© 1995 American Heart Association, Inc.
Articles |
Local Continuity of Myocardial Blood Flow Studied by Monochromatic Synchrotron Radiation–Excited X-ray Fluorescence Spectrometry
From the Department of Physiology (H.M., M.C., S.H., H.S., Y.S., M.U.-M., H.N.), Tokai University School of Medicine, Bohseidai Isehara, Kanagawa, Japan, and the National Laboratory for High Energy Physics (A.I.), Ibaraki, Japan.
Correspondence to Hidezo Mori, MD, Department of Physiology, Tokai University School of Medicine, Bohseidai Isehara, Kanagawa 259-11, Japan.
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Abstract |
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Abstract We have developed a monochromatic synchrotron radiation–excited system for two-dimensional mapping of x-ray fluorescence evoked from heavy element–loaded microspheres, which can evaluate myocardial blood flow in small contiguous regions with a small methodological error: 10.8±2.4% of the average of difference of the dual flow for 7- to 10-mg myocardial tissue (4 dogs). The fractal D value obtained from the slope of the log relative dispersion–log mass plot was 1.21±0.08 for a voxel size of 7 to 1260 mg (5 dogs) and that for a voxel size of 2.5 to 40 mg (1.12±0.06) was smaller than that for a voxel size of 40 to 1280 mg (1.25±0.14, P<.05, ANOVA, 4 dogs). The distance–correlation coefficient relation for paired myocardial regions was attenuated (correlation analysis), and the correlation coefficients between the original grouping and the two aggregates of the adjacent regions were dissociated (extended correlation analysis) under reduction of coronary perfusion pressure (6 dogs). Suppression of myocardial contraction with lidocaine (3 dogs) and vasodilation with adenosine partly improved the distance–correlation coefficient relation under reduced coronary perfusion pressure. Thus, an x-ray fluorescence system designed for precise flow measurement shows that the fractal nature of local flow distribution can be extended into regions smaller than previously reported, that in these regions the flow becomes more homogeneous, and that the self similarity and continuity of local flow are attenuated by the reduction of coronary perfusion pressure and improved by contractile suppression and coronary vasodilation.
Key Words: microsphere • myocardial ischemia • microcirculation • fractal analysis
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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Blood flow distribution in small myocardial regions of 40 to 200 mg has been studied by means of radioactive microspheres.1 2 3 These studies, as well as recent computer simulations by VanBavel and Spaan,4 indicate a continuity of local flows, suggest a close relation of local flow to coronary vascular anatomy, and point out that more precise measurement of regional flow and direct comparison of regional flow with anatomic features are much needed. According to the report by Bassingthwaighte et al,5 the functional microvascular unit of the myocardium weighs between 0.2 and 1 mg, and according to VanBavel and Spaan,4 the estimated myocardial mass per end coronary vascular segment is 19.3 µg. These divergent conclusions indicate that a more precise method for the evaluation of regional flow is required. The radioactive microsphere technique has a disadvantage in measuring flow in smaller regions, because the tissue has to be cut into discrete samples to count the radioactivity. Cutting tissue into tiny regions of <100 mg is tedious and also makes comparison of the regional flow with the results of anatomic investigations difficult. In addition, a section of 100-mg mass might have several different flow domains. A few years ago, we developed a system for flow measurement using monochromatic synchrotron radiation–excited x-ray fluorescence spectrometry and heavy element–loaded microspheres and reported preliminary results.6 7 The improved method described in the present study does not require cutting the tissue into tiny regions and can more accurately evaluate flow in smaller myocardial regions (<10 mg) than with previously described methods. In the present study, we quantified the methodological errors for the flow measurement in regions smaller than had been used before with monochromatic synchrotron radiation and heavy element–loaded nonradioactive microspheres and then applied the methods to evaluate the self similarity and local continuity of myocardial blood flow distribution.
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Materials and Methods |
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General Surgical Procedures
Fourteen dogs weighing 8.6 to 22.0 kg were anesthetized by intravenous administration of pentobarbital (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 to 20 mL/kg, the respiration rate at 15 to 25/min, and the oxygen administration rate at 1 to 4 L/min to adjust the arterial oxygen level to 100 to 200 mm Hg and the carbon dioxide level to 30 to 40 mm Hg. We added sodium bicarbonate intravenously as needed to maintain the pH of the arterial blood at 7.35 to 7.45. Bipolar electrodes for cardiac pacing were sutured onto the left atrial appendage to adjust the heart rates in dogs 6 through 11, in which the repeated measurements of regional blood flow were performed.
