Am J Physiol Heart Circ Physiol
281: H448–H456, 2001.
O2 release from erythrocytes flowing in a narrow
O2-permeable tube: effects of erythrocyte aggregation
NORIHIKO TATEISHI, YOJI SUZUKI, IWONA CICHA, AND NOBUJI MAEDA
Department of Physiology, School of Medicine, Ehime University,
Shigenobu, Onsen-gun, Ehime 791-0295, Japan
Received 5 October 2000; accepted in final form 8 February 2001
O2 TRANSFER FROM ERYTHROCYTES to tissues is influenced
by the diffusion process of O2 that has been dissociated
from the erythrocytes to the tissues. The flow behavior
of erythrocytes in microvessels and/or capillaries might
be related to the diffusion process; the pathophysiological flow conditions of erythrocytes may especially interfere with O2 diffusion. Such conditions are also
important for understanding the nature of O2 transfer
from erythrocytes to tissues. As is well known, the
plasma (cell-free) layer formed along the blood vessel
wall enhances erythrocyte flow by reducing frictional
interaction with the endothelial cells of blood vessels
(10, 19), but O2 released from erythrocytes must be
transferred through the cell-free layer via diffusion.
The cell-free layer thickness changes with the flow
behavior of erythrocytes, and this behavior is modified
by the rheological properties of the cells such as hematocrit, deformability, and aggregation (19).
The O2 transfer from erythrocytes to tissues in the
microcirculatory network is the result of a complex
process in which a substantial fraction of O2 is exchanged in the arterioles and venules, although the
major site of O2 delivery is the capillaries (7, 24). In
some tissues, more O2 is transferred from arterioles
than capillaries (6); for this reason, studies of O2 release are physiologically important in microvessels as
well as capillaries. The dynamics of such O2 transfer
have been studied by measuring the oxygenation state
of hemoglobin in erythrocytes and the flow velocity of
erythrocytes in single capillaries and/or microvessels
(7, 20). We have constructed a system composed of a
scanning spectrophotometer and an inverted microscope to record the absorption spectrum of flowing
erythrocytes in single microvessels (28). The flow velocity of the cells has been simultaneously determined
by adopting the method of dual-spots cross correlation,
and the diameter of microvessels has been measured
on a digitized video image obtained with an image
processor (28). The rate of O2 release (VO2 /dt) from
erythrocytes was determined on the basis of the change
of the absorption spectra obtained at two points on the
microvessel: the flow velocity of the cells and the diameter of the microvessels.
This paper describes the physiological importance of
flow behavior of erythrocytes in the O2 transfer from
cells to tissues in microvessels. For this purpose, the O2
released from flowing erythrocytes was measured using narrow O2-permeable tubes, and the flow behavior
of the erythrocytes was modified by the addition of
high-molecular-weight dextran, which expanded the
cell-free layer by accelerating erythrocyte aggregation
in the central flow axis. This study concludes that
Address for reprint requests and other correspondence: N. Maeda,
Dept. of Physiology, School of Medicine, Ehime Univ., Shigenobu,
Onsen-gun, Ehime 791-0295, Japan (E-mail: [email protected].
ac.jp).
The costs of publication of this article were defrayed in part by the
payment of page charges. The article must therefore be hereby
marked ‘‘advertisement’’ in accordance with 18 U.S.C. Section 1734
solely to indicate this fact.
diffusion; cell-free layer; spectrophotometry; dextran; image
processing
H448
0363-6135/01 $5.00 Copyright © 2001 the American Physiological Society
http://www.ajpheart.org
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Tateishi, Norihiko, Yoji Suzuki, Iwona Cicha, and
Nobuji Maeda. O2 release from erythrocytes flowing in a
narrow O2-permeable tube: effects of erythrocyte aggregation. Am J Physiol Heart Circ Physiol 281: H448–H456,
2001.—The effects of erythrocyte aggregation on O2 release
were examined using O2-permeable fluorinated ethylenepropylene copolymer tubes (inner diameter, 25 ␮m; outer diameter, 100 ␮m). Measurements were performed using an apparatus built on an inverted microscope that contained a
scanning-grating spectrophotometer with a photon count detector connected to two photomultipliers and an image processor through a video camera. The rate of O2 release from
the cells flowing in the narrow tube was determined based on
the visible absorption spectrum and the flow velocity of the
cells as well as the tube size. When the tube was exposed to
nitrogen-saturated deoxygenated saline containing 10 mM
sodium dithionite, the flowing erythrocytes were deoxygenated in proportion to the traveling distance, and the deoxygenation at a given distance increased with decreasing flow
velocity and cell concentration (hematocrit). Adding Dextran
T-70 to the cell suspension increased erythrocyte aggregation
in the tube, which resulted in suppressed cell deoxygenation
and increased marginal cell-free-layer thickness. The deoxygenation was inversely proportional to the cell-free-layer
thickness. The relation was not essentially altered even
when the medium viscosity was adjusted with Dextran T-40
to remain constant. The rate of O2 release from erythrocytes
in the tube was discussed in relation to the O2 diffusion
process. We conclude that the diffusion of O2 from erythrocytes flowing in narrow tubes is inhibited primarily by erythrocyte aggregation itself and partly by thickening of the
cell-free layer.
O2 RELEASE FROM RBC AGGREGATES DURING FLOW
erythrocyte aggregation (or the axial accumulation of
the cells) and/or thickening of the cell-free layer decreases O2 diffusion.
MATERIALS AND METHODS
viscometer (model E; Tokyo Keiki, Tokyo). All experiments
were carried out at 25°C.
