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Am J Physiol Heart Circ Physiol 286: H2386-H2392, 2004. First published December 11, 2003; doi:10.1152/ajpheart.00682.2003
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Relationship between arterial diameter and perfused tissue volume in myocardial microcirculation: a micro-CT-based analysis

Nasser M. Malyar, Mario Gössl, Patricia E. Beighley, and Erik L. Ritman

Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, Minnesota 55905

Submitted 29 July 2003 ; accepted in final form 8 December 2003


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
The volume of myocardial tissue that is perfused by an epicardial coronary artery has been shown to be predictably related to the diameter of the epicardial arterial lumen. However, to what extent the intramyocardial microvasculature follows the epicardial rules remains unclear. To explore the relationship between the diameter of coronary arterioles and their subsequent perfused myocardial volumes, we quantified the volume of nonperfused myocardium resulting from an embolized arteriole of a certain diameter. We injected a single dose of microspheres selected from one of nine possible microsphere combinations (10, 30, and 100 µm diameter, each at three possible doses) into the left anterior descending coronary and/or left circumflex arteries of seven anesthetized pigs. At postmortem, the coronary arteries were infused with a radiopaque silicon polymer. Embolized myocardium (1 cm3) was scanned with a microcomputerized tomography scanner and resulted in three-dimensional images that consisted of 20 µm/side cubic voxels and a subvolume of the specimen with 4 µm/side cubic voxels. Image analysis provided the number and volumes of myocardial perfusion defects for each size and dose of microspheres. The smallest individual myocardial perfusion defects, which correspond to the volume of myocardium perfused by a single embolized arteriole, were found to be 0.0004 ± 0.0002, 0.02 ± 0.004, and 0.62 ± 0.099 mm3 for the 10-, 30-, and 100-µm microspheres, respectively. The number of myocardial perfusion defects in the embolized myocardium was inversely related to the dose of the injected microspheres. This reflects a clustering behavior that is consistent with a random distribution process of the individual embolized perfusion defects.

coronary; perfusion; defect; microspheres; microcomputer tomography

THERE IS A LARGE INTERINDIVIDUAL variation in the volume of myocardium that is perfused by each of the three epicardial coronary arteries (8, 21). However, when the luminal cross-sectional area of any of these arteries is related to the volume of muscle it perfuses, a predictable relationship between these two variables results (9, 12). Information such as the relationship between vessel luminal diameter and perfused tissue volume can be useful for risk stratification, e.g., for estimating the sizes of the area at risk and the final infarct after occlusion of an epicardial artery. To what extent this relationship in the myocardial microvasculature follows the epicardial arterial rule, i.e., what volume of myocardial tissue is perfused by a single arteriole of a certain diameter, is not known.

Such information may help to increase our understanding of the entities of myocardial microcirculation such as differences in susceptibility to ischemia (i.e., why the occurrence of myocardial ischemia during increased oxygen demand differs among individuals despite maximal vasodilation of the coronary microvasculature) and the poor correlation between epicardial artery stenosis and its physiological impact on myocardial contractile function (2, 22). Moreover, it may help us evaluate the impact of pathomorphological changes of the myocardial microcirculation on myocardial function, where the number of vessels per unit of myocardial volume is decreased such as occurs in cardiomyopathies and hypertrophy.

To date, this question has been addressed by rather indirect estimates of the structural anatomical data of the coronary arterial tree (1, 5). Imaging modalities such as computerized tomography (CT), X-ray angiography, single photon emission CT (SPECT), magnetic resonance imaging (MRI), and echocardiography do not have sufficient spatial resolution to study single vessels of the intramyocardial microcirculation.

X-ray microcomputed tomography (micro-CT) is a technique that allows detailed analysis of the three-dimensional (3-D) morphometry of the coronary tree in intact tissues (6, 7). We used micro-CT to localize and quantify the distribution, size, and number of myocardial perfusion defects within transmural myocardial "biopsies" of ~1–1.5 cm3 after coronary microembolization with microspheres of three different diameters. We used microembolization of individual arterioles to characterize the volume of myocardial tissue that was not perfused due to lodging of a microsphere in the supplying arteriole. This volume was taken to correspond to the volume of myocardium that was supplied by the embolized arteriole because there was little collateralization in porcine myocardium (4, 23). We also used pigs as animal models, because their epicardial coronary artery anatomy is very similar to that of humans (21).


