357
Heterogeneity of Red Blood Cell Perfusion in
Capillary Networks Supplied by a Single
Arteriole in Resting Skeletal Muscle
C.G. Ellis, S.M. Wrigley, A.C. Groom
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Abstract Flow heterogeneity within capillary beds may have
two sources: (1) unequal distribution of red blood cell (RBC)
supply among arterioles and (2) unique properties of RBC flow
in branching networks of capillaries. Our aim was to investigate
the capillary network as a source of both spatial and temporal
heterogeneity of RBC flow. Five networks, each supplied by a
single arteriole, were studied in frog sartorius muscle (one
network per frog) by intravital video microscopy. Simultaneous
data on RBC velocity (millimeters per second), lineal density
(RBCs per millimeter), and supply rate (RBCs per second) were
measured continuously (10 samples per second) from video
recordings in 5 to 10 capillary segments per network for 10
minutes by use of automated computer analysis. To quantify
heterogeneity, mean values from successive 10-second intervals
were tabulated for each flow parameter in each capillary segment
(ie, portion of capillary between successive bifurcations), and
percent coefficient of variation (SD/mean. 100%) was calculated
for (1) spatial heterogeneity among vessels (CV,) every 10
seconds and for the entire 10-minute sample and (2) temporal
heterogeneity within vessels for every capillary segment and for
the mean flow parameter. Analysis of these data indicates that
(1) capillary networks are a significant source of both spatial and
temporal flow heterogeneity, and (2) continuous redistributions
of flow occur within networks, resulting in substantial temporal
changes in CV,, although a persistent spatial heterogeneity of
perfusion still exists on a 10-minute basis. In most networks, CV,
decreased as supply rate within the network increased, thus
indicating that rheology plays a significant role in determining the
perfusion heterogeneity. (Circ Res. 1994;75:357-368.)
Key Words * spatial heterogeneity * temporal
heterogeneity * microcirculation * capillary networks .
flow redistribution
T he most striking feature of the microcirculation
of skeletal muscle, to the person who views it
for the first time through a microscope, is the
large variability in perfusion among individual capillaries. Some capillaries appear to have few red blood cells
(RBCs) traveling at high velocities, whereas other vessels have a continuous train of RBCs traveling very
slowly. Closer examination reveals that this apparent
simple relation between RBC velocities and lineal densities (number of RBCs per millimeter) does not hold;
there are vessels with almost any combination of low
and high velocity and lineal density. This situation is
further complicated by the fact that flow is not steady
but fluctuates with time within each vessel.
For the past decade and a half there have been
numerous studies that have attempted to quantify this
heterogeneity of perfusion and to determine its physiological significance.1-5 Heterogeneity has been expressed in terms of the relative dispersion (SD/mean, ie,
the coefficient of variation) of one or more hemodynamic parameters such as RBC velocity (millimeters
per second), hematocrit (percent), RBC content (lineal
density in RBCs per millimeter), or RBC supply rate
(RBCs per second).6 The variability among vessels has
been termed the spatial heterogeneity, and the variabil-
ity with time within each vessel, the temporal heterogeneity.4 The physiological significance of spatial heterogeneity has been linked with the efficiency of tissue
oxygenation and capillary exchange of diffusible solutes.67 Thus, one would expect that spatial heterogeneity should be under some form of regulatory control in
response to changes in metabolic demand or oxygen
delivery to the microvasculature. To date, research into
this area has yielded contradictory results.1,8-'1
The physiological significance of temporal heterogeneity has been less clear, although it likely affects the
efficiency of microvascular exchange. Our understanding of the properties of the microvasculature that lead
to flow heterogeneity and how these properties might be
regulated is far from complete.12
To understand how the heterogeneity of perfusion
might be regulated or altered, one needs to consider the
potential sources of this heterogeneity. Although
Krogh13 considered the capillary as the smallest independent controller of capillary perfusion, more recent
studies have indicated that control lies entirely within
the arteriolar tree.14 Even in passive microvascular
networks, such as the mesentery, the level of perfusion
within groups of capillaries reflects the distribution of
perfusion among the arterioles feeding these capillary
beds." Temporal heterogeneity has usually been associated with vasomotion,15 ie, the rhythmic contraction
and relaxation of arterioles. Thus, the arteriolar tree
appears to be a major component in determining both
the spatial and temporal heterogeneity of capillary
perfusion.
Another source of heterogeneity may be the capillary
network. Conceptually, the microvasculature has been
Received October 21, 1993; accepted April 19, 1994.
From the Department of Medical Biophysics (C.G.E., S.M.W.,
A.C.G.), University of Western Ontario, and The J.P. Robarts
Research Institute (C.G.E., A.C.G.), London, Ontario, Canada.
Correspondence to Dr Christopher G. Ellis, Department of
Medical Biophysics, University of Western Ontario, London,
Ontario, Canada N6A 5C1.
©) 1994 American Heart Association, Inc.
358
Circulation Research Vol 75, No 2 August 1994
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described as being composed of a number of parallel
flow paths between artery and vein.6 However, the
capillary bed is made up of networks of interconnected
diverging and converging capillary segments. This arrangement provides numerous alternate routes for
blood flow to follow, and as a consequence, the level of
flow in individual capillary segments must be quite
different. This type of spatial heterogeneity has been
referred to as the longitudinal heterogeneity in capillary
segment flow6 or between proximal and distal capillaries.11 We have also reported considerable dynamic
variability in capillary flow, which is apparently unrelated to vasomotor activity and which we believe to have
originated within the capillary network itself.2
It is likely that all four aspects of heterogeneity
(arteriolar, capillary network, spatial, and temporal) are
interrelated. However, to date, no experimental studies
have been designed to account for this possibility. Most
experiments have studied spatial heterogeneity by using
measurements of one or more flow parameters from a
limited number of capillary segments selected at random.8'9 These studies cannot distinguish between the
arteriolar and capillary network component of heterogeneity.11'16 Two studies in which data were collected
from all arteriolar, capillary, and venular segments of
the mesentery required up to 30 minutes for one data
set. These experiments cannot distinguish between spatial and temporal components of the heterogeneity.
The goal of the present study was to examine the
spatial and temporal heterogeneity of RBC perfusion
arising within the capillary network, independent of
heterogeneity introduced by unequal flow distributions
among arterioles. This was accomplished by simultaneously measuring RBC velocity, lineal density, and supply rate in individual capillary segments of networks
supplied by a single arteriole. By studying such networks, we were able to demonstrate that the capillary
network is a source of perfusion heterogeneity, and by
measuring all three flow parameters, we were able to
show that rheology plays a significant role in determining this heterogeneity.