Hemoglobin concentration and O2 saturation. The Vo2 /dt
values for erythrocytes in the narrow tube were measured
during a steady flow as previously described (28) and as
shown in Fig. 1. The apparatus consisted of an inverted
microscope containing an objective lens with ⫻40 magnification (ULWD CDPlan 40PL; Olympus Optics), a scanninggrating spectrophotometer with a sensitive photon-counting
detector (USP-410; Unisoku, Osaka), and a computer (PC386V; Epson, Tokyo). The light intensity of a halogen lamp in
the microscope was controlled by a current stabilizer (NLO
18-10; Takasago, Tokyo). The spectrophotometer was connected to the microscope eyepiece through a thin light guide
(diameter, 0.4 mm) made of quartz and was operated by the
computer. The grating was scanned by 508 steps over the
wavelength range of 499.2–600.8 nm with a gate time of 20
ms/step for photon counting; data was obtained every 0.2 nm.
One visible spectrum from a 5-␮m-diameter spot over the
centerline of the narrow tube was recorded within 20 s. The
detector counted 1 ⫻ 103 to 3 ⫻ 106 photon/s. A measuring
spot on the narrow tube within the visual field of the microscope was fixed on a monitor (PVM-1371; Sony, Tokyo)
through a video camera attached to the vertical eyepiece
(DXC-930; Sony) by sliding the stage of the microscope and/or
by rotating the cylindrical mirror.
The O2 saturation of erythrocytes during flow was determined by a modified method of Tateishi and colleagues (28).
In brief, after converting the light intensity to optical density
(OD), a numerical filtering was carried out to maximize the
signal-to-noise ratio by taking a moving average of nine
successive data points (i.e., data obtained in the range of
⫾0.8 nm). Thus one absorption spectrum constituted 51 OD
points every 2 nm. Because a spectrum from flowing cells
originates from both oxyhemoglobins and deoxyhemoglobins
and light scattering, the OD at a particular wavelength is
expressed by
OD ⫽ 关Eoxy 䡠 S ⫹ Edeoxy 䡠 共1 ⫺ S兲兴共c 䡠 d兲 ⫹ B
where S is the fraction of oxyhemoglobin (i.e., the O2 saturation); Eoxy and Edeoxy are the molar extinction coefficients of
oxyhemoglobin and deoxyhemoglobin, respectively; (c 䡠 d) is
the hemoglobin content [c is hemoglobin concentration supposing that the hemoglobin is distributed homogeneously in
a flowing erythrocyte column with the diameter, d, c can be
calculated by (c 䡠 d)/d when d is determined as described
below]; and B is a correction term for light scattering. After
converting the equation to
OD ⫽ 共Eoxy ⫺ Edeoxy兲 䡠 S 䡠 共c 䡠 d兲 ⫹ Edeoxy 䡠 共c 䡠 d兲 ⫹ B
Fig. 1. Apparatus for measurements of O2 release and flow behavior
of flowing erythrocytes in a narrow tube, constructed on an inverted
microscope. Absorption spectrum of the flowing cells was determined
with a spectrophotometer, flow velocity of the cells was determined
with photomultipliers, and distribution of the flowing cells was
determined with an image processor. See the text for details. RBC,
red blood cells.
(1)
(2)
the [S 䡠 (c 䡠 d)], (c 䡠 d), and B values were calculated by multipleregression analysis using 51 data points in the spectrum.
Flow velocity of erythrocytes. The flow velocity of erythrocytes in a narrow tube was determined as described previously (28). In brief, the light intensity changes in two spots
(diameter, 3 ␮m; separation distance, 3.4 ␮m) on the centerline of the narrow tube were conducted to two photomultipliers with fine light guides (diameter, 200 ␮m; separation
distance, 250 ␮m) connected to another eyepiece of the microscope. As described by Baker and Wayland (1), the cross
correlation between the changes of light intensity from two
spots was calculated with a computer by varying the time
delay for erythrocyte flow between the two spots. The flow
velocity of the cells (v) was estimated by dividing the distance
between the spots by the time delay to yield the maximum
correlation.
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Perfusion of erythrocytes through narrow tubes. Narrow
O2-permeable tubes [inner diameter (D), 25 ␮m; outer diameter, 100 ␮m; lengths, 300 and 500 mm] were produced from
fluorinated ethylenepropylene copolymer at Hirakawa Hewtech (Ibaraki, Japan) as described by Kubota and colleagues
(16). One end of the narrow tube was fixed with an adhesive
that passed through a 22-gauge needle (length, 200 mm), and
the open end of the needle was connected to a reservoir of
erythrocyte suspension. The narrow tube together with another portion of the needle (length, ⬃100 mm) was placed
horizontally between two wide glass plates with a short gap
(⬃2 mm) on the stage of an inverted microscope (IMT-2;
Olympus Optics, Tokyo), as shown in Fig. 1. The erythrocyte
suspension in the reservoir was mixed gently and constantly
with a magnetic stirrer. The gap between the two glass plates
was filled with isotonic phosphate-buffered saline [PBS; in
mM: 50 NaPO3, 90 NaCl, 5 KCl, and 6 glucose (pH 7.4); 285
mosM], and the gap was continuously perfused with the
saline via a peristaltic pump (SJ-1215; Atto, Tokyo). O2
release from erythrocytes in the tube was induced by perfusion of the suspension with nitrogen-bubbled saline containing 10 mM sodium dithionite. The narrow tube was not
permeable to sodium dithionite.
Fresh human erythrocytes from a healthy donor (N.
