Detection of Coronary Stenoses and Quantification of the Degree and Spatial Extent of Blood Flow Mismatch During Coronary Hyperemia With Myocardial Contrast Echocardiography
Background We hypothesized that the degree and spatial extent of blood flow mismatch in beds supplied by stenoses that are not flow-limiting at rest can be quantified with myocardial contrast echocardiography (MCE) using left atrial (LA) and right atrial (RA) injections of contrast during pharmacologically induced coronary hyperemia.
Methods and Results In 12 open-chest dogs, MCE was performed and myocardial blood flow (MBF) was measured by use of radiolabeled microspheres at baseline and during phenylephrine-induced coronary hyperemia. In the presence of this drug, stenoses were placed during different stages on the left anterior descending (LAD) and left circumflex (LCx) coronary arteries, and MCE and MBF assessments were performed. LA injections of 2 mL of 0.5 billion/mL microbubbles (mean diameter, 4.3 μm) were performed at each stage in all 12 dogs, and RA injections of 10 mL of 6 billion/mL microbubbles (mean diameter, 3.7 to 5.3 μm) were administered in 7 dogs. MCE images in which the contrast disparity between the LAD and LCx beds was maximal were digitally subtracted from precontrast images, and mean videointensities in these beds were measured after the dynamic range of gray-scale intensities was increased in the subtracted image and the image was color coded. The region showing hypoperfusion during LAD stenosis was planimetered and expressed as a percentage of the myocardial area in the short-axis slice. There was an excellent correlation between the LAD/LCx bed videointensity ratio and LAD/LCx bed MBF ratio (y=0.5x+0.44, r=.91, P<.001) during 57 LA injections. There was also an excellent correlation between the hypoperfused bed size on MCE during LA injection of contrast in the presence of LAD stenosis and the hypoperfused myocardium as determined by radiolabeled microspheres (y=0.8x+4.2, r=.90, P<.001, SEE=2.4, n=11). The anterior myocardium was opacified in 6 dogs receiving RA injections of contrast, and the hypoperfused area during LAD stenosis correlated closely with that determined by radiolabeled microspheres (y=0.86x+3.4, r=.93, P<.01).
Conclusions Coronary stenoses, which are not flow limiting at rest, can be detected and the degree and spatial extent of blood flow mismatch during pharmacologically induced coronary hyperemia can be quantified with MCE using LA and RA injections of contrast. Thus, it is possible that the severity of coronary stenoses and the quantum of myocardium in jeopardy could be quantified in the future with MCE using venous injection of contrast.
We have previously demonstrated that it is possible to opacify the myocardium on two-dimensional echocardiography (2DE) from left atrial (LA) and right atrial (RA) injections of sonicated albumin microbubbles.1 We have also demonstrated that both risk area during coronary occlusion and infarct size during coronary reperfusion can be quantified with myocardial contrast 2DE (MCE) using LA and RA injections of contrast.2 More recently, we have shown that background-subtracted myocardial videointensity reflects regional myocardial blood volume (MBV) when the dose of microbubbles injected is within the linear range of the relation between microbubble concentration and videointensity.3
The present study was performed to test the following hypotheses: (1) coronary stenoses that are not flow-limiting at rest can be detected with MCE during pharmacologically induced hyperemia using LA and RA injections of contrast, and (2) the degree and spatial extent of blood flow mismatch in the myocardium supplied by these stenoses can be quantified by this approach.
The study was approved by the Animal Research Committee at the University of Virginia and conformed to the American Heart Association Guidelines for Use of Animals in Research. Twelve adult mongrel dogs were anesthetized with 30 mg/kg sodium pentobarbital (Abbott Laboratories), intubated, and ventilated with a respirator pump (model 607, Harvard Apparatus). Additional anesthesia was administered during the experiment as needed. A 7F catheter was placed in the right femoral artery for recording of arterial pressure and withdrawal of arterial reference blood samples. This catheter was connected to a multichannel recorder (model 4568C, Hewlett-Packard) via a fluid-filled transducer (model 1280C, Hewlett-Packard). Another 7F catheter was placed in the left femoral vein for intravenous administration of phenylephrine HCl and fluids as needed.