   MATERIALS AND METHODS
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 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
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This study was reviewed and approved by the Mayo Foundation's Institutional Animal Care and Use Committee in accordance with the National Institutes of Health guidelines.

Animal preparation. Eight female domestic pigs (mean body wt, 31.2 ± 0.8 kg) were initially anesthetized as described previously (15). The left internal jugular vein and the left carotid artery were isolated by cut-down technique. Under fluoroscopic control, a guide-catheter tip was placed in the left main coronary artery to perform coronary angiography and monitor proximal coronary artery pressure. The tip of a 2.2-F dual-lumen infusion catheter was placed in the proximal left anterior descending artery (LAD) or the left circumflex artery (LCX) between the first and second diagonal branches to selectively infuse microspheres and drugs. During the entire procedure, heart rate, arterial blood pressure in the aortic root, and data from a three-lead ECG were continuously recorded. Sonicated polymer microspheres (Duke Scientific; Palo Alto, CA) of one size and one dose of nine possible combinations (see Table 1) were slowly injected into the LAD over 2–3 min. In two of the seven animals, the LCX was also embolized to complete the protocol of three different sizes by three different doses of microspheres. The fatal dose of microspheres was established empirically in previous experiments (15). In those studies, repetitive doses of microspheres of one size were injected into the LAD until the animals died due to pump failure. The number of microspheres required for the fatal effect was chosen as the fatal dose. In the present study, the number of microspheres injected was given as a fraction of the fatal dose to enhance the chances that the animals would survive the experimental procedure.


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  		Table 1. Protocol of coronary microembolization in pigs

 
Preparation of micro-CT specimens. Four hours after injection of microspheres, the animals were euthanized with a fatal dose of Sleepaway (Fort Dodge Laboratories; Fort Dodge, IA). The hearts were excised, and the LAD and/or LCX were cannulated and subsequently flushed with heparinized saline (5,000 IU/100 ml). A lead chromate-containing, self-hardening silicone polymer (Microfil; Flow Tech; Carver, MA) was infused into the embolized artery at 100 mmHg of pressure using a Harvard infusion pump. The hearts were fixed by immersion in 10% formalin for 24 h. After the polymerization of Microfil within the vasculature, three transmural blocks (volume of each biopsy, ~1–1.5 cm3) from the myocardium within the embolized perfusion territory (see Table 1) were cut out and dehydrated by 75, 85, and 95% alcohol and absolute alcohol at 15-min intervals before being embedded in paraffin wax for subsequent micro-CT scan.

Micro-CT scanner. The micro-CT scanners used were previously described in detail (7, 17). Myocardial samples were scanned at 0.49° angular increments, which provided 721 views around 360°. The 3-D images of the entire specimen were generated with the bench-top micro-CT and consisted of 20 µm/side cubic voxels. A selected region within one specimen for each size of microspheres was rescanned with the micro-CT scanner on the x2B beam line of the Brookhaven National Laboratories National Synchrotron Light Source (NSLS). This scanner was configured to generate images of 4 µm/side cubic voxels and was therefore sufficient for visualizing the 10-µm arterioles (Fig. 1). From these images, we could directly measure the smallest myocardial perfusion defects for each size of microsphere.



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  		Fig. 1. Maximum-intensity projections of our in-house bench-top microcomputed tomography (micro-CT; left) and a Brookhaven National Laboratories National Synchrotron Light Source (NSLS) micro-CT image (right) of porcine myocardium with radiopaque (white) polymer in the microvasculature, which was injected after embolization with quarter- and half-fatal doses of 10-µm microspheres, respectively. Note the parallel orientation of the arterioles (10–15 µm in diameter) in the NSLS image (right), which are not visible in the laboratory-based micro-CT image (left).

