Vol. 277, Issue 6, H2353-H2362, December 1999
Intramyocardial vascular volume distribution studied by
synchrotron radiation-excited X-ray fluorescence
Yukiko
Nakajima1,
Noboru
Akizuki1,
Yoko
Kimura1,
Hiroki
Kohguchi1,
Akira
Tanaka1,
Mitsuaki
Chujo1,
Naoichiro
Hattan1,
Yoshiro
Shinozaki1,
Atsuo
Iida2,
Shunnosuke
Handa1,
Hiroe
Nakazawa1, and
Hidezo
Mori1
1 Department of Physiology,
Tokai University School of Medicine, Bohseidai, Isehara, Kanagawa
259-1193; and 2 Photon Factory,
Institute of Materials Structures Science, Ko-Energy Kasokuki
Kenkyukiko, Tsukuba 305-0801, Japan
 |
ABSTRACT |
We evaluated the vascular volume distribution
with fine resolution (0.1-1.3 mg myocardial tissue) in the
sagittal plane of the left ventricle by using the microsphere filling
method in 21 dogs. The coronary arterial volume density in the sagittal plane did not exhibit normal distribution and was characterized by
variability among the outer-to-inner layers and within the layers
(+2SD/
2SD > 80 times), and the median values in the layers ranged from 4.7 to 22.9 nl/mg myocardial tissue. The fractal analysis of vascular volume revealed a self-similar nature with a fractal dimension (D value) similar to that of
flow distribution (1.20 ± 0.05 and 1.24 ± 0.09 for vascular
volume and flow distribution, respectively) and had a more marked
variability than the flow. The correlation of the regional vascular
volume between adjacent regions decreased as the distance increased.
However, the correlation coefficients in the endocardial-to-epicardial
direction were significantly higher than those in the
anterior-to-posterior direction (P < 0.05 by paired t-test). In conclusion,
we determined intramyocardial vascular volume density in the sagittal
plane, and the distribution revealed considerable variability,
self-similarity, and asymmetry in the correlation among the adjacent
regions. These observations could be related to the characteristics of
the intramural coronary vascular network.
coronary artery; fractal analysis; microcirculation; microsphere
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INTRODUCTION |
BASSINGTHWAIGHTE ET AL. (3, 20) initially reported a
self-similarity, and Austin et al. (1) a profound spatial heterogeneity and local continuity, in coronary blood flow distribution using radioactive microspheres and/or molecular tracer methods.
Mori et al. (14), using heavy element-loaded microspheres and
synchrotron radiation-excited X-ray fluorescence (SR-XF) spectrometry,
and Matsumoto et al. (13), using a molecular tracer method and precise detecting system (imaging plate), expanded these observations by
achieving a finer resolution. The coronary blood flow distribution is
dependent on the anatomic features of vessels, extravascular compression, and vascular tone (2, 9). Regional vascular volume
reflects the local resistance to coronary flow (5). The coronary
vascular volumes at systole and diastole were analyzed histologically
(11) and by using albumin labeled with radioactive tracers (7).
Penetrating transmural arteries (PTAs) penetrate the heart wall toward
the inner layers along the sagittal plane and are considered to be a
crucial vascular segment for supplying blood to the subendocardial
muscle (6). Thus flow and vascular volume distribution in the sagittal
plane of the left ventricle (LV) should be analyzed.
However, in the previous studies described above, neither
flow nor vascular volume distribution has been evaluated on the
horizontal myocardial surfaces, except in the report by Mori et al.
(14), which described a flow distribution analysis in the sagittal
plane of the LV.
In the present study, we analyzed the variability within and between
the outer and inner layers, self-similarity, and local continuity in
intramyocardial vascular volume distribution in the sagittal myocardial
plane using the microsphere filling method. In the present
method, the analytical range of the vascular size can be altered by
applying microspheres of different sizes (15 and 60 µm) to plug
vessels, and the relative vascular volume can be converted to an
absolute value (µl/mg tissue) by applying a particular calibration method.
