Quantification of Myocardial Blood Flow With Ultrasound-Induced Destruction of Microbubbles Administered as a Constant Venous Infusion

Assume, first, that microbubbles are administered intravenously as a continuous infusion at a constant rate and concentration. After steady state is achieved, assume that all microbubbles within an ultrasound field are destroyed by a single ultrasound pulse (Fig 1) and that the elevation (thickness) of the ultrasound beam E is uniform. If new microbubbles enter this field with a flat profile at a velocity v, then the distance (d) they will travel within the beam elevation (Fig 1B through 1E) will be given by the following equation:where t is the PI of ultrasound.

Because VI is proportional to the effective microbubble concentration within the beam thickness at any PI (when the relation between the two is linear¹³ ), it will be proportional to d/E. Substituting for d, from equation 1, VI is proportional to vt/E. At a constant v, VI increases with t until a specific PI, T, is reached (Fig 2A), at which the microbubbles have just sufficient time to fill the entire beam thickness (Fig 1E). Then,As shown in Fig 2A, when the PI exceeds T, VI will remain constant. This plateau phase will reflect the effective microbubble concentration within the myocardial microcirculation. At any given concentration of intravenously infused microbubbles, the VI at the plateau phase will be proportional to the sum of CSA of microvessels (a) within the beam thickness.

The model predicts a sharp demarcation between the upslope and plateau phases of the PI-VI relation (Fig 2A). In reality, however, neither the beam elevation nor the degree of microbubble destruction are expected to be entirely uniform. The profile of the microbubbles also is not expected to be entirely flat. The actual relation between VI and PI is therefore more likely to be curvilinear as shown in Fig 2B and can be described by the following exponential function:where y is VI at a PI t, A is the plateau VI, and β is the rate constant that determines the rate of rise of VI.

Because the slope of the tangent to the curves is given by dv/dt=AβE^−βt, the slope at the origin (t=0) is Aβ. As shown in Fig 2A, this slope is also equal to A/T. Therefore,Eliminating T between equations 2, and 4 results in:Thus, for a given beam elevation (thickness at a given distance from the transducer), the mean velocity of microbubbles is proportional to β. If flow, f, occurs through an area, a, then:If E is constant, then a will be proportional to A. Therefore, with rearrangement of equation 6 and substituting for v from equation 5, we get:When E is constant,From equation 5 it is obvious that if E is known, then v can be expressed in cm · s⁻¹. Similarly, if the microvascular CSA is known, then A can be expressed in cm². The product of A and v will then represent f in mL · s⁻¹.

Ex vivo experiments with explanted veins were initially performed to determine the efficacy of microbubble destruction in a flowing system and to evaluate the optimal PI required to detect flow differences from VI measurements. Because of the large CSA and low resistance of the ex vivo veins, the flow rates used were much higher than those in the microcirculation. To evaluate flow rates seen within the myocardium, in vitro experiments were performed with hollow-fiber bundles that had CSA more akin to that of microvessels. This system was also used to derive the PI versus VI relation at multiple flow rates. To test the model in vivo, we first used an experimental setup in which MBF could be altered without changing CBV. Subsequently, a preparation was used in which changes in MBF were caused solely by changes in CBV. Finally, a coronary stenosis model that more closely resembles the clinical situation was used.

All catheters were connected to fluid-filled pressure transducers, which, like the flowmeter, were connected to a multichannel recorder (model ES2000; Gould Electronics). Epicardial coronary artery flows and all pressure signals were acquired digitally at 200 Hz into an 80386-based personal computer via an eight-channel analog-to-digital convertor (Metrabyte). The signals were displayed on-line using Labtech Notebook (Laboratory Technologies).²

Comparisons between more than two stages were performed with repeated measures ANOVA, whereas those between two stages were made with Student’s t test. All correlations were performed using least-squares linear regression analysis. Differences were considered significant at P<.05.