 
Image analysis. Image analysis was performed using the Analyze software package (Biomedical Imaging Resources; Mayo Clinic). One specimen per size and dose of microsphere was analyzed completely. From the remaining two specimens per size and dose of microsphere, a volume of 100–200 mm3 was analyzed, and the obtained values were normalized to 1 g of embolized myocardium. The 3-D images were analyzed as follows: contiguous image slices of 200-µm thickness (each slice consisting of either 20-µm cubic voxels) or 40-µm thickness (each slice consisting of 4-µm cubic voxels) were displayed with a maximum-intensity projection. The areas in the myocardium that lacked Microfil (which represented perfusion defects) due to microembolization were manually outlined in these images generated in x-, y-, and z-dimensions and were saved as 3-D binary object maps; the voxels that indicated perfusion defects were labeled as 1, and those outside the outlined areas (that represented perfused myocardium) were labeled as 0 (Fig. 2). The corresponding voxels in each of the three binary object maps were then multiplied with one another to generate a fourth 3-D object map in which the nonperfused territories, which were spatially coincident in all three binary maps, were represented by the value 1 (Fig. 3). From these 3-D object maps, we directly obtained the individual and total volumes of myocardial perfusion defects as well as the number of perfusion defects for each size and dose of microsphere.



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  		Fig. 2. Manual tracing of the Microfil-lacking areas in the micro-CT images of 200-µm-thick slabs of myocardium that were computed from stacked "sagittal," "coronal," and "transversal" CT sections. One representative myocardial perfusion defect is outlined; its course is shown through consecutive micro-CT slices.

 


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  		Fig. 3. Color-labeled three-dimensional (3-D) representation of the distribution of myocardial perfusion defects in micro-CT images of porcine myocardium after embolization with 10-, 30-, or 100-µm microspheres (µsph), each at the half-fatal dose. Color allows better discrimination of individual perfusion defects.

 
Extraction of microspheres in embolized tissue. Once the myocardial "biopsies" were scanned with the micro-CT scanner, the same specimens were weighed, hydrolyzed with an alkaline solution (EZ-Trac; Los Angeles, CA), and treated according to the Ultrasphere extraction protocol from EZ-Trac. The numbers of microspheres in the samples were counted using a microscope and a slide with Neubauer ruling and were normalized to 1 g of embolized myocardial tissue.

Statistical analysis. Continuous variables are presented as means ± SD. A two-tailed, paired Student's t-test was used for comparison of hemodynamic variables before and after microembolization. A single-factor ANOVA was used to compare total numbers and volumes of myocardial perfusion defects for different sizes and doses of microspheres. A P value of <=0.05 was considered significant.


   RESULTS
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 MATERIALS AND METHODS
 RESULTS
DISCUSSION
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General findings. One animal was lost due to refractory ventricular fibrillation during the embolization procedure. The mean heart weight at postmortem was 150 ± 8.4 g. Systolic blood pressure remained unchanged (111 ± 11 vs. 110 ± 13 mmHg; P > 0.05), but heart rate increased significantly during intracoronary infusion of adenosine (77 ± 19 vs. 98 ± 20 beats/min; P < 0.001). Tables 1, 2, and 3 present the results for each pig.


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  		Table 2. Hemodynamic parameters at baseline and after intracoronary infusion of adenosine and microspheres

 

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  		Table 3. Volume and number of smallest myocardial perfusion defects resulting from coronary microembolization with three different sizes and doses of microspheres in pigs

 
Individual and total volumes and numbers of myocardial perfusion defects in relation to microsphere size. For results including the total number and volume of myocardial perfusion defects, see Figs. 4 and 5. Coronary microembolization led to a continuous spectrum of different sizes of myocardial perfusion defects. The smallest individual perfusion defects measured in the NSLS micro-CT images were found to be 0.0004 ± 0.0002, 0.02 ± 0.004, and 0.62 ± 0.099 mm3 for the 10-, 30-, and 100-µm microspheres, respectively. As illustrated in Table 3, no statistical differences were found (P > 0.05) regarding the smallest size of myocardial perfusion defects caused by one size of microsphere; nor were any differences identified within any one animal, between animals, or between the LAD and LCX perfusion territories. The largest contiguous perfusion defects were 76, 178, and 410 mm3 for the 10-, 30-, and 100-µm microspheres (at the half-fatal doses), respectively. The highest number of perfusion defects (3,860 defects/g of embolized myocardium; this number is not included in Fig. 5) was found in a specimen that was embolized with 10-µm microspheres and scanned with the NSLS micro-CT scanner. Increasing the microsphere size and dose resulted in a decrease in the total number of perfusion defects (Fig. 5). Plotting the logarithm (log) of the number of perfusion defects against the log of the geometric mean size of myocardial perfusion defects within each size range resulted in a linear log-log relationship (Fig. 6).



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  		Fig. 4. Micro-CT-derived nonperfused volumes of myocardial perfusion defects in relation to doses and sizes of injected microspheres. Note that the embolized, nonperfused myocardial volume increased linearly with increasing size and dose of injected microspheres.