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METHODS |
General Surgical Procedures and Experimental Protocol
Twenty-one dogs weighing 7.1-22.0 kg were anesthetized by
intravenous administration of pentobarbital sodium (30 mg/kg), and ventilation was maintained by an artificial
respirator via an endotracheal tube. We set the tidal volume in the
range of 15-20 ml/kg, the respiration rate at 15-25
breaths/min, and the oxygen administration rate at 1-4 l/min to
adjust the arterial oxygen and carbon dioxide levels to 100-150
and 30-40 mmHg, respectively. We added sodium bicarbonate
intravenously as needed to maintain the pH of the arterial blood at
7.35-7.45.
Analysis of intramyocardial vascular volume distribution (15 dogs).
We analyzed the intramyocardial vascular (IMV) volume distribution in
12 dogs and performed a preliminary protocol to validate the present
method (microsphere filling method) in the remaining 3 dogs. In one of
the three dogs used for validation of the microsphere filling method,
we determined whether our SR-XF spectrometry (14) could detect a single
microsphere with a diameter of 15 µm in myocardial tissue, to test
whether the present method had adequate sensitivity to detect coronary
arterioles with a diameter of 15 µm in tissue. We injected 1 × 106 zirconium-loaded microspheres
into the left atrium in the dog. After the dog was killed, the heart
removed, and the LV free wall fixed in Formalin solution for several
days, we took a portion of the free wall for two-dimensional (2-D) XF
mapping as described below. For the validation protocol in the second
and third dogs, the left circumflex coronary artery (LCX) was plugged
with 3 and 5 × 108
iodide-loaded microspheres (15 µm). We then compared the 2-D XF
mapping images of thin myocardial slices (20-30 µm) with the microscopic images (resolution level <5 µm) of coronary arterioles and the angiographic images of intramyocardial and epicardial coronary
arteries (resolution level 30 µm) taken with the SR angiographic system (14, 16) to assess the completeness of microsphere filling of
the intramyocardial coronary arterial trees. With this angiographic
system, monochromatic SR with an energy level just above the
K-absorption (33.30 keV) edge of iodine was used as an X-ray source,
and a high-definition video system with a camera having a
high-sensitivity tube was coupled with a fluorescent screen as a
detector. This system allowed depiction of small vessels with diameters
as small as 50 µm (16, 17).
In the 12 dogs used for vascular volume analysis, intramyocardial and
epicardial coronary arteries were filled retrogradely with microspheres
(15 µm or 60 µm in diameter) and loaded with a heavy element
(zirconium or bromide), and the intramyocardial microsphere
distribution was analyzed by XF spectrometry using monochromatic SR as
an excitation source. Heavy elemental activity of microspheres plugging
the coronary arteries is considered to be an index of the vascular
volume of intramural coronary vessels, of which the smallest vascular
diameter for the measurement was determined by the size of microsphere
used. We performed a left thoracotomy and pericardiotomy. A bypass was
set between the left subclavian artery and the LCX. Coronary blood flow
was monitored by an electromagnetic flowmeter preset in the bypass. We
injected bromide- or zirconium-loaded microspheres with diameters of 15 µm (8 dogs) or 60 µm (4 dogs) into the LCX. The total amount of injected microspheres was 3-5 × 108 for 15-µm microspheres and 1 × 107 for 60-µm
microspheres. These microsphere numbers, divided into >10 doses, were
injected via the bypass. In the four dogs, 15-µm microspheres were
injected after complete cardiac arrest was induced with intravenous
pentobarbital and potassium chloride (neither vascular tonus nor
myocardial compression). In the other eight dogs (4 dogs injected with
15-µm microspheres and the remaining 4 dogs with 60-µm
microspheres), the initial injection was started while the heart was
beating. However, within the initial three doses, ventricular
fibrillation developed. The remaining doses were injected under the
condition of cardiac arrest. Several milliliters of saline were
injected between each dose to plug vessels without space.
Analysis of local myocardial flow distribution.
In six dogs we performed a left thoracotomy and pericardiotomy and
placed a catheter in the left atrium (LA) via the appendage and another
catheter to monitor blood pressure (BP) in the descending aorta. Dual
microspheres (Sekisui Plastic, Tokyo, Japan) loaded with yttrium or
zirconium and with a diameter of 15 µm (1 × 107 microspheres for each) (13)
were stirred in 0.1% SDS solution and injected slowly into the LA via
the catheter for 2 min. The injection of microspheres was repeated
three to four times at 2-min intervals (total amount of each
microsphere: 3-4 × 107). Mori et al. (15)
previously confirmed that this amount of dual microspheres could be
injected into the LA without causing a marked hemodynamic effect.