Experimental Protocol and Specific Surgical Procedures
Effects of More Than the Usual Amount of Microspheres on
Hemodynamic Variables and Temporal Variations in Myocardial Flow
Distribution (3 Dogs)
In the main experimental protocol (dogs 1 through 11 in Table 1
), we used more than the usual number of microspheres
to improve the resolution of flow measurement. Therefore, we tested the
effects of these microsphere injections on hemodynamic variables and
temporal variations in myocardial flow in contiguous small regions in 3
dogs. Changes in aortic pressure, coronary perfusion pressure, and
coronary blood flow during the injection and the degrees of reactive
hyperemia after 15-second occlusion of the bypass before and
after the microsphere injection were evaluated in 2 dogs. In one dog
(Fig 1, top), we repeated intra-atrial injections of
2x107 bromine-loaded microspheres four times, leaving a
short interval of 2 to 3 minutes between the injections. This
microsphere injection procedure was exactly the same as that used in
dogs 2 through 5 for the quantification of the methodological errors.
In the other dog (Fig 1, bottom), we set a bypass between the left
subclavian and left circumflex arteries, monitored coronary blood flow
with an in-line electromagnetic flowmeter, and repeated intracoronary
infusion of 1x106 heavy element (bromine)–loaded
microspheres in a bolus dose three times, with a 15-minute interval
between the injections in order to simulate the protocol of microsphere
injections in the 6 dogs in which we evaluated local continuity of flow
(dogs 6 through 11 in Table 1). In these dogs, we injected 5 to
12x105 microspheres into the coronary artery in a single
dose or in two divided doses, waited for 15 minutes, and repeated the
injection three times at maximum. One milliliter of 0.05% SDS solution
containing single doses as described above was prepared in 1-mL
syringes. Each injection of the 1-mL solution took place over 1 to 2
minutes. The solution was stirred by moving a small steel ball in the
syringe with a magnet attached to the outside of the syringe in order
to avoid poor mixing of the microspheres throughout the injection. The
same microsphere injection procedure was performed in the 11 dogs of
the main protocol (dogs 1 through 11; see below). The numbers of
microspheres per injection and in total in the 11 dogs of the main
protocol were equal to or less than the values for these 2 dogs.
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In one dog with the same experimental setup as in dogs 1 through 5 (Fig 2), we studied the temporal variability of regional flow
under adenosine treatment (100
µg · kg-1 · min-1 into left atrium)
by injecting two sets of microspheres sequentially with an interval of
10 minutes. First, we injected 25 million 39Y-loaded
microspheres into the left atrium, which were divided into two doses,
and 10 minutes later, we injected the same number of
35Br-loaded microspheres. There were not any obvious
differences in the heart rate or in aortic pressure between these two
injections. Temporal relative dispersion was calculated while changing
the mass of the aggregated myocardial spots in the range of 44 to 792
mg.
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Evaluation of Methodological Errors and Fractal Analysis (Dogs 1
Through 5)
We quantified methodological errors (precision of the
measurements) and analyzed self similarity of myocardial flow
distribution with fractal analysis8 in the 5 dogs with
dual flow measurements. We measured dual flows with two simultaneously
injected sets of heavy element–loaded nonradioactive microspheres into
the left atrium under autoregulatory conditions in 5 dogs (dogs 1
through 5, Table 1
). After performing a left thoracotomy and a
pericardiotomy, a 3F plastic catheter (length, 5 cm) was introduced
into the left atrium via the appendage. We performed two-dimensional
mapping of x-ray fluorescence on the short axial slices of the left
ventricle containing the dual microspheres and calculated the
variability of the dual relative flows (Fig 3, left).
Dog 1 was designed to have the largest stochastic error sources for the
flow measurement; dog 2, the smallest among the 5 dogs. We injected 15
million of each of the dual heavy element–loaded microspheres into the
left atrium (divided into two doses) and counted the x-ray fluorescence
of each myocardial spot for 30 seconds in dog 1. We used two sets of
either 35Br-, 39Y-, 40Zr-, and/or
41Nb-loaded microspheres made by Sekisui Plastic Co Ltd
(except for dog 2, 53I- and 56Ba-loaded
microspheres).6 7 As described previously, these
microspheres have a specific gravity of 1.29 to 1.61, mean diameters of
14.8 to 15.7 µm, and SDs of 1.5 to 2.3 µm, with a good sphericity,
as can be seen in the photograph shown in Fig 2 of our previous
study.6 We increased the number of microspheres to 3.0 to
4.0x107 and the counting time of the x-ray fluorescence to
50 to 100 seconds in dogs 2 through 5. In addition, the efficiency of
x-ray fluorescence was also improved by using 53I- and
56Ba-loaded microspheres in dog 2. These two microspheres
are characterized by higher elemental concentrations (53I,
37%; 56Ba, 29%) than the other microspheres (11% to
15%) and less attenuation of x-ray fluorescent signals in tissue;
x-ray fluorescence from 56Ba, 53I,
41Nb, 40Zr, 39Y, and
35Br was attenuated to 90%, 88%, 68%, 65%, 62%, and
46% of the original intensities, respectively, by H2O with
a 2-mm depth.6 7 The calculated numbers of the
microspheres, assuming the fraction of the microspheres trapped in the
coronary circulatory system to be 5% of the microspheres injected,
were 103 for the smallest (dog 1) and 227 for the largest (dog 2).