Materials and Methods
Animal Preparation
Five mature frogs (Rana pipiens) weighing -'-:50 g were
anesthetized with a 20% urethane solution injected into the
dorsal lymph sac (35 mg/10 g body wt). During the course of
the experiment, anesthesia was maintained by 0.05-mL injections of urethane through a small cannula inserted under the
ventral skin. With each frog, a sartorius muscle was exposed by
removing the overlying skin. The transparent connective tissue
surrounding the muscle was left intact to minimize surgical
trauma to the muscle. The frog was placed in the supine
position on the stage of a Wild Makroskop (M420) and left at
room temperature. The exposed muscle was covered with a
plastic coverslip to isolate the tissue from the surrounding
environment. The surface of the muscle was epi-illuminated
using a Schott fiberoptic light source (KL1500) with both a
green filter and a heat filter. Images of the microvasculature
associated with the superficial muscle fibers were recorded on
videotape with a Panasonic video camera (WV-1550) and a
Panasonic videocassette recorder (WV-9240XD). The images
were viewed on a Panasonic black and white monitor (WV5410). After surgery, the flow in the microvasculature was
allowed to stabilize for a period of up to 1 hour. For each
muscle, a capillary network was chosen that permitted hemo-
dynamic analysis of at least five capillary segments in a
network supplied by a single arteriole. A capillary segment was
defined as the section of capillary between two branch points.
A capillary network was defined as the group of capillary
segments originating from near the terminal end of a single
arteriole (see Fig 1). Video images of the RBC flow in the
network were recorded for at least 10 minutes. The size of the
field of view was '0.8x0.6 mm, with the capillaries oriented
vertically on the monitor.
Analysis of Video Images
RBC velocity (millimeters per second) and lineal density
(content, RBCs per millimeter) were measured in each capillary segment from the video recordings by use of automated
computer analysis routines. To ensure that the sampling of
each capillary segment began at the same point in time, an
audio cue was placed on one of the audio channels of the
videotape. Sampling of the videotape began when the computer system detected the audio cue. Thus, by replaying the
videotape, "simultaneous" data on RBC velocity and RBC
lineal density were obtained for each capillary segment. RBC
velocities were measured in a single capillary by use of a
spatial correlation technique.17"8 The spatial correlation technique was able to measure positive, zero, and negative RBC
velocities over the physiological range of velocities found in
capillaries. RBC lineal densities were measured using a videodensitometric method.18'9 Since this technique did not attempt to detect individual cells, the lineal density could be
measured in capillaries even with continuous trains of RBCs.
Both velocity and lineal density were sampled every sixth
video field (ie, rate of 10/s) for 10 minutes (total of 6000
samples per parameter per vessel). RBC supply rate was
calculated for every sample interval from the product of
velocity and lineal density.218 For the analysis presented in
"Results," the data are presented as 10-second mean values
for successive 10-second time intervals (ie, each mean is
computed from an independent set of data).
All statistical calculations were performed with SYSTAT
(Systat Inc). The schematic diagram was produced using
CORELDRAW (Corel Inc). Graphs were plotted using SIGMAPLOT (Jandel Scientific) and arranged for publication using
CORELDRAW. Tables were generated using EXCEL (Microsoft
Inc).
Results
Video images of RBC flow in resting sartorius muscle
were recorded from five capillary networks supplying
superficial muscle fibers (one network per frog). Networks in which five or more capillary segments, with
straight portions at least 140 ,um long, could be included
in a single field of view were selected at random. RBC
velocity, lineal density, and supply rate were measured
from the video recordings for 10 minutes in each
capillary segment (number of segments per network: 9,
10, 5, 6, and 8). The architecture of a typical network is
shown in Fig 1. The capillary segments were identified
with a two-digit code, the first digit representing branching order (1, 2, 3 ...) and the second digit specifying the
particular segment within each branching order. In the
field of view represented by Fig 1, it was possible to
record the flow simultaneously in all segments except 31
and 32.
The flow heterogeneity found in such a network may
be appreciated visually from three-dimensional (3D)
presentations of the flow data, as illustrated in Fig 2. In
this figure, data for RBC velocity, lineal density, and
supply rate are plotted as 10-second mean values for
each capillary segment. To highlight the differences in
v- ~ ~en~~2~4 ~ ~ ~ ule
Ellis et al Heterogeneity of Perfusion in Capillary Networks
arteriole
e12
20
25
FIG 1. Schematic of capillary network 1. Direction of flow is
indicated by the arrows. Each segment has been identified with
a two-digit code, the first digit indicating whether it is a first-,
second-, or third-order vessel and the second digit specifying
the particular segment within each branching order.
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blood perfusion among capillaries, a line has been
drawn at each time interval connecting the values for all
capillary segments. The graph of RBC supply rate
shows the considerable temporal and spatial fluctuations that exist within the network, and closer inspection
reveals persistent differences between vessels (eg,
"mountain ranges" versus "valleys"). The contribution
of velocity and lineal density to the heterogeneity of
RBC supply rate can be easily recognized by comparing
the 3D plots for all three parameters. For example, at
time 0, capillary segments 23 and 25 show an almost
3-fold difference in RBC supply rate; this is due almost
entirely to a 2.5-fold difference in lineal density and
only a slight difference in velocity. In contrast, the
difference in RBC supply rate between capillary segments 12 and 13 is due primarily to a difference in
velocity. The vessels with the highest lineal densities, 24
and 25, arise from the most distal section of the
arteriole. The graph of relative supply shows the supply
rate for each segment relative to the total RBC supply
rate to the network, ie, relative to the estimated arteriolar input to the network. The 10-second mean arteriolar RBC supply rates were estimated from the measured RBC supply rates in individual capillary segments
on the basis of a simple mass balance of RBCs; ie, only
one segment from each flow path between arteriole and
venule was included in the summation. For example, in
network 1 (Fig 1), the arteriolar input was estimated
from capillary segments 11 and 20 through 25. When
359
expressed as a relative supply rate, some vessels show a
reduced temporal variability, whereas others do not
(compare vessels 23 through 25 with vessel 11).
To quantify flow heterogeneity, 10-second mean values for each flow parameter were tabulated for all
capillary segments in each network, as illustrated in
Table 1 for RBC supply rate. From these data, one can
compute the mean+SD values for the entire network at
each 10-second interval (rows) and for each capillary
over the entire 10-minute period (columns). The 10second mean arteriolar RBC supply rates were also
included in the supply rate tables for calculation of the
relative supply rates. For RBC velocity and lineal
density, similar tables were constructed, excluding all
reference to the supplying arteriole.
The heterogeneity for each capillary flow parameter
can be quantified in terms of the coefficient of variation
(CV%= SD/mean * 100%). This heterogeneity can be
resolved into two components, spatial (among capillaries, CVs) and temporal (CV,). In Table 1, the spatial
heterogeneity has been computed for each 10-second
interval (individual rows) as well as for the entire
10-minute data set (row of 10-minute mean values).
The 10-second CVS values indicate how spatial heterogeneity varied with time, whereas the 10-minute CV,
value indicates the persistent spatial heterogeneity
within the network. The temporal heterogeneity has
been computed for each capillary (individual columns)
as well as for the mean capillary flow in the entire
network (column of 10-second mean values). The 10minute CV, values for capillaries indicate how the
temporal heterogeneity varied among capillaries,
whereas the 10-minute CVt value for the mean capillary
flow indicates how the mean perfusion of the network
varied with time. The overall heterogeneity of capillary
flow (CVo) is computed from the entire set of values in
the table (rows and columns). CVO indicates the variability of capillary perfusion due to both spatial and
temporal factors. Repeated random samples of capillaries at different points in time during the 10-minute
interval would approximate CVO.
