Annals of Biomedical Engineering, Vol. 28, pp. 884–896, 2000 Printed in the USA. All rights reserved.

0090-6964/2000/28共8兲/884/13/$15.00 Copyright © 2000 Biomedical Engineering Society

Problems of Coronary Flow Reserve JULIEN I. E. HOFFMAN Department of Pediatrics and Cardiovascular Research Institute, University of California, San Francisco, CA (Received 22 October 1999; accepted 10 March 2000)

to demonstrate autoregulation 共at two levels of myocardial function兲, and then repeated the measurements of flow at different perfusion pressures after dilating the vessels by producing ischemia. The effects of changing CFR were probably first reported in 1974 by Gould and colleagues.49,50 They showed that as a coronary artery was progressively narrowed, resting 共autoregulated兲 flow did not change at first, but maximal flow 共achieved by injecting a vasodilator兲 decreased progressively. It was only near complete occlusion, when CFR was almost absent, that autoregulated flow decreased. The normal coronary conductogram 关Fig. 1共A兲兴 shows the normal relationship between mean coronary perfusion pressure and left ventricular myocardial blood flow for basal 共resting, autoregulated兲 flow A and for flow through maximally dilated myocardial vessels M. The difference between the two flows at any given perfusion pressure is the coronary flow reserve, and their ratio is the coronary flow reserve ratio. The line relating coronary perfusing pressure to flow in maximally dilated myocardial vessels reaches zero flow at a positive pressure 共termed P zf or P f ⫽0 ) that is normally about 10 mm Hg. Whether this pressure is determined by vessel closure, as in a Starling resistor, or is a function of intramyocardial vascular time constants is still under debate.60 Under most circumstances, coronary venous pressure is about 6–12 mm Hg. If we were to plot coronary arterial minus coronary venous pressure 共the driving pressure兲 on the X axis of these graphs, then the slope of the pressure–flow lines would indicate conductance 共the reciprocal of resistance兲. Because coronary venous pressure is usually small in comparison to coronary arterial pressures over 50 mm Hg, the slopes of the upper parts of the pressure–flow lines shown in Fig. 1 can be interpreted as conductances. Below coronary arterial pressures of 50 mm Hg, the actual conductances are lower than shown in Fig. 1. There is one disadvantage in plotting flow against driving pressure. For any given driving pressure, an increase in absolute pressures dilates the coronary vessels53 and increases conductance. It would be possible to allow for this issue by plotting flow against coronary arterial pressure with a family of dif-

Abstract—Coronary flow reserve is used to aid understanding why myocardial oxygen consumption may fail to meet demand. Its general aspects are well known, but the problems of using it are not. This manuscript describes three important factors that need to be considered when assessing coronary flow reserve. 共1兲 Maximal flow is usually achieved by giving either increasing doses or else what is thought to be a maximal dose of a vasodilator, or by examining peak reactive hyperemia. Evidence that both these approaches are flawed is provided. 共2兲 Existing methods in humans allow only total reserve to be determined, but this might be inadequate because changes in total reserve might not reflect changes in subendocardial flow reserve. 共3兲 Because there is marked heterogeneity of flow reserve in the left ventricle, measuring total flow reserve does not indicate when small regions are becoming ischemic. More basic research is needed to overcome these difficulties. © 2000 Biomedical Engineering Society. 关S0090-6964共00兲00908-5兴

Keywords—Reactive hyperemia, Maximal vasodilatation, Adenosine, Papaverine, Fractional flow reserve, Flow heterogeneity, Regional myocardial blood flow.