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Correlation Analysis and Extended Correlation Analysis (Dogs 1
Through 11)
We compared local continuity and self similarity of flow
distribution between conditions of autoregulation (dogs 1 through 7)
and reduced coronary perfusion pressure (dogs 6 through 11) by applying
correlation analysis and extended correlation analysis,
respectively. We compared the degree of correlation of flows in paired
regions with reference to their intervening distances in correlation
analysis and determined whether the correlation coefficients for
adjacent pairs or nonadjacent regions would be the same for
different-sized groupings of the data in extended correlation
analysis.9 10 In dogs 6 through 11, we reduced
coronary perfusion pressure, measured local flow with microspheres, and
applied correlation analysis and extended correlation analysis.
These results were compared with those under autoregulatory (7 dogs [1
through 7]), and reduced coronary perfusion pressure conditions (6
dogs [6 through 11]). In 2 dogs (dogs 6 and 7), we evaluated the
correlation of local flow under both autoregulatory and reduced
coronary perfusion pressure conditions. In 4 dogs (dogs 8 through 11),
we tested whether contractile suppression with local lidocaine
administration (1 mg/min IC, 3 dogs [8 through 10]) or metabolic
vasodilatation with local adenosine administration (5
µg · kg-1 · min-1 IC, 3 dogs [8,
9, and 11]) modified the correlation. The blood flow of the left
circumflex arteries was reduced to 30% to 65% of baseline by reducing
coronary perfusion pressure to 30 to 40 mm Hg with a screw
constrictor around the bypass (Table 1). The coronary perfusion
pressure was kept at the same level throughout each microsphere
injection period and between the repeated measurements. Microspheres (7
to 12x105) in single or divided doses, as described above,
were injected into the bypass to evaluate regional flow distribution.
We left a 15-minute interval between the repeated injections of the
microspheres and confirmed a reactive hyperemia of >150% of
the baseline value after a 15-second occlusion of the bypass several
minutes before each microsphere injection. Left atrial pacing was
needed to adjust the heart rates during the repeated measurements only
in dog 8.
Myocardial Sample Preparation
After completing the experimental protocol, we killed the
dogs by an overdose of intravenous pentobarbital. In dogs 6 through 11,
the region perfused by the bypass was stained with Evans blue solution
immediately before pentobarbital administration. We then excised and
sliced the hearts by means of a meat-slicing machine into short axial
rings with a thickness of 
5 mm from the base to apex. Then we
removed the papillary muscles and weighed the slices. We selected
contiguous basal and middle short axial slices of the left ventricular
free wall for synchrotron radiation–excited x-ray fluorescence
spectrometry. Mechanical stress and contractile function can be
considered homogeneous within these regions but not for the atria, the
right ventricle, interventricular septum, or apical free
wall.11 We confined the measurements to posterior segments
of basal and middle short axial slices stained well with Evans blue
(central ischemic region) in dogs 6 through 11. We flattened the short
axial slices to 1.5 to 2.5 mm in thickness with two acrylic plates
while keeping them in 10% formalin solution for several days and then
dried the rings in room air for a few days (except for dog 2, whose
rings were maintained under vacuum conditions with
P2O5 for 24 hours). We divided each short axial
ring into two or three contiguous segments (anterior, mid, and
posterior regions) as shown in Fig 3, left, and weighed again. These
drying procedures reduced the tissue weight to 60% to 80% (25% in
dog 2) of the original value with a minimal change in their
cross-sectional area. The condensing elemental concentration in dog 2
was one more factor for increasing the efficiency of x-ray
fluorescence. Flattening with two acrylic plates allowed us to obtain
the segments of highly homogeneous thickness. We measured the thickness
of each segment at three sites (both sides and central portion) and
calculated the mean and SD for each segment. The coefficient of
variation (100xSD/mean) of the thickness among the three sites in each
slice was <5%, and the coefficient of variation for the mean
thickness among the measured slices was <8%.
X-ray Fluorescence Spectrometry
The synchrotron radiation used was derived from the positron
storage ring (Photon Factory, National Laboratory for High Energy
Physics) with an acceleration energy of 2.5 GeV and an average beam
current of 300 mA. As shown in Fig 3, right, we converted the
continuous synchrotron radiation via beam line 4A, a bending magnet
source, to 20.5-keV monochromatic x-ray to evoke x-ray fluorescence
from 35Br, 39Y, 40Zr, and
41Nb (dogs 1 and 3 through 11) and that via beam line 14C,
a vertical wiggler source, to 50-keV monochromatic x-ray to evoke
fluorescences from 56Ba and 53I (dog 2).