A left lateral thoracotomy was performed, and the heart was suspended in a pericardial cradle. The proximal portions of the left anterior descending (LAD) and the left circumflex (LCx) coronary arteries were dissected free from the surrounding tissues, and custom-designed reversible snares were placed loosely around them. Doppler flow probes (2 mm, series SB, Transonics) were placed on these vessels proximal to the snare and were connected to a digital flowmeter (model T206, Transonics). A 7F catheter was placed in the LA for injection of microbubbles and radiolabeled microspheres. The RA was also cannulated with a similar catheter for microbubble injections.
Myocardial Contrast Echocardiography
MCE was performed with a phased-array system (RT5000, General Electric Medical Systems) with a 5-MHz transducer. A saline bath served as an acoustic interface between the heart and the transducer. Gain settings were optimized initially and were held constant throughout each experiment. A maximal dynamic range of 72 dB was used. Imaging was performed at the midpapillary muscle short-axis level at a depth setting of 8 cm, and the data were recorded on 1.25-cm VHS videotape with a high-fidelity video recorder (Panasonic AG6200, Matsushita Electrical Co).
Sonicated albumin microbubbles (Albunex, Molecular Biosystems, Inc) were used for the LA injections.4 These bubbles have a mean diameter of 4.3±0.3 μm and a concentration of 0.5 billion/mL. Two mL of this agent and 3 mL of saline flush (total volume of injectate, 5 mL) were administered as a bolus over 1 second with a power injector (model 3000, Liebel-Flarsheim). We have previously shown that 2 mL of Albunex is the optimal LA dose for myocardial opacification.3 At this dose, a maximal signal-to-noise ratio is achieved without significant attenuation in the anterior myocardium. For RA injections, 10 mL of 3.7- to 5.3-μm bubbles with a concentration of 6 billion/mL was used. These bubbles were custom-designed for us by Molecular Biosystems, Inc, and were hand-injected as a bolus as previously described.1 2
MCE images were analyzed with an off-line computer (Mipron, Kontron Electronics)5 and were transferred from videotape to the image memory of the computer in a 244×244×8 bit format. For LA injections, end-systolic frames were used for analysis. These frames were selected because the left ventricular cavity is the smallest in these frames and the amount of contrast in the left ventricular cavity is the least, resulting in the least posterior wall attenuation. A precontrast frame and a similar frame with maximal disparity in the contrast effect between the LAD and LCx beds were selected and aligned by computer cross-correlation as previously described.5 Each pixel in the digitally subtracted image showing an increase in intensity was assigned a gray-scale value from 0 to 255 and was then assigned colors whereby gradations of red to orange, to yellow, to white, represented increasing gray-level values.1 2 The color coding of each pixel was performed in reference to the brightest pixel in each image, which was assigned a gray-scale value of 255. Pixels showing either no change or a decrease in gray level were not color-coded, and the left ventricular cavity was masked out.
The LAD and LCx beds were defined on MCE as regions demonstrating relative color deficiency during LAD and LCx stenoses, respectively, and transmural regions of interest (ROI) were placed over them. An attempt was made to include as much of the LCx bed as possible without including areas that were subject to attenuation from the presence of contrast in the left ventricular cavity. Care was also taken not to include the speckled epicardial and endocardial borders. The average size of the ROI over the LAD bed was 1766±488 pixels, and that over the LCx bed was 1392±371 pixels.
The LAD perfusion defect size varied with the severity of the stenosis; it was planimetered in each dog only during placement of the more severe stenosis and was expressed as a percentage of the myocardial area in the short-axis slice. Because of attenuation of the posterior wall, the posterior border of the LCx bed could not be defined; thus, the LCx perfusion defect size was not measured.
Unlike LA injections, end-systolic frames could not be used for RA injections because the myocardial contrast effect was significantly less in systole than in diastole. Furthermore, because of poor signal-to-noise ratio, subtraction of single precontrast and postcontrast frames did not result in optimal images. Therefore, as previously described,1 2 three consecutive end-diastolic precontrast frames were averaged to improve the signal-to-noise ratio, and three consecutive contrast-enhanced end-diastolic frames were similarly averaged. The averaged precontrast frame was digitally subtracted from the averaged postcontrast frame, and the subtracted image was assigned colors as described above. Since the posterior myocardium was attenuated during RA injections, ROI were placed only over the LAD bed and the hypoperfused zone was measured only during LAD stenosis. Because of posterior wall attenuation, a precontrast short axis frame was selected for the measurement of the myocardial area.