Table 1 depicts the efficacy of ultrasound in destroying microbubbles in a flowing system. The number of microbubbles from just proximal and distal to the transducer location were similar when no ultrasound was transmitted. At PI of 33 and 200 ms, virtually no bubbles were seen distal to the transducer. When the PI was increased to 1000 ms, bubble destruction was less.

Fig 5 illustrates the importance of using the correct PI for the detection of flow differences based on VI measurements. Although the concentration of microbubbles in both veins was identical, there was a fourfold difference in the flow between the two veins. Fig 5A and 5B depict images acquired at PI of 33 and 200 ms, respectively. At the short PI, more bubbles have replenished the ultrasound beam elevation in the vein with higher compared with lower flow (Fig 5A), allowing for flow differences in the two veins to be noted. In comparison, when the PI was prolonged, the bubbles completely replenished the ultrasound beam elevation in both veins, and flow differences in the two veins were no longer seen (Fig 5B). Obviously, the optimal PI for distinguishing different flows depends on the flow rates themselves.

Fig 6 illustrates the PI versus VI relations at different flow rates in the hollow fiber bundles. It is obvious that for any flow, several PIs were required to derive the values of β and A. VI increased more rapidly and reached a plateau at a shorter PI when flows were higher (Fig 6A). An excellent linear relation was noted between the value β from the fitted functions and flow measured in the tubing (Fig 6B).

Fig 7 depicts VI data using solutions with three different microbubble concentrations at a constant flow rate of 30 mL · min⁻¹. Two important points are evident from these data. First, as long as the relation between microbubble concentration and VI remains within the linear range,¹³ β reflects velocity and is not affected by the concentration of microbubbles infused intravenously. Second, because changing microbubble concentration within the fibers is equivalent to changing the number of fibers containing the same concentration of microbubbles, these results indicate that the measurement of A actually reflects fiber CSA.

Using a PI >1000 ms, both myocardial and LV video intensities remained unchanged during constant infusions of microbubbles over 5 to 12 minutes. The relations between VI and infusion rate (which denotes microbubble concentration) for both the LV cavity and myocardium are shown in Fig 8. There was an initial rapid rise of VI in the LV cavity as microbubble concentration increased. As the concentration continued to increase, however, the LV VI reached a plateau. Appreciable myocardial opacification was noted only during this plateau phase when microbubble concentration in the LV cavity was high. When the linear portion of the relation between microbubble concentration and VI from the LV cavity was extrapolated to the level at which myocardial VI was similar to that noted in this study, the myocardial/LV cavity VI ratio was 8%. Because the LV cavity contains only blood, these data indicate that the estimated MBV is 8%. Thus, despite the nonlinear relation between microbubble concentration and VI, myocardial VI can be calibrated as a percentage of the VI in the LV cavity.

Fig 9 depicts images obtained at a constant LAD flow of 65 mL · min⁻¹ at four incremental PIs in one group 1 dog. The color-coding algorithm used to illustrate the data has been described previously.¹⁵ Shades of red, progressing to hues of orange, yellow, and then white, represent incremental myocardial contrast opacification. At the shortest PI, no contrast was seen in either the LAD or LCx beds, indicating that the PI was too short to allow replenishment of detectable amounts of microbubbles in either bed. At a higher PI, the VI in the LAD bed increased progressively and reached a plateau at longer PI. Initial opacification of the LCx bed was seen at a higher PI than the LAD bed, and its rate of rise is also slower, indicating a lower microbubble velocity in the LCx bed.

Fig 10A illustrates the VI versus PI plots from the LAD bed at five different flows in one dog. As the LAD flow was increased, the value of β also increased. Fig 10B shows the excellent relation between β and LAD flow in the same dog. Similar results were found in all other dogs (Fig 11) with an average correlation between β and mean coronary flow in all seven dogs of r=.91 (range, .77 to .97).

These results pertain to imaging in end systole only. In the three dogs in which imaging was also performed in end diastole, no differences were found between the value of β derived at end systole or end diastole. Because the interval between the “bubble destruction” and “imaging” pulses can span several cardiac cycles, the rate of replenishment of the ultrasound beam elevation by microbubbles reflects an average of that from different phases of the cardiac cycle, which can explain these findings.