Monochromatization was made by using double Si(111) and double Si(220)
crystal monochromators for BL-4A and BL-14C,
respectively.12 13 The spectra of x-ray fluorescent
signals, as shown at the top of Fig 3, right (K fluorescence peaks),
were detected by a Si(Li) detector (Ortec Co Ltd) with an active area
of 12 mm2 connected to a pulse-height analyzer with 1024
channels (NAIG), processed by a computer (PC 9801 RX, NEC), and stored
on floppy disk for later analysis. We adjusted the beam shape of
the monochromatic synchrotron radiation into a rectangle (1 to
2–to–1 in length ratio) by using a pair of slits (0.5 to 4.0 mmx0.5
to 2.0 mm). The horizontal angle between the incident radiation and the
detector was set at 90° to minimize the background level of x-ray
fluorescence spectrometry mainly due to Compton scattering. Because the
incidental angle to the sample was 45°, the beam width along the
horizontal axis became 
times larger at the myocardial
sample than at the slits. We performed two-dimensional mapping of x-ray
fluorescence on the myocardial segments by using a computer-aided
movable sample holder with a minimum pulse movement of 1 µm for both
the horizontal and vertical axis. The horizontal axis was set exactly
along the anterior-to-posterior direction; the vertical axis, along the
endocardial-to-epicardial direction or vice versa. We left tiny copper
wires at the four corners of each myocardial segment and used the x-ray
fluorescence from the copper (K
peak of 9.0 keV) as a marker to
identify the beam position on each segment. The number of spots on
which x-ray fluorescence spectrometry was performed ranged from 109 to
400 spots, with the mean spot weight ranging from 6 to 42 mg and the
total mass from 1.1 to 8.4 g (Table 1). In dog 2, we repeated
measurement of x-ray fluorescence on the 32 spots of mean spot weight
of 2.5 mg (total, 80 mg tissue) with the finest resolution.
We quantified the peak heights of the elemental x-ray fluorescences,
Compton scattering (large arrowhead in the top of Fig 3, right), and
elastic scattering (small arrowhead in Fig 3, right) from each
myocardial spot. The peak height of Compton scattering linearly
reflects the irradiated mass; that of elastic scattering, the intensity
of the primary monochromatic x-ray.12 13 14 We took care to
prepare each myocardial segment with a homogeneous thickness for x-ray
fluorescence spectrometry as described above. Therefore, the relative
variability of the irradiated mass indicated by Compton scattering was
<4%. To correct the intensity of x-ray fluorescence in each spot with
reference to the precise relative weight for the data analysis
described below, we corrected the x-ray fluorescence (XF) counts from
each myocardial spot to the mean Compton scattering of the whole spots
by Equation 1 and then obtained the relative regional flow in percent
fluorescence (mass-corrected percent x-ray fluorescence) by Equation 2.
 | (1) |
 | (2) |
90 hours. Therefore, the change in the intensity of
primary x-ray for the measurement taking less than a few hours can be
ignored, but the long-lasting measurements >6 hours in total in dogs 3
through 7 and 9 cannot. In these measurements, we used the ratio (peak
Compton scattering/peak elastic scattering) as a correction factor
instead of the Compton scattering peak to obtain mass-corrected x-ray
fluorescence, because the intensity of primary x-ray linearly
correlates with intensities of elemental x-ray fluorescence and Compton
scattering.12 13 14
Data Analysis
Evaluation of Methodological Errors (5 Dogs) and the Method of
Aggregating Spots
In dogs 1 through 5, we quantified the average percent
difference between the dual measurements (RDm)8 as an
index for the methodological errors (precision of the measurement) and
compared it with stochastic error by the following
equation15 16 17 :
 | (3) |
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 | (4) |
 | (5) |
As additional indices for the measured methodological errors (precision
of the measurement), we obtained the square root of the mean residual
error from linear regression analysis (Sy.x) and the SD of the
differences of the dual measurements (SD of d from the method of Bland
and Altman18 ) and compared them with RDm. After
determining the measured and stochastic errors for the original 21-mg
spots in dog 1, 10-mg (2.5-mg) spots in dog 2, and 7- to 9-mg spots in
dogs 3 through 5, we obtained numerically the x-ray fluorescence
activity and the mass for the aggregated myocardial spots up to 1 g,
except for dog 2 (140-mg aggregated mass for the 10-mg spot
analysis and 20-mg mass for the 2.5-mg spot analysis) and
repeated the determination of the measured errors and the calculation
of stochastic errors as described above. In dogs 3 through 5, each
slice consisted of 10*10 spots along transmural and horizontal
directions (Fig 3, left). Then, the mass of the aggregated spots 1*2
(and 2*1), 2*2, 2*3 (and 3*2), 3*3, 4*4, 5*5, 7*7,
9*9, and 10*10 were created. We selected two different ways of
grouping the adjacent spots, leaving the spots at epicardial and
anterior corners or at the endocardial and posterior corners excluded
from the analysis for 3*3, 4*4, 7*7, and 9*9 and obtained a
mean of two calculated error indices. We did not combine the spots from
different segments. These principles were essentially maintained for
the other dogs as well (dogs 1, 2, and 6 through 11).