Tateishi; mean cell volume 88.6 fl; mean cell hemoglobin
concentration 34.2 g/dl; mean cell hemoglobin 30.3 pg) suspended in the isotonic PBS containing 4 g/dl of bovine serum
albumin were perfused through the tube under hydrostatic
pressure.
The flow behavior of erythrocytes in the narrow tube was
modified by the addition of 0–4.0 g/dl of Dextran T-70 (mol
wt, 70,400; Pharmacia Fine Chemicals, Uppsala, Sweden) in
the suspending medium, which induced cell aggregation in
the central flow axis of the tube (25). In some experiments,
the viscosity of the suspending medium was adjusted to 2.7
cP by supplementation with 0–5.2 g/dl of Dextran T-40 (mol
wt, 40,100; Pharmacia Fine Chemicals). The viscosity was
measured at shear rates of 3.8–380 s⫺1 with a cone-plate
H449
H450
O2 RELEASE FROM RBC AGGREGATES DURING FLOW
For the determination of the cell-free-layer thickness, the
D and d values were measured using the digitized video
image incorporated into an image processor (PIP-4000; ADS
Tech, Nara, Japan) combined with the computer according to
a previous method (28, 29). Because of the heterogeneous
distribution of erythrocytes in the narrow tube, the values
obtained for eight successive video frames were averaged to
get one measured value for d; the SD of d measured in eight
successive video frames was within 5%. The thickness of the
cell-free layer was calculated as (D ⫺ d)/2.
Statistical analysis. Statistical significance was determined by the Mann-Whitney U-test and by covariance analysis.
RESULTS
The “two-spots velocity” generally overestimates the true
mean velocity. Baker and Wayland (1) used a factor of 1.6 to
convert this velocity to a mean value. This seems accurate for
a fully developed Poiseuille radial dependence, but the
blunter velocity profiles that probably exist in the present
experiments would require a different value, probably ⬍1.6.
The degree of bluntness of the velocity profile in different flow
conditions of the cells is discussed later (see Erythrocyte
Distribution and Velocity Profile in Narrow Tubes).
Rate of O2 release: VO2/dt. The VO2 /dt values for erythrocytes were determined as previously described (28). In brief,
VO2 /dt estimated in the flow distance (L) of a narrow tube
(D ⫽ 25 ␮m in this study) is expressed as
VO2 /dt ⫽ 共S1 ⫺ S2兲 䡠 C 䡠 Q/共␲ 䡠 D 䡠 L兲
Factors Affecting O2 Release from
Flowing Erythrocytes
Traveling distance of erythrocytes. The S value of the
erythrocyte suspension (hematocrit, 30%) was determined at various points of the tube at a constant
cell-flow velocity (0.5 mm/s). In the present experiment, the boundary portion between the tube exposed
to a deoxygenated environment and the 22-gauge needle connected to the tube was the starting point (traveling distance ⫽ 0) for the measurements. The steady
flow of the cells and thus the steady formation of the
cell-free layer was obtained in the boundary portion.
The typical original absorption spectra (i.e., before numerical filtering) and the calculated S values for flowing cells obtained at traveling distances of 10, 100, and
(3)
where S1 and S2 for hemoglobin (0 ⬍ S ⬍ 1) are measured at
the upstream and downstream points, respectively; C is the
averaged concentration of hemoglobin in the narrow tube
[(c 䡠 d)/D], and Q is the flow volume [(␲ 䡠 D2 /4)v]. For greater
accuracy, the averaged values calculated at upstream and
downstream points were used for C and Q, respectively.
VO2 /dt is defined as (amount of released O2)/(inner surface
area of the tube)/(time) and is expressed as mol 䡠 m⫺2 䡠 s⫺1.
Flow dynamics of erythrocytes. The flow behavior of erythrocytes in the narrow tube was analyzed as described previously (25, 29, 30) using the apparatus as shown in Fig. 1. All
information on the flowing cells was recorded on a video tape
(SLHF-705; Sony) as we observed the study on the monitor
through the video camera.
Fig. 3. Change in deoxygenation of flowing erythrocytes with traveling distance in the narrow tube after the tube was exposed to a
deoxygenated environment (n ⫽ 5). Erythrocyte suspensions (30%
hematocrit) were perfused through the tube as described in Fig. 2.
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Fig. 2. Typical absorption spectrum of flowing erythrocytes in a
narrow tube(inner diameter, 25 ␮m; outer diameter, 100 ␮m) obtained before a numerical filtering. Erythrocytes (30% hematocrit)
suspended in isotonic saline containing 4 g/dl bovine serum albumin
were perfused at a velocity of 0.48 ⫾ 0.07 mm/s through the narrow
tube under a hydrostatic pressure of 130 cmH2O. O2 release from the
flowing cells was induced by exposing the tube to nitrogen-saturated
isotonic saline containing 10 mM sodium dithionite. Spectra were
obtained at traveling distances of 10, 100, and 200 mm. OD, optical
density; ␭, wavelength.
Two narrow, O2-permeable, fluorinated ethylenepropylene copolymer tubes (D ⫽ 25 ␮m) were conveniently
used as a model of microvessels. O2 release from erythrocytes flowing in the narrow tube was induced by
exposing the tube to nitrogen-saturated saline containing 10 mM sodium dithionite. All measurements were
carried out after a steady flow of erythrocytes was
attained in the narrow tube (actually, a few minutes
later, after perfusion of the cell suspension). The results for the measurement of S under specific experimental conditions using the tubes were reproducible
within a SD of 3%.
