# Local Continuity of Myocardial Blood Flow Studied by Monochromatic Synchrotron Radiation–Excited X-ray Fluorescence Spectrometry

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## Abstract

*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.

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.

## Materials and Methods

### 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 2×10^{7} 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 1×10^{6} 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 12×10^{5} 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.

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 _{39}Y-loaded microspheres into the left atrium, which were divided into two doses, and 10 minutes later, we injected the same number of _{35}Br-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.

#### 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 analysis^{8} 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 _{35}Br-, _{39}Y-, _{40}Zr-, and/or _{41}Nb-loaded microspheres made by Sekisui Plastic Co Ltd (except for dog 2, _{53}I- and _{56}Ba-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 4.0×10^{7} 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 _{53}I- and _{56}Ba-loaded microspheres in dog 2. These two microspheres are characterized by higher elemental concentrations (_{53}I, 37%; _{56}Ba, 29%) than the other microspheres (11% to 15%) and less attenuation of x-ray fluorescent signals in tissue; x-ray fluorescence from _{56}Ba, _{53}I, _{41}Nb, _{40}Zr, _{39}Y, and _{35}Br was attenuated to 90%, 88%, 68%, 65%, 62%, and 46% of the original intensities, respectively, by H_{2}O 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).

#### 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 12×10^{5}) 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 P_{2}O_{5} 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 (100×SD/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 _{35}Br, _{39}Y, _{40}Zr, and _{41}Nb (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 _{56}Ba and _{53}I (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 mm^{2} 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 mm×0.5 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 (Kα 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. The intensity of synchrotron radiation decays slowly with a time constant of ≈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 equation^{15} ^{16} ^{17} : where n_{d} and n_{c} are calculated mean numbers of microspheres and of mean x-ray fluorescence counts per spot, respectively.

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 Altman^{18} ) 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: where RDobs is the observed coefficient of variation.

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: where m_{ref} equals 1 g and 1−D is the slope of the regression line.

#### 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. All animal studies were performed following “The Guide for the Care and Use of Laboratory Animals” (Department of Health, Education, and Welfare publication No. [NIH] 86-23, revised 1985).

## Results

### 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 2×10^{7} 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 8×10^{7} microspheres in total. As shown in Fig 1⇑, bottom, three intracoronary infusions of 1×10^{6} 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 3×10^{6} 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 (RDτ) was calculated on the basis of the following formula: where RDτm is observed RD including temporal variability (RDτ) and methodological error (RDm). This formula was derived by modifying the formula reported by Bassingthwaighte et al^{8} :

There was an obvious dissociation between stochastic error and RDτ,m or RD (Fig 2⇑), in contrast to the close correlation of stochastic error and RDm in the methodological error protocol described later. The RDτm and RDτ of the temporal dual flows were substantially large in the mass range of 44 to 176 mg (17% to 12% for RDτ,m and 14% to 11% for RDτ, 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).

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 Altman^{18} (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⇑.

### 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⇓.

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 (*r*_{1}=2^{3−2D}−1) ranged from 1.07 to 1.20 (1.13±0.05) under autoregulatory conditions (dogs 1 through 7).

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⇑).

## Discussion

### 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 colleagues^{2} ^{3} and Bassingthwaighte and colleagues^{1} ^{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 al^{6} 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 al^{19} 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 al^{20} 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 _{35}Br-loaded nonradioactive microspheres having a diameter of 60 μm and _{41}Nb-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 al^{16} 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 (RDτ 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 colleagues^{5} ^{8} have reported that the RDτ can be described by the equation of 6.26∗mass^{−0.233}, giving an RDτ 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 al^{5} 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} Chilian^{23} 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 colleagues^{2} ^{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).

## Acknowledgments

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.

- © 1995 American Heart Association, Inc.

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- Local Continuity of Myocardial Blood Flow Studied by Monochromatic Synchrotron Radiation–Excited X-ray Fluorescence SpectrometryHidezo Mori, Mitsuaki Chujo, Shuichi Haruyama, Hiroyasu Sakamoto, Yoshiro Shinozaki, Minhaz Uddin-Mohammed, Atsuo Iida and Hiroe NakazawaCirculation Research. 1995;76:1088-1100, originally published June 1, 1995https://doi.org/10.1161/01.RES.76.6.1088
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- Local Continuity of Myocardial Blood Flow Studied by Monochromatic Synchrotron Radiation–Excited X-ray Fluorescence SpectrometryHidezo Mori, Mitsuaki Chujo, Shuichi Haruyama, Hiroyasu Sakamoto, Yoshiro Shinozaki, Minhaz Uddin-Mohammed, Atsuo Iida and Hiroe NakazawaCirculation Research. 1995;76:1088-1100, originally published June 1, 1995https://doi.org/10.1161/01.RES.76.6.1088