MBF was increased in group 2 dogs solely by increasing CBV via intracoronary infusion of vasodilators (adenosine and acetylcholine). The doses of the drugs infused were sufficient to increase LAD flow without any changes in LCx flow or mean arterial pressure (Table 2). During peak hyperemia, both LAD flow and radiolabeled microsphere-derived MBF in the LAD bed increased approximately threefold compared with baseline. An excellent correlation was found in all dogs between the value of β and LAD flow as well as radiolabeled microsphere-derived MBF in the LAD bed (r=.88, P<.001). Despite large increases in MBF caused by the vasodilators, no significant change in A was found, indicating that microvascular CSA within the myocardium did not change appreciably (Table 2). As shown in Fig 12A, the relation between radiolabeled microsphere–derived MBF and MCE derived MBF (Aβ) was excellent.

The protocol could not be completed in one group 3 dog due to hemodynamic instability, and the distal coronary catheter resulted in a myocardial infarction in another dog, so the data from the remaining seven dogs are presented in Table 3. There were three stages for each dog: baseline and two separate stenosis stages. Before hyperemia, the pressure gradient across the stenosis increased with increasing stenosis severity, but MBF and all other hemodynamic data remained unchanged. Likewise, the mean values of A, β, and Aβ also did not change at any stage compared with the nonstenosed bed. Thus, like MBF, microbubble velocity and myocardial microvascular CSA remain constant at rest in the presence of non–flow-limiting coronary stenosis.

In the presence of exogenously induced hyperemia with WRC-0470, there were no significant changes in mean aortic pressure or heart rate at any stage compared with the corresponding baseline stage. As expected, the pressure gradient across the stenosis increased significantly (P<.001) in the presence of hyperemia compared with baseline, and this increase was higher for more severe stenoses. MBF to the stenosed bed also increased in all stages with hyperemia, but the maximal hyperemic flow attained before placement of a stenosis was significantly greater (P<.01) than that during either stenosis stage. An excellent correlation was found between β and radiolabeled microsphere–derived MBF for all dogs (mean, r=.93; range, .70 to .99). The value of A from the stenosed bed was lower (P=.05) compared with the control bed with increasing levels of stenosis. The correlation between radiolabeled microsphere–derived MBF and MCE-derived MBF (Aβ) for all dogs was excellent (average, r=.93; range, .71 to .99). As shown in Fig 12B, an excellent correlation was also found between the Aβ ratio from the stenosed versus normal bed and the radiolabeled microsphere–derived MBF ratio from the two beds. All the points lie practically on the line of identity except for two outliers (○). In these two dogs, the value of A in the control bed was artificially reduced as a result of lateral wall attenuation, resulting in an apparent “increase” in the Aβ ratio compared with the stenosed bed.

When microbubbles are injected as a discrete bolus directly into a coronary artery, their mean transit rate reflects the MBF/CBV relation.^{1 2} When they are administered intravenously, the input function of the myocardium is the time-intensity curve from the LV cavity. As a result of dispersion of the microbubbles through the myocardial microvasculature, the myocardial output function should be wider than the input function. A number of factors, however, make the myocardial output function appear paradoxically narrower than the input function.

Ultrasound systems have a threshold below which microbubbles are not detected.¹³ This threshold results from suppression of electronic “noise,” a narrow dynamic range, and compression of the signal to display it on the video monitor. To be detected in the myocardium, therefore, the concentration of microbubbles in the LV cavity must be very high. Because the number of microbubbles in the myocardium is much lower than that in the LV cavity, the threshold effect makes the time-intensity curve from the myocardium appear narrower than that from the LV cavity.¹³ This phenomenon makes it impossible to deconvolve the latter from the former, precluding the measurement of the MBF/CBV relation during venous infusion of microbubbles.