 


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  		Fig. 5. Laboratory-based micro-CT-derived data for numbers of myocardial perfusion defects in 1 g of embolized porcine myocardium. Note the inverse relationship between the size and number of injected microspheres and the number of resulting perfusion defects, which indicates clustering of microembolism-induced perfusion defects.

 


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  		Fig. 6. Confined NSLS- and laboratory-based micro-CT-derived data of the numbers and sizes of myocardial perfusion defects (MPD) for microspheres of 10, 30, and 100 µm diameter. Linear log-log relationship allows estimation of the numbers and sizes of perfusion defects beyond the resolution limit of the laboratory-based micro-CT, i.e., we can accurately predict the volume of myocardium supplied by a single precapillary arteriole.

 
Extraction of microspheres in embolized myocardial tissue. For the total number of injected microspheres per artery and the number of extracted microspheres in 1 g of embolized myocardial tissue, see Table 1.

We divided the micro-CT-derived nonperfused myocardial volume by the number of extracted microspheres in the same specimen to obtain the average volume of nonperfused myocardium that was caused by a single microsphere lodged in an arteriole of corresponding diameter. The nonperfused volumes were calculated to be 0.0008 ± 0.00006, 0.027 ± 0.0018, and 0.95 ± 0.12 mm3 for the 10-, 30-, and 100-µm microspheres, respectively.


   DISCUSSION
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
GRANTS
 REFERENCES
 
In this study, we used our lab-based micro-CT (an imaging technique with excellent resolution and ability to scan a relatively large volume of myocardium) to quantify the relationship between the luminal cross-sectional areas of different-sized intramyocardial arterioles and the volumes of myocardial tissue that these arterioles perfuse.

Microembolization was performed during maximal vasodilatation with adenosine (100 µg·kg–1·min–1), because with incomplete vasodilatation, the nonpatent vessels would open and compensate for the occluded arterioles. Each myocardial perfusion defect would then be enveloped uninterruptedly by patent microvessels.

Embolization with different sizes and doses of microspheres resulted in a wide range of myocardial perfusion-defect sizes. The smallest perfusion defect, as derived directly from the high-resolution NSLS micro-CT images, was found to be 0.0004 mm3 in the 10-µm microsphere embolization. The largest contiguous perfusion defect was 410 mm3 and was found in the sample embolized with 100-µm microspheres at the half-fatal dose. The underlying mechanism for the continuous spectrum of perfusion-defect sizes and for the inverse relationship between the number of injected microspheres and the number of resulting perfusion defects (see Fig. 5) likely has three bases. First, the random distribution of individual arteriolar perfusion defects results in a clustering behavior of microembolization such as is observed in other random dispersion processes (11, 20). As the number of injected microspheres increases, the possibility of adjacent arterioles being occluded also increases and results in a decrease in the number and an increase in the mean size of the individual perfusion defects (see Fig. 6). The fact that the log of the perfusion defect number plotted against the log of the mean size results in a log-log linear relationship supports this random clustering effect. A second plausible cause is that the branching geometry is not symmetrical (i.e., daughter branches are not of equal size and angles to mother segments), so preferential flow distribution results in an inhomogeneous distribution of microspheres due to the locally increased chance that adjacent arterioles will be embolized. To exclude this mechanism, we would need to perform image analysis well beyond the scope of the goal of this study, which was to give the minimal perfusion-defect size associated with occlusion of an arteriole of a selected diameter. A third possibility is that microspheres clump within the arteries and hence occlude arterioles larger than the diameter of a single microsphere, which would result in larger perfusion defects. In our study, we found little evidence of this plausible mechanism.

With the use of this approach and assuming that each injected microsphere results in one isolated ischemic perfusion territory, the smallest myocardial perfusion defect estimated from our bench-top micro-CT images (0.0006 mm3) was very similar to the smallest defect derived directly from the NSLS images (0.0004 mm3). Interestingly, when the total micro-CT-derived nonperfused myocardial volume is divided by the number of microspheres that were found in the same specimen by direct counting of the digested specimen, the obtained value (0.0008 mm3) is close to the values obtained from the log-log plot and the NSLS micro-CT images. These values are consistent for a terminal arteriole (of 8–10 µm diameter) perfusing the basic functional unit (Krogh cylinder) of the myocardium (10). Moreover, the smallest perfusion defect in the 10-µm microsphere embolization (0.0006 mm3), which we assume was caused by a single microsphere, was related to the smallest perfusion defect in the 100-µm microsphere embolization (0.62 mm3) by a factor of 10–3. This ratio is consistent with observations noted in previous publications. In a recently published study from our laboratory (15), the decrease in intramyocardial blood volume (blood volume was used as a surrogate for nonperfused myocardial volume under maximal vasodilation) due to embolization of 100-µm arterioles was related to embolization of 10-µm arterioles by a factor of 1,000.