H451
O2 RELEASE FROM RBC AGGREGATES DURING FLOW
decreasing hematocrit from 40 to 30% (see Table 2)
owing to the accelerated axial accumulation of the
flowing cells (25, 26, 29), but the thickness was not
greatly increased by further decreases in hematocrit.
Inhibition of O2 Release by Erythrocyte Aggregation
200 mm after exposure of the tube to the deoxygenated
environment are shown in Fig. 2. The deoxygenation of
erythrocytes increased in proportion to the traveling
distance, as is shown in Fig. 3.
Flow velocity of erythrocytes. When the flow velocity
of the erythrocytes was increased, the deoxygenation of
flowing cells at a traveling distance was suppressed, as
shown in Fig. 4 and Table 1. However, VO2 /dt was
significantly increased as shown in Table 1. Furthermore, the cell-free-layer thickness slightly but significantly increased with increasing flow velocity (see Table 1) as was previously reported (26). The increment of
the thickness was not as prominent, possibly due to the
high medium viscosity (including 5.2 g/dl of Dextran
T-40) in these experimental conditions.
Hematocrit. When hematocrit decreased, the deoxygenation of flowing erythrocytes at a traveling distance
was accelerated, as shown in Fig. 4 and Table 2. As
expected, VO2 /dt decreased significantly with decreasing hematocrit, from 40 to 30%. However, the rate was
not altered between hematocrit levels of 30 and 20%
(see Table 2), possibly due to the counterbalance between the degree of deoxygenation and the hemoglobin
content in the present experimental conditions. The
cell-free-layer thickness was markedly increased with
Deoxygenation of Flowing Erythrocytes and
Cell-Free-Layer Thickness
Summarizing the experiments using Dextran T-70
in Figs. 5 and 6, a linear relationship between the S for
flowing erythrocytes and the cell-free-layer thickness
was observed, as shown in Fig. 7. Namely, the O2
release from flowing cells was inhibited by cell aggregation accompanied with the increase of in cell-free-
Table 1. Effect of flow velocity on rate of O2 release from erythrocytes flowing in narrow tube
Flow Velocity, mm/s
Cell-free-layer thickness, ␮m
O2 saturation, %
Hemoglobin content, M ⫻ ␮m
Flow velocity, mm/s
Rate of O2 release, mol 䡠 m⫺2 䡠 s⫺1
n
0.5
1.0
2.0
3.30 ⫾ 0.14
41.4 ⫾ 1.4
0.094 ⫾ 0.004
0.50 ⫾ 0.03
0.069 ⫾ 0.005
13
3.41 ⫾ 0.10
65.6 ⫾ 1.8
0.115 ⫾ 0.004
0.99 ⫾ 0.06
0.098 ⫾ 0.009*
14
3.61 ⫾ 0.14
76.2 ⫾ 2.7
0.120 ⫾ 0.003
1.98 ⫾ 0.04
0.142 ⫾ 0.019*†
13
Values are means ⫾ SD. All measurements were carried out at 100-mm traveling distance using a narrow tube of 25 ␮m inner diameter.
n, Number of measurements for O2 saturation, hemoglobin content, flow velocity, and thus rate of O2 release. Erythrocyte suspension of 30%
hematocrit was perfused. Statistical significance was determined by Mann-Whitney U-test: * P ⬍ 0.0001 vs. 0.5 mm/s; † P ⬍ 0.0001 vs.
1.0 mm/s.
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Fig. 4. Effects of flow velocity of erythrocytes and hematocrit on the
O2 saturation (S) of the flowing cells. Erythrocyte suspensions of 20%
(E), 30% (‚), and 40% (䊐) hematocrit in isotonic saline containing 5.2
g/dl Dextran T-40 and 4 g/dl bovine serum albumin (medium viscosity, 2.7 cP) were perfused through the narrow tube. Values were
determined at a 100-mm traveling distance after the tube was
exposed to nitrogen-saturated isotonic saline containing 10 mM
sodium dithionite.
The flow behavior of erythrocytes in the narrow tube
was modified by inducing erythrocyte aggregation in
the flow by addition of Dextran T-70. Furthermore,
Dextran T-40, which did not induce cell aggregation,
was used to examine the effects of medium viscosity on
O2 release from flowing cells and the cell-free-layer
thickness.
With increasing concentrations of Dextran T-70 in
the erythrocyte suspension, deoxygenation of the flowing cells was reduced and the thickness of the cell-free
layer increased, as shown in Fig. 5. However, the
deoxygenation of flowing cells and the cell-free-layer
thickness were not modified by Dextran T-40, even
though Dextran T-40 has the same medium viscosity
as Dextran T-70 (see Fig. 5). The significant difference
in cell deoxygenation between the Dextran T-70 and
Dextran T-40 experiments was clearly observed above
2 g/dl of Dextran T-70, where the differences in the
cell-free-layer thickness became evident and the erythrocyte aggregation was visible in the central flow axis.
Furthermore, the Dextran T-70-dependent changes
in the deoxygenation of erythrocytes and the cell-freelayer thickness were not essentially altered even when
the medium viscosity was adjusted to remain constant
(at 2.7 cP) by the addition of Dextran T-40, as shown in
Fig. 6.
VO2 /dt values for flowing cells were slightly but significantly decreased in the presence of Dextran T-70,
as shown in Table 3, and were not significantly altered
by increasing the medium viscosity with Dextran T-40.