Sample Preparation
In the dog used for detecting a single microsphere, the flattened LV
free wall (1 cm × 1 cm × 2 mm) was used for XF
spectrometry. In the dog used for validating microsphere filling of the
coronary arterioles, a rectangular block (1 × 1 × 2 mm) was
obtained from the midportion of the LV free wall. Several thin samples
of 20-30 µm in thickness were then obtained from the block and
used for microscopic observation, after which 2-D XF mapping was
applied to the same samples. In the dog used for validating microsphere (I labeled) filling of larger coronary arterial segments, the heart was
fixed in Formalin solution. Two weeks later, radiography using
monochromatic SR (33.3 keV energy) was applied. This system allows
visualization of coronary vessels with diameters as small as 50 µm.
In the 12 dogs used for analysis of IMV volume distribution in the
sagittal myocardial plane, the hearts were excised and kept in 10%
Formalin solution for 1 wk. After the week of fixation, we
dissected out a rectangular block (1 × 1 × 2 cm in
endocardial-to-epicardial, circumferential, and base-to-apex
directions, respectively) from the LV free wall. Care was taken to
include the first or second marginal branches of the LCX along the
base-to-apex direction on the epicardial surface in these blocks. We
divided this block into several thin sagittal slices with a thickness
of 1-2 mm. All of these slices included a cross-sectioned marginal
branch at the top and the endocardial surface at the bottom. We
selected three to five contiguous myocardial slices from each heart to be used as samples for XF spectrometry (see Fig.
3B in Ref. 14). It was thought that
small intramyocardial vessels with a diameter of >15 µm would be
plugged with microspheres of 15 µm in diameter (8 dogs). In four of
the eight dogs, an epicardial surface slice of 1 mm in thickness was
prepared in addition to three sagittal slices to obtain a calibration
factor for the conversion of relative to absolute vascular volume. In
these epicardial slices, microscopic photographs were taken to
calculate the segmental vascular volume of epicardial vessels with a
diameter of 300-600 µm by using a cylindrical model. After the
determination of XF, the activity of the same segments gave us a
calibration factor for the conversion of relative to absolute vascular
volume density (nl/mg tissue). In the remaining four dogs, in which
microspheres with a diameter of 60 µm were plugging the vessels, the
self-similarity in the coronary vessels with a diameter of 
60 µm
(coronary arterial tree without microcirculatory segments of <60 µm
in vessel diameter) was analyzed. According to the data by Kassab et
al. (12), coronary arterial segments with a diameter of <65 µm have
more critical pressure drop and flow reduction than the larger segments.
We killed the six dogs used for analysis of the local myocardial flow
distribution on the short axial plane of the LV with an overdose of
intravenous pentobarbital, excised the hearts, and sliced them into
short axial rings with a thickness of 5-6 mm from base to apex. We
removed the papillary muscles and weighed each slice. We selected the
contiguous basal and middle short axial slices of the LV free wall for
SR-XF spectrometry. We flattened the short axial slices to 1.5-2.5
mm in thickness with two acrylic plates while keeping them in 10%
Formalin solution for several days. We divided each short axial ring
into two to three segments (anterior, mid, and posterior regions) and
weighed them for XF spectrometry (14).
XF Spectrometry Using Monochromatic SR
SR-XF spectrometry was carried out as described in our previous report
(14). We performed 2-D XF mapping and quantified the peak heights of
the elemental XF values, Compton scattering, and elastic scattering
from each myocardial spot. The elemental XF values of the heavy
element-loaded microspheres plugging the vessels reflect the vascular
volume in the measured spots. However, the measured XF values were not
normalized for the precise spot weight. In addition, the intensity of
the primary monochromatic X-ray also affects the efficiency of the XF
values, because the intensity of the primary monochromatic X-ray decays
slowly (time constant of ~90 h). Spectrometry of the XF values can
give us information concerning the spot weight and primary X-ray
intensity; the peak height of Compton scattering linearly reflects the
evoked myocardial mass, and that of elastic scattering gives the
intensity of the primary monochromatic X-ray. The XF counts from
individual myocardial spots were corrected by the mean of the Compton
scattering intensity divided by elastic scattering intensity
(correction factor in Eq. 1), and
then the percent mass-corrected XF (relative regional vascular volume
or flow) was calculated using Eq. 2.
|
(1)
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|
(2)
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Data Analysis
IMV volume distribution.