INTRODUCTION Coronary flow reserve 共CFR兲 is a useful concept for understanding why myocardial oxygen consumption may fail to meet demand. By definition, CFR is the difference between basal 共autoregulated兲 and maximal flow at any given perfusion pressure. If measured as the absolute difference, it has the same units as the flow measurements, for example, ml/min/g. CFR can also be measured in dimensionless units by dividing maximal by autoregulated flow; this is the CFR ratio. One way of understanding CFR is to plot the coronary conductogram, that is, displaying the coronary flow–pressure relationship for both autoregulated and maximal flow on the same figure. In the conductogram, the CFR at any coronary perfusion pressure can be evaluated. The first investigators to examine this relationship were probably Shaw and colleagues89,107 who cannulated the coronary artery in dogs, changed perfusion pressures Address correspondence to Julien I. E. Hoffman, MD, Professor of Pediatrics 共Emeritus兲, Box 0544, University of California, San Francisco, CA 94143; electronic mail: [email protected]

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Problems of Coronary Flow Reserve

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FIGURE 1. Coronary conductograms: „A… Normal left ventricle. A 1 and M 1 indicate the autoregulating and maximally dilated pressure–flow relations, respectively. CFR100 and CFR70 show the coronary flow reserve at mean perfusing pressures of 100 mm Hg „about 300 mlÕmin… and 70 mm Hg „about 200 mlÕmin…, respectively. The arrow labeled B 1 indicates the approximate pressure at which autoregulation fails. „B… An increase in autoregulated flow from A 1 to A 2 reduces CFR from CFR1 „about 300 mlÕmin… to CFR2 „about 200 mlÕmin…. Note that because the pressure–flow line during maximal vasodilatation slopes up to the right, the increased autoregulated flow fails at a higher pressure „ B 2 … than when normal „ B 1 …. The lines for normal values are thin, and the lines for abnormal values are thick. Adjacent parallel lines indicate the same values that are separated for clarity. „C… If the slope of the pressure flow line during maximal vasodilatation halves from normal „ M 1 … down to M 2 , the coronary flow reserve is decreased from CFR1 „about 300 mlÕmin… to CFR2 „about 100 mlÕmin…. The change of slope has the effect of increasing the pressure at which autoregulation fails from B 1 to B 2 . Note that halving the normal maximal conductance has a greater effect on CFR than doubling the normal autoregulated flow. The lines for normal values are thin, and the lines for abnormal values are thick. Adjacent parallel lines indicate the same values that are separated for clarity. „D… When the normal line of the pressure– flow relation during maximal vasodilatation „ M 1 … has a parallel shift to the right „ M 2 … due to a rise in the zero flow pressure, it reduces the CFR from CFR1 „about 300 mlÕmin… to CFR2 „about 230 mlÕmin…, and also increases the pressure at which autoregulation fails from B 1 to B 2 . The lines for normal values are thin, and the lines for abnormal values are thick. Adjacent parallel lines indicate the same values that are separated for clarity. „E… The combination of a doubling of autoregulated flow from A 1 to A 2 and a halving of the slope of the pressure–flow line during maximal vasodilatation from M 1 to M 2 causes a dramatic decrease in CFR from CFR1 „about 300 mlÕmin… to CFR2 „about 25 mlÕmin…. The pressure at which autoregulation fails has changed from about 40 mm Hg at B 1 to about 100 mm Hg at B 2 . Under these circumstances, some regions of the heart may be ischemic at normal perfusing pressures. The lines for normal values are thin, and the lines for abnormal values are thick. Adjacent parallel lines indicate the same values that are separated for clarity.

ferent lines for different coronary venous pressures, or plotting flow against driving pressure with a family of different lines representing different absolute coronary arterial pressures. The utility of such graphs has not been explored. There are three ways in which CFR can be reduced at any perfusion pressure. One is by an increase in resting flow from A 1 to A 2 关Fig. 1共B兲兴. This increase can occur for any of the reasons given in Table 1. The second is a decrease in the slope of the pressure–flow relation through maximally dilated vessels from M 1 to M 2 关Figure 1共C兲兴. This decrease is usually secondary to an increase in resistance to flow through these maximally dilated vessels, but this is not always so. Maximal flow is decreased if coronary venous pressure rises, despite normal or even decreased vascular resistance.53 Maximal

flow per gram is also reduced with ventricular hypertrophy when muscle mass increases without a corresponding increase in the vascular bed; here, too, absolute resistance is not decreased.90,91,95,118 Factors that might TABLE 1. Coronary flow reserve: Increased basal flow. Exercisea Fever Increased inotropyb

