1113
Redistribution of Red Blood Cell Flow in
Microcirculatory Networks by Hemodilution
A.R. Pries, A. Fritzsche, K. Ley, and P. Gaehtgens
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The effect of isovolemic hemodilution on red blood cell flow distribution was studied in complete
self-contained microvessel networks of the rat mesentery. Hematocrit, diameter, and length of all vessel
segments as well as the topological structure were determined in control networks (systemic hematocrit,
0.54) and after hemodilution (systemic hematocrit, 0.30). Hemodilution was performed by exchanging
blood with hydroxyethyl starch (MW 450,000; 6%) or homologous plasma. With hemodilution, the
decrease of microvessel hematocrit exceeded that of systemic hematocrit. The average discharge
hematocrit in capillaries was 79%o of systemic hematocrit in the control group and 73% with hemodilution
(p<O.OOl). The heterogeneity of capillary hematocrit within the network, expressed by the coefficient of
variation, increased from 0.4 to 0.7. By using the morphological and topological data of four networks, the
distribution of hematocrits was also calculated using a hydrodynamic flow model. The modeling results
were found to be in close agreement with the experimental data. This indicates that the observed changes
can be deduced from established rheological phenomena, most of all phase separation at arteriolar
bifurcations. The changes in hematocrit distribution after hemodilution are accompanied by a redistribution of red blood cell flow within the network: relative to total red blood cell flow, red blood cell flow in
the distal capillaries of the network increases by about 40%o at the expense of the proximal capillaries that
are close to the feeding arteriole and that exhibit the highest red blood cell flow under control conditions.
This redistribution leads to a more homogeneous red blood cell flow distribution between proximal and
distal regions of vessel networks with hemodilution, which might serve to increase tissue oxygenation in
regions endangered by underperfusion. (Circulation Research 1992;70:1113-1121)
KEY WoRDs * hemodilution * microcirculation * networks * flow pathways * hematocrit
I ntentional hemodilution has evolved as a clinically
accepted therapy of a number of disorders with
impaired peripheral perfusion.' The beneficial effects reported have been attributed to increased peripheral perfusion caused by reduced blood viscosity and
possibly peripheral vasodilation. The present study will
mainly focus on effects resulting from changes in the
rheological properties of the blood after hemodilution,
which will affect the perfusion characteristics of all
tissues both in the presence and absence of vascular
reactions.
At a given driving pressure and oxygen saturation of
hemoglobin, oxygen delivery to a tissue is proportional
to the hematocrit of the systemic blood divided by the
flow resistance. The latter, in turn, is the product of
geometric hindrance of the vascular bed and blood
viscosity. Because of the dependence of blood viscosity
on hematocrit, oxygen delivery or red blood cell flow to
a vascular network is a nonlinear function of hematocrit
with a maximum at the so-called optimal hematocrit.
There is considerable variation in the determined values
of the optimal hematocrit: in experiments in which
From the Department of Physiology, Freie Universitat Berlin,
FRG.
Supported by the Deutsche Forschungsgemeinschaft (Pr 271/
1-1, Pr 271/1-2).
Address for correspondence: Dr. A.R. Pries, Department of
Physiology, Freie Universitat Berlin, Arnimallee 22, D-1000 Berlin
33, FRG.
Received July 29, 1991; accepted January 29, 1992.
changes of vessel diameters are unlikely (e.g., in maximal dilatation), the optimal hematocrit was reported to
be in the range of 0.5,2,3 whereas in tissues in which
vasodilatory reserve was available, values in the range
of 0.3 were found.4-6 The latter findings have served as
a rationale to advocate intentional hemodilution as a
means to alleviate tissue malperfusion in peripheral
ischemic disease.' Because it is not clear whether insufficiently perfused tissue areas representing the target
zones of intentional hemodilution retain vasodilatory
capacity, it appears uncertain whether the concept of
optimal hematocrit is adequate to explain the positive
effects of hemodilution.
Hemodilution not only changes oxygen-carrying capacity and viscosity of the blood, but also influences the
distribution of hematocrit and red blood cell flows within
microvascular networks. Under physiological conditions,
the volume concentration of red blood cells in microvessels (HT) is much lower than the systemic hematocrit
(H,)7-12 In addition to a low mean value, the HT values
show a substantial heterogeneity.9-1' It has been suggested in some studies that in hemodilution the average
capillary HT falls less than Hy, and red blood cells are
distributed more homogeneously to the individual microvessels.13-18 Both effects are supposed to improve
tissue oxygenation. However, all of the cited studies are
based on hematocrit measurements in selected subpopulations of microvessels. In view of the large heterogeneity of flow and hematocrit distribution characterizing
microvascular networks,9-"1920 it is very difficult to
1114
Circulation Research Vol 70, No 6 June 1992
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select a group of vessels that is truly representative of the
entire vascular bed. Even if such selection of vessels were
possible in the control state, during hemodilution redistribution of cell and plasma flows within the network
would invalidate the chosen set of selection criteria.