H452
O2 RELEASE FROM RBC AGGREGATES DURING FLOW
Table 2. Effects of hematocrit on rate of O2 release from erythrocytes flowing in narrow tube
Hematocrit, %
Cell-free-layer thickness, ␮m
O2 saturation, %
Hemoglobin content, M ⫻ ␮m
Flow velocity, mm/s
Rate of O2 release, mol 䡠 m⫺2 䡠 s⫺1
n
20
30
40
3.77 ⫾ 0.10
26.6 ⫾ 1.4
0.075 ⫾ 0.004
0.50 ⫾ 0.02
0.068 ⫾ 0.005
19
3.30 ⫾ 0.14
41.4 ⫾ 1.4
0.094 ⫾ 0.004
0.50 ⫾ 0.03
0.069 ⫾ 0.005‡
13
1.91 ⫾ 0.07
57.0 ⫾ 1.5
0.157 ⫾ 0.005
0.50 ⫾ 0.03
0.084 ⫾ 0.007*†
14
Values are means ⫾ SD. All measurements were carried out at a flow velocity of 0.5 mm/s at 100-mm traveling distance using a narrow
tube of 25 ␮m inner diameter. Hemoglobin content and n as in Table 1. Statistical significance determined by Mann-Whitney U-test: * P ⬍
0.001 vs. 20% hemocrit; † P ⬍ 0.001 vs. 30% hematocrit; * P ⬍ 0.05 vs. 20% hematocrit, not significant.
DISCUSSION
Movement of O2 from the erythrocytes to the tissues
has been considered to take place exclusively at the
capillary level. However, this idea changed after Duling and Berne’s observations (6), and, in some tissues,
arterioles may be a greater source of O2 than capillaries (27). As recently reviewed, gas-diffusive transfer
from arterioles to capillaries, among capillaries (7, 24),
and in postcapillary venules (13) may play an important role in regulating homogeneous tissue oxygenation. Thus O2-permeable artificial narrow (D ⫽ 25
␮m) tubes made of fluorinated ethylenepropylene copolymer are useful for the study of dynamic O2-release
processes.
Experiments Using Narrow O2-Permeable Tubes
The experimental setups that employ O2-permeable
tubes having D ⫽ 25 ␮m are different from in vivo
conditions of microvessels with D ⫽ 25 ␮m in three
Fig. 5. Effects of Dextran T-70 and Dextran T-40 on the deoxygenation of erythrocytes (A) and the thickness of the cell-free layer (B).
Concentrations of Dextran T-70 (average mol wt, 70,400; 0–4.0 g/dl;
E) or Dextran T-40 (average mol wt, 40,100; 0–5.2 g/dl; ‚) in erythrocyte suspension (30% hematocrit) containing 4 g/dl bovine serum
albumin were graduated in the same medium viscosity (1.5–2.7 cP).
Suspension was perfused at an erythrocyte-flow velocity of 0.50 ⫾
0.07 mm/s (n ⫽ 70) through the narrow tube. Values were measured
at a 100-mm traveling distance after exposure of the tube to the
deoxygenated environment. Number of measurements, 10 ⫾ 1 for S
and 720 ⫾ 100 for cell-free layer thickness. Significantly different S
values between Dextran T-70 and Dextran T-40, P ⬍ 0.002 at 1.8 cP
and P ⬍ 0.001 at ⱖ2.1 cP.
Fig. 6. Effects of Dextran T-70 on deoxygenation of erythrocytes (A)
and thickness of the cell-free layer (B). Measurements in the presence of Dextran T-70 were carried out under the same experimental
conditions as in Fig. 5 except the medium viscosity was adjusted by
the supplement of Dextran T-40 to be constant (2.7 cP). Values were
measured at a 100-mm traveling distance after exposure of the tube
to the deoxygenated environment. Significantly different S values
between 0 g/dl of Dextran T-70 and 1 g/dl of Dextran T-70: P ⬍ 0.001.
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layer thickness. In the present experimental conditions, the relationship between S (percent) and cellfree-layer thickness (T; ␮m) could be approximately
expressed as the linear equation S ⫽ 6.4T ⫹ 22 (r ⫽
0.842).
H453
O2 RELEASE FROM RBC AGGREGATES DURING FLOW
Table 3. Effects of Dextran T-70 and Dextran T-40 on rate of O2 release
from erythrocytes flowing in narrow tube
Cell-free-layer thickness, ␮m
O2 saturation, %
Hemoglobin content, M ⫻ ␮m
Flow velocity, mm/s
Rate of O2 release, mol 䡠 m⫺2 䡠 s⫺1
n
No Dextran
Dextran T-40
(5.2 g/dl)
Dextran T-70
(4.0 g/dl)
3.30 ⫾ 0.09
42.5 ⫾ 1.6
0.103 ⫾ 0.005
0.49 ⫾ 0.05
0.073 ⫾ 0.010
11
3.24 ⫾ 0.11
42.0 ⫾ 1.3
0.100 ⫾ 0.004
0.52 ⫾ 0.02
0.076 ⫾ 0.007‡
10
4.48 ⫾ 0.13
51.0 ⫾ 1.7
0.101 ⫾ 0.015
0.51 ⫾ 0.03
0.064 ⫾ 0.011*†
10
Values are means ⫾ SD. All measurements were carried out at a flow velocity of 0.5 mm/s at 100-mm traveling distance using a narrow
tube of 25 ␮m inner diameter. Erythrocyte supsension of 30% hematocrit was perfused with or without dextran to examine effects of
erythorycte aggrebation and medium viscosity on rate. Hemoglobin content and n as in Table 1. Statistical significance determined by the
Mann-Whitney U-test: * P ⬍ 0.05 vs. no dextran; † P ⬍ 0.02 vs. 5.2 g/dl Dextran T-40; ‡ P ⬍ 0.05 vs. 5.2 g/dl Dextran T-40, not significant.
