM, A. J. (1960). The adhesiveness of human blood platelets in vitro. Stand. J. Clin. Lab. Invest. 12 (Suppl. 51), l-l 17. KARNIS, A., AND MASON, S. G. (1967). The flow of suspensions through tubes. VI. Meniscus effects. J. Colloid Interface Sci. 23, 120-133. MCPHERSON, V. J., ZUCKER, M. B., FRIEDBERG, N. M., AND RIFKIN, P. L. (1974). Platelet retention in glass bead columns: further evidence for the importance of ADP. Blood 44,411-425. O’BRIEN, J. R., AND HEYWOOD, J. B. (1967). Some interactions between human platelets and glass: von Willebrand’s disease compared with normal. J. Clin. Pathol. 20, 56-64. VEILENS, G. (1938). The distribution of leucocytes in the vascular system. Acta Pathol. Microbial. &and. Suppl. XxX111, 159-190. WHITMORE, R. L. (1959). The viscous flow of disperse suspensions in tubes, In “Rheology of Disperse Systems” (C. C. Mills, ed.), pp. 49-60. Pergamon, New York. ZUCKER, M. B., RIFKIN, P. L., FRIEDBERG, N. M., AND COLLER, B. S. (1972). Mechanisms of platelet function as revealed by the retention of platelets in glass bead columns. Ann. N. Y. Acad. Sci. 201, 138-144.
RESEARCH
Platelet
HARRY
9, 304-309 (1975)
Retention Test: at the Advancing
Accumulation of Corpuscles Blood-Air Interface’
L. GOLDSMITH*, PAUL L. RIFKIN, AND MARJORIE B. ZUCKER
McGill University Medical Clinic, Montreal General Hospital, Montreal, Quebec H3G 1A4, and the Departments of Pathology and Medicine, New York University School of Medicine, New York, N. Y. 10016 Received August 12, 1974 The hematocrit of the first drops of EDTA human blood emerging from a column of glass beads was greater than that in the syringe reservoir. Relative to the reservoir concentration the increase was greater at lower hematocrits, similar results being obtained with ghost cells suspended in plasma. The number concentration of platelets in platelet-rich plasma was also appreciably greater in the first drops than in the reservoir, but in whole blood there was no significant accumulation of platelets in the first drops. The results may be explained by postulating an accumulation of blood cells at the advancing suspension-air interfaces in the channels of the column of beads, similar effects having been previously observed at the advancing meniscus of suspensions of rigid spherical particles flowing through glass tubes.
INTRODUCTION When native, heparinized or titrated blood is passed through a column of glass beads at an appropriate rate, platelets are retained (Hellem, 1960; Bowie et al., 1969; Coller and Zucker, 1971). The mechanism of platelet retention is poorly understood. It was originally thought that ADP released from erythrocytes was responsible. However, recent evidence suggests that the released ADP comes from platelets (McPherson et al., 1974) and that the role of the erythrocytes is to produce a marked lateral dispersion of plasma and platelets which greatly increases the frequency of collisions between platelets and the beads and with each other (Goldsmith, 1971; Zucker et al., 1972). Our interest in this test prompted us to study the changes in hematocrit and platelet count of the first drops of blood passingthrough the column of glass beads. This led to the finding that there was always a significant increase in red cell concentration in the first drop issuing from the column, an observation made earlier with longer columns by O’Brien and Heywood (1967). This and subsequent experiments with ghost cells and platelet-rich plasma form the subject of this paper. METHODS The method for passing blood through a column of beads was based on that of Bowie et al. (1969)asmodified by Coller and Zucker (1971). However, to avoid retention 1 This work was supported in part by USPHS Grant Nos. HL-12859 and S-TOl-AM-05283 from the National Heart and Lung Institute. 2 Research Associate of the Medical Research Ccuncil of Canada. 304 Copyright 0 1975 by Academic Press, Inc. All rights of reproduction Printed in GreatBritain
in any form reserved.