Results from the analysis of the 10-second data from
all five networks are summarized in Table 2, in terms of
10-minute mean values and their corresponding CV
velocity
(mm/s)
0.4
0.3
02
0.1
242
capillary
segment
FIG 2. Three-dimensional plots of velocity, lineal
density, supply rate, and relative supply vs capillary segment ID vs time for capillary network 1.
RBC indicates red blood cells. ID refers to the
two-digit code identifying each capillary segment
(see Fig 1 legend).
360
Circulation Research Vol 75, No 2 August 1994
TABLE 1. Mean Values of Red Blood Cell Supply Rate Over Successive 10-Second Intervals for Each Capillary of the
Network Throughout a 1 0-Minute Period
10-Second Values
Estimated
RBC Supply Rate in Capillary Segments, RBCs/s
Arteriolar
CV,
SD,
Mean,
Input,
%
25
24
RBCs/s RBCs/s
23
...
13
12
11
RBCs/s
Time, s
0
10
20
30
10.2
13.2
13.6
12.9
1.9
3.1
2.1
2.1
560
570
580
590
15.5
14.8
16.8
17.9
2.4
2.6
3.4
3.5
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10-Minute
mean SD
1 0-Minute
2.1
1.6
2.1
2.3
2.1
0.8
1.1
1.1
0.9
2.5
3.6
2.4
1.1
...
3.1
3.1
2.2
3.4
2.3
1.0
44.7
44.5
...
...
2.9
3.0
2.4
2.6
3.7
2.8
2.6
2.8
1.2
1.1
46.5
37.8
2.300
0.92s
40.16,
2.5
..
0.8
1.4
2.6
3.3
2.6
3.2
3.7
3.2
...
1.5
2.5
1.9
1.8
2.1
2.2
2.2
4.0
3.6
...
2.0
4.7
5.0
2.5
...
...
14.42±+1.74 2.51+0.60 2.54+0.47 3.71±0.55 ... 2.40+0.48 1.95+0.41
12.04
24.08
18.67
14.76
47.3
2.8
3.3
3.1
3.1
1.9
...
20.08
20.94
3.44+0.38
49.8
46.5
42.4
0.25t 0.990
10.91
1 0.74t
...
43.040
CVt, %
RBC indicates red blood cell; CV, coefficient of variation; subscript a, the overall statistic computed from the data as a whole, both rows
and columns; subscript s, the spatial statistic calculated from the row of 1 0-minute mean values; and subscript t, the temporal statistic
calculated from the column of 10-second mean values for all capillaries.
The arteriolar supply of RBCs to the network is estimated from individual capillary supply rates based on a mass balance of RBCs.
Mean, SD, and CV are computed for each column yielding the 1 0-minute mean and 1 0-minute temporal CV values for the arteriolar input
and for each capillary. The same calculations are performed on each row of capillary data yielding the successive 1 0-second mean and
1 0-second spatial CV values. The seven values in the lower right corner (values with subscripts) are statistics calculated from the entire
1 0-minute data set.
values (temporal, spatial, and overall) for the three flow
parameters and for the estimated arteriolar input. In all
cases, the temporal CV values were much less than the
spatial values, so that spatial and overall CV values were
similar. However, a two-way ANOVA of the data for
each of the five networks (arranged as in Table 1, time
versus capillary number) showed that temporal variations, based on 10-second intervals, made a small but
statistically significant (P<.005) contribution to the
overall heterogeneity of capillary network perfusion.
This reflects the presence of a degree of temporal
variation that was consistent across the entire network.
The statistics compiled from the mean data for all five
networks (not weighted with respect to the number of
capillaries in a network) indicates the variability in
these parameters among networks.
The CV, values for RBC supply within each network
of capillaries (CVcap) were comparable in magnitude to
those of their arteriolar input (CVinput) (Table 2). However, analysis of the 10-second data on the basis of
individual capillaries showed that although some vessels
exhibited similar temporal heterogeneity to the input
(CVcap/CVinput, 1), others displayed much greater heterogeneity (CVcap/CVinput, > >1).
Fig 3 shows that the capillaries with a greater heterogeneity were primarily those with RBC supply rates
<20% of the input supply rate. The capillary segment
order is also shown in Fig 3, and there appears to be no
relation between the location of the segment in the
network and the degree of temporal heterogeneity. The
question arises whether the capillaries having a high
temporal heterogeneity are those with a low RBC
velocity, a low RBC lineal density, or a combination of
both. This issue is explored in Fig 4, which shows a 3D
plot of the relative temporal heterogeneity CVcap/CVinput
versus velocity and lineal density. It is clear that the
highest relative temporal heterogeneity occurred in
those capillaries having a combination of low RBC
velocity and low RBC lineal density. Conversely, the
lowest relative temporal heterogeneity (ie, z-1.0) was
found in vessels with the highest velocity and lineal
density. A multilinear regression analysis (CVcap/
CVinp,t ao+a, v+a2 n, where v is velocity and n is
lineal density) showed that there is a significant relation
between relative temporal heterogeneity and both velocity (P<.001) and lineal density (P=.011), with
r=.693. The relative heterogeneity fell more rapidly
with increasing velocity than with increasing lineal
density.
The spatial heterogeneity of perfusion for each 10second interval (10-second CV,) showed considerable
variability during the 10-minute sample interval. Fig 5
(upper panels) shows histograms of 10-second CV, for
velocity, lineal density, and supply rate in capillary
network 1. The source of the variability in spatial
heterogeneity was explored by testing the correlation
between the 10-second CV, and the 10-second data on
arteriolar input, mean velocity, mean lineal density, and
Ellis et al Heterogeneity of Perfusion in Capillary Networks
361
TABLE 2. Summary of Statistics for Red Blood Cell Velocity, Lineal Density, and Supply Rate for the Entire 10-Minute
Sample Interval for All Five Capillary Networks and for the Estimated Arteriolar Input to Each Network
Statistics Compiled From All
Five Networks
Network
1
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Capillary RBC supply parameter
Number of capillary segments analyzed
9
Velocity
Mean, mm/s
0.15
CV, %
Temporal
6.4
Spatial
38.8
Overall
40.2
Lineal density
Mean, mm/s
14.9
CV, %
Temporal
14.0
Spatial
33.3
Overall
38.3
Supply rate
Mean, mm/s
2.3
CV, %
Temporal
10.7
Spatial
40.2
Overall
43.0
Estimated arteriolar input to network
Number of capillary segments used in input
7
Supply rate
Mean, mm/s
14.4
Temporal CV, %
12.0
RBC indicates red blood cell; CV, coefficient of variation.
2
10
0.12
0
20
~~~
0
CV, %
5
6
8
...
...