Erythrocyte Distribution and Velocity Profile
in Narrow Tubes
To understand O2 release from cells in the narrow
tube, the erythrocyte distribution and velocity profile
within the lumen of the tube must be taken into consideration. Deviation of the centerline hematocrit from
the true discharge hematocrit depends on the erythrocyte distribution within the lumen and also on the
velocity profile (8): the centerline hematocrit (or hemoglobin concentration, c) is lower than the true discharge hematocrit (or hemoglobin concentration, C) for
parabolic velocity profiles but higher than the true
discharge hematocrit for blunt velocity profiles.
Table 4 shows the degree of bluntness of the velocity
profile that can be represented by the ratio of c:C,
which was calculated using the results in Tables 1, 2,
and 3. The higher this ratio, the more blunt are the
velocity profiles. An increase in velocity leads to a more
blunt velocity profile, whereas an increase in the discharge hematocrit is apt to lead to a less blunt velocity
profile. Interestingly, an increase in erythrocyte aggregation in the presence of Dextran T-70 leads to a more
blunt velocity profile. The degree of bluntness in the
presence of the dextrans may depend on the concentration, the hematocrit, and the flow velocity. For blunt
velocity profiles, the ratio of c:C would also decrease if
the erythrocyte distribution tended to be more uniform
(i.e., a blunt heme profile). Hence the present results
may also be interpreted as an increase in the bluntness
of the heme profile for blunt velocity profiles.
For practical distribution of S, hemoglobin concentration, and velocity, the centerline S value can be
shown to be close to the true discharge value. Hence we
may regard the value of the centerline S as the discharge S. This is exactly true if the distribution of S is
uniform, which was the case in this study.
Factors Affecting O2 Release from Erythrocytes
in the Narrow Tube
Fig. 7. Relationship between S of flowing erythrocytes and cell-freelayer thickness (T) observed in the narrow tube when erythrocyte
aggregation was induced by Dextran T-70. Data are from Fig. 5
(F, medium viscosity varied) and Fig. 6 (E, medium viscosity kept
constant with Dextran T-40). Relationship between S (percent) and T
(␮m) can be approximately expressed by the linear equation S ⫽
6.4T ⫹ 22 (r ⫽ 0.842).
Some fundamental factors affecting O2 release from
flowing erythrocytes in the narrow tube were first
analyzed in this study using an apparatus constructed
in our laboratory (28). In brief, first, O2 release from
flowing cells was increased in proportion to the travel-
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primary ways. First, the thickness of the tube walls
was much greater than in microvessels, thus O2 diffusion to the surrounding media was more reduced. In
this regard, the narrow tube was less elastic than
microvessels. The elasticity of the tube affects the flow
behavior of the erythrocytes and thus changes the flow
resistance: the hematocrit-dependent changes in the
cell-free-layer thickness were much smaller in the lesselastic microvessels (21) and thus in the tube. Furthermore, the narrow tube has a smooth inner surface
whereas microvessels have an irregular surface with
endothelial cells; additionally, the two differ in chemical characteristics. These variations cause different
kinds of cell flow and flow resistance (26). Second, the
flow velocity (0.5–2 mm/s) was less than in microvessels (⬃3 mm/s). This influence may be assumed by
extrapolation of the present results (see Table 1).
Third, the tube length was much greater than the
microvessel length; therefore, although an equilibrated
flow of the cells occurred in the narrow tube, it might
not be achieved in the microvessels.
Despite these differences in physiological conditions,
the narrow O2-permeable tube is a convenient model
for fundamental analyses of O2 transfer from erythrocytes to tissues with regard to cell-flow dynamics.
H454
O2 RELEASE FROM RBC AGGREGATES DURING FLOW
Table 4. Effects of flow velocity, hematocrit, and
erythrocyte aggregation on the degree of bluntness
of the velocity profile
Experimental Variable
Values
Effect of flow velocity at 30% hematocrit
Flow velocity (v), mm/s
Cell-free-layer thickness [(D ⫺ d)/2], ␮m
Width of erythrocyte column (d), ␮m
Hemoglobin content (c 䡠 d), M ⫻ ␮m
Hemoglobin content/width of erythrocyte
column (c), mM
Discharge hemoglobin concentration (C),
mM
c/C
0.5
1.0
2.0
3.30
3.41
3.61
18.4
18.2
17.8
0.094 0.115 0.120
5.12
6.33
6.75
6.36
6.36
6.36
0.81
1.00
1.06
Effect of hematocrit at 0.5 mm/s flow velocity
c/C
1.01
0.80
0.87
Effect of erythrocyte aggregation at 30% hematocrit
and 0.5 mm/s flow velocity
Dextran
None
T-40
T-70
Cell-free-layer thickness, ␮m
3.30
3.24
4.48
Width of erythrocyte column, ␮m
18.4
18.5
16.0
Hemoglobin content, M ⫻ ␮m
0.103 0.100 0.101
Hemoglobin content/width of erythrocyte
column, mM
5.60
5.40
6.31
Discharge hemoglobin concentration, mM
6.36
6.36
6.36
c/C
0.88
0.85
0.99
All data are from Tables 1, 2, and 3, which were obtained using a
narrow tube of 25 ␮m inner diameter (D). Note that c/C is also equal
to hematocrit in erythrocyte column (calculated from centerline
measurements) divided by discharge hematocrit.
ing distance in the tube in the present experimental
conditions because of a longer exposure to the deoxygenated environment (see Fig. 3). The mechanism for
the linear decrease in S in these experiments is unknown; however, it may be explained by both the PO2
gradient from the outer surface (zero) to the inner
surface of the tube and the inhomogeneous distribution
of the cells in the tube (such as cell-free-layer formation and axial accumulation of the cells) under a steady
flow. It may be also noted that under steady flow, O2
dissociation from the cells was not in an equilibrium
state at an O2 tension near the inner wall of the tube.