We performed two analyses of the obtained data. First, we observed the
relative vascular volume distribution (mass-corrected XF values) from
the outer to the inner layers (epicardial, outer middle, inner middle,
and endocardial) in the sagittal myocardial plane and calculated their
logarithmic values. We described the logarithmic mass-corrected XF
values of the four layers using a histogram and compared their
parameters (mean value and standard deviation of the populations) in
eight dogs. We applied this procedure to the results with both 15-µm
(4 dogs, 16 slices) and 60-µm microspheres (4 dogs, 15 slices) to
assess whether the vascular volume of arterioles with a diameter of 15 or 60 µm alters the intramyocardial vascular distribution. In the
remaining four dogs with 15-µm microspheres (12 slices), the relative
distribution of vascular volume was converted to the absolute value
(nl/mg tissue) using a calibration slice from each of the previous four
dogs, and the same analysis as that used for relative distribution was applied.
Fractal analysis.
To perform a fractal analysis in the sagittal myocardial plane, we
created the mass range by regularly aggregating the adjacent spots. As
summarized in Table 1, the mean mass of
individual spots ranged from 0.11 to 1.06 mg and the number of spots on
each slice ranged from 400 to 4,160. The stochastic error of
measurement can be calculated from the following equations and used as
an alternative for measurement error (14)
|
(3)
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|
(4)
|
where
nd is the number
of microspheres in the measured mass, and
|
(5)
|
where
nc is the number
of XF values counted in the measured mass. To obtain the spatial
relative dispersion (RDs;
error-corrected coefficient of variation) for IMV volume, we used
Eq. 6
|
(6)
|
where
RDobs is the standard deviation of
mass-corrected XF values divided by the mean, in each mass. Total
measurement error (stochastic error) was 5.23 ± 1.28% for 15-µm
microspheres and 14.26 ± 2.86% for 60-µm microspheres. We then
plotted RDs against the mass
(weight) in log scale for each myocardial slice (43 slices, 12 dogs).
We calculated the linear regression slope for the plots and obtained
the fractal dimension (D) value from
Eq. 7 for each slice
|
(7)
|
where
m is the measured mass,
mref is the
reference mass (1 g), and 1 D is the slope of the regression
line. Fractal analysis for coronary blood flow
distribution was performed by exactly the same method as described in
our previous report (14). The mass of individual spots ranged from 4.0 to 10.0 mg, the number of spots was 100 in all slices, and the number
of spots in an aggregated mass increased to 100. The fractal
D value was calculated for each dog
(3-4 slices each).
Correlation analysis.
We compared local correlation in IMV volume between the
endocardial-to-epicardial direction and the circumferential direction. The method was essentially same as that used for the correlation analysis of regional blood flow described in our previous report (14).
We applied linear correlation analysis to the vascular volume of the
paired myocardial regions that were the same distance apart in the
anterior-to-posterior (circumferential or horizontal) direction (unit
distance 
10, distance range from 250 µm to 2.5 mm) and in the
epicardial to endocardial (sagittal) direction (unit distance 10,
distance range from 250 µm to 2.5 mm). We then plotted the
correlation coefficients of the pair volumes against the distance.
All animal studies were performed following "The Guide for the Care
and Use of Laboratory Animals, Tokai University School of Medicine."
| |
RESULTS |
The computer graphic image shown in Fig.
1A was
constructed from a 2-D distribution of XF activity of zirconium in
myocardial tissue with a thickness of 2 mm (a scanning area of 40 × 40 spots, spot size of 8 × 8 µm). In a spot near the
center of the scanning area, the strongest positive zirconium
fluorescence was observed associated with weaker fluorescence in the
adjacent spots. This could be recognized as a single zirconium-labeled
microsphere in the myocardial tissue due to the similarity in size (15 µm). In Fig. 1B, microscopic and
computer graphic (XF mapping) images of an arteriole filled with
iodide-loaded microspheres are shown for comparison. In
the microscopic image, a series of microspheres is aligned along the
vascular wall. This indicates that the diameter of the vascular segment
is ~15 µm. The computer graphic images show similar arteriolar
structural features. In the angiographic images shown in Fig.