0.15
0.24
0.16
0.16
0.05
27.47
28.88
11.02
32.62
34.72
3.18
7.30
7.42
22.39
21.37
18.3
22.5
22.9
24.9
20.70
4.03
19.49
14.0
42.2
51.0
10.0
41.8
40.6
8.1
29.0
28.6
13.5
20.0
28.1
11.92
33.26
37.32
2.71
9.31
9.49
22.75
28.00
25.42
2.5
3.2
5.6
4.1
3.54
1.35
38.14
18.3
67.6
71.2
15.3
42.0
43.1
11.4
49.8
47.8
15.1
36.8
42.1
14.16
47.28
49.44
3.12
12.32
12.37
26.06
25.01
8
3
4
6
17.0
18.8
9.7
16.7
16.5
12.6
20.2
13.7
15.56
14.76
3.88
2.89
24.93
19.60
capillary
segment
70 1st
2nd
4
0 ~~~v 3rd
4th
~~~~v
40
SD
11.0
29.1
31.3
0
20
Mean
10.1
28.3
28.5
2
0
5
15.0
25.0
28.7
43
4
12.6
41.9
44.9
mean supply rate. The lower panels in Fig 5 show the
correlation of the 10-second CV, for velocity, lineal
density, and supply rate with the arteriolar input. The
. .
3
60
capillary supply rate
(% artenolar input)
FIG 3. Temporal variation of capillary supply rate (CVap/CVinput,
where CV is coefficient of variation, cap is capillary supply, and
input is arteriolar input) as a function of red blood cell supply rate
expressed as a percentage of the input supply rate. The data
have been pooled from all five networks. The order of the
capillary segment from which the data were obtained is indicated
by the different symbols shown in the legend.
22.03
results for all five networks have been summarized in
Table 3. Each network was found to have a considerable
dispersion of 10-second CV, values. Three of the five
networks showed a modest correlation between the
spatial heterogeneity of RBC supply rate within the
network and the estimated arteriolar input to the network. Two networks showed a correlation between the
heterogeneity of velocity and of lineal density with the
input as well. In all of these cases, the heterogeneity of
perfusion decreased as the input to the network increased. Since RBC supply rate is determined both by
velocity and lineal density, we tested to see whether the
heterogeneity of RBC supply rate correlated with these
two parameters by use of multilinear regression analysis
[10-second CV, =a-+
ao (10-second mean velocity) + a2
(10-second mean lineal density)]. The results of this
analysis are given in Table 3. Only networks 1 and 2
showed a significant correlation.
Network 5 demonstrated very unique behavior compared with the networks studied. During the first 400
seconds (Fig 6) the spatial heterogeneity showed the
same behavior as the other three networks (spatial
heterogeneity was negatively correlated with arteriolar
input), but during the last 200 seconds the behavior was
Circulation Research Vol 75, No 2 August 1994
362
tions to the population of capillary segments within a
network supplied by a single arteriole.
20
"/7elde
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3D Plots
The first goal of the present study was to determine
whether the capillary network is a source of spatial and
temporal heterogeneity of RBC flow. The 3D plots in
Fig 2 provide a simple means of visualizing the heterogeneity and attempt to answer this question. The obvious heterogeneity of perfusion in these plots cannot be
due to differences in RBC supply among individual
arteriolar networks, since the capillary network analyzed for these graphs originated from a single arteriole.
The presence of a persistent spatial heterogeneity
among the capillaries within the network can easily be
appreciated from the distinct "mountain ranges and
valleys." The temporal heterogeneity within individual
vessels can be appreciated from the "peaks" in the
mountain ranges and the "dips" in the valleys.
Did this spatial heterogeneity originate in the capillary network? For two pairs of second-order capillaries,
segments 20/21 and 22/23, the answer is clearly yes,
since in each case the flow from the parent vessel was
divided very unequally between the daughter branches.
For the other capillaries, the answer is not as simple,
since this network contained four inputs from the
supplying arteriole, ie, four first-order capillary segments (Fig 1, segments 11 through 13 and the parent of
vessels 24 and 25). Several of these vessels show distinct
differences: segment 13 had the highest velocity; segments 24 and 25, the highest lineal density; and segments 13 and 25, the highest supply rates. From the 3D
plots we cannot tell whether these differences were a
passive result of the geometry of the network and of the
rheology or whether the flow was being actively controlled by the supplying arteriole to each individual
first-order vessel, ie, the activity of capillary "sphincters." More detailed analysis of the data given below
will help to answer this question.
Did the temporal heterogeneity originate in the capillary network? We can attempt to answer this question
by comparing the temporal heterogeneity in the network with that in the supplying arteriole. This can be
done only in terms of RBC supply rate, since RBC
velocities and lineal densities in the arteriole could not
be estimated from the capillary data. Moreover, we
were unable to measure these parameters directly.
IZsk
&C'5Z
FIG 4. Three-dimensional plot of the relative temporal heterogeneity of supply rate (CVap/CVinput, where CV is coefficient of
variation, cap is capillary supply, and input is arteriolar input) vs
velocity vs lineal density. The origin of the plot is shown by the
arrows in the lower back corner of the graph. The plane at
CVap/CVnput= 1.0 indicates the level at which the temporal
heterogeneity of the capillary equals that of the input. The
distance between a data point and this plane is indicated by the
thin vertical line. The location of the point in the velocity versus
lineal density plane is shown by a small + drawn in perspective.
All values above the plane are white; all values below the plane
are shaded gray. RBC indicates red blood cells.
reversed (the heterogeneity followed the change in
arteriolar input [positive correlation]). The spatial heterogeneities of all three flow parameters during the final
200 seconds were correlated with the arteriolar input
and the mean value of each parameter (Table 4).
Discussion
Several strategies could be used to evaluate different
aspects of the spatial heterogeneity of RBC flow in a
capillary bed. For example, one could focus on the
distribution of perfusion among capillary segments intersecting a cross section of the muscle or on the
dispersion of flow based on capillary segments yielding
a mass balance. Alternatively, one could estimate the
heterogeneity of perfusion in the entire population of
capillary segments at the surface of the muscle, as most
previous investigators have done. We have chosen a
different strategy, one that allowed us to distinguish
between potential sources of heterogeneity present in
these previous studies. We have restricted our observavelocity
O15
1T
~010-
10-
0
20
40
80
60
0
0
20
10-s spatial CV
40
60
80
10-s spatial CV
60
&
10-s spatial CV
60
X0'
t
60
40
t-f i
-
'
40
I
0
0
30-
20
10
12
FIG 5. Variation of the spatial heterogeneity of red
blood cell (RBC) perfusion (10-second spatial coefficient of variation [CV] values for velocity, lineal density, and supply rate) in capillary network 1 displayed
as histograms in the upper panels and as scatterplots
vs the estimated arteriolar input to the network in the
lower panels. The solid and dashed lines in the
scatterplots indicate the least-squares regression line
and its 95% confidence intervals, respectively. The
results of the regression analysis are given in Table 3.
~~~~~~~~~5
5
0
supply rate
lineal density
14
16
18
artenolar supply rate
RBCIs
20
20
10
12
14
16
18
supply rate
artenolarRBC/s
20
20
10
o
:
0
12
14 16
18
arteriolar supply rate
RBC/s
20
Ellis et al Heterogeneity of Perfusion in Capillary Networks
363
TABLE 3. Variation in the 10-Second Spatial Coefficients of Variation in Each Capillary Network for Red
Blood Cell Velocity, Lineal Density, and Supply Rate
Network
Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017
2
3
4
5
1
%
CV
of
velocity,
1 0-Second spatial
31.1
26.1
41.8
44.9
29.0
Mean
2.6
5.5
6.8
7.0
6.3
SD
12.1
21.9
29.6
22.5
28.0
Minimum
62.9
41.8
44.2
54.5
35.1
Maximum
0.42
...