Second, increases in erythrocyte-flow velocity suppressed deoxygenation of the cells at given traveling
distance (see Fig. 4) due to reduced exposure times to
the deoxygenated environment. However, VO2 /dt was
increased (see Table 1) because of the longer traveling
distance of the cells within the deoxygenated environment. As previously described (Rate of O2 release:
VO2/dt), VO2 /dt can be expressed as (amount of O2
released per unit of traveling distance) ⫻ (traveling
distance per unit time); an increase in flow velocity will
decrease the former term (see Fig. 4) but increase the
latter term. When the latter overcomes the former with
Process of O2 Release from Erythrocytes
in Narrow Tube
VO2 /dt is an operational parameter in the state of
steady flow of erythrocytes. This parameter is affected
by 1) dissociation of O2 from hemoglobin in the cells,
2) diffusion in the cells including the membrane, 3)
diffusion in plasma, and 4) passage across the wall of
the narrow tube.
Dissociation of O2 from hemoglobin. The dissociation
rate of O2 from hemoglobin is physiologically affected
by pH, PCO2, 2,3-diphosphoglycerate concentration in
erythrocytes, and temperature (31). The present study
was carried out using fresh blood.
Cell diffusion. As is generally recognized, the biconcave-disc shape of erythrocytes minimizes the diffusion
distance of O2 from inside to outside the cells. However, O2 release from the cells depends on the flow
velocity (15, 28), because O2 diffusion in deformable
cells is enhanced by stirring within the interior (20).
As opposed to the single-cell situation, aggregation of
cells reduces the surface area-to-volume ratio of the
aggregate for O2 release; therefore, the diffusion of O2
embedded in large aggregates will be retarded, even if
high shear flow stirs the aggregate interior and intracellular hemoglobin facilitates the O2 diffusion. Recently it was shown that clustered distribution of
erythrocytes results in the reduction of CO diffusion
capacity in alveolar capillaries (12), which may be
essentially related to the substantial resistance of encapsulated hemoglobin (as a cell) to O2 transport (3).
The present experiment clearly shows retardation of
O2 release with the progress of erythrocyte aggregation.
Erythrocyte membranes may not limit O2 diffusion
as has been postulated experimentally and theoretically (17, 31), but the stagnant (unstirred) layer surrounding the cells would be a barrier for O2 diffusion
(3, 15). The flow in the present experiment was laminar
with a low Reynolds number, and thus would be less
effective regarding mixing of the cell interior and reduction of the stagnant layer as compared with turbulent flow (9). However, in erythrocyte aggregates, such
a stagnant layer may have an important role in O2
transfer.
Diffusion in plasma. The reaction rate between carbon monoxide and myoglobin depends on the reciprocal
of the solvent viscosity (11, 22). However, at least in
the present experimental conditions, the effects of medium viscosity on the diffusion of O2 are ruled out,
because VO2 /dt was not significantly reduced by change
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Hematocrit
0.2
0.3
0.4
Cell-free-layer thickness, ␮m
3.77
3.30
1.91
Width of erythrocyte column, ␮m
17.5
18.4
21.2
Hemoglobin content, M ⫻ ␮m
0.075 0.094 0.157
Hemoglobin content/width of erythrocyte
column, mM
4.30
5.11
7.41
Discharge hemoglobin concentration, mM
4.24
6.36
8.48
an increase in flow velocity, VO2 /dt is increased (see
Table 1).
Third, the deoxygenation of flowing erythrocytes accelerated with decreasing hematocrit (see Fig. 4), possibly due to the stirring of the cells despite the accelerated axial accumulation of the cells (and thus the
increased cell-free-layer thickness). However, VO2 /dt
was decreased because of the reduced number of cells
(see Table 2).
H455
O2 RELEASE FROM RBC AGGREGATES DURING FLOW
Interpretations in Terms of a Simple
Mathematical Description
The process of O2 release from blood flowing at the
mean velocity of v̄ through a tube of inner radius R may
be described by
Cv៮ ␲R 2 dS/dz ⫽ ⫺K关S共R兲/␤ ⫺ Pe兴
(4)
where ␤ is the slope of the O2 dissociation curve and Pe
is the PO2 at the outer radius of the tube (Pe ⫽ 0 in this
study). K is the overall mass-transfer coefficient comprising the intraluminal and extraluminal resistances
to O2 transport. Figure 3 shows that the entire process
of O2 unloading occurs over a period of 400 s, which
suggests that the O2 transport process is governed by
the resistance of the surrounding polymer rather than
the intraluminal resistance. Hence the value of K is
equal to the conductivity of the outer shell of the tube.
This also implies that the intraluminal gradients are
negligible and that S is uniform across the lumen.
Therefore the above equation becomes
Cv៮ ␲R 2 dS/dz ⫽ K[⫺S/␤].
(5)
If the discharge S at z ⫽ 0 is 1, the variation of S
along the length of the tube is expressed as
S ⫽ exp[⫺Kz/共Cv៮ ␲R2␤兲].