The present study attempts to overcome these problems by determining hematocrit, length, diameter, and
topological position of all vessel segments in complete
networks of the terminal vascular bed comprising large
numbers of flow pathways from arterioles to venules.
The hematocrit data are compared with predictions of a
hydrodynamic flow model21 that is based on established
rheological data on blood viscosity and phase separation
at bifurcations. These model calculations also enable
the analysis of red blood cell flow distribution and thus
oxygen delivery.
The rat mesenteric microcirculation was chosen for
this study because most of the precapillary microvessels
lack smooth muscle cells.22 Moreover, spontaneous
changes of vasomotor tone are not observed. Therefore,
the changes in perfusion pattern determined in this
vascular bed mainly reflect changes of blood rheology
that are operative in all tissues and add to effects
exerted by organ-specific active control mechanisms.
Materials and Methods
Animal Experiments
Male Sprague-Dawley rats (body mass, 300-460 g)
were anesthetized with ketamine (100 mg/kg i.m.) after
premedication with atropine (0.1 mg/kg i.m.) and pentobarbital sodium (20 mg/kg i.m.). The trachea, left
carotid artery, and jugular vein were cannulated with
polyethylene tubing. Throughout the experiment, all
animals received an intravenous infusion (24
ml kg- . hr-1) of physiological saline containing 0.3
mg/ml pentobarbital sodium to maintain anesthesia and
prevent an increase of HSYS. Arterial blood pressure,
heart rate, and central venous pressure were monitored
continuously. HSY (heparinized microhematocrit tubes)
and red blood cell counts (Coulter Dn, Herts, UK) were
determined before and after hemodilution steps and at
approximately 30-minute intervals during intravital microscopy in blood samples drawn from the carotid
-
catheter.
Animals were allocated to a control (CTRL, n =5)
and two hemodilution (DIL, n=6) groups. Isovolemic
hemodilution was performed either with homologous
plasma (PLASMA group, n =3) or with hydroxyethyl
starch solution (60 g/l, MW 450,000/0.7 in physiological
saline; Fresenius, Wiesbaden, FRG; HES group, n=3).
Homologous plasma was obtained by bleeding an anesthetized donor rat through the carotid catheter and
centrifuging the blood at 3,000g. Hemodilution was
performed in two steps by exchanging 10% (2.4-3.3 ml)
and then 11.5% (2.7-3.8 ml) of estimated blood volume
(8% of body mass) in the PLASMA group, and 11%
(3.4-3.8 ml) and 13% (4.0-4.5 ml) of estimated blood
volume in the HES group, respectively. Each hemodilution step was performed by simultaneously withdrawing (from the carotid catheter) and infusing (through
the jugular catheter) the specified volumes in approximately 10-15 minutes with a 15-minute interval between dilution steps. The resulting H, after hemodilution ranged between 0.30 and 0.35 in the PLASMA
and between 0.29 and 0.325 in the HES group.
The CTRL group remained untreated and showed
values of HSYS between 0.48 and 0.51. Mean red blood
cell volume in the carotid blood, as calculated from red
blood cell concentration and hematocrit, was 54±2 fl in
the CTRL group as well as in the PLASMA group,
while the HES group exhibited mean red blood cell
volume values of 48±1 fl.
For intravital microscopy, the mesentery was cautiously exteriorized through an abdominal midline incision, spread over a Lucite stage, and superfused with
thermostated (37°C) bicarbonate-buffered saline (composition, millimoles per liter: NaCl 132, KCl 4.7, CaCl2
2.2, MgC12 1.2, and NaHCO3 18, equilibrated with 5%
CO2 in N2, pH 7.3-7.4). Microscopy was performed
using a Leitz intravital microscope modified for telescopic imaging23 and equipped with a Leitz SW 25/0.6
saltwater immersion objective, a projection eyepiece
(f=268 mm, Leitz) and a transfer lens (f=300 mm,
Xenar, Schneider, Kreuznach, FRG), and a video camera (model 1005, RCA, Lancaster, Pa.). The mesenteric
microcirculation was transilluminated with monochromatic blue light (BG12 color glass and MA 3-0.3,
448-nm small band interference filter; Schott, Mainz,
FRG). Simultaneous recordings were obtained on videotape (Sony U-matic) and on black-and-white film
(AGFAPAN 100 professional, Agfa, Leverkusen,
FRG). The final magnification on the target of the video
camera and the film plane of the photographic camera
was x28, yielding a field of view of approximately
300x400 ,um on the video monitor. Scanning microvessel networks in the fat-free portion of the mesentery
(area between 25 and 80 mm2) took approximately 30
minutes and resulted in up to 300 photographs that
were assembled into photomontages.