Fractal Analysis (5 Dogs [1 Through 5])
Fractal analysis was applied to dogs 1 through 5. We
calculated single values of spatial relative dispersion (RDs,
error-corrected coefficient of variation) of flows for the individual
myocardial spots and the variously aggregated adjacent spots (ranging
from 21 to 1260 mg in dog 1, from 10 to 280 mg and from 2.5 to 20 mg in
dog 2, and from 7–9 to 700–900 mg in dogs 3 through 5). RDs was
calculated by using the following formula:
 | (6) |
By plotting RDs against the mass in log scale and then calculating the
linear regression slope for the plots, we obtained the fractal D value
by the following formula:
 | (7) |
Correlation Analysis and Extended Correlation Analysis (Dogs 1
Through 11)
We analyzed the relation between the degree of correlation of
flows in the adjacent regions and their distances (correlation
analysis). We first obtained individual or aggregates of myocardial
spots with sufficiently small (nearly 10% or less) RDm or stochastic
error in each experiment as a unit region for the analysis:
individual spots of 6 to 13 mg (dogs 2 through 7 and 9), two aggregated
spots of 48 to 84 mg (dogs 8, 10, and 11), and five aggregated spots of
105 mg (dog 1). We applied linear correlation analysis to the flows
of the paired myocardial unit regions that were the same distance apart
along the anterior-to-posterior direction (horizontal distance, 1 to 20
mm) or along the endocardial-to-epicardial direction (transmural
distance, 1 to 10 mm). We then plotted the correlation coefficients of
the pair flows against the distances.
According to the reports by Bassingthwaighte and
colleagues,9 10 self similarity can be tested by
determining whether or not the correlation coefficients for the
adjacent pair of regions or nonadjacent neighbors are the same for
different-sized groupings of the data (extended correlation
analysis). We compared the correlation coefficient
(r)–distance relation for the two different levels of
resolution (the original grouping and two aggregates of the adjacent
regions) under autoregulatory (dogs 1 through 7) and reduced coronary
perfusion pressure (dogs 6 through 10) conditions. Fractal dimension D
can be estimated by the autocorrelation function directly with Equation 8.9 10 Therefore, we calculated fractal D values for some
of the dogs (6 and 7) in which dual flow measurements were not
performed but self similarity was estimated by extended correlation
analysis, as for dogs 1 through 5.
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Effects of Injection of More Than the Usual Amount of Microspheres on Hemodynamic Variables and Temporal Variation of Myocardial Flow Distribution (3 Dogs)
As shown in Fig 1
, top, four left atrial injections of
2x107 microspheres, which simulated the protocol in dogs 1
through 5 (determination of methodological precision and fractal
analysis) without repeated flow measurement, slightly increased
aortic pressure, coronary perfusion pressure, and coronary blood flow
during the injections. However, these variables returned to the
preinjection level within several minutes. There was no significant
difference in the amount of reactive hyperemia before and 10
minutes after the injection of 8x107 microspheres in
total. As shown in Fig 1, bottom, three intracoronary infusions of
1x106 microspheres, which simulated the protocol in
dogs 6 through 11 (correlation analysis and extended correlation
analysis) with two or three repeated flow measurements, did not
produce any significant change in aortic pressure, coronary perfusion
pressure, or mean coronary blood flow. There was no marked difference
in the amount of reactive hyperemia after a 15-second occlusion
of the bypass circuit among the periods before, 10 minutes after the
first microsphere injection, and after the third injections (a
cumulative dose of 3x106 microspheres). In dogs 6
through 11, we confirmed an overshoot of coronary blood flow to >150%
of the preocclusion flow level after the 15-second occlusion in the
period 10 minutes after each microsphere injection.
In the remaining dog, temporal relative dispersion (RD
) was
calculated on the basis of the following formula:
 | (9) |
m is observed RD including temporal variability (RD)
and methodological error (RDm). This formula was derived by modifying
the formula reported by Bassingthwaighte et al8 :
 | (10) |
There was an obvious dissociation between stochastic error and
RD,m or RD (Fig 2), in contrast to the close correlation of
stochastic error and RDm in the methodological error protocol described
later. The RDm and RD of the temporal dual flows were
substantially large in the mass range of 44 to 176 mg (17% to 12% for
RD,m and 14% to 11% for RD, respectively); in contrast, the
stochastic error was quite small even for the individual myocardial
spots of 44 mg (10.2%). These results indicate that the present
protocol can detect temporal variability in small regions of <100 mg
under adenosine infusion.
Evaluation of Methodological Errors (5 Dogs)
Dual flow measurements with two simultaneously injected sets of
microspheres in dogs 1 through 5 demonstrated that the methodological
errors in the present method of measuring flows in small contiguous
regions (7 to 10 mg) were small (10.8±2.4%) and that the number of
microspheres used and the length of counting the x-ray fluorescence
were the major determinants of the degree of error. RDm decreased
exponentially as the mass increased in dogs 1 and 2, and log–log scale
plotting revealed a significant linear correlation (r=.994
and P<.0001 in dog 1; r=.898 and
P<.015 in dog 2), as shown in Fig 4.