(6)
This equation may be used to analyze the variation
of S with distance, z, along the tube and also to analyze
the effect of velocity on S at a given location, z ⫽ Z. If
the exponential term is expanded, then we obtain
S ⫽ 1 ⫺ Kz/共Cv៮ ␲R 2 ␤兲 ⫹ 关Kz/共Cv៮ ␲R 2 ␤兲兴 2
⫺ 关Kz/共Cv៮ ␲R 2 ␤兲兴 3 · · ·
(7)
Note that the nature of the variation of S from 1 to 0
is dictated by the number of terms in the expansion
that are important. For the case when K/(Cv̄␲R2␤) is
small (as appears to be the case in this work), the
entire range of variation of S is linear. The value of z
when S goes to 0 is that at which the second term is
equal to 1; thus (Cv̄␲R2␤)/K. As the permeability increases or velocity decreases, the third and fourth
terms become important and the variation of S with z
is nonlinear. In this case, the value of z at which S falls
to 0 is that at which the sum of the second, third, and
fourth terms is equal to 1, and so on. As shown in Fig.
4, it can easily be explained from the above analysis
that S increases in a hyperbolic fashion with an increase in the flow velocity.
A surprising finding in the present study is the
increase in S at a given axial location with an increase
in cell-free-layer thickness. As discussed above, because O2 transport is governed by diffusion through
the surrounding tube, a change in the intraluminal
transport resistance via the change in the cell-freelayer thickness should not have a significant impact on
O2 transport and hence S. From the analysis presented
above, we may infer that a possible explanation for this
observation exists in the velocity measurements. As
shown in Table 4, erythrocyte aggregation induced by
Dextran T-70 either led to a more blunt velocity profile,
or an already blunt velocity profile led to a more uniform heme distribution. A combination of these two
effects could have caused the interpretation of the
observed dual-spot velocity in terms of the mean velocity of blood flow to change. Therefore, although the
measured dual-spot velocity was kept constant, the
actual mean velocities could be different in the control
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in medium viscosity with Dextran T-40 (see Table 3).
Furthermore, the reduction in deoxygenation of erythrocytes by Dextran T-70 (see Fig. 5) was not significantly altered by the addition of Dextran T-40 (see
Fig. 6).
The cell-free plasma layer formed by axial accumulation of deformable erythrocytes (10) is important for
the maintenance of blood flow as a lubricating layer (2).
The cell-free layer is significantly thick in microvessels, and thus the layer may be a kind of barrier for O2
transfer from erythrocytes to tissues, especially at reduced microvessel hematocrit (14).
The great majority of the resistance to O2 transport
in arterioles of D ⬎ 20 ␮m is distributed in the cell-free
plasma layer as was demonstrated experimentally
(23). Furthermore, the importance of the plasma layer
in O2 transfer to tissues may be indirectly suggested by
the acceleration of O2 transfer by the shear-induced
plasma motion (4, 5).
As demonstrated in the present experiment, the
thickness of the cell-free layer increased with decreasing hematocrit and with increasing flow velocity because of the accelerated axial accumulation of the cells
(19, 29). However, the cell-free layer was hardly related to O2 release from the erythrocytes (see Tables 1
and 2) based on our difficulty in ruling out other factors
affecting O2 release.
On the other hand, a good relationship between the
cell-free-layer thickness and the deoxygenation of
erythrocytes was obtained in the experiment of cell
aggregation using high molecular weight dextrans (see
Fig. 7). Erythrocyte aggregation induced by Dextran
T-70 increased the cell-free-layer thickness, which has
been demonstrated previously (25). Thickening of the
cell-free layer reduced the deoxygenation of the flowing
cells (see Figs. 5 and 6) and thus the amount of O2
released from the cells (see Table 3). These results may
include the effects of the flow-velocity profile for a
narrow tube, which are possibly modified by cell aggregation. In these experiments, the effect of medium
viscosity on O2 release was ruled out, as explained in
the preceding paragraphs. Furthermore, the flow velocity and hematocrit are maintained as constant.
Passage across the wall of the narrow tube. The
100-␮m wall thickness of the tubes (much thicker than
microvessel walls) is important as a barrier to O2
diffusion. The gradient profile of O2 tension from the
outer to the inner surface of the tube is not clear in the
present experimental conditions. The flow behavior of
erythrocytes in the tube may modify the gradient. The
present experimental results include these effects,
which need to be clarified in the future.
H456
O2 RELEASE FROM RBC AGGREGATES DURING FLOW
The authors thank Dr. K. Kubota (Department of Medicine, Kusatsu Branch Hospital, Gumma University School of Medicine) for
the generous suggestion of the preparation of narrow fluorinated
ethylenepropylene copolymer tubes.
This work was supported in part by grants from the Ministry of
Education, Science, Sports, and Culture of Japan and from the
Ehime Health Foundation.
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and erythrocyte aggregation-induced cases. It is possible that the actual mean velocities in the erythrocyte
aggregation case are higher, which would lead to a
higher S value.
The present study demonstrated that narrow O2permeable fluorinated ethylenepropylene copolymer
tubes are a useful tool for the dynamic study of O2
transfer from flowing erythrocytes. Furthermore, the
present study clearly demonstrated that in the narrow
tube the diffusion of O2 from flowing erythrocytes was
inhibited primarily by erythrocyte aggregation and
partly by thickening of the cell-free layer. Modification
of the rheological properties of the erythrocytes during
flow will provide further evidence for understanding
the dynamics of O2 transfer from the cells to the tissues
in relation to the flow behavior of the cells.