group
Data Analysis
The number of vessel segments (defined as the section of a vessel between two branch points) per network
ranged between 334 and 913 in the CTRL group,
between 431 and 550 in the PLASMA group, and
between 328 and 456 in the HES group. Segment
diameters and lengths were measured from photomicrographs. Flow direction and microvessel hematocrit were
obtained from video recordings.9 24 The method of
photometric hematocrit measurement used is based on
the determination of optical density in the vessel segment at an isosbestic wavelength of hemoglobin (448
nm) by using a digital video image analysis system.25
Calibration of the method with capillary glass tubes
perfused with blood of known hematocrit allowed determination of both microvessel hematocrit (tube hematocrit, HT) and discharge hematocrit (HD), assuming
that the Fahraeus effect in vivo is equal to that in the
calibration tubes. In the HES group, a correction for the
observed change in mean red blood cell volume was
applied. In most (85%) of the vessels with diameters
below 8 ,um, HT was determined from photomicrographs
by counting the number of red blood cells in a given
length of the vessel. HD was then derived from HT by
using literature data of the Fahraeus effect in vitro.2' In
these smallest vessels the photometric method was used
only if HTwas too high to allow cell counting.
Pries et al Hemodilution and Flow Distribution
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Vascular networks were divided into arteriolar and
venular vessel trees on the basis of flow directions in
individual vessel segments. Segments connecting two
divergent branch points and linked to an input vessel of
the network via diverging branch points were classified
as arteriolar. A corresponding definition using converging branch points defined the venular segments. Segments connecting the divergent arteriolar tree with the
convergent venular tree (arteriovenous segments9'26)
were classified as "capillaries" regardless of their diameter or other morphological criteria. This definition of
capillaries is purely topological and therefore includes
vessel segments whose morphological and hydrodynamic properties vary. The mean capillary diameter of
all networks analyzed in this study was 9.6+±2.5 ,ttm,
whereas individual values ranged from 4.5 to 21 ,gm.
When capillaries were seen to form meshes creating
divergent bifurcations downstream of a convergent bifurcation, only the initial capillary branch connected to
the arteriolar tree was included in the analysis; less than
1% of all capillaries was seen to form such meshes. One
network of the CTRL group and two networks of the
HES group consisted of two arteriolar trees that could
be analyzed independently. All other networks were fed
by one large inflow arteriole only.
The topological position of each microvascular segment in the arterial tree is represented by its generation
number, which equals the number of branch points
between this segment and the inflow arteriole of the
vessel tree plus one.9,26 Based on this generation
scheme, consecutive complete flow cross sections were
defined through which the blood entering a vessel tree
must pass: the complete flow cross section number "x"
consists of all arteriolar and capillary segments of
generation x plus the capillaries of lower generation
numbers.9 Depending on the maximum generation
number reached in a tree, this type of analysis yields
about 20 complete flow cross sections, the most distal
flow cross section being identical to the population of
capillaries.
Model Calculations
A hydrodynamic model simulation was used to calculate the distribution of red blood cell and plasma flow in
four microvascular networks (two networks from the
CTRL group, one network each from the PLASMA and
HES groups). The model calculations are based on the
individual morphology and topology of each network
and the rheological laws derived from literature data.2'
The network data bases list diameter, length, and
individual feeding or draining segments for all segments
in a microvascular network. For segments entering or
leaving the network, measured hematocrit and estimated volume flow values were used as boundary
conditions. For each network analyzed with the model,
inflow hematocrit could be manipulated to match the
experimental values of both DIL and CTRL groups.
The volume flow in the main arteriolar inflow vessel was
set to correspond to measurements reported in the
literature for vessels of the appropriate dimensions.27
For additional input or output segments, the volume
flow values were calculated based on the volume flow in
the main arteriolar inflow vessel in proportion to the
1115
number of capillaries fed by or drained by the respective
inflow or outflow vessel.
Rheological phenomena represented in the hydrodynamic model were the phase separation effect at arteriolar branch points and the variation of apparent blood
viscosity with hematocrit and vessel diameter (Fahraeus-Lindqvist effect). For the nonproportional distribution of red blood cells and plasma at arteriolar branch
points (phase separation), a parametric description was
used that is based on data obtained from arteriolar
bifurcations in the rat mesentery in previous studies.21,28
According to these data, the hematocrit difference
between the daughter vessels of a bifurcation is determined by the diameter and hematocrit of the feeding
vessel, the relation between the diameters of the daughter vessels, and the flow split at the bifurcation.
An equation similar to that given by Pries et a12' was
used to estimate the relative apparent viscosity of blood
in a microvessel (77rel) as a function of HD and vessel
diameter (D, in micrometers). This equation was fitted
to experimental data available in the literature
eHD a-)
l
71rel= +e45 a ' (220e l
217D+2-17245e-071D 065
D 4
VD-W)
(1)
with
a=3.9/(1+e-2.374* (D-5.054))
(2)
a correction factor that was previously shown to
optimize the agreement between model results and
experimental data.2' In the present study, W ranged
between 2.4 and 3.4 ,um.