CELL ACCUMULATION
AT BLOOD-AIR
INTERFACE
305
of platelets in the column, blood was drawn into a plastic syringe containing 0.013 ~1 15 % K,HEDTA per ml blood instead of heparin. The contents were mixed by rolling the syringe between the palms 15 times in each of two planes. The syringe was placed on a Harvard pump and the blood forced at a rate of 5.7 ml/min through a column made of plastic tubing 41.3 cm long, 0.30 cm internal diameter containing 3.9 g glass beads (3M Co., 070-5005), 0.047 cm mean diameter. Other details of the method have been reported elsewhere (Coller and Zucker, 1971). In preliminary experiments it was noted that the first drop or two of EDTA-treated blood passing through a column of unwashed beads usually clotted presumably because of residual calcium on the unwashed beads. Therefore the beads were washed with 0.1% EDTA followed by distilled water, or with water alone and dried overnight at 100°C before filling the columns. Washing did not affect platelet retention as measured with heparinized blood. Drops emerging from the column fell serially onto Parafilm and were covered with a Petri dish containing moist paper; microhematocrits and duplicate platelet counts were carried out immediately on the drops and on the reservoir of blood remaining in the syringe after it was thoroughly mixed. The platelets in 1 square millimeter of a hematocytometer chamber were counted under phase contrast as described by Brecher and Cronkite (1950). Judging by their results, the reproducibility of duplicate counts was about &8 % (Brecher et al., 1953). The “plasma platelet count” was calculated by dividing the whole blood platelet count by (I-hematocrit). Experiments were also performed on platelet-rich plasma. In these, platelets were counted using a Coulter Counter Model B with a 70 pm orifice tube (Bull et al., 1965). The hematocrit was increased in some experiments by centrifuging the blood at about 300 g for 10 min, removing some platelet-rich plasma, and remixing. This avoided packing the erythrocytes or platelets tightly. In other experiments, the hematocrit was lowered by adding platelet-poor plasma to whole blood. Ghost cells were prepared by lysis in 20 mosmolar phosphate buffer (Dodge et al., 1963; Zucker et al., 1972). The number concentration of cells was determined under phase contrast using a hematocytometer. RESULTS The hematocrit cI of the first drop of blood emerging from the column was always considerably higher than that of the blood in the reservoir syringe, c,. A typical outflow curve of hematocrit against drop number is shown in Fig. 1. After the first drop, the hematocrit fell, usually reaching the reservoir concentration by the fourth or fifth drop, i.e., by the time 0.2-0.25 ml of blood had passed through the column. Sometimes, as illustrated in Fig. 1, the hematocrit of the fourth and fifth drops fell a little below that of the reservoir, although the mean concentration in drops 4-7 was statistically not significantly different from that in the reservoir. Table 1 gives mean values of the increase, c,-c,, and relative increase, (cl-c,)/cO, in red cell concentration of the first drop within various ranges of hematocrit, increasing from 13 to 57 %. Similar results were obtained with platelet-rich plasma, as shown by the second curve (open circles) in Fig. 1. In seven experiments in which the reservoir concentration n, varied from 4.1 x lo5 to 8.7 x lo5 cells/pi, the mean relative increase in platelet con-
306
GOLDSMITH,
RIFKIN,
AND
ZUCKER
centration of the first drop was 25.6% + 2.1 % (SD). In contrast, the platelet number concentration n, calculated for the plasma in the first drops of whole blood was not significantly different from that in the reservoir syringe over a range n, from 1.4 x lo5 to 5.6 x IO5 cells/PI (Table 1).
44
L ,-c Reservoir
A2
;
40
0
. I
2
3
5
4
Drop
6
7
a
9
’ 500
IO
w
Number
FIG. 1. Hematocrit in the first drops of whole blood (filled circles) and platelet concentration m the first drops of platelet-rich plasma (open circles) emerging from a column of glass beads. TABLE 1 RED CELL AND PLATELETCONCENTRATION CHANGESIN FIRST DROPOF BLEND
Red cells Hematacrit, %
Platelets No. of cells/p1 plasma x low3 (calculated)’
Mean increase in first drop Reservoir, No. of c, range runs 13-19 20-29 33-39 4G44 45-49 50-57
11 8 10 8 11 5
Cl-CO 4.4 + 0.2” 6.7 + 0.4 9.3 rf: 0.6 9.9 ?I 0.6 10.3 k 0.6 9.2 + 0.7
(cl-3/to,
%
29.1 + 1.1” 28.4 _+1.4 25.5 + 1.6 23.9 f 1.6 22.3 + 1.4 17.5 * 1.1
Mean increase in first drop Reservoir, No. of runs n, range 140-380 390-560
9 9
nt-% -1.4 + 10.8” -3.2+ 3.2
h-no)/&,
%
-1.8 + 4.2” -2.9 -t 2.6
ROne standard deviation. b In 18 experiments in which the hematocrit varied from 17 to 57; obtained by dividing whole blood platelet count by (1-hematocrit).
The data on red cells, summarized in Table 1, are plotted in Fig. 2 and it is evident that there is a considerable scatter in the values of the relative increase in red cell concentration in each hematocrit range. Nevertheless, as indicated by the mean values in Table 1, there was a significant increase in the relative accumulation of cells with decreasing hematocrit until reservoir concentrations below 20% were reached. As
CELL ACCUMULATION
AT BLOOD-AIR
INTERFACE
307
shown in Table 2, a similar effect of concentration was seenin experiments carried out with suspensionsof red cell ghosts in plasma. With platelet-rich plasma, however, no such trend could be discerned, but it should be remembered that the particle volume concentration in these runs only ranged from 0.36 to 0.69% (assuming a mean corpuscular volume 8 pm3).