Comparison of the results from these 2 dogs revealed that the
methodological errors indicated by RDm were reduced in dog 2 by
increasing the number of microspheres (103 versus 227 per 10 mg) and
extending the x-ray fluorescent counting time (30 versus 100 seconds).
For example, the RDm for the 42-mg mass in dog 1 was 16.4% (the arrow
in the left panel of Fig 4), and in contrast, the RDm for the 40-mg
mass in dog 2 was 5.2% (the arrow in the right panel of Fig 4). Even
the RDm for the individual mass (10 mg) in dog 2 was <10% (7%). The
RDm for dogs 3 through 5 fell between those of dogs 1 and 2, as did the
number of microspheres per 10 mg heart tissue (109 to 212 microspheres)
and x-ray fluorescence per spot-counting time of 50 seconds, as shown
in Table 2. There was also a significant linear
correlation between the stochastic error and RDm plotted in log–log
scale (r=.991 to .956 and P<.0001 in dogs 1
through 5) characterized by small SDs of the data from the regression
line (Sy.x, 0.97% to 0.40%) and the slope of the regression lines
around 1.0 (1.16 to 0.79).
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Increase in the mass of the aggregate of the spots also reduced the
other two indices for the variability of dual flows: Sy.x of the linear
regression analysis and the SD of difference by the methods of
Bland and Altman18 (Fig 5 and Table 2). A
10-fold increase in mass (21 to 210 mg) reduced both Sy.x and the SD of
the difference (SD of d) from 23.4% to 9.8%, but these two indices
were slightly bigger than RDm (19.7% to 8.7%) throughout the range of
the mass of aggregates, as shown at the top of Fig 5 and Table 2.
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Fractal Analysis
Fractal analysis confirmed that the self-similar nature of
coronary blood flow distribution can be extended and that flow
distribution becomes more homogeneous in smaller regions than has been
reported in previous studies.2 8 The fractal analysis
in 5 dogs, in which the RDs values for the mass of the individual and
of aggregates were analyzed in the ranges of 21 to 1260, 10 to 280, 7
to 700, 9 to 900, and 7 to 700 mg (dogs 1, 2, 3, 4, and 5,
respectively) demonstrated a negative linear correlation
(r=.93 to .98) between the mass and the RDs (log scale) and
gave fractal D values of 1.21±0.08. Thus, resolution-dependent change
of flow variance and moderate local continuity of the flows were
confirmed. The results of fractal analysis obtained from 4 of the 5
dogs (dogs 2 through 5), in which individual voxel size was set at 
10
mg (7 to 10 mg), are shown in Fig 6.
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The fractal analysis in the range of 2.5 to 40 mg in dogs 2 through 5 revealed a smaller D value of 1.12±0.06 (P<.05 by ANOVA and Fisher's test) than those for the 40- to 1260-mg analysis in the same 4 dogs (1.25±0.14).
Correlation Analysis and Extended Correlation Analysis
As shown in Fig 7 and Table 3, the
correlation coefficient of the paired flows was the highest for the
adjacent paired regions (side by side) and became lower for the
nonadjacent neighbors, as the number of the units between the paired
regions increased (dog 6). Comparisons of the correlation
coefficients for the original grouping (open squares) and for the two
aggregates of the adjacent regions (asterisk in Fig 7) were almost
equal under autoregulatory conditions (left panels of Fig 7 and Table 3). That is, the levels of resolution did not affect the results of the
correlation analysis under autoregulatory conditions. Reduction of
coronary perfusion pressure weakens the correlation for the adjacent
and nonadjacent neighbors along both directions (right panels of Fig 7). Essentially the same results as found for dog 6 were obtained for
the other 9 dogs (dogs 1 through 5 and 7 through 10 as shown in Table 3), in 8 of which correlation analysis was applied under either
autoregulation (dogs 1 through 5) or reduced coronary perfusion (dogs 8
through 10). The calculated D value
(r1=23-2D-1) ranged from 1.07 to
1.20 (1.13±0.05) under autoregulatory conditions (dogs 1 through
7).
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) and two aggregates of the adjacent regions (*). Bottom,
Horizontal distance–correlation coefficient relation. Correlation
coefficients for original grouping and aggregates of two adjacent spots
are almost identical under autoregulatory conditions but dissociated
under reduced coronary perfusion pressure. The dissociation of the
correlation coefficient and unit distance under reduced coronary
perfusion pressure shown in this figure and in Table 3
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In 4 dogs (8 through 11), intracoronary administrations of lidocaine
(Fig 8A) or adenosine (Fig 8B) partly restored the
distance–correlation coefficient relation and increased the
endocardial-to-epicardial flow ratio (P<.05, ANOVA). The
characteristic observations in modification of myocardial blood flow
distribution by lidocaine treatment were that it modified predominantly
the distance–correlation coefficient relation along the
endocardial-to-epicardial direction (left graphs of Fig 8A) and did not
increase blood flow of the left circumflex artery in any of these 3
dogs (Table 1). There was either no obvious modification in the
distance–correlation coefficient relation along the
anterior-to-posterior direction (dogs 8 and 10, right upper graph of
Fig 8A) or a less obvious modification than that along the transmural
direction (dog 9, right lower graph of Fig 8A) in 3 dogs. Adenosine
administration enhanced the correlation coefficients along both the
horizontal and transmural directions in 2 of the 3 dogs (dogs 8 and 11,
upper graphs of Fig 8B) with an increase in the total blood flow of the
left circumflex artery (P<.05, ANOVA, Table 1).