W is
Results
Hemodilution reduced mean hematocrit in the capillaries (segments connecting the arteriolar with the
venular vessel trees) to a similar extent in the HES and
PLASMA groups (Table 1). Average capillary HT in the
HES and PLASMA groups decreased more than HY,,
i.e., the ratios HT/He,. and HD/HSYS decreased. The
dispersion of capillary HT/H0y, and HD/HsY, increased as
reflected by an elevation of the standard deviations and
coefficients of variation. The distributions of HT/Hsys
and HD/Hsy in the dilution groups (PLASMA, HES,
and DIL) were tested against that of the CTRL group
by using the nonparametric U test (Wilcoxon-MannWhitney), which is mainly sensitive to differences of the
median. These tests indicated statistically significant
differences (p<0.001). In contrast, no significant difference was found between the PLASMA and HES groups
(p=0.66 and p=0.89).
Both for the experimental and for the model results,
the hematocrit distributions obtained after hemodilution were flatter and exhibited lower mean values
compared with those of the CTRL group (Figure 1).
Because the differences between the distributions obtained in the PLASMA and HES groups were small and
the medians showed no statistically significant difference, the results of experimental hemodilution will be
given for the combined DIL group in the following.
Figure 1 demonstrates that the model results exhibit a
Circulation Research Vol 70, No 6 June 1992
1116
TABLE 1. Statistical Parameters for Capillary Hematocrits
No. of
No. of
arteriolar
No. of
HT
HD
HD/HSYS
HT/H,Y.
networks
trees
median
median
Group
CV
median
median
capillaries
CV
5
801
0.48
6
0.23
0.45
0.37
0.78
CTRL
0.40
3
PLASMA
3
491
0.12
0.37
0.88
0.20
0.63
0.75
308
HES
3
5
0.13
0.40
0.61
0.21
0.67
0.58
DIL
6
799
8
0.12
0.39
0.70
0.21
0.65
0.70
CV values given are valid for the normalized hematocrit values (HT/H,,, HD/H,), but the corresponding values for HT and HD differ by
less than 2%. HT, tube hematocrit; HT/HV,,, HT normalized with respect to systemic hematocrit (H,y,); HD, discharge hematocrit; HD/Hsy,,
HD normalized with respect to HS,,; CTRL, control; PLASMA, group hemodiluted with homologous plasma; HES, group hemodiluted with
hydroxyethyl starch solution; DIL, the two hemodiluted groups.
Downloaded from http://circres.ahajournals.org/ by guest on June 15, 2017
higher number of capillaries in the lowest hematocrit
classes. This is due to the prediction of significant
numbers of segments with zero hematocrit by the
model. Such capillaries are presumably underrepresented in the experimental results because they are
difficult to detect in the analysis of photomontages or
video recordings obtained during the experiments.
Figure 2 shows hematocrit distributions for the subgroup of capillaries with diameters less than 8 ,um, most
z
W
W
IL
W
O
0.3
1
m
.
1
1
1
1
MODEL
n:
Mean:
-, A*X
,'
"
Lr
0.2 -
\DIL
,
,,
ok
\
1
CTRL
587
0.76
0.386
0.508
Std:
C.V.:
--
4..
DIL
587
0.664
0.45
0.677
'
X~~~~
z
WO0.2
v~iA
1
0.5
1
1
ECTRL
W
%1.
L /
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uv .r
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I
0.3
%
"w TR
0.1 -
of which (approximately 85%) were analyzed by direct
cell counting. In agreement with the findings for the
complete capillary group, the hematocrit distribution
exhibits lower median values and higher coefficients of
variation after hemodilution compared with control
conditions.
Figure 3 shows the average HD normalized with
respect to the inflow hematocrit of the networks for the
consecutive flow cross sections of arteriolar vessel trees
from the inflow arteriole to the level of the capillaries.
In the averaging procedure, the HD values were
weighted by the individual cross-sectional area of the
vessel segments. Since by definition total blood flow
through the tree passes through each of the consecutive
complete flow cross sections, a flow-weighted average
HD always equals the inflow hematocrit. If, on average,
those vessel segments of a complete flow cross section
that exhibit high flow velocities also exhibit high HD
values (such vessels may correspond to functional red
blood cell shunts as described in the literature), red
blood cells will travel faster through that cross section
than will plasma. As a consequence, the mean areaweighted HD will be lower than the inflow hematocrit of
the vessel tree. This effect has been called the network
Fahraeus effect.9 As shown in Figure 3, the hematocrit
reduction caused by the network Fahraeus effect in-
-
U-
1
<0.1-
1.5
HD/Hsys
FIGURE 1. Graphs showing frequency distributions of discharge hematocrit (HD) normalized with respect to systemic
hematocrit (Hsys) in capillary vessels. Data have been allocated to equally spaced HD/HSys classes. Upper panel: Experimental results in the control (CTRL) and two hemodiluted
(DIL) groups. Hemodilution was performed either with homologous plasma (PLASMA group) or with hydroxyethyl
starch solution (HES group). Lower panel: Distributions
predicted by the flow model for input hematocrit levels
corresponding to those found in the experimental groups
CTRL and DIL.