...
0.73
...
Correlation with input*
...
...
...
...
0.40
Correlation with mean velocityt
10-Second spatial CV of lineal density, %
24.7
38.0
46.3
43.5
30.0
Mean
6.2
3.4
3.2
5.5
10.7
SD
30.9
35.3
22.6
12.5
24.6
Minimum
37.4
37.4
50.5
52.8
84.3
Maximum
0.35
...
...
0.63
...
Correlation with input*
...
...
0.46
...
0.59
Correlation with mean lineal densityt
10-Second spatial CV of supply rate, %
44.4
50.6
44.3
72.3
40.6
Mean
6.5
8.0
4.9
4.3
6.5
SD
27.0
56.6
33.5
39.7
29.2
Minimum
52.7
56.8
89.0
61.6
55.0
Maximum
0.49
...
0.66
0.50
...
Correlation with input*
0.47
...
0.61
...
...
Correlation with mean supply ratet
0.71
...
0.59
...
...
Correlation with velocity and lineal density*
CV indicates coefficient of variation.
*Linear regression of 10-second spatial CV values with arteriolar red blood cell supply rate; tLinear regression of
1 0-second spatial CV values with corresponding mean velocity, lineal density, or supply rate; and tMultilinear regression
of 1 0-second spatial CV values with mean velocity and mean lineal density. Regression coefficient is reported for significant
correlations (P<.01). All significant correlations show a negative slope, ie, a negative correlation.
Comparison of the 3D plots of absolute (RBCs per
second) versus relative (percent input) RBC supply
rates (Fig 2) can be made on the basis of the following
premise. The plot of relative supply was constructed on
the assumption that consistent temporal fluctuations in
flow across the network, which most likely originated in
the supplying arteriole, would be removed when the
data were plotted as a percentage of the input. Fluctuations originating within the network would not be
coordinated and hence would be unaffected by normalizing the data in this manner. There are four segments,
b
a
30
60
60
p
10-s CV
Q-1
'P
Ut
13 and 23 through 25, in which the dynamic variations in
supply have been obviously reduced, and there are at
least three capillary segments, 11, 12, and 22, which had
large temporal variations in supply rate that have not
been appreciably affected (the responses in other vessels are hidden by those with the highest flow). Thus,
some, but not all, of the temporal heterogeneity of RBC
supply did have its origins in the network.
The 3D plots, when used together with the schematic
of the network layout, can provide useful insights into
the heterogeneity of capillary flow. However, to inves-
50
input
o
25
40
0
15
0
50
>
4't0 @0
_. U
20 t1*'
30
20
O-Pt
200
4
time (s)
g
P
0
30
20
00~
~
30
o0
-
16
20
090
~~~
o
-
24
arteriolar input (RBC/s)
FIG 6. Variation of the spatial heterogeneity of red
blood cell (RBC) supply rate (10-second spatial coefficient of variation [CV]) in capillary network 5 as a
time-series plot in panel a and as a scatterplot vs the
estimated arteriolar input in panel b. In panel a, the
estimated arteriolar input supply rate is also plotted
(dashed line). In panel b, the white circles represent
data from the first 400 seconds, and the black circles
represent the data from the final 200 seconds. The
solid and dashed lines in the scatterplots indicate the
least-squares regression line and its 95% confidence
intervals, respectively, for the two sets of data. The
regression line has a negative slope for the white
circles and a positive slope for the black circles.
364
Circulation Research Vol 75, No 2 August 1994
TABLE 4. Correlation of 10-Second Spatial Coefficients of Variation Versus the Arteriolar Input or
the Corresponding Velocity, Lineal Density, or Supply Rate in Capillary Network 5 for Two
Time Periods
Time Interval
0 to 400 Seconds
Downloaded from http://circres.ahajournals.org/ by guest on June 16, 2017
r
Independent Variables
Slope
10-Second spatial CV of velocity
0.67
-ve
Input supply rate
0.43
-ve
Mean velocity
10-Second spatial CV of lineal density
...
...
Input supply rate
...
...
Mean lineal density
10-Second spatial CV of supply rate
0.38
-ve
Input supply rate
...
...
Mean supply rate
0.62
Both mean velocity and mean lineal density
+ve, -ve
CV indicates coefficient of variation; -ve, negative; and +ve, positive.
Regression coefficient and sign of slope reported for significant correlations (P<.01).
tigate the factors affecting the heterogeneity, more
detailed analysis of the data, such as presented in Table
1, is required. This analysis yields quantitative values for
the spatial and temporal components of the heterogeneity, which then can be correlated with the flow
parameters.
Analysis of Spatial Heterogeneity
The hemodynamic data have been presented as mean
values for successive 10-second intervals. This interval
was selected for a number of reasons. First, since each
10-second CV value is computed from the mean±SD of
100 "instantaneous" data values per capillary, we can
have considerable confidence in the validity of spatial
heterogeneity estimates. Second, since this interval
exceeded the mean RBC transit time through a capillary segment, each successive time period corresponded
to a new set of RBCs within the segment. Thus,
temporal variations due to the heartbeat and to discrete
events such as the passage of RBCs through bifurcations
or capillary constrictions were removed. Furthermore,
this averaging interval corresponds to that frequently
reported by others in the literature (note that the
analysis of 10-second mean data for the 10 minutes may
be considered to be equivalent to 59 sequential analyses
of a single capillary network). We have shown previously that using 10-second mean data reduces the
temporal CV for a single vessel to between 30% and
60% of the value obtained from instantaneous data.2
Calculation of the spatial CV of network perfusion
for successive 10-second intervals allows one to follow
changes in spatial heterogeneity over prolonged periods
of time (eg, 10 minutes in the present study). Interestingly, even under resting conditions there existed up to
a threefold variation in spatial CV for RBC velocity and
lineal density and up to a twofold variation for RBC
supply rate. Thus, as we expected, within the network
there exists a continuous redistribution of RBC flow
among capillaries. However, the fact that each 10minute CV, value fell within the range of its correspond-
400 to 590 Seconds
r
Slope
0.68
0.78
+ve
+ve
0.72
0.68
+ve
+ve
0.8
0.81
0.82
+ve
+ve
+ve, +ve
ing 10-second values confirms that an inherent spatial
heterogeneity of perfusion persists within each capillary
network. Although this inherent heterogeneity cannot
be abolished, it can be diminished to some extent by
flow redistribution, as evidenced by the fact that some of
the 10-second CV, values were considerably smaller
than the 10-minute value. The lower limit of the histograms in Fig 5 (minimum CV values listed in Table 3)
may represent the maximum degree of homogeneity
that can be achieved.