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferences |
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New Observations From the Present Study
Several new observations were derived from the present study. First, we demonstrated that a method of monochromatic synchrotron radiation–excited x-ray fluorescence spectrometry with heavy element–loaded microspheres can be used to evaluate myocardial blood flow distribution in contiguous small regions with sufficiently small methodological errors (Figs 4
and 5 and Table 2). Second, the fractal
nature of myocardial flow distribution was confirmed in the
analysis with an individual spot size of <10 mg, and it was
suggested that local flow may become more homogeneous in smaller
regions (fractal analysis in Fig 6). Third, reduced coronary
perfusion pressure attenuates the self-similar nature of flow
distribution, and local correlation of flow (correlation analysis
and extended correlation analysis in Fig 7 and Table 3). Fourth,
suppression of myocardial contraction with lidocaine and metabolic
vasodilatation with adenosine partly improves the correlation of local
flow under reduced coronary perfusion pressure (Fig 8).
Evaluation of the Present Method
In the present study, we were able to measure the regional
flow in 7- to 10-mg myocardial spots with a sufficiently small
methodological error (10.8±2.4% of RDm). Hoffman and
colleagues2 3 and Bassingthwaighte and
colleagues1 5 8 9 10 have measured regional flows in
myocardial regions of 40- to 200-mg mass by radioactive microspheres.
This difference in sample mass does not indicate a greater sensitivity
in detecting small amount of tracers in small samples by the
present method than by the radioactive method. The reason is that
the number of microspheres (Poisson distribution error) that can be
used without significant alterations in hemodynamic conditions is a
major limiting factor for flow measurement in small regions with
microspheres, instead of being a result of counting errors in the
methods. The advantage of the present method lies in not being
required to cut the tissue into tiny samples. The relative variability
in sample weights can be corrected by the peak height of Compton
scattering or by the ratio of Compton scattering to elastic scattering
during x-ray fluorescence spectrometry. One other important observation
related to the methodological errors in the present study is the
good linear correlation of stochastic errors to the actually measured
index for the variability of the dual flows (RDm). Therefore,
methodological errors for the flow measurement with a single set of
microspheres can be estimated by this relation.
One major criticism concerning the present microsphere technique
might be whether deposition of the heavy element–loaded microspheres
is proportional to blood flow. This issue relates to the
reproducibility of the method and the rheological effects of the
microspheres. The reproducibility of the radioactive microsphere method
has been extensively studied by dual injection of the microspheres, and
the methodological errors have been found to be substantially smaller
than the actually observed spatial heterogeneity of
blood flow.1 2 15 16 17 The difference in the dual flows
measured by heavy element–loaded nonradioactive microspheres is also
small, as described above, and Mori et al6 have recently
reported a good correlation between the flows measured with radioactive
and heavy element–loaded microspheres. Concerning the rheological
effects of radioactive microspheres, Utley et al19
reported that microspheres with a diameter of 15 µm do not deposit
preferentially in areas of high flow compared with microspheres with a
diameter of 50 µm, and Bassingthwaighte et al20
reported a slight tendency for preferential deposit in regions of high
flow even in the measurement with microspheres with a diameter of 15
µm by comparing them with a molecular microsphere. In preliminary
experiments, we compared the dual flow measured with
35Br-loaded nonradioactive microspheres having a diameter
of 60 µm and 41Nb-loaded microspheres with a diameter of
15 µm. The dual flows for the myocardial regions with a mean mass of
1200 mg revealed a significant linear correlation (r=.97,
P<.01). However, the flow measured with the 60-µm
microspheres was 30% greater than the flows measured with the
15-µm microspheres.
One other criticism concerning the present microsphere technique
might be the possible impairment of the microcirculation due to the
large amount of microspheres. In two preliminary experiments, we
investigated the hemodynamic effects induced by an equal or greater
number of the microspheres than used for the main protocol (dogs 1
through 11). Left atrial administration of 80 million microspheres
produced only a transient increase in systemic and coronary perfusion
pressure and coronary blood flow (Fig 1, top). Intracoronary
administration of 3 million microspheres did not reveal any significant
change in these values (Fig 1, bottom). Neither the left atrial nor
intracoronary administration of more than the usual amount of
microspheres affected the degree of reactive hyperemia after a
15-second occlusion of the coronary arterial flow. Austin et
al16 reported that a cumulative dose of 20 million
radioactive microspheres injected into the left main coronary artery
did not affect the temporal stability of the flow measurements.