Even if the threshold effect were not present, the transit rate of intravenously administered microbubbles would not reflect their dispersion through the myocardium. Microbubbles injected into a peripheral vein first disperse through the cardiac chambers and pulmonary vasculature before reaching the coronary circulation. Compared with the central circulation, further dispersion of the bubbles through the much smaller coronary circulation is therefore insignificant. Consequently, the resulting output function is not much different from the input function,⁴ and this difference cannot be resolved by ultrasound. Thus, the measured myocardial output function invariably reflects the dispersion of bubbles in the large central circulation (and hence provides a measure of cardiac output¹⁶ ) rather than the mean myocardial transit rate.⁴

The novelty of our approach is that it does not rely on tracer kinetic principles to quantify myocardial perfusion. Destruction of microbubbles and measurement of their reappearance rate within the myocardium during a continuous infusion provide an estimation of mean myocardial microbubble velocity. Similarly, the plateau VI at long PI reflects microvascular CSA. The product of the two provides an estimation of MBF.

The independent estimation of both microbubble velocity and microvascular CSA afforded by our approach also has many advantages, as demonstrated in our study. In situations in which MBF changes are not associated with alterations in CBV, such as in the group 1 dogs, the plateau VI did not change and alterations in MBF were reflected only by changes in microbubble velocity. Similarly, in situations in which MBF changes are associated with changes in CBV but not MBV, the plateau VI should not change. The two examples of this phenomenon in our study occurred during direct coronary infusion of vasodilators in the group 2 dogs and in the presence of non–flow-limiting stenosis at rest in the group 3 dogs. In both instances, reliance on changes in VI alone would have led to errors in the estimation of MBF.

An interesting observation from this study is that when vasodilators were infused directly into a coronary artery, increases in MBF and microbubble velocity were not associated with changes in myocardial microvascular CSA. These real-time in vivo results are identical to those of Crystal et al¹⁸ and Eliasen and Amtorp.¹⁹ In their experiments, the mean myocardial transit rate of red blood cells increased during adenosine infusion, implying that the increase in MBF occurred via increase in CBV, but no changes in MBV were found. The microvessels that are imaged within the myocardium and that constitute MBV are predominantly capillaries,¹⁷ with dimensions or numbers that are not altered by direct coronary infusion of adenosine. Taken together, the results of these studies indicate that direct coronary injection of adenosine increases MBF by dilating microvessels which form a small portion of the MBV or are not present within the myocardia. Thus, by determining both CBV (measurement of the mean transit rate of microbubbles after an intracoronary bolus injection^{1 2} ) and MBV (measurement of microvascular CSA during an intravenous infusion of microbubbles), MCE could be used to separate changes in capillary dimension or density from those of larger microvessels.

In the presence of coronary stenoses, both microvascular CSA and microbubble velocity were found to be less in the stenosed versus the normal bed during hyperemia. These findings supports those of Canty et al,²⁰ who measured changes in MBV with the use of computed tomography. In the presence of coronary hyperemia, arteriolar dimensions increase with a consequent increase in MBF. In the stenotic bed, however, hyperemia is associated with an increase in the resistance across the bed compared with when no stenosis is present. Thus, a partial collapse of microvessels is likely to occur distal to the arterioles.⁶ Our results indicate that one potential site of this phenomenon is the capillary bed.

From the ex vivo experiments, we showed that differences in flow velocity can be detected using a single PI. This approach, however, has two limitations. First, because the magnitude of MBF and the degree of MBF mismatch between beds are not known a priori, the PI used may not be optimal to display the maximal disparity in MBF between the beds. As shown in the ex vivo experiment (Fig 5), use of a PI that is too short or too long may obscure VI disparities. Second, even if optimally timed, a single PI can provide only an assessment of the relative degree of flow mismatch. Multiple PIs are required to quantify myocardial microbubble velocity.

We have shown that the myocardial microbubble velocity can be derived from the PI versus VI relation during a continuous venous infusion. Derivation of the absolute value of MBV or microvascular CSA, however, is more involved. First, the VI within the myocardium depends on the concentration of microbubbles infused in the vein. Second, as shown in Fig 8, at concentrations required to produce myocardial opacification, the relation between microbubble concentration and VI within the LV cavity is no longer in the linear range. Thus, unlike other techniques,²¹ expression of myocardial VI as a percentage of that obtained from the LV cavity does not provide an accurate estimation of MBV with MCE.