1C, the epicardial coronary arterial
branches with diameters of a few millimeters and the PTAs with
diameters of 100-500 µm can be visualized. There was no
inhomogeneity within any of the vascular images. The results shown in
Fig. 1 confirm that an intramyocardial arterial system with a diameter
range of 15 µm to several hundred micrometers can be filled
thoroughly with microspheres and that their heavy elemental activity
can be analyzed for determination of IMV volume.
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Fig. 1.
Results of validation protocol. A:
computer graphic image of single microsphere detected by X-ray
fluorescence (XF) spectrometry. B:
microscopic image (right) of an
arteriole filled with iodide-loaded microspheres (surrounded by blue
outline, detailed in inset) and its
computer graphic image (left)
created by distribution of heavy elemental activity.
C: marginal branches (arrows) and
their penetrating transmural arteries (arrowheads). Radiographic image
was created by synchrotron radiation microangiography. Coronary
arterial tree was filled with iodide-loaded microspheres 15 µm in
diameter. Note that there is no inhomogeneity of iodide contrast in
these vascular images.
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Vascular volume distributions from the outer to inner layers in the
sagittal myocardial plane revealed quite a skewed distribution in the
normal scale (Fig.
2A,
left); in contrast, the distribution returned to normal in the log scale (Fig.
2A,
right). As shown in Table
2, the median values of
absolute vascular density (cumulative data from 3 myocardial slices)
ranged from 4.7 to 22.9 nl/mg tissue (0.47-2.29 vol%, assuming
the relative density of myocardial tissue as 1.0). The
distribution of the high-density regions (>90% in percentile) was
contiguous and treelike in shape, and the density decreased in general
from the epicardial to the endocardial direction in each slice. Such
vascular density distribution could be recognized as the PTAs and their
major branches. These regions are responsible for the large variability
of the whole vascular volume distribution (mean coefficient of
variation: 153 ± 15% in 4 dogs), and the coefficient of variation
decreased to 99 ± 33% in the remaining <90% regions in
percentile. The relative vascular volume (log XF count)
distribution analyzed under the arrested, and the initially beating and
finally arrested conditions (beating-arrested) measured with 15- and
60-µm microspheres revealed a normal distribution in the log scale in
all of the epicardial, mid, and endocardial regions (Fig.
2B). The differences in relative XF
activity (relative vascular volume) were statistically significant for
all pairs of layers among the four layers in all 12 dogs (Table
3). The ratios of the epicardial XF
intensity in the outer-middle, inner-middle, and endocardial layers
ranged from 58% (dog no. 4, outer middle) to 96% (dog no. 3, outer
middle) in the arrested hearts, from 94.6% (dog no. 8, outer middle)
to 117.9% (dog no. 5, endocardial) in the beating-arrested hearts with
15-µm microspheres, and from 80.1% (dog no. 9, endocardial) to
113.9% (dog no. 12, endocardial) with 60-µm microspheres. The
epicardial vascular density was higher than the endocardial values in
all four arrested hearts and in two of four and three of four
beating-arrested hearts with 15- and 60-µm microspheres,
respectively.
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Fig. 2.
Distributions of vascular volume from outer and inner layers shown as
histograms. A: absolute vascular
density distribution (left, normal
scale) and relative density distribution
(right, log scale) from an arrested
heart. B: relative distributions
measured with 15-µm (left) and
60-µm microspheres (right) from a
beating-arrested heart.
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Fractal analysis in the sagittal myocardial plane confirmed that the
IMV volume distribution has self-similarity (fractal nature) and that
its fractal dimension is almost identical to or slightly smaller than
that of the myocardial blood flow distribution at baseline (Fig.