Hypoxemia Anemia Left shift of oxygen dissociation curve

Tachycardiaa,b Thyrotoxicosis Hypertrophya,b

Fetal hemoglobin Alkalosis Carboxyhemoglobin Abnormal hemoglobins

a

May increase zero flow pressure. May also reduce maximal flow.

b

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JULIEN I. E. HOFFMAN TABLE 2. Coronary flow reserve: Decreased maximal flow. Increased blood viscosity

Small vessel disease

Polycythemia Macroglobulinemia

Systemic lupus erythematosus Aortic stenosis

Abnormal cardiovascular function

Hypertension a

High left ventricular diastolic pressure Low aortic pressure–aortic incompetence Pericardial tamponadea

Hypertrophic cardiomyopathy Diabetes mellitus Idiopathic Cigarette smoking

Marked increase in contractilityb

Large vessel disease

a,b

Tachycardia Left ventricular hypertrophya,b Right ventricular hypertrophya,b,c

Atherosclerosis Thrombosis

a

May increase zero flow pressure. May also increase basal flow. c If acquired after early childhood. b

cause maximal flow to decrease are given in Table 2. The third is a parallel shift to the right in the pressure– flow relation through maximally dilated vessels due to an increase in zero flow pressure 关Fig. 1共D兲兴. Factors known to cause such a shift are listed in Table 3. It is possible for two or more factors to operate simultaneously, and then there will be a more dramatic reduction in CFR 关Fig. 1共E兲兴. These concepts and the various factors that reduce CFR were summarized in two publications by Hoffman,57,59 and another by ter Keurs.114 A point of particular importance is that as CFR decreases the ischemia that eventually occurs is predominantly subendocardial.42,44,60 One point of importance, shown clearly in the diagrams, is that any factor that reduces CFR increases the perfusion pressure at which autoregulation fails in the subendocardium. In extreme instances, subendocardial ischemia can occur at normal perfusing pressures.

The mechanisms underlying this selective subendocardial vulnerability to ischemia are beginning to be elucidated. The factors responsible for subendocardial vulnerability to ischemia may be divided into those that reflect the longer pathways for blood to enter and leave the subendocardium than the subepicardium; those associated with differences in regional stresses, strains, and intramyocardial tissue pressure; and those microvascular variations in responsiveness to stretch, nerve stimulation, and external agonists.20,30,65–67,74,75 Because the last of these sets of factors probably is inactive during maximal vasodilatation, it will not be discussed further here. The role of pathway length was explored by Chilian18 who compared maximally dilated coronary vessels in the subendocardium and subepicardium of arrested pig left ventricles. He found that the resistances of small arteries and veins were higher in the subendocardium, presumably related to the greater path lengths from epicardium to

TABLE 3. Coronary flow reserve: Right shift of zero flow line. Increased left ventricular diastolic pressurea Increased right ventricular diastolic pressure ⬎10 mm Hg Pericardial tamponadea Increase in coronary sinus and venous pressure ⬎10 mm Hg with normal right ventricular diastolic pressure, e.g., after Fontan–Kreuzer operation for tricuspid atresia

␤-adrenergic blockade or ␣-adrenergic stimulationa Left and right ventricular hypertrophya Tachycardiaa Some anesthetic agents, e.g., nitrous oxide a

May also reduce maximal flow.