0-J
00
a
0.5
1
1.5
2
HT/ Hsys
FIGURE 2. Graph showing frequency distribution of tube
hematocrit (HT) normalized with respect to systemic hematocrit (HSYS) in capillary vessels with diameters less than 8 ,um.
In this diameter group 84% (control, CTRL) and 87%
(dilution, DIL) of the experimental hematocrit measurements
have been made by direct cell counting. Control: n=147,
median=0.45, CV=0.49; dilution: n=301, median=0.30,
CV=0.94.
l-
-
., .|'l~ ~ ~ ~
1
1
EXPERIMENT
1.0 -
CTRL
0.19 -
0
C
1._0
.II
1117
Pries et al Hemodilution and Flow Distribution
fi
a
a
1 9a
I
a
-
.0
MODEL
1.0 0.9
lr
CTRL
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-P0
0
T
T
1
1
I
I
16
8
12
COMPLETE FLOW CROSS SECTION
4
I
1
20
20
FIGURE 3. Graphs showing mean area-weighted discharge
hematocrit (1D4) normalized with the discharge hematocrit in
the feeding vessel (HDinflow) for the consecutive flow cross
sections of arteriolar vessel trees (network Fahraeus effect).
The complete flow cross section x is given by all arteriolar
segments of the generation xplus all capillaries ofgenerations
less than or equal to x. Shown are sliding means (±SEM) over
three flow cross sections. Upper panel: Experimental data for
control conditions (CTRL, six vessel trees) and after hemodilution (DIL, eight vessel trees). Lower panel: Model calculations for matched inflow hematocrits (four vessel trees). The
difference between CTRL and DIL is statistically significant
for flow cross section levels above eight in the experimental
data and above 11 in the model results (t test, p<0.01).
creases along the consecutive complete flow cross sections and is more pronounced in the hemodilution
experiments compared with control conditions. The
difference is statistically significant (t test, p< 0.01) for
all cross sections above eight in the experimental data
and above 11 in the model results. This indicates that
hemodilution causes the development of a stronger
positive correlation between hematocrit and flow velocity along the consecutive complete flow cross sections.
Application of the hydrodynamic flow model to the
experimental data allows the extension of the analysis to
parameters requiring the knowledge of volume flow that
was not experimentally available. Figure 4 compares the
flow-weighted average HD of the blood passing through
the capillaries and arterioles of a given generation. In
both CTRL and DIL groups, the general pattern is
similar: the main arterioles of the proximal generations
carry blood with a hematocrit close to the HD inflow.
These vessels give rise to capillary side branches that
exhibit reduced hematocrits caused by phase separation. As a consequence, the hematocrit increases in the
continuing arteriolar vessel tree. Because this process
continues up to the most distal vessel generations, there
is a substantial hematocrit buildup along the arteriolar
vessel tree, and the capillaries in the latest generations
0
5
10
15
GENERATION
20
25
FIGURE 4. Graphs showing mean flow-weighted discharge
hematocrit (HDg, right ordinate) and TH normalized with the
discharge hematocrit in the feeding vessel (IDQIHDinflow, left
ordinate) for arteriolar (ART) and capillary (CAP) vessel
segments in arteriolar vessel trees (n=4) as a function of
vessel generation (sliding mean+±SEM). The difference of
ART values between control and hemodilution is statistically
significant for generation levels above nine (t test, pc<0.01).
exhibit HD values exceeding the inflow value. This leads
to a preferential distribution of red blood cells to
capillaries with high generation numbers and therefore
to the long flow pathways. This so-called pathway
effect29 is much stronger after hemodilution than in
control conditions, as indicated by a hematocrit increase
by about 68% of the systemic value after hemodilution
compared with 35% for the control. Hence, hemodilution enhances longitudinal hematocrit heterogeneity
between proximal and distal capillaries in hemodiluted
networks.
In spite of the hematocrit increase with generation
number, mean capillary erythrocyte flow decreases
from the most proximal to the most distal generations in
the control situation (Figure 5). This is due to the
dominating effect of the decrease in flow velocity along
the arteriolar tree.21 However, the redistribution of red
blood cells to long flow pathways effected by hemodilution will tend to counteract the effect of flow velocity;
hemodilution therefore leads to a reduction of the
longitudinal heterogeneity of red blood cell flow.