3). The plotting of the
relative dispersion of regional vascular volume measured against mass
in the log scale revealed a linear relationship with the slope
(a) of the regression line being
0.20 ± 0.05 (mean values) in the arrested hearts and 0.22 ± 0.06 in the beating-arrested hearts. The fractal
D values defined by 1 a (1.20 ± 0.05 and 1.22 ± 0.06, Table 4) were almost identical to or
slightly lower than that of the analysis of relative dispersion of the
regional myocardial flow (1.24 ± 0.09, n = 6 dogs). Elimination of the
vascular volume of microcirculatory vessels with diameters of
15-60 µm from the measurements did not affect the fractal
D value. As shown in Table 4, the
vascular volume distribution measured with 60-µm microspheres yielded
results (D value: 1.23 ± 0.04)
almost identical to those measured with 15-µm microspheres. Any
relative dispersions of the vascular volume were larger than those of
the myocardial flow, as indicated representatively by the
RDs at 10-mg mass in Fig. 3
(50-200% in volume and 20-30% in flow). The variability of
RDs between the myocardial slices or among the dogs was larger in the beating-arrested hearts than in the
arrested hearts, although there were no differences in the slopes of
the fractal regression lines (Fig. 3,
B-D).
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Fig. 3.
Fractal analyses of myocardial blood flow in beating hearts
(A; n = 6 dogs), intramyocardial vascular volume in arrested hearts
(B; n = 4 dogs), and intramyocardial vascular volume in beating-arrested
hearts as measured with 15-µm (C;
n = 4 dogs) or 60-µm microspheres
(D; n = 4 dogs). In
A, the mass-flow dispersion relation
was analyzed for each dog; in
B-D, the mass-intramyocardial
vascular (IMV) volume dispersion (%) was analyzed for each myocardial
slice. RD, relative dispersion.
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As shown in Fig. 4, the correlation
coefficient of the paired volume measured with 15-µm microspheres in
the sagittal myocardial plane was the highest for the adjacent paired
regions with a unit (250 µm) distance and became lower as the
distance between the paired regions increased. The degree of
correlation coefficient reduction along the endocardial-to-epicardial
(transmural) direction was less marked than that in the
anterior-to-posterior (horizontal) direction (Fig. 4). The correlation
coefficient in the transmural direction was kept at a higher level than
that along the horizontal direction. The correlation coefficient
decreased to <0.2 by the second (for arrested hearts) or fourth (for
beating-arrested hearts) unit distance in the horizontal direction,
whereas in the transmural direction the correlation coefficient was
maintained >0.2 to the eighth distance (for both arrested and
beating-arrested hearts). The correlation coefficients in the
transmural direction were significantly higher than those in the
horizontal direction at the first to the tenth and the first to the
eighth unit distances of the arrested and beating-arrested hearts,
respectively (P < 0.05 by paired
t-test).
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Fig. 4.
Results of correlation analysis from arrested hearts
(A) and beating-arrested hearts
(B). Correlation coefficients were
plotted against unit distance. * Correlation coefficients at unit
distances are significantly higher along transmural (Trans) than
horizontal (Horizon) direction (P < 0.05, paired t-test).
 Significant difference between arrested and
beating-arrested hearts (P < 0.05).
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DISCUSSION |
IMV volume in the sagittal myocardial plane could be analyzed by
applying SR-XF spectrometry and the microsphere filling method (Fig. 1)
with a resolution of <1.0 mg. The present analysis demonstrated the
following new findings. IMV volume density was variable within and
among the layers, and its median value ranged from 4.7 to 22.9 nl/mg
myocardial tissue (or 0.47-2.29 vol%). Coexistence of arterioles
and major segments (PTAs and their branches) in the sagittal slices
could be considered as one of the reasons for the extreme variability.
The IMV volume density had a fractal nature with almost the same
fractal D values as the local
myocardial blood flow (Fig. 3 and Table 4). The fractal
D value was not modified by the
microsphere size (60 µm vs. 15 µm) or the conditions under which
the microsphere injection was started (arrested or beating-arrested).
There was a closer local continuity in the endocardial-to-epicardial
than in the anterior-to-posterior direction (Fig. 4). These
observations could be related to characteristics of the intramural
coronary vascular network.
Consideration of Model
Our method of assessing the IMV volume distribution has several
differences from those of previous reports (7, 11, 19, 21, 22). The
major advantages of this method are that the analysis was done in the
sagittal plane of the LV free wall, that the relative volume
distribution can be converted to the absolute value by measuring
epicardial vessels with known volume, and that the analytic range with
reference to the vascular size can be altered by applying different
microsphere sizes. The region selected for the measurement was confined
to a relatively small portion of the LV free wall (4.65 g in each
dog) as shown in Table 1. In addition, the vascular volume measurement
was confined to the arterial system with a diameter as low as 15 µm.