Problems of Coronary Flow Reserve

endocardium. This disadvantage was overcome by a lower microcirculatory resistance in the subendocardial microvessels, thus explaining why in the arrested heart subendocardial perfusion exceeds subepicardial perfusion.44,116 The role of mechanical forces during cardiac contraction has been explored by numerous investigators,19,42,58,60 but will be discussed briefly here in relation to the studies of Flynn et al.44 These investigators found that when the heart went from arrest to beating at different heart rates, subendocardial flow decreased but subepicardial flow increased. The decrease in subendocardial flow with increased heart rate was originally reported by Domenech and Goich35 who attributed this decrease to the reduction in the time for diastolic perfusion of the subendocardium. The increase in subepicardial flow, however, cannot be explained by a temporal effect, for then flow in this region should either be reduced or at least unchanged. The explanation given by Flynn et al. was based on the finding that there was no systolic flow recorded in small epicardial arteries at their point of penetration into the myocardium; the systolic flow observed at the origin of the coronary arteries is stored in the epicardial arteries and does not contribute to systolic perfusion of the muscle. Therefore the increase in subepicardial flow with beating must have been due to retrograde flow from the deeper muscle of the left ventricle. This retrograde flow, in turn, was thought to have been due to the greater compression of subendocardial than subepicardial vessels by systolic tissue pressure which is near systolic cavity pressure at the endocardium and near atmospheric pressure at the epicardial surface. Such a gradient in intramyocardial tissue pressure had long been predicted from theoretical considerations,3,4,17,87 and was supported by many experimental observations that, despite technical problems,92,104 were remarkably consistent.2,10,33,52,54 One major consequence of these differential tissue pressures is that the subendocardial vessels become partially emptied of blood in systole and so become narrower. Therefore at the onset of the next diastole, they offer much more resistance to flow than do the wider subepicardial vessels. Given a long enough diastolic perfusion time and a high enough diastolic perfusion pressure, all the myocardial layers will be adequately perfused. However, an inadequate diastolic perfusion time or pressure will lead to inadequate subendocardial perfusion in the face of adequate inflow to the more superficial muscle layers. There is much direct and indirect support for the hypothesis put forward by Flynn et al.44 Goto et al.46 found that during barium-induced systolic cardiac arrest, left ventricular subendocardial vessels were half the diameter that they were during diastolic arrest, whereas in the subepicardium there was little change from systole to diastole. In the beating heart, direct observation of subepicardial microvessels5 showed constancy of diameter

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throughout the cardiac cycle, with acceleration of flow in the small arteries in midsystole and in the venules in late systole. Studies reported by Kajiya and colleagues previously121 and in this issue confirm these findings and added the narrowing of the subendocardial arteries in systole. This hypothesis also explains the observed effects of changes in contractility on regional myocardial blood flow.64,84 An increase in contractility increases intramyocardial tissue pressures, especially in the subendocardium.2,34 This increase would be expected to compress the subendocardial vessels more forcefully and therefore squeeze more blood out of the subendocardium. In fact, with increases in contractility, the retrograde flow can be so much increased that a flow meter on the origin of the left coronary artery shows retrograde systolic flow.68 More complete emptying of subendocardial vessels in systole would narrow them and increase their resistance to diastolic reflow even more than occurs normally, so that an increase in contractility tends to decrease subendocardial and increase subepicardial flow. Although most studies of CFR have been done in animals, there has been some application of the concept to make decisions about the treatment of human disease. These applications cover two large groups: global myocardial ischemia with normal extramural coronary arteries, and regional ischemia with one or more narrowed extramural coronary arteries. When there is localized coronary arterial disease, additional concepts have been introduced by Gould and his colleagues.31,48 They divided CFR into two components, stenosis flow reserve 共SFR兲 that depends only on stenosis geometry, and myocardial flow reserve 共MFR兲 that is a function of myocardial work, aortic blood pressure, vasoactive substances, collateral flows, venous pressures, and the size of the regional myocardial vascular bed. In addition, they also introduced concepts of absolute and relative CFR. Absolute CFR is the ratio of basal-to-maximal flow in the target artery. Because of the many factors that can affect CFR and MFR, it may be difficult to interpret the value for CFR if it is in an intermediate range. Relative CFR relates the CFR in the target artery to the CFR in another presumably normal artery. As both values are determined in the same patients, the various factors that can interfere with the interpretation of CFR are common to both measurements. If the ratio of these two CFRs is near 1, then the target and the reference artery have the same CFR and both are presumably normal. On the other hand, many patients have diffuse arterial disease 共for example, patients with diabetes or systemic lupus erythematosus兲,110 and showing that two arteries have the same CFR does not prove that they are both normal; they could both be equally abnormal. The notion of SFR and MFR has been extended to the concept of fractional flow reserve 共FFR兲 that will be discussed in detail below.