Myocardial Blood Flow Measurement
Approximately 2×106 11-μm radiolabeled microspheres (Dupont Medical Products) suspended in 4 mL 0.9% saline solution/0.01% Tween 80 were injected into the LA at each stage. Reference samples were withdrawn from the femoral artery over 130 seconds with a constant-rate withdrawal pump (model 944, Harvard Apparatus). At the end of the experiment, the short-axis slice of the left ventricle corresponding to the MCE image was cut into 16 wedge-shaped pieces, and each piece was divided into endocardial, midwall, and epicardial portions. The papillary muscles were included in the endocardial portions. All samples were counted in a well counter with a multichannel analyzer (model 1282, LKB Wallac). Corrections were made for activity spilling from one window to the next with a custom-designed computer program.6
Flow to each myocardial sample was calculated from the equation Qm=(Cm×Qr)/Cr, where Qm is myocardial flow (mL/min), Cm is tissue counts, Qr is rate of arterial sample withdrawal (mL/min), and Cr is counts in the arterial reference sample.7 Transmural blood flow (mL · min−1 · g−1) was derived by dividing the sum of flows to the individual segments by their combined weight. Myocardial blood flow (MBF) to the LAD and LCx beds was calculated by averaging transmural flows in the segments that demonstrated reduced flows during LAD and LCx stenosis, respectively. Segments interspersed between the two beds and demonstrating intermediate levels of flow during stenosis were not included in the analysis. For the stage with severe LAD stenosis, the combined weight of the hypoperfused segments was expressed as a percent of the weight of the entire short-axis slice.
Each dog was studied at baseline and during coronary hyperemia induced by an intravenous infusion of 0.4 to 0.8 mg · kg−1 · min−1 of phenylephrine HCl (Schein Pharmaceuticals). We have previously shown that phenylephrine HCl increases MBF by increasing MBV and that these two are closely coupled.3 Stenoses of different severities were created on the LAD during continuous infusion of phenylephrine, and the degree of severity was judged by reduction in hyperemic LAD flow recorded on the Doppler flow probe. The LAD stenoses were then reversed, and a stenosis was created on the LCx during the continuous infusion of phenylephrine HCl. The degree of stenosis was again judged with the Doppler flow probe. Radiolabeled microspheres were injected into the LA, and the aortic pressures were recorded at each stage. MCE was performed with LA injection at each stage but with RA injection only during phenylephrine-induced hyperemia before and after an LAD stenosis was placed. The dog was then killed, the heart was excised, and the slice corresponding to the image on MCE was processed to determine MBF.
All data were analyzed with RS/1 (Bolt, Beranek, and Newman) resident on a minicomputer (VAX4000, Digital Equipment Corp) and were expressed as mean±SD.8 Comparisons between MCE and other measurements were made by linear regression analysis. Statistical significance was defined as P<.05 (two-sided).
A total of 57 LA injections were analyzed in the 12 dogs. In 1 dog, the LAD was small and could not be dissected. In the remaining 11 dogs, moderate to severe LAD stenosis was created that reduced the mean LAD flow to approximately two fifths of maximal hyperemic flow (mean MBF of 2.0±1.5 mL · min−1 · g−1 during coronary hyperemia). In only 3 dogs did LAD flow reach below resting levels during placement of severe stenosis. In addition to the severe stenosis, a mild LAD stenosis was also created in 8 dogs that reduced hyperemic flow to approximately two fifths (mean MBF of 2.1±1.2 mL · min−1 · g−1 during coronary hyperemia). In 11 dogs, moderate LCx stenoses were placed that resulted in the reduction of hyperemic flow by about one half; in 1 dog, we were unable to dissect the LCx.
Tables 1⇓ and 2⇓ depict the hemodynamic, MBF, and MCE data for LA injections during baseline and LAD and LCx stenoses. As would be expected, MBF increase during hyperemia was associated with an increase in blood pressure induced by phenylephrine. Videointensity in the LAD and LCx beds changed during phenylephrine infusion in relation to changes in MBF. At baseline, although MBF was lower than during stenoses placed in the presence of phenylephrine, videointensities in the myocardial beds supplied by these vessels were higher during stenoses. This phenomenon occurred because videointensities in the subtracted images were adjusted relative to the brightest pixel in each image. At baseline, the brightest pixel and the least bright pixel were not very different; during stenosis placed in the setting of coronary hyperemia, the difference between the two was significantly greater, which resulted in a lower pixel intensity in the stenotic bed even when absolute flow in that bed was higher than at baseline.