In addition, we confirmed in dogs 6 through 11 that the degree of
reactive hyperemia was not altered by repeated injection of
microspheres. The temporal variability of the flows under adenosine
treatment (RD of 11% to 14% for 44- to 132-mg mass in Fig 2) was
not apparently different from those with radioactive
microspheres.21 22 Bassingthwaighte and
colleagues5 8 have reported that the RD can be
described by the equation of 6.26*mass-0.233,
giving an RD of 10.8% for a 100-mg mass.
Self Similarity and Local Continuity of Myocardial Flow
Fractal analysis in dogs 1 through 5 demonstrated a negative
linear correlation between the logarithmic RDs and the logarithmic mass
with a D value of 1.21±0.08 (Fig 6), and extended correlation
analysis demonstrated that the levels of resolution did not affect
the results of correlation analysis under autoregulatory conditions
(Fig 7 and Table 3). These results confirmed the self-similar nature of
myocardial flow distribution during autoregulation, and the fractal D
value of 1.21 in mean suggested a moderate local continuity of flow in
the range of 7- to 1200-mg voxel size, as initially reported by
Bassingthwaighte et al.8 The significantly smaller D value
for 2.5- to 40-mg voxel size than for 40- to 1260-mg voxel size
suggested the possibility that the flow distribution in the smaller
regions might be more homogeneous. Bassingthwaighte et al5
have suggested the possibility that fractal plots might bend toward a
plateau in smaller myocardial regions close to functional microvascular
units of 0.2 to 1.0 mg. More precise analysis would be required to
demonstrate distinct homogeneous flow distribution in the smaller
myocardial regions (<1 mg). Applying the present x-ray
fluorescence system to molecular microspheres loaded by heavy element
might be an ideal methodology for this purpose.
The attenuation of correlation in both directions and the dissociation
of the correlation coefficients between the original grouping and the
two aggregates of the adjacent regions under reduced coronary perfusion
pressure (Table 3 and Fig 7) indicated that continuity of local flow
and the self-similar nature of flow distribution were attenuated by a
reduction of coronary perfusion pressure. Lidocaine and adenosine
treatment partially restored the correlation of local flow and the
increased endocardial-to-epicardial flow ratio under reduced coronary
perfusion pressure. However, their effects were different in certain
aspects. Lidocaine produced a predominant effect on transmural
correlation and was not accompanied by an increase in total coronary
blood flow (Fig 8A and Table 1). Adenosine treatment partially
recovered the correlation of local flow along both directions with an
increase of coronary blood flow (upper graphs of Fig 8B and Table 1).
These results suggest that extravascular compression due to a
heterogeneous impairment of myocardial contraction
aggravates transmural flow distribution during ischemia, as well as
heterogeneity of the vascular reserve.3
Chilian23 has reported a lower coronary arterial pressure
and a rather smaller microvascular resistance in the subendocardium
than in the subepicardium and interpreted these results as evidence for
impediment of flow at the penetrating transmural artery and a
compensating lower resistance in the subendocardial microvascular
structures. Our observations suggest a possible effect of
heterogeneous impairment of myocardial contraction on the
penetrating transmural arteries and their branches,24 and
this produces a heterogeneous impediment of flow
distribution across the myocardial wall. Austin and
colleagues2 25 have reported a difference in
autocorrelation analysis between the endocardial and epicardial
layers and an improvement of correlation by lidocaine. However, they
did not apply autocorrelation analysis on short axial slices of the
left ventricle.
In conclusion, the present study demonstrates the usefulness and
accuracy of a synchrotron radiation–excited x-ray fluorescence system
for measuring relative flows in small contiguous regions and provides
several characteristic observations with reference to the self
similarity and local continuity of myocardial blood flow. The fractal
nature of myocardial flow distribution was extended into smaller
regions (down to 7 to 10 mg) than has been previously reported (>40
mg), and the possibility that local flow becomes more homogeneous in
smaller regions is suggested. The self similarity and the continuity of
local flow are attenuated by reduction of coronary perfusion pressure
and partly restored by the addition of lidocaine (contractile
suppression) or adenosine (vasodilation).
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Acknowledgments |
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This project was approved by the National Laboratory for High Energy Physics, Tsukuba, Japan, as a joint research program (89-148, 91-232, and 93-236) and partly supported by research aid from the Tokai University School of Medicine and the Ministry of Education, Science, and Culture, Japan (94-06807063). We deeply thank Dr J.I.E. Hoffman for his criticism in preparing the manuscript, Dr Akihiko Yamakawa for his cooperation in this project, and Dr Kevin Boru for editing the manuscript. We also thank Y. Shinozaki, Y. Takahari, and M. Takada for their technical assistance.
Received May 19, 1994; accepted February 13, 1995.
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References |
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