In other words, this method does not allow assessment of capillary
vessels, venous vessels, or arterioles with a diameter <15 µm. We
injected a certain amount of microspheres into the dogs under arrested
conditions with intravenous KCl or under beating-arrested heart
conditions. In the latter group, microsphere injection of less than
one-third of the total amount caused ventricular fibrillation followed
by cardiac standstill in 1 min, and the remaining two-thirds or more were injected under arrested heart conditions. Concerning the completeness of microsphere filling of the coronary vascular network, we performed a validation protocol as described in Fig. 1. We eliminated the XF activities from the epicardial rims (0.5-1.0 mm
in width) from the analysis. Therefore, our analysis was confined to
the activities of intramural vessels. In other words, the results were
not affected by the activities of the epicardial coronary branches. We
minimized the methodological error for volume measurement (5.23 ± 1.28% for the beating-arrested hearts with 15-µm microspheres), defined as the square of the distribution error plus the square of the
counting error, compared with those of flow measurement (10.8 ± 2.4%) in this study. The Poisson distribution error was small (3.17 ± 1.27%), because there was a large number of microspheres in each
measurement spot. The counting error was also adequately minimized
(2.90 ± 1.08%), because XF counting per spot was substantial. The
high-sensitivity SR-excited system (14, 15) allowed us to obtain a
large number of regional activities (400-4,160 spots/slice) of XF
with a relatively short counting time per spot (1-5 s) and substantial XF activity per spot.
IMV Distribution
The present study demonstrated IMV volume density in absolute values
(nl/mg tissue) and its variability within the layers and among the
layers (Fig. 2 and Table 2). The absolute vascular density on a
sagittal slice ranged from 4.7 to 22.9 nl/mg tissue (0.47-2.29
vol%). The coronary arterial volume density (20 µl/g myocardial
tissue) calculated by Kassab et al. (12), which is based on their
morphometric analysis, is close to the upper limit of the present
vascular density. Kassab et al. measured the whole coronary arterial
system from the left main coronary artery to the capillaries; in
contrast, our measurement was confined from the PTAs to arterioles with
a diameter of 15 µm. The contiguous high-density regions (>90% in
percentile) on the slices probably reflected PTAs and their branches
and are responsible for the large variability (153% in mean CV) of the
density distribution. The differences in relative IMV volume were
statistically significant for every pair of the four layers in all
eight dogs. There have been numerous studies on IMV volume using direct
morphometric or indirect microsphere detecting methods. However, the
results were variable. Judd and Levy (11) and Goto et al. (7) reported that total volume was greater in the epicardial than in the endocardial layers of rat and rabbit hearts, respectively. Hyde and Buss (10) found
no transmural gradient of the intramyocardial blood volume in canine
hearts. Wusten et al. (22) and Weiss and Conway (21) found a
significant transmural gradient in arterial plus arteriolar volume,
favoring the subendocardium, using rabbits and dogs, respectively. One
noteworthy point in this study is that we measured only small myocardial regions of the heart (measured total mass of 0.63-4.65 g for each dog) in both the analysis with 60-µm microspheres and that
with 15-µm microspheres, but not in the whole heart. However, we
found a profound heterogeneity of IMV volume even in the small regions.
Fractal Analysis
The present fractal distribution of the IMV volume in the sagittal
plane of the LV free wall indicated that self-similarity in vascular
branching is maintained throughout the intramyocardial coronary artery
system down to the microcirculatory level (15-µm vessel diameter).
The fractal nature of the myocardial blood flow distribution was
initially reported by Bassing-thwaighte and colleagues (3, 4, 8) and
then extended by Mori et al. (14) to a smaller region with an
individual spot size as small as 2.5 mg using XF spectrometry.
Matsumoto et al. (13) achieved the finest resolution by using a
molecular tracer and a precise detecting system (imaging plate). The
present report is the first study directly describing the fractal
nature of the intramyocardial vascular volume distribution. The fractal
D value for the vascular volume
distribution (1.20 ± 0.05 and 1.22 ± 0.06 for beating-arrested hearts in Table 4) was almost identical to that for the blood flow
distribution (1.24 ± 0.09). VanBavel and Spaan (19) and Bassingthwaighte et al. (4) initially reported that a fractal dichotomous branching network model correlated well with flow distribution in baboons and sheep and obtained a similar fractal value
(fractal dimension of 1.16-1.22). Recently, Tanaka et al. (18)
reported that self-similarity in diameter reduction, as for branching,
was almost identical between the intramural and epicardial coronary
arterial networks. To evaluate the effects of vascular tonus and/or
extravascular compression (remaining 2 of the 3 major determinants of
coronary flow) on the complexity in the fractal baseline flow, fractal
analysis of flow measured under lidocaine or adenosine administration
may be required in the future.