If the spatial heterogeneity seen in the network is due
to network geometry and rheological mechanisms, then
the distribution of RBC flow within the network should
be influenced by factors such as the RBC input to the
network and by the number and velocity of RBCs within
the network. Fig 5 presents convincing data that this was
the case for network 1. As the RBC input to the network
increased, the spatial heterogeneity (CV,) of RBC
supply rate decreased. Two other networks showed
similar results (Table 3). The spatial heterogeneity of
velocity and of lineal density also was reduced in two
networks as the RBC input increased. Furthermore,
only one network (3) did not show a correlation with at
least one of the flow parameters. The level of RBC
input to the networks in the present study only accounted for 10% to 50% of the variability in the
10-second CVs values. The remaining variability may
have been due to other factors, such as transient white
blood cell plugging of individual flow paths or changes
in vascular resistance or pressure on the venous side of
the network. Or it may have been due to a limitation in
the measurements themselves. The arteriolar input was
estimated from the supply rates in individual capillary
segments. Since it requires a finite time for cells to move
from one location to the next, our estimate of the
dynamics of the cell input to the network may be
distorted. However, we did observe that some vessels
(eg, segment 13, network 1) that were not included in
the calculation of the input supply rate did correlate
well with the dynamics of the estimated input. The
Ellis et al Heterogeneity of Perfusion in Capillary Networks
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estimated arteriolar input to the network should not be
confused with the total RBC supply rate in the arteriole.
The supplying arteriole delivers RBCs to other capillary
networks as well. The correlations of spatial heterogeneity with mean velocity, mean lineal density, and mean
supply rate should be valid, since these values represent
events that were measured within the network.
Why did not all of the networks show the same
behavior? Network 3 showed no correlation between
the measures of heterogeneity and the rheological
parameters that might affect spatial heterogeneity. This
network had the fewest capillary segments (five), composed of two groups of capillaries with no interconnections between them. Other than differences in geometry, there was no obvious reason for the lack of
correlation. Network 5 did show the same correlation as
the other three networks during the first 400 seconds
and the opposite correlation during the final 200 seconds. The combination of behaviors led to the lack of
correlation for the data set as a whole. Inspection of a
set of 3D plots for this network, of the type shown in Fig
2, revealed that one first-order segment, and thus the
segments downstream from it, received a greater proportion of the input to the network than the other
vessels during the last 200 seconds of the sample. This
"imbalance" in perfusion led to the positive correlation
shown in Fig 6 and summarized in Table 4. The
imbalance was not due to a higher than usual supply of
RBCs to the network, since the input did not rise above
earlier levels (Fig 6) and it did not appear to steal flow
from the other first-order capillaries downstream, since
these vessels maintained approximately the same level
of flow during this period of time. The change in RBC
supply also occurred without a change in velocity and
was entirely due to an increase in lineal density. We may
speculate that the supplying arteriole actively diverted
additional RBCs to this first-order segment, for a brief
period of time, in response to local metabolic demand
or that a passive event such as the transient plugging of
another capillary out of the field of view caused RBCs
to enter this vessel.
Changes in mean RBC velocity for a network should
reflect changes in driving pressure relative to the hemodynamic resistance across the network. It is interesting
that the values of 10-second CV, for velocity were not
correlated with the mean velocity in any of the networks
(except for network 5 during the flow imbalance, Table
3). This can be interpreted as indicating that changes in
driving pressure and/or hemodynamic resistance across
the network did not significantly alter the heterogeneity
of pressure gradients and/or resistance within the network. In contrast, increasing the number of RBCs
entering the network did decrease the spatial heterogeneity of velocity. We interpret this to mean that rheological mechanisms associated with the passage of an
increased number of RBCs through the network resulted in a more uniform distribution of segmental
driving pressures relative to flow resistance.
Our previous estimate of spatial heterogeneity of
RBC supply rate2 included interarteriolar and animalto-animal variation, whereas in our present estimate
these variations have been excluded. Nevertheless, the
mean network spatial CV of 47% (Table 2) reported in
the present study amounted to more than two thirds of
our previous global estimate of 66% for frog sartorius
365
(and 67% for rat gracilis) muscle. The implication is
that the capillary network itself is a significant source of
the spatial heterogeneity of RBC supply in capillaries
across the frog sartorius muscle.
Analysis of Temporal Heterogeneity
One might expect the global temporal variability of
RBC perfusion within the network to arise from variations in the arteriolar supply. This expectation was
confirmed by the similarity of temporal CVs for the
entire network to those for the estimated arteriolar
input and by the ANOVA, which indicated consistent
temporal variations throughout the capillary network.
However, the spatial heterogeneity results also indicated another source of heterogeneity, the temporal
redistributions of RBC flow among capillaries. This was
seen particularly with capillaries that carried <20% of
the total RBC input, for these vessels showed temporal
CV values up to four times that of the arteriolar supply.
Vessels with a high relative heterogeneity of perfusion
were characterized by low velocity and low lineal density of RBCs (Fig 4). However, the magnitude of the
relative heterogeneity appeared to depend more on
velocity than on lineal density. The underlying mechanism for this behavior may depend on a number of
factors. Flow of RBCs in capillary segments with a low
driving pressure across them (as indicated by a low
velocity of flow) will be sensitive to irregularities in
capillary luminal cross section20 that are due to the
finite energy required for the deformation of RBCs.
Moreover, at each capillary bifurcation the distribution
of cells to vessels with a low velocity may be highly
variable compared with the vessel with the higher
velocity.
Summary
How are we able to explain the degree of spatial and
temporal heterogeneity we found in these networks?
We believe that the topology of the networks is one
important factor. For example, at a diverging capillary
bifurcation, the blood flow in the parent capillary must
be divided between the daughter vessels. In terms of
RBC supply rate, the sum of the supply rates in the two
daughter vessels must equal that of the parent. A
homogeneous distribution of cells between the two
daughter vessels would reduce the supply rate in these
segments to half of that in the parent. The level of RBC
velocity in the daughter vessels relative to the parent is
more difficult to predict, since this is determined by the
relative cross-sectional areas of the daughter vessels to
that of the parent (and by the relative velocity of the
RBCs to that of the blood flow as a whole). The RBC
lineal density in the daughter vessels is then determined
by the supply rate and by the velocity in each vessel:
lineal density (RBCs per millimeter)=supply rate
(RBCs per second)/velocity (millimeters per second).
There are situations when a daughter vessel can have
either a much lower or much higher lineal density than
the parent. The distribution of RBCs at branch points is
further exaggerated by the phase separation of plasma
and RBCs at bifurcations. The daughter vessel with the
higher blood flow rate tends to receive an even greater
proportion of the RBCs than one would predict simply
from the blood flow distribution.21 Thus, even if the
arteriolar supply to all first-order capillary segments (ie,
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Circulation Research Vol 75, No 2 August 1994
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capillaries branching directly from the arteriole) were
homogeneous, one would measure a spatial heterogeneity of perfusion from either a random sample of the
capillary bed or from a network analysis.