Fig 1⇓ illustrates color-coded images from four stages in a dog after LA injection of contrast. During baseline (panel A), MBF to the LAD bed was 0.93 mL · min−1 · g−1, and that to the LCx bed was 1.34 mL · min−1 · g−1; the LAD/LCx bed MBF ratio was 0.73. A greater preponderance of yellow is seen in the lateral than in the anterior wall. The background-subtracted videointensity in the anterior wall was 163, whereas that in the lateral wall was 173, with an LAD/LCx bed videointensity ratio of 0.94. During phenylephrine HCl–induced hyperemia (panel B), MBF to the two beds was nearly identical (2.7 and 2.6 mL · min−1 · g−1, respectively), with an LAD/LCx bed flow ratio of 1.03. Both beds show increased preponderance of whites and oranges. The background-subtracted videointensity in the anterior wall was 203, whereas that in the lateral wall was 207, with an LAD/LCx bed videointensity ratio of 0.98. In the presence of an LAD stenosis (panel C), MBF to the LAD bed was reduced to 0.51 mL · min−1 · g−1, and that to the LCx bed was 1.34 mL · min−1 · g−1. The LAD/LCx bed flow ratio was 0.38. A lack of oranges and whites is noted in the LAD (arrow) compared with the LCx bed. The background-subtracted videointensity in the anterior wall was 91, whereas that in the lateral wall was 153, with an LAD/LCx bed videointensity ratio of 0.60. During LCx stenosis (panel D), MBF to the LAD bed was 2.7 mL · min−1 · g−1 and that to the LCx bed was 1.35 mL · min−1 · g−1, with an LAD/LCx bed flow ratio of 2.0. This time, a lack of oranges, yellows, and whites is noted in the LCx (arrow) compared with the LAD bed. The background-subtracted videointensity in the anterior wall was 174, and that in the lateral wall was 111, with an LAD/LCx bed videointensity ratio of 1.6.
Fig 2⇓ illustrates the relation between LAD/LCx MBF ratio and LAD/LCx bed background-subtracted videointensity ratio during the 57 LA injections in all the 12 dogs. The relation is linear over a wide range of values (0 to 4), and the correlation is highly significant. Fig 3⇓ depicts the relation between perfusion defect size as a percent of myocardial area in the short-axis slice versus the weight of the hypoperfused segments as a percent of the total myocardial weight of that slice in the 11 stages with moderate to severe LAD stenosis. The relation is linear, with an excellent correlation coefficient, indicating that the perfusion defect size during LA injection of contrast in the presence of a stenosis corresponds to the amount of myocardium receiving relatively lower flow during pharmacologically induced coronary vasodilation.
Right Atrial Injections
We were able to perform RA injections in only 7 dogs because of unavailability of the custom-designed bubbles for all animals. Myocardial opacification was noted during phenylephrine-induced hyperemia in 6 of the 7 dogs, a success rate in accordance with our previous experience.1 2 Table 3⇓ depicts MBF and background-subtracted videointensity in the LAD bed before and after LAD stenosis in the presence of phenylephrine HCl in the 6 dogs with successful myocardial opacification. It is apparent that the videointensity is decreased in the presence of reduced MBF to the LAD bed. In only 1 dog was the LAD flow during stenosis below the resting level.
Fig 4⇓ illustrates end-diastolic color-coded images from two stages from a dog after RA injection of contrast. Both stages are during phenylephrine HCl–induced hyperemia. The first stage (panel A) is before the placement of LAD stenosis, when MBF to the LAD bed was 5.1 mL · min−1 · g−1 and the background-subtracted videointensity was 100 relative units. The second stage (panel B) is after placement of the LAD stenosis, when MBF to the LAD bed was 1.3 mL · min−1 · g−1 and the background-subtracted videointensity was 37 relative units. Both images demonstrate the significant posterior wall attenuation that is noted with end-diastolic frames, since the number of microbubbles in the left ventricular cavity is much more during end diastole than during end systole (see Fig 2⇑).
Fig 5⇓ illustrates the relation between perfusion defect size as a percentage of myocardial area in the short-axis slice versus the weight of the hypoperfused segments as a percentage of the total myocardial weight of that slice during moderate to severe LAD stenosis. The relation is close, indicating that perfusion defects during RA injection of contrast show the extent of myocardium receiving relatively lower flow in the presence of moderate stenosis during pharmacologically induced coronary hyperemia.