An alternative method for deriving MBV or microvascular CSA is depicted in Fig 8 and is in the range reported with the use of other methods.^{2 21} If the sizes of the regions of interest and the ultrasound beam elevation are known, MBF can be calculated in absolute terms. Let us assume that a 1-cm² rectangular region of interest is placed over the myocardium and that the ultrasound beam elevation is 0.5 cm; therefore, the volume of tissue being examined is 0.5 cm³. Using the volume fraction of blood estimated above, MBV will be 0.04 mL. The average myocardial microbubble velocity at rest in our dogs was 0.6 cm · s⁻¹. Tissue flow as derived in equation 7 will therefore be 0.012 mL · s⁻¹, or 0.72 mL · min⁻¹, which is consistent with values derived using radiolabeled microspheres in these dogs.

Because the ultrasound beam profile is not homogeneous along its entire length, it is essential to have the exact value of the beam elevation at all image depths in order to quantify microbubble velocity. This value can be calibrated at different depths using an in vitro system in which both the flow and CSA are known. It may also be possible to “defocus” the beam or alter its profile so the beam thickness becomes more uniform at all depths. In this manner, MBF can be compared from different myocardial beds. We attempted to standardize our comparisons by choosing regions of interest at similar imaging depths.

Cardiac translation, caused by base-to-apex systolic shortening, results in different short-axis planes of the heart being imaged at different times in the cardiac cycle. If imaging is performed using apical views, there also is counterclockwise rotation of the heart during systole. Thus, in either view, the plane in which microbubble destruction occurs may not be precisely the same in which imaging subsequently occurs. This problem can be avoided if both microbubble destruction and imaging are performed at the same point in the cardiac cycle. The entire PI versus VI curve can potentially be constructed using PIs that are multiples of one cardiac cycle. Microbubble destruction and imaging will then occur in the same phase of the cardiac cycle (either end diastole or end systole). Quiet respiration can be used to minimize cardiac motion caused by respiration, and images from the same part of the respiratory cycle can be selected for analysis.

Several PIs are required to derive values for A and β, necessitating several minutes of image acquisition, which makes it essential for systemic hemodynamics and MBF to be stable for a long period. Thus, to produce steady state hyperemia, we selected an intravenous infusion of an adenosine agonist rather than a single venous injection of dipyridamole, because peak hyperemia may not be sustained by the letter. Such an approach may be indicated in the clinical setting as well.

The VI versus PI relations in this study are based on a steady state of microbubble concentration. Unlike a bolus administration of a large dose of microbubbles, in which recirculation of microbubbles is seen,^{4 5 6} prolonged infusions at low concentrations do not change either LV cavity or myocardial VI. It is possible that at these concentrations, the reticuloendothelial system is able to clear the microbubbles from the circulation at a rate that is similar to their intravascular replenishment. Even if a small number of microbubbles escape entrapment, they may not be sufficient to cause an appreciable change in myocardial VI.

Given the <1-mm axial resolution of echocardiography, it may be possible to measure the transmural distribution of MBF. Such an analysis will need the incorporation of both A and β because VI measurements alone were shown not to represent transmural distribution of MBF.²² The exception to this finding is the situation on which there is damage of the microvessels, so changes in MBF are simply due to changes in microvascular density.²³ Similarly, phasic changes in MBF could also be estimated using this technique if short PI or narrow-beam elevations are used. Abnormalities in phasic changes in MBF may make it possible to detect coronary stenosis at rest without recourse to provocative testing.²⁴

We have defined a novel method for measuring microbubble velocity and microvascular CSA that is based on bubble destruction by ultrasound. Measurement of these variables provides a quantitative assessment of MBF using a venous infusion of microbubbles, a technique that is likely to become clinically feasible in the near future. Although these data were derived from the myocardium, this method can be applied to any tissue accessible to ultrasound and therefore has the potential for quantifying perfusion in many organ systems.