These arguments did not take into account variations
in vascular resistance due to the geometry of the
network that would further contribute to the spatial
heterogeneity. The geometry of the capillary network in
frog sartorius muscle has been studied by Plyley et al.22
Analysis of the fundamental structure of the diverging
and converging vessels revealed that the number of
branch points per capillary path, from arteriole to
venule, formed a Poisson distribution and that the
capillary segment lengths formed an exponential distribution. Both findings indicate that branch points are
distributed randomly along each capillary path. Furthermore, for this same muscle Safranyos et al,23 have
reported a wide range of capillary diameters, and Ellis
and colleagues24'25 have demonstrated considerable
changes in luminal cross-sectional area along capillaries. One would expect that the complexity of such a
capillary network must lead to an inherent spatial
heterogeneity of vascular resistances and thus of flow
among vessels, even for a simple newtonian fluid. In
addition, for networks perfused by blood, we would
predict the spatial heterogeneity to be dynamic because
of the two-phase nature of capillary blood flow. As
RBCs enter and leave a capillary segment, they alter the
resistance to flow within that segment, and this phenomenon would lead to a redistribution of blood flow and of
RBCs between daughter branches at diverging bifurcations. This is the most likely explanation of temporal
changes in the spatial heterogeneity of blood flow that
we observed.
This explanation of the spatial and temporal heterogeneity of RBC flow derives solely from the passive
rheological properties of blood in capillary networks.
This concept is supported by the dynamic simulation of
Kiani et a126 for blood flow in capillary networks, which
demonstrates that flow within a given vessel varies with
time even when the driving pressure across the network
is fixed.
Discussion of the Present Study Related to Others
The approach to studying flow heterogeneity has
varied considerably among different research groups. In
most cases, experiments have been designed to study
the spatial heterogeneity of perfusion (variation in flow
among capillaries) rather than the temporal heterogeneity (variation in flow with time in individual capillaries). To obtain a representative measure of the distribution of blood flow among capillaries, RBC velocities
have been sampled randomly from capillaries on the
muscle surface. Most velocity measurements are reported to represent approximately a 10-second mean
value for each vessel. In some of these studies, care has
been taken to determine the "true" spatial heterogeneity by measuring the velocity distribution at one fixed
point in time within one muscle region9; others have
pooled data that have been sampled at different times
and from different muscles.' Since these two studies
obtained contradictory results, it has been proposed
that their disagreement was due to this fundamental
difference
in
sampling strategy.9 Another approach
has
been to study entire capillary networks and to measure
the distribution of RBC velocities,4 content, and supply
rate27 within these networks. In these studies, the spatial
distributions of flow parameters were measured simultaneously in all vessels. More recently, entire microvascular networks of arterioles, capillaries, and venules
(with up to 1000 vascular segments) have been analyzed
in rat mesentery under normal conditions16 and after
isovolemic hemodilution.1" Because of the vast size of
the mesenteric networks, hemodynamic data could not
be sampled simultaneously in all vascular segments
(data collection required up to 30 minutes with 300
individual fields of view). The fact that the network
analysis of the effect of hemodilution on spatial heterogeneity disagreed with almost all previous studies
based on a random sample of capillaries highlights the
important issue of how to obtain representative data to
properly investigate flow heterogeneity under a variety
of conditions.
It is interesting that the overall CV in the present
study was very similar to the 10-minute spatial CV, even
though the overall CV included the temporal variability
as well. Does this mean that a random-sample strategy
at different points in time is as valid as a strategy that
samples at a specific point in time? No, because of the
redistribution of flow within the network, each value
sampled at a different point in time would represent a
value from a different state of heterogeneity. The
resulting data would be very difficult to interpret.
However, there are also problems with the CV calculated at a specific point in time, since it represents only
one state of the muscle. A number of values should be
calculated to get a better estimate of the true mean
spatial heterogeneity for a given situation in a specific
muscle.
The network analysis of the mesenteric microvasculature required at least 30 minutes and 300 individual
fields of view to complete, ie, 6 seconds per field,
which is slightly less than the 10-second interval used in
the present study. From our analysis, we would predict
that even a passive network such as the mesentery
would show dynamic redistributions of flow over the
course of the 30-minute sample. The montage of images
may actually represent a series of snapshots of the
microvascular network at various stages of flow distribution. The fact that hemodilution had such a profound
effect on the hematocrit distribution and the spatial
heterogeneity of perfusion of the mesenteric network
indicates that passive rheological events do have the
potential to cause dynamic redistributions of flow within
this microvasculature.
In the present study, an increase in RBC supply to the
network was accompanied, in most cases, by a decrease
in the spatial heterogeneity of RBC perfusion. This
result may be interpreted to indicate that the fractional
distribution of RBCs at capillary bifurcations depends
not only on the flow distribution, as reported in the
literature,21 but also on the magnitude of the RBC
supply in the parent vessel. During periods of low RBC
input to the network, RBCs would be found primarily in
preferential flow paths through the network, whereas
during periods of high RBC input, the distribution
would be more uniform among all flow paths.
Would we expect to see the same situation in mammalian muscle? From our previous comparative study
between frog and rat,2 we found a surprisingly close
Ellis et al Heterogeneity of Perfusion in Capillary Networks
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agreement between the mean values of RBC velocity
and supply rate. The difference in lineal density was
almost entirely accounted for by differences in RBC
size. Furthermore, the heterogeneity of the flow parameters was also very similar. Since the flow and the
architecture of capillary networks in rat skeletal muscle
appears to be similar to that in frog, we would expect
the above conclusions to be valid for mammalian muscle
also. However, we do not have enough data as yet to
determine how important the precise network geometry
is in determining the spatial and temporal heterogeneity. Also, significant arteriolar activity, such as arteriolar
vasomotion, which is seen more often in mammalian
muscle,15 may easily dominate both the spatial and
temporal heterogeneity described in the present study.
Heterogeneity and Microvascular Exchange
Spatial heterogeneity in the literature is associated
with the efficiency of exchange processes. Do our measurements of spatial heterogeneity accurately reflect the
ability of the microvasculature to deliver oxygen and
exchange diffusible solutes with the tissue? If exchange
occurs only between a capillary and the tissue volume
surrounding it, then the measures of spatial heterogeneity used in the present study are likely very important.
However, if diffusive exchange occurs among capillaries
such that a number of capillary segments are collectively
responsible for exchange with a volume of tissue, then
the measures of spatial heterogeneity used in the present study and in the literature will be misleading.
Ellsworth and colleagues28'29 have presented results
indicating that oxygen exchange in resting skeletal
muscle occurs among capillaries28 and between arterioles and capillaries.29 Thus, a resting muscle may be
able to tolerate what appears to be a very significant
degree of spatial heterogeneity, because it is the integrated supply of a group of capillaries that determines
the tissue oxygenation, not the supply in each capillary
independent of its neighbors. However, if the oxygen
demands of the tissue increase, then the degree of
diffusive exchange among microvessels will decrease,
and spatial heterogeneity will become important. The
level of heterogeneity that the tissue was able to tolerate at rest may now result in local regions of ischemia.
In organs that actively regulate their blood supply in
response to tissue demands, such as skeletal muscle, one
would predict that the heterogeneity of perfusion due to
the arteriolar tree can be actively regulated. Although
the heterogeneity arising within the capillary network
likely cannot be directly regulated, it can be modified as
indicated above. Thus, the increase in RBC supply to a
capillary network that would occur with an increase in
blood flow should reduce the heterogeneity within each
network; ie, the distribution of 10-second spatial CV
values should shift toward some minimum value. However, even under conditions of high arteriolar supply,
not all of the heterogeneity can be removed because of
the basic geometric structure of a branching network.