The redistribution of red blood cell flow results from
a redistribution of flow velocity and hematocrit to the
benefit of distal capillary generations. This is shown in
Figure 6, in which a value of unity indicates that the
relative change of the respective parameter in the
capillaries of a given generation level equals that found
in the inflow arteriole of the network on hemodilution.
For all parameters, the ratios are close to unity for
generations between 9 and 17. This demonstrates that in
1118
Circulation Research Vol 70, No 6 June 1992
_J
c-J
0
_i
LL
_ilU
0
_J
a
W
m
W
E
N
2:
cr
0
z
_j
(-
-J
10
15
GENERATION
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FIGURE 5. Graph showing red blood cell (RBC) flow
(sliding mean+±SEM) in capillaries of a given generation
divided by the average capillary RBC flow (total RBC flow
through the network divided by the number of capillaries in the
network).
the intermediate generations of capillaries the changes
of velocity, hematocrit, and red blood cell flow resulting
from hemodilution directly reflect the corresponding
changes in the main feeding vessels. A comparison
between proximal and distal capillaries, however, indicates the longitudinal redistribution of red blood cell
and plasma flow. Both flow velocity and HD show
reductions of about 17% in the proximal capillaries
during hemodilution, while the more remote capillary
segments experience a corresponding increase. As a
consequence, the relative erythrocyte flow after hemodilution is elevated (approximately +40%) in the
most distal capillaries at the expense (approximately
-30%) of the proximal capillaries close to the feeding
arteriole.
Discussion
The results presented demonstrate that hemodilution
leads to a redistribution of red blood cell and plasma to
the various flow pathways through microvascular networks, thereby influencing the transfer characteristics of
vascular beds. This in turn affects the residence times
for different blood components in the vessels of a
network and therefore hematocrits: with hemodilution,
average capillary HT decreases more than H,S,. This is
accompanied by an increase in overall hematocrit heterogeneity as represented by the coefficient of variation
(Table 1). These findings contrast with reports in which
an increase of HT/H,S was found with decreasing
also are at variance with the notion that
H,y.13-18They
the increase of HT/Hy, under hemodilution is combined
with a "more uniform spatial distribution of RBC
throughout the true capillary level.'3 It is important to
investigate the apparent contradiction between these
findings and interpretations, since it has been suggested
that a more homogeneous distribution of hematocrit is
relevant for the clinical effects of hemodilution.'
Hematocrit Distribution
The average HT in the capillaries of a microvascular
network may differ from the inflow or the HYS as a result
of two major effects.9'30,31 The vessel Fahraeus effect
C
XX
t
1.2
I- T
U.
0.
0.6
0
5
10
15
20
25
GENERATION
FIGURE 6. Graphs showing flow velocity (top panel), discharge hematocrit (HD, middle panel), and erythrocyte
(RBC) flow (bottom panel) during hemodilution divided by
the respective value under control conditions (DIL/CTRL) for
capillaries of different generations. The ratios obtained were
normalized with respect to the ratio between the respective
parameters in the feeding arterioles (sliding mean±SEM).
Asterisks indicate significant difference from unity (two-tailed
t test, p<0.01).
leads to a reduction of individual vessel hematocrit, HT,
relative to the discharge hematocrit, HD. The network
Fahraeus effect, on the other hand, reduces the areaweighted HD of a complete flow cross section relative to
the HD in the feeding arteriole, H,Y,.
From in vitro experiments with blood-perfused glass
tubes, the vessel Fahraeus effect is known to be more
pronounced at reduced hematocrits.32,33 This is explained by the enhanced axial migration of red blood
cells.34,35 If these results are applicable to blood flow in
vivo, the vessel Fahraeus effect would tend to decrease
HT/HSs, with hemodilution. The expected influence of
the vessel Fahraeus effect on HT/Hs,, is, however, small.
The network Fahraeus effect is generated by a positive
covariance of flow velocity and hematocrit in the microvessels constituting a complete flow cross section.36
The correlation between flow velocity and hematocrit,
in turn, depends on the extent of phase separation at
the diverging arteriolar bifurcations: at a bifurcation,
the daughter branch with the higher volume flow gen-
Pries et al Hemodilution and Flow Distribution
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erally receives blood with an increased hematocrit and
vice versa.2837 This phase separation effect generates a
positive covariance between hematocrit and flow velocity in the daughter branches of a bifurcation and also
among vessels constituting the consecutive flow cross
sections of a network. The reduction of the mean
area-weighted HD normalized with respect to HS,Y by the
network Fahraeus effect therefore increases with the
number of branch points passed and shows a maximum
at the capillary level (Figure 3).