Unlike other techniques used for myocardial perfusion imaging, in which the tracer is either extracted by myocytes (201Tl or sestamibi used for nuclear myocardial imaging9 10 ) or enters the extravascular space (radiopaque dyes used for digital subtraction angiography and cine-computed tomography11 12 ), microbubbles act as true intravascular tracers that remain within the intravascular space during their transit through the myocardium.13 14 We have previously demonstrated that the measured concentration of microbubbles within the myocardium (so long as they are adequately mixed with blood before entering the coronary circulation), expressed as videointensity in that bed, correlates with MBV of that bed.3
In the present study, we show that in a model in which MBF and MBV are closely coupled (such as during the administration of catecholamines), the ratio of background-subtracted videointensity from two myocardial beds correlates with the ratio of MBF to those beds during LA injection of contrast. In “Appendix A,” we attempt to explain mathematically the occurrence of a linear relation between background-subtracted videointensity from two myocardial beds and relative MBV to those beds. We assume that the relation between background-subtracted videointensity and microbubble concentration was linear in our study. We used just enough microbubbles to cause a mild change (10 to 50 relative units in the original 2DE image) in videointensity, which would relate linearly with changes in microbubble concentration within tissue.3
As long as autoregulation remains intact, there are two major mechanisms by which MBF increases via an increase in MBV (Fig 6⇓). The first mechanism is recruitment of microvessels,15 and the second is microvessel dilatation.16 17 During any particular condition, one mechanism may be predominant or both may play significant roles in increasing MBF. In “Appendix A” and Figs 7⇓ and 8⇓, we show that, in either case, the relation between videointensity ratio between two myocardial beds is linearly related to the ratio of MBV of the two beds.
An interesting observation from our study is that myocardial videointensity decreases in the presence of a coronary stenosis. This decrease in videointensity could be explained by two possible mechanisms. The first mechanism implies that MBV actually diminishes during pharmacologically induced hyperemia in a bed supplied by a stenosis that limits an increase in flow to that bed compared with a normal bed. In previous experiments, we calculated MBV by dividing MBF measured with radiolabeled microspheres by microbubble transit rate (volume=flow/transit rate).3 18 We found that the calculated MBV of the bed supplied by the stenotic vessel actually decreased in the presence of pharmacologically induced hyperemia.3 18 Recent studies using direct16 19 20 21 22 and indirect11 12 observations of the coronary microvasculature have demonstrated that coronary microvessel size is both flow- and pressure-dependent. The pressure gradient across a stenosis that is not flow-limiting at rest is minimal, and the microvessels actively dilate to maintain MBF.16 19 In the presence of coronary hyperemia, however, the same stenosis becomes flow-limiting and results in a greater pressure gradient,16 resulting in a decrease in both flow and pressure, which can cause a decrease in microvessel size and hence, MBV.20 21 Although earlier studies using direct observations of the microvasculature had demonstrated the effect of flow and pressure on arteriolar size alone,20 recent studies have shown the same effect even in venules,21 which may be an important autoregulatory site and may be responsible for a significant fraction of the MBV during pharmacologically induced coronary hyperemia.22
Since in our study we did not measure microvessel size and MBV directly, we have to entertain another possible explanation for the linear relation between the background-subtracted videointensity and MBF ratios in the two beds. In “Appendix B,” we attempt to explain mathematically the basis of such a relation in the absence of a decrease in MBV in the bed supplied by the stenotic vessel. It is apparent from our discussion that for MBF ratios <4.0, a linear relation is possible between MBF and videointensity ratios even when the MBVs of the two beds are equal. It should be noted, however, that such a relation is possible only when videointensity is measured, as was done in our study, at the moment of maximal disparity in the contrast effect between the two beds. It could be argued that since MBVs of the two beds are equal in this model, the transit rate ratios should theoretically provide a linear relation over a wider range of MBF ratios compared with videointensity ratios.14 Because of the great variability in the input function after venous injection, however, the derivation of myocardial transit rates may not be accurate and thus may not be a reliable indicator of MBF.3
Critique of Our Methods
To correlate background-subtracted videointensity to MBV, it is imperative that the relation between microbubble concentration and videointensity be linear. In the 2DE system we used, this relation is almost linear at videointensity levels <50 units; above this level, the relation becomes flat.3 We have previously shown that when 2 mL of Albunex is injected into the LA, the relation between myocardial videointensity and microbubble concentration is linear and attenuation does not occur in the anterior myocardium.3
The videointensity values reported in this study were not obtained from the original 2DE data but rather from the digitally subtracted images, in which these values were readjusted over a wider dynamic range to accentuate minor differences in videointensities. Consequently, the videointensity values reported in this study are several times higher than the original values and reflect only relative changes. Our results are also influenced by the computer algorithms used for color-coding, which have been optimized to enhance subtle differences in videointensities so as to clearly define the borders between high and low flows. In this study, we were able to separate zones with as little as 15% difference in hyperemic flow, which is significantly superior to other imaging techniques.