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JULIEN I. E. HOFFMAN TABLE 4. Methods for determining CFR in humans. Acquisition time

Measured value

Inert gas

Long (20–40 min)

Flow/100 g LV or part of LV

All LV, or designated regions

Poor

Complicates interpretation

110,111,113

Suction Doppler

Short

Velocity

Ill-defined region supplied by artery

Poor

Not assessed

37,38,82,83

Transthoracic echocardiogram

Short

Velocity

Ill-defined region supplied by artery

Poor

Not assessed

13,61,77,94

Trans-esophageal echocardiogram

Short

Velocity, ? flow

Ill-defined region supplied by artery

Fair

Not assessed

24,56,105

Coronary sinus thermodilution

Short

Flow

Ill-defined region of left ventricle

Poor

Not assessed

45,96a

Doppler tipped wire

Short

Velocity, ? flow

Ill-defined region supplied by artery

Fair

Not assessed

1,43,63,76

Pressure tipped wire

Short

Pressure

Ill-defined region

Fair

Not assessed

26,27,29,99,106

Method

Region assessed

Spatial resolution

Effect of heterogeneity

Supplied by artery

References

112

Angiography: video-densitometry, digital angiography

Short, but processing time long

Density as surrogate for volume

Designated regions

High

Not assessed

25,28,55,93,97

Angiography: frame counting

Short

‘‘Velocity’’

Fairly good

High

Not assessed

81

Angiography; instantaneous hyperemic diastolic flow

Short

Velocity

Region supplied by artery

Poor

Not assessed

21,22,32,79,80

Fast CT

Short

? flow

Designated regions

Very high

Possibly assessed

119,120b

MRI

Long

? flow

Designated regions

Very high

Possibly assessed

69,78

PET scanning

Variable

Flow/100 g LV

Designated regions

Fair

Assessed

11,14,36,103

a

Method not applied to flow reserve. Technique assessed, but not for flow reserve.

b

METHODS FOR DETERMINING CFR IN HUMANS At present, these are only partly satisfactory. The methods and their major features are summed up in Table 4. Each method may have variations designed to overcome some of the shortcomings, but none are ideal. In particular, the ability to define subendocardial CFR is still lacking, although it is possible that fast CT or even MRI will one day be able to make these measurements.

PROBLEMS IN DETERMINING CFR There are three aspects of CFR that need to be addressed. 共1兲 How is maximal flow achieved?

共2兲 How do we interpret a decrease in CFR for the whole heart when what we really need is the subendocardial CFR? 共3兲 How useful is CFR in assessing regional ischemia? Maximal Flow This is achieved by intravenous or intracoronary injection of a vasodilator 共contrast medium, adenosine, dipyridamole, papaverine, nifedipine兲 or by examining reactive hyperemia after temporary coronary arterial occlusion. The latter is done usually in animal studies, but has been done in humans at the time of surgery.37,38,82,83 The opportunity for measuring reactive hyperemia during angioplasty exists, but there are no reports of it being done without surgery when the coronary arteries are normal.