. i---L1
I,.
40
20 Reservoir
60
Hemotocrit,
CO, %
FIG. 2. Relative increase in hematocrit of the first drop of blood as a functionrof the reservoir concentration.
TABLE 2 ACCUMULATION
OF GHOST CELLS IN FIRST SUSPENSION
DROP
OF
Ghost cells, PI-’ x 10m3 Reservoir no
First drop n1
nl-no
3350
5250 6750 6350 7200
1900 1750 1320 680
8000
1000
5ooo 5030 6520 7000
n,-no no % 57 35 26
10 14
DISCUSSION When the blood first enters the column of dry beads, it advancesin a seriesof small channels eachhaving an air-blood interface. It has beenknown for sometime that when dilute suspensionsof neutrally buoyant spheresflow through narrow, empty circular tubes there is an accumulation of particles at the advancing liquid-air meniscus, the contrary being true at the receding meniscus when the tube empties (Whitmore, 1959; Bhattacharji and Savic, 1965; Karnis and Mason, 1967). A theoretical analysis of the streamlines followed by particles in the region at, and immediately behind the meniscus (Bhattacharji and Savic, 1965), showed that the particles arriving at the interface on centrally located streamlines at velocities faster than the meniscus move radially
308
GOLDSMITH, RIFKIN, AND ZUCKER
outward and return on slower moving paths nearer the tube walls. As a result, there is a net gain of particles at the meniscus and for some distance behind it. The particle paths were measuredexperimentally (Karnis and Mason, 1967)in dilute suspensionsof rigid spheres(c, < 2%) and found to be in substantial agreement with the theory. The observations were extended to concentrations as high as 40% and it was found that the rate of accumulation of spheresat the interface increased with increasing reservoir concentration, although the relative increase in meniscusconcentration at a given time was greater at lower reservoir concentrations. It was also noted that the rate of accumulation was greater the larger the ratio of sphere to tube diameter. The above phenomenon was earlier qualitatively observed in whole blood flowing through glass tubes by Fahraeus (1928) and Vejlens (1938). It appears reasonable then to suppose that the observed increase in hematocrit in the first drops of blood issuing from the column is due to the accumulation of red blood cells at the air interfaces of the numerous little channels as the blood percolates through the tube. A gross estimate of the mean channel thickness within the column can be made assuming an interstitial volume of 42 %, as experimentally found by Cronberg (1967), and dividing the total bead surface area (199 cm”) into the total interstitial volume (1.23 cm3). This yields an average channel thickness of 61 pm, only eight times the diameter of the erythrocyte and -20 times that of the platelet. From the results of model experiments (Karnis and Mason, 1967), one would have expected a much more rapid accumulation of red cells and ghost cells than that of platelets; however no runs with platelets were possible at comparable volume concentrations. Nevertheless, the results do show some of the effects expected: thus the relative increasein red cell and ghost cell concentrations in the first drop was somewhat greater at lower reservoir concentrations. No such effect was observed in the plateletrich plasma, presumably becausethe volume concentrations were very low and covered too small a range. At a given hematocrit, the relative increase in red cell concentration in the first drop exhibited considerable scatter (Fig. 2). This is likely due to the fact that one is dealing with a multitude of small, noncylindrical and nonuniform channels in which separate streams of blood flowing at locally varying rates continually meet and diverge again. Nor can the conditions in the column be expected to be exactly reproduced from one run to the next. The result that platelets did not accumulate in the first drops of whole blood is of interest. Presumably, this is evidence of the much faster arrival of the larger red cells at the menisci. In addition, there is the effect of red cells on platelets during flow; as shown by model studies in tubes (Goldsmith, 1971), continual interactions between red cells result in marked lateral displacements of the platelets and one would expect numerous collisions with the beads.The resultant mixing of platelets within the blood will tend to offset their accumulation at the advancing meniscus, such as occurred in the absenceof red cells. ACKNOWLEDGMENTS The authors are indebted to the members of the Columbia University Seminar on Biomaterials for useful discussions, Sook-Ja Kim and Larry Marcus for their technical assistance and Hedi Podbere for typing the manuscript.
CELL ACCUMULATION
AT BLOOD-AIR
INTERFACE
309
REFERENCES BHATTACHARII, S., AND SAVIC, P. (1965). Real and apparent non-Newtonian behaviour in viscous pipe
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