In our data, the variability in the vascular volume was more marked
than that of the tissue flow (compare
RDs at 10 mg in Fig. 3) as
described in the report by Kassab et al. (12). They calculated that the
variability of blood volume distribution in the coronary arterial
segments below arterioles with a diameter of 17 µm was >100% in
terms of the coefficient of variation; in contrast, the variability at
1-mg mass in the blood volume distribution in the present study was
much more (log 2.7; ~500%), as shown in Table 4. This difference
seems to be related, at least in part, to the coexistence of arterioles
and larger vascular segments such as the PTAs and their major branches
in a small sample region, as discussed previously.
Local Correlation of IMV
The local correlation analysis in the sagittal myocardial plane
demonstrated that the local vascular volume had a stronger local
correlation in the transmural than in the horizontal direction, or, in
other words, poorer local continuity of vascular volume (local
resistance) distribution in the horizontal direction. Recently, Tanaka
et al. (18) demonstrated that the reduction ratio of vascular diameter
(daughter/mother) was much smaller at the junction of the PTAs
(daughter segments) and their mother segments of the epicardial
coronary arteries than those at branching points within the intramural
and epicardial coronary arterial systems. Furthermore, the diameter
change in the proximal segments of PTAs did not relate to the order of
branching off from the epicardial coronary arteries. Tanaka's
observation explains the results in the present correlation analysis; that is, the lack of relation between the PTA size and the
order of sequence contributes to poor correlation in the horizontal direction. Self-similarity in diameter reduction as for branching was
maintained within the PTA system, and these arterial systems arise from
the epicardial site and penetrate the heart perpendicularly toward the
endocardium. These findings contribute to the higher correlation in the
transmural direction. These results indicate that the intramyocardial
coronary arterial system has inherently closer structures in the
transmural than in the horizontal direction. In our previous report
(14), a correlation analysis of myocardial blood flow showed no such
difference in the transmural direction or the horizontal direction. In
addition, relatively maintained local continuity of the myocardial
blood flow was markedly decreased under ischemic conditions. This means
that other factors add additional complexity to the myocardial flow
distribution in the transmural direction while the heart is beating.
Austin et al. (2) applied autocorrelation analysis in the horizontal
myocardial slice in the arrested and beating hearts, the latter with
and without vascular tone, and concluded that coronary vasomotor tone,
without apparent regard for coronary anatomy or the mechanical effects
of cardiac contraction, appears to be the sole determinant of
myocardial blood flow under resting conditions. However, they did not
precisely analyze autocorrelation in the sagittal plane except for the
analysis among the three layers. Myocardial contraction produces
retrograde flow through PTAs (17). This retrograde flow causes a
variability in flow along the transmural direction (2). The closer
correlation in vascular volume along the transmural direction is
effective in ameliorating the contraction-dependent increase of flow
variability along the direction.
| |
ACKNOWLEDGEMENTS |
This project was approved by the National Laboratory for High
Energy Physics, Tsukuba, Japan, as a joint research program (93G241,
95G113, and 96G229) and was supported by Grants-in-Aid 07557060, 07807073, 07807363, and 09670756 for Scientific Research from the
Ministry of Education, Science, and Culture, Japan; JSPS-RFTF-97I00201 from The Japanese Society for the Promotion of Science; and Tokai University School of Medicine Project Research (1977).
| |
FOOTNOTES |
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Address for reprint requests and other correspondence: H. Mori,
Dept. of Physiology, Tokai Univ. School of Medicine,
Bohseidai, Isehara, Kanagawa 259-11, Japan (E-mail:
coronary{at}keyaki.cc.u-tokai.ac.jp).
Received 15 June 1998; accepted in final form 10 June 1999.
| |
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ABSTRACT
INTRODUCTION