Pharmacological increases in MBF could also have been achieved with vasodilators such as adenosine and dipyridamole. In the presence of these drugs, although maximal increase in MBV can occur, MBF becomes dependent primarily on the coronary driving pressure.23 Nevertheless, even if absolute MBF is altered in the presence of coronary vasodilators because of changes in systemic pressure, relative MBV and hence relative MBF to two beds need not be affected.24
The aim of this study was not to demonstrate that myocardial opacification is easily possible using RA injections of sonicated albumin microbubbles. In fact, the bubbles used in this study for RA injection are highly concentrated, and their use is not advisable in the clinical setting. The aim of the study was to define the principles based on which LA and RA (and hence, presumably venous) injections of contrast could be used for the detection of coronary stenoses that are not flow-limiting at rest and for the quantification of the degree and spatial extent of flow mismatch that occurs in the presence of these stenoses during pharmacologically induced coronary hyperemia. It is very likely that such an approach will be used when venous contrast agents become available. Newer contrast agents have recently been shown to result in reproducible myocardial opacification from venous injection when smaller doses and concentrations are used.25 26 27 The principles advocated in this article could also be applied to the use of these agents.
MCE in the cardiac catheterization laboratory has usually been performed with direct intracoronary injections of microbubbles. The results of our present study suggest that injection of microbubbles into a chamber such as the left ventricle could be used to determine the physiological significance of coronary stenoses. Preliminary data from our laboratory demonstrate that injection of microbubbles into the aortic root also provides similar results.18 24 Unlike the situation with LA, venous, and left ventricular injection of contrast, attenuation is not a problem when contrast is injected into the aortic root.
Although the newer contrast agents25 26 27 result in less posterior wall attenuation, this phenomenon will always occur as long as there are microbubbles in the left ventricular cavity. Different imaging planes (such as apical views) could be used to better define the posterior wall. In case of difficulties in adequately imaging the posterior wall or in acquiring overall high-quality images from the transthoracic approach, the transesophageal approach could prove useful. Further experimental and clinical studies are necessary to define the clinical utility of MCE for the detection of coronary disease and estimation of the ischemic burden by use of venous injection of contrast.
In this section, we show how the ratios of videointensities from different myocardial beds correlate with MBV ratios in those beds. As shown in Fig 6⇑, the two mechanisms by which MBV increases are microvessel recruitment14 and microvessel dilatation.15 16
where α/2 is the mean transit rate of the microbubbles through the ROI, then the time-intensity curve from n number of vessels lying within the same ROI will have the form y=nAte−αt. If two ROI have n1 and n2 number of vessels, respectively, each of the same radius (Fig 6B⇑), then the corresponding time-intensity curves would be y1=n1Ate−αt and y2=n2Ate−αt, respectively.
Dividing the time-intensity curve from one bed by that from the other, we get y1/y2=n1/n2. Since in this model of microvessel recruitment, MBF (f) is proportional to MBV (v) and hence α is the same in both ROI, the ratio of the videointensities from the two beds at any given time will relate to the ratio of number of microvessels and thus MBV in the two beds (Fig 7A⇑). In practical terms, the measurement of peak videointensities is easy, and because α is constant in this model, peak intensities occur at the same time in both beds (Fig 7B⇑).
Unlike recruitment, mathematical modeling of microvascular dilatation is more complex. Not only does f change because of change in v, but α also changes. Thus, the value A in the gamma-variate function also changes. According to Poiseuille’s law,29 flow (f) through a tubing is proportional to the fourth power of the radius of the tubing and, therefore, the second power of volume (v) of the tubing, provided that there is a constant pressure gradient across the tubing and the flow through it is laminar. Then,
where k1 is a constant.