Earlier investigations have demonstrated that phase
separation increases with decreasing hematocrit.-83839
It can therefore be expected that hemodilution will
enhance the network Fahraeus effect and increase
heterogeneity of hematocrit distribution. The expected
changes are quantitatively described by the flow model
and are in close agreement with those found in the
experimental data. This indicates that the experimental
data presented here for complete networks and their
dependence on systemic hematocrit can be explained by
the basic rheological mechanisms incorporated into the
model, i.e., the Fahraeus-Lindqvist effect and phase
separation at arteriolar bifurcations.
The obvious discrepancy between the present results
and the majority of data available in the literature may
in part be related to the fact that in these studies
measurements have been made in a limited number of
vessels rather than in complete networks. In larger
arteriolar vessels, an increase in hematocrit heterogeneity as well as the concomitant decrease in HT/Hsy,
after hemodilution might not be found, since phase
separation is not prominent in vessels of this size.11,14 If,
on the other hand, the analysis is based on measurements in capillaries,15-18 the selection procedure used
will have a strong influence on the results.20 In most
experimental situations, exact morphological or topological information is not available, and therefore the
decision whether a vessel segment is considered a
capillary bears some degree of uncertainty. Specifically,
a nonrandom selection procedure may favor distal capillaries because of their low flow velocities, thereby
leading to an underestimation of the prevalent heterogeneity. Such an unbalanced selection could also influence the magnitude and even the direction of changes in
the measured parameters with hemodilution. The present measurements, for example, indicate that a determination of HD/RYS in distal capillaries would suggest
an increase with hemodilution despite the fact that the
overall capillary HD/R,, decreases (Table 1, Figure 6).
Although the discrepancies to previous reports cannot be rigorously accounted for, the validity of the
general conclusion presented in this study for complete
networks is supported by the compatibility between
experimental data and modeling results that are based
on accepted rheological laws. In addition, similar reactions on hemodilution could be shown for both the
topologically defined group of capillaries and for the
subgroup of capillaries with diameters less than 8 ,gm
(Figure 2). In this morphologically defined subgroup,
which might be more closely related to the capillaries as
defined in other studies, the majority (approximately
85%) of hematocrit measurements was made by direct
cell counting, a method that was also used in most of the
studies cited from the literature.
1119
In reconciling the present study with previous reports
in the literature, a number of possible sources for
discrepancies can be identified. In addition to the
strategy used for selecting vessel segments discussed
above, the choice of species and tissue, the hemodilution protocol, and the methods used for hematocrit
measurement may be relevant. Preparation technique
and the hemodilution protocol could also influence
changes of vascular tone accompanying the reduction on
systemic hematocrit, depending on the species and
tissue used. Such changes, which are absent in the
present preparation, would influence distribution of red
blood cell flow pathways through microvascular networks by redistribution of volume flow. Finally, the
intensity of red blood cell aggregation might affect cell
plasma separation at microvascular bifurcations and
therefore hematocrit distribution. If hemodilution is
carried out with a diluent altering red blood cell aggregation, this may introduce additional effects that are not
seen in the present experiments with a species that has
extremely low red blood cell aggregation tendency.
Cell Flow Distribution
In the mesentery, the capillaries of the different
generations are distributed in an onion skin-like pattern
around an arteriole (Figure 7). Capillaries with high
generation numbers are located in distant regions of the
tissue relative to the input arteriole and vice versa. On
average, the pressure gradient per capillary will therefore decrease with increasing generation level. The
resulting low flow rate in the distal capillaries also leads
to a low red blood cell flow despite high discharge
hematocrits (Figure 5). This distribution of red blood
cell flows is modified by hemodilution: capillaries of
high generation levels feeding the most distant areas of
the tissue get an increased share of the total red blood
cell flow through the network (Figure 6). Because these
vessels exhibit the lowest absolute values of erythrocyte
flow in the control state, the redistribution tends to
homogenize the dispersion of erythrocyte flow to the
different tissue regions.
The homogenization of red blood cell flow distribution to different tissue regions is, however, not accompanied by a reduction of the overall heterogeneity of
red blood cell flow in the capillaries. In contrast, the
coefficient of variation of red blood cell flow increases
during hemodilution (Table 2). Only the "longitudinal"
component of the coefficient of variation (CV,), i.e., the
heterogeneity between proximal and distal capillaries of
a network, decreases on hemodilution. This longitudinal
heterogeneity is caused by the asymmetrical topological
structure of the microvascular bed and by the cumulative effect of phase separation at successive bifurcations.
One way to quantify longitudinal heterogeneity is to
correlate a given parameter determined for all capillaries with their generation numbers and calculate the
respective coefficient of correlation. Based on this correlation coefficient, CV, can be determined from the
systematic variance of the parameter X with capillary
generation number. As shown in Table 2, the correlation coefficient of the correlation between red blood cell
flow and generation shifts to less negative values after
hemodilution, leading to a decrease in the absolute
value of the respective correlation coefficient and the
1120
Circulation Research Vol 70, No 6 June 1992
3,
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10~
~
~
~
~
~
~ ~
~
~~~~~~~~~~~~~~~~~~~~~~~.