Finally, the vessels that could be recruited were the
capillaries with the greatest dynamic variability relative
to the input. These vessels were also found to have the
lowest RBC velocities. A low RBC velocity indicates
that the driving pressure relative to the hemodynamic
resistance across these segments must be small. Thus,
these capillaries will be the most susceptible to plugging
367
by leukocytes or stiffened RBCs20 at low flow rates. If
these vessels are lost, then the ability of the network to
reduce its heterogeneity and increase its efficiency for
exchange will be impaired, and in fact the heterogeneity
will shift toward higher values.
Conclusions
The key concepts that can be derived from this
analysis are as follows: (1) Capillary networks are a
significant source of both spatial and temporal heterogeneity of capillary perfusion. (2) Redistribution of
RBC flow occurs within the capillary network, resulting
in a wide range of spatial heterogeneity values, although
persistent spatial heterogeneity does remain because of
the network geometry. (3) In most networks, the spatial
heterogeneity decreased as the input of RBCs to the
network increased, indicating the importance of the
rheological properties of blood in capillary networks.
(4) There are preferential flow paths within each network that follow the dynamics of the arteriole, and there
are other pathways or individual segments that have the
lowest percentage of the input supply rate when the
supply is low but can be recruited to carry more RBCs
when the supply to the network increases. (5) These
vessels, which can be recruited, have the greatest dynamic variability.
Acknowledgments
This study was supported by separate grants to Drs Ellis and
Groom from the Heart and Stroke Foundation of Ontario. Dr
Ellis is a Career Investigator of the Heart and Stroke
Foundation.
References
1. Damon DH, Duling BR. Are physiological changes in capillary
tube hematocrit related to alterations in capillary perfusion heterogeneity? Int J Microcirc Clin Exp. 1987;6:309-319.
2. Ellis CG, Wrigley SM, Potter RF, Groom AC. Temporal distributions of red cell supply rate to individual capillaries of resting
skeletal muscle, in frog and rat. Int J Microcirc Clin Exp. 1990;9:
67-84.
3. Klitzman B, Johnson PC. Capillary network geometry and red cell
distribution in hamster cremaster muscle. Am J Physiol. 1982;242:
H21 1-H219.
4. Tyml K, Ellis CG, Safranyos RG, Fraser S, Groom AC. Temporal
and spatial distributions of red cell velocity in capillaries of resting
skeletal muscle, including estimates of red cell transit times.
Microvasc Res. 1981;22:14-31.
5. Tyml K. Capillary recruitment and heterogeneity of microvascular
flow in skeletal muscle before and after contraction. Microvasc Res.
1986;32:84-98.
6. Duling BR, Damon DH. An examination of the measurement of
flow heterogeneity in striated muscle. Circ Res. 1987;60:1-13.
7. Gaehtgens P. Heterogeneity of capillary perfusion. Blood Vessels.
1991;28:197-200.
8. Damon DH, Duling BR. Evidence that capillary perfusion heterogeneity is not controlled in striated muscle. Am J Physiol. 1986;
248:H386-H392.
9. Tyml K. Red cell perfusion in skeletal muscle at rest and after mild
and severe contractions. Am J Physiol. 1987;252:H485-H493.
10. Tyml K, Budreau CH. Effect of isovolemic hemodilution on microvascular perfusion in rat skeletal muscle during a low flow state. Int
J Microcirc Clin Exp. 1992;11:133-142.
11. Pries AR, Fritzsche A, Ley K, Gaehtgens P. Redistribution of red
blood cell flow in microcirculatory networks by hemodilution. Circ
Res. 1992;70:1113-1121.
12. Gaehtgens P. Why networks? Int J Microcirc Clin Exp. 1992;11:
123-132.
13. Krogh A. The number and distribution of capillaries in muscles
with calculations of the pressure head necessary for supplying the
tissue. J Physiol. 1919;52:409-415.
368
Circulation Research Vol 75, No 2 August 1994
14. Sweeney TE, Sarelius IH. Arteriolar control of capillary cell flow
in striated muscle. Circ Res. 1989;64:112-120.
15. Slaaf DW, Tangelder GJ, Teirlinck HC, Reneman RS. Arteriolar
vasomotion and arteriole pressure reduction in rabbit tenuissimus
muscle. Microvasc Res. 1987;33:71-80.
16. Pries AR, Secomb TW, Gaehtgens P, Gross JF. Blood flow in
microvascular networks: experiments and simulation. Circ Res.
1990;67:826-834.
17. Tyml K, Sherebrin MH. A method for on-line measurements of
red cell velocity in microvessels using computerized frameby-frame analysis of television images. Microvasc Res. 1980;
20:1-8.
18. Ellis CG, Tyml K, Groom AC. Computer-assisted analysis of video
images: a new tool for microvascular measurements. In: Baker CH,
Nastuk WL, eds. Microcirculatory Technology. New York, NY:
Academic Press Inc; 1986:229-244.
19. Ellis CG, Fraser S, Hamilton G, Groom AC. Measurement of the
lineal density of red blood cells in capillaries in vivo, using a
computerized frame-by-frame analysis of video images. Microvasc
Res. 1984;27:1-13.
20. Secomb TW. Flow dependent rheological properties of blood in
capillaries. Microvasc Res. 1987;34:46-58.
21. Pries AR, Ley K, Claassen M, Gaehtgens P. Red cell distribution
at microvascular bifurcations. Microvasc Res. 1989;38:81-101.
22. Plyley MJ, Sutherland GL, Groom AC. Geometry of the capillary
network in skeletal muscle. Microvasc Res. 1976;11:161-173.
23. Safranyos RGA, Ellis CG, Tyml K, Groom AC. Heterogeneity of
capillary diameters in the skeletal muscle of the frog. Microvasc
Res. 1983;26:151-156.
24. Ellis CG, Tyml K, Burgess W. Quantification of red cell movement
in microvessels: a new application of interactive computer
graphics. Microvasc Res. 1987;33:428-432.
25. Ellis CG, Tyml K, Strang BK. Variation in axial velocity profile of
red cells passing through a single capillary. Adv Exp Med Biol.
1989;248:543-550.
26. Kiani MF, Cokelet GR, Sarelius IH. Effect of diameter variability
along a microvessel segment on pressure drop. Microvasc Res.
1993;45:219-232.
27. Groom AC, Ellis CG, Wrigley S, Potter RF. Architecture and flow
patterns in capillary networks of skeletal muscle of frog and rat. In:
Popel AS, Johnson PC, eds. Microvascular Networks: Experimental
and Theoretical Studies. Basel, Switzerland: S Karger AG; 1986:
61-76.
28. Ellsworth ML, Popel AS, Pittman RN. Assessment and impact of
heterogeneities of convective oxygen transport parameters in capillaries of striated muscle. Microvasc Res. 1988;35:341-362.
29. Ellsworth ML, Pittman RN. Arterioles supply oxygen to capillaries
by diffusion as well as by convection. Am J Physiol. 1990;258:
H1240-H1243.
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Heterogeneity of red blood cell perfusion in capillary networks supplied by a single
arteriole in resting skeletal muscle.
C G Ellis, S M Wrigley and A C Groom
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Circ Res. 1994;75:357-368
doi: 10.1161/01.RES.75.2.357
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