The values for the smallest myocardial perfusion defect for each size of microsphere were within a small range (see Table 3). No statistical differences were observed (P > 0.05) regarding the smallest perfusion defect for any one size of microsphere either between different animals or between LAD and LCX perfusion territories. The small interanimal variation regarding the smallest perfusion defect in our study is consistent with interindividual variation in the number of arterioles per unit of myocardium in porcine myocardium (10). Studies on other species (13, 14, 16) have shown that the number of capillaries per unit area of myocardium is 2,500–3,500/mm2 of myocardium and hence is similar to the number in pigs. Eng et al. (5) embolized the myocardium of dogs with 25- or 50-µm-diameter microspheres to test the effects of various drugs on the embolism-induced myocardial necrotic lesions. The necrotic myocardial lesions after coronary microembolization were ~0.023 and 0.074 mm3 for the 25- and 50-µm microsphere embolizations, respectively. These values are consistent with those obtained in our study. However, the extrapolation of our results in pigs to other species can only serve as an estimation of the myocardial volume perfused by a single arteriole of a certain diameter. Additional studies in other species are needed to better define this issue.

Finally, our results are also consistent with a bifurcational branching geometry in the presence of Murray's law (19), which holds that the daughter-branch diameters (Dd) are related to mother-branch diameters (Dm) by approximately Dm = Dd x 21/3, such that D100 = D10 x 210, which indicates that a 100-µm-diameter arteriole (D100) should perfuse 1,024 arteriolar branches of 10 µm (D10) diameter. The values we obtained with three different methods suggest that the volume of myocardial tissue supplied by a terminal arteriole is between 0.0004 and 0.0008 mm3.

Limitations of this study.

Our values for the sizes of myocardial perfusion defects that result from embolization of arterioles do not necessarily equal the sizes of the myocardial necrotic lesions that resulted from microembolization. Although it is well known that pigs have very few native collaterals, we cannot exclude that this factor might affect to some extent the final perfusion-defect size. Some of the 10-µm microspheres probably passed through the myocardial microcirculation into the systemic circulation. This may have led to underestimation of the total embolized myocardial volume in a sample and also to a lower number of recovered microspheres. However, the main goal, which was to determine what volume of myocardium is perfused by a single arteriole of 10 µm in diameter, was not hampered by this phenomenon.

In conclusion, the results of our study provide a directly measured, quantitative relationship between vessel size and perfused myocardial tissue volume in porcine coronary microcirculation. Our findings may serve as the basis for additional studies to quantify this relationship under pathological conditions.

Our quantitative results, such as the sizes and numbers of microemboli and the associated micro-infarcts in a perfusion territory, may also help in the exploration of some of the apparently contradictory and discrepant consequences of selective microvascular obstruction (e.g., in coronary microembolization after coronary interventions), such as perfusion-contraction uncoupling and infarct size-myocardial dysfunction mismatch (3) as was emphasized in a recent review (18).


   GRANTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
REFERENCES
 
This study was funded in part by National Institutes of Health Grants HL-43025 and EB-000305. High-resolution images were scanned at the National Synchrotron Light Source, Brookhaven National Laboratory, which is supported by the Department of Energy, Division of Materials Sciences, and Division of Chemical Sciences under Contract DE-AC02-98CH10886.


   ACKNOWLEDGMENTS
 
The authors thank Julie M. Patterson for illustrations.


   FOOTNOTES
 

Address for reprint requests and other correspondence: E. L. Ritman, Dept. of Physiology and Biomedical Engineering, Alfred 2-409, Mayo Clinic, 200 First St. SW, Rochester, MN 55905 (E-mail: elran{at}mayo.edu).

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. Section 1734 solely to indicate this fact.


   REFERENCES
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 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
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 REFERENCES
 

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