9 13 20
FIGURE 7. Diagrams of the arteriolar vessel tree in the rat mesentery. Solid lines indicate arteriolar segments; dashed lines
indicate capillaries. Left panel: The generation number of every capillary is given. Right panel: Contour lines have been drawn
to indicate tissue regions supplied by capillaries of the generation numbers indicated at the bottom of the panel.
longitudinal heterogeneity described by CV,. The
changes in red blood cell flow distribution are due to a
weaker negative correlation between velocity and generation corresponding to a decrease in CV,, while in
parallel a more positive correlation between hematocrit
and generation is established and the corresponding
value for CV, increases.*
The values of CV, are low compared with the overall
coefficient of variation, despite the substantial longitudinal dispersion demonstrated in Figure 6. This reflects
the uneven frequency distribution of capillary generation levels. As shown in Figure 8, the largest number of
capillaries is found in the intermediate generation range
*The absolute values for the coefficient of variation of capillary
flow velocity reported here for the rat mesentery are considerably
higher than the average values of about 0.6 given in the literature
for striated muscle.l9.2040 This might be related to differences in
the angioarchitecture of the investigated tissues and to the fact
that in the present study strict topological criteria were used to
define capillaries.
(between eight and 16), where longitudinal redistribution of red blood cell flow with hemodilution is minimal.
The comparatively low number of capillaries with low or
high generation numbers limits the influence of longitudinal hematocrit redistribution on CV,. However,
changes of red blood cell flow in these subgroups of
capillary vessels are functionally relevant, since capillaries of given generation levels almost exclusively supply specific tissue regions (Figure 7).
The discrepancy between the effects of hemodilution
on overall and longitudinal heterogeneity of red blood
cell flow shows that an exclusive analysis of global
statistical parameters might miss functionally relevant
phenomena because of the complex relations among
morphological, topological, and hemodynamic parameters within a microvascular network.
In tissues in which adjustments of vascular tone can
occur in response to changes of supply conditions, the
redistribution pattern described here may be modified.
However, in a number of pathological states such as
TABLE 2. Heterogeneity of Velocity, Hematocrit, and Red Blood Cell Flow in the Capillaries of Three Networks Analyzed Using the
Hydrodynamic Flow Model
CV
Group
CTRL
Velocity
1.65±0.74
HD
r(XIGEN)
QRBC
Velocity
HD
QRBC
-0.25±0.14
-0.16±0.14
0.57±0.22
Velocity
0.73±0.36
0.66±0.35
0.89±0.06
CV,
HD
0.07±0.06
QIIBC
0.52±0.02 1.97±0.37 -0.44±0.07 0.08±0.14
0.52±0.36
DIL
1.62±0.62 0.68±0.07 2.24±0.35 -0.39±0.09 0.18±0.11
0.13+0.09 0.41±0.35
0.89±0.10 1.98+1.05
DIIJCTRL 1.01±0.06 1.31±0.10 1.14±0.03
2.63±1.47 0.64±0.24
Values are mean±SEM. CV, overall coefficient of variation; r(xiGEN), correlation coefficient for the correlation between the respective
parameter (X) and the generation number; CV,, longitudinal component of coefficient of variation (to calculate CV,, the residual variance
of the parameter X with respect to the generation was subtracted from its overall variance; CV, was then given as the square root of that
longitudinal variance divided by the mean value of X); HD, discharge hematocrit; QRC, red blood cell flow; CTRL, control; DIL, the two
hemodiluted groups.
Pries et al Hemodilution and Flow Distribution
z
40-
W
W
Li.
20-
0-
0
5
10
15
GENERATION
20
25
FIGURE 8. Graph showing frequency distribution of generation levelfor capillary segments in the four networks used for
model calculations (n=587,
mean =12.8,
CV=O.334).
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chronic ischemia, the remaining vasodilative reserve is
probably minimized or not recruitable. Improvements
of tissue oxygenation by hemodilution in the absence of
vasomotor adjustments, which have for instance been
demonstrated in skeletal muscle with chronically reduced blood supply,41,42 must be attributed to passive
rheological mechanisms. These mechanisms are on one
hand related to the effect of hematocrit on viscosity and
oxygen-carrying capacity of the blood ("optimal hematocrit") and on the other hand to the effect of hematocrit
on the distribution of red blood cell flow in microcirculatory networks as described here.
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Redistribution of red blood cell flow in microcirculatory networks by hemodilution.
A R Pries, A Fritzsche, K Ley and P Gaehtgens
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Circ Res. 1992;70:1113-1121
doi: 10.1161/01.RES.70.6.1113
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