Thus, unlike recruitment, in which an increase in the number of microvessels by twofold results in an increase in MBV by twofold, in the case of microvascular dilatation, an increase in microvascular radius by twofold will result in an increase in MBV by fourfold.
To mathematically describe A in Equation 1, one must relate the microbubble concentration to f. If w is the total number of bubbles injected into the LA, c is the cardiac output, and f is flow through an ROI (Fig 6A⇑), then the number of microbubbles, m, entering the ROI is given by the equation:
According to the Stewart-Hamilton equation,30
where a is the area under the time-intensity curve obtained from a myocardial bed and k2 is a constant.
Applying Equation 7 to two different myocardial beds of volumes v1 and v2 (Fig 6C⇑) and corresponding background-subtracted videointensities of i1 and i2, respectively, we get
The ratio of videointensities in the two beds is independent of B but is dependent on v1/v2, k1, and t. Since the moment of the greatest disparity in contrast effect between the two beds is the easiest and most practical to determine (Fig 8A⇑), we simulated time-intensity curves for i1 and i2 for various values of v1 and v2 at this time.
For simulation of data, k1 was derived from previously published data by Wu and colleagues.11 In this article, the relation between f and v was determined to be v=9.5f1/2. Therefore, f=(1/9.52)v2, or f=0.011v2, or k1=0.011. Substitution of this value of k1 in Equations 8 and 9 allowed generation of time-intensity curves for i1 and i2 for various values of v1 and v2. Plotting the ratio of i1/i2 against v1/v2, we find that the two are closely related (Fig 8B⇑). Although theoretically the relation is quadratic, in practical terms, because of the value of k1, the relation is almost linear.
In this section, we demonstrate how measuring relative videointensities within different myocardial beds correlates with relative MBF to those beds even when MBV is equal in both beds. At baseline, the time-intensity curves from ROI placed on these beds will be identical as microbubbles transit these beds (Fig 9A⇓). Now let us assume that the microvessels in both beds are maximally dilated, resulting in an equal increase in MBV in both beds (Fig 9B⇓). Let us also assume that the vessel supplying bed A has no stenosis and thus, MBF to this bed increases in proportion to the increase in MBV. Assume that MBV increases by 2.5 times and MBF by 5 times. The time-intensity curve from this bed, therefore, will have a higher peak and a narrower width than during baseline (Fig 9B⇓). Let us now assume that the vessel supplying bed B has a stenosis such that, although the MBV is 2.5 times that at baseline, MBF increases to only 1.25 times that at baseline. The time-intensity curve from this bed will have a lower peak and a greater width compared with baseline and compared with that derived from bed A (Fig 9B⇓).
The background-subtracted videointensities (i1 and i2) from the two myocardial beds can be described by i1=A1te−α1t and i2=A2te−α2t.
The difference in videointensities between the two beds, z, is
from which we get
The ratio of videointensities from the two beds when the difference in videointensities is maximal is given by
We numerically obtained values for T from Equation 17 for various values of α1 and α2 and substituted these in Equation 16 to obtain the ratio of videointensities (i1/i2) at the time of maximal disparity in the videointensities. A plot of i1/i2 versus α1/α2 is shown in Fig 9C⇑ (since volume is maximal in both beds, α equals f). It can be noted that the relation between videointensity and α ratios from the two beds is linear up to an α ratio of approximately 4.0, which may explain the good correlation between MBF ratio and videointensity ratio in Fig 2⇑ even if MBV did not decrease with a decrease in MBF. When the flow ratios are >4, one would not expect a linear relation between these ratios.
This study was supported in part by grants from the National Institutes of Health (R01-HL-48890), Bethesda, Md; the Virginia Affiliate of the American Heart Association, Glen Allen, Va; and Molecular Biosystems, Inc, San Diego, Calif; and an equipment grant from General Electric Medical Systems, Milwaukee, Wis. Dr Ismail was the recipient of a fellowship training grant from the Virginia Affiliate of the American Heart Association, and Dr Kaul is an Established Investigator of the American Heart Association, Dallas, Tex.
Presented in part at the 66th Scientific Sessions of the American Heart Association, Atlanta, Ga, November 8-11, 1993.
- Received May 26, 1994.
- Accepted August 19, 1994.
- Copyright © 1995 by American Heart Association
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