Problems of Coronary Flow Reserve

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TABLE 5. Coronary flow reserve: Effect of different agents †data taken from Bookstein and Higgins „Ref. 12…‡. Agent or action

Dose

Reactive hyperemia

Conductance ratio 3.84

Papaverine

5 mg 10 mg

3.7 3.84

ATP

60 ␮g 180 ␮g

4.15 4.08

Papaverine⫹ATP

5 mg(P)⫹60 ␮g(ATP) 10 mg(P)⫹60 ␮g(ATP) 16 mg/min(P)⫹200 ␮g/min(ATP)

5.53 6.53 7.87

The major issue that arises when giving vasodilators is whether maximal vasodilatation has been achieved. In animals, this is often done by demonstrating that the dose of vasodilator has abolished reactive hyperemia. Alternatively, in both animals and humans, increasing doses of the agonist are given until there is no further increase in coronary flow. This implies that coronary flow can be measured rapidly after each dose, and precludes the long duration inert gas techniques for measuring coronary blood flow. In humans, the only practical method is using a Doppler-tipped wire inserted into the coronary artery.39 Sometimes the higher doses of agonist produce ischemic pain or arrhythmias, and the procedure cannot be continued. Some investigators have used a single average dose of an agonist based on previous experience, but this may be unreliable because some patients need more than the average dose for maximal vasodilatation. Even if a maximal dose of a vasodilator is given, the question still arises whether flow is indeed maximal. In a study done on conscious dogs, Vlahakes et al.117 measured diastolic pressure–flow relations during maximal vasodilatation obtained with adenosine and verified by noting the abolition of reactive hyperemia. When phentolamine, an ␣-adrenergic receptor antagonist, or isoproterenol, a ␤-adrenergic receptor agonist, was given, flow increased at any given pressure. When phenylephrine, an ␣-adrenergic receptor agonist was given, flow decreased at any given pressure. In general, the pressure–flow lines were parallel, and the mechanism appeared to be an increase in zero flow pressure. Whether this effect is mediated through changes in intramyocardial blood time constants60 or venous waterfalls60,115 is not known. One can argue that the effect of isoproterenol was mediated by changes in myocardial contractility 共although these should have decreased maximal flows兲, and that the effect of phenylephrine was mediated by superimposing ␣-adrenergic mediated vasoconstriction. The mechanism of the effect of phentolamine, however, is more difficult

to evaluate; ␣-adrenergic receptors do not affect myocardial contractility in adults. Is it possible that any given vasoactive agonist acts on only part of the circulation; for example, on arteries and not veins, or preferentially on larger but not smaller arteries? We know of several differences between arteries and veins. There is more nitric oxide synthase in coronary arteries than coronary veins, and the veins but not the arteries contain dipeptidyl peptidase 共angiotensin converting enzyme兲. Some studies have already demonstrated that combinations of vasodilators with different actions can achieve higher flows than can any of them alone,12 as shown in Table 5. For example, the combination of ATP and papaverine demonstrated greater CFR 共and therefore greater vasodilatation兲 than either alone, even in larger doses. Of interest is that CFR in that study was greater with these agonists than with reactive hyperemia. Two other factors of more importance in the heart than in other organs are the effect of changes in heart rate and myocardial contractility. As heart rate increases resting flow rises,41 and maximal flow tends to be reduced by the shortened diastolic perfusion time. However, for relatively small changes in heart rate 共and aortic blood pressure兲, average coronary flow reserve does not appear to change much.86 Contractility is a more important source of variability. Decreases in contractility are known to increase subendocardial blood flow, and increases in contractility perhaps to inhibit these flows.64,84 Contractility is difficult to control, especially in human subjects, and the differences in CFR found in different studies in normal subjects may be related to differences in contractility. In dogs, Gould and colleagues50 observed CFR ratios of 3.5–4.5, and we have found the CFR ratio to vary from about 3 to 7.6 Bookstein and Higgins12 observed ratios of 1.1–3.1 with renografin, 2.5–3.8 with papaverine, 2.6–4.1 with ATP in modest doses, but 7 with high-dose ATP, and 7.9 with ATP plus papaverine. In human subjects, Marcus and

890

JULIEN I. E. HOFFMAN

colleagues82,83 found it to be about 4.5 共range 3.8–7.5兲 under anesthesia, Tauchert and Hilger113 found an average of 4, and Strauer109 found it to be just under 5. The value of reactive hyperemia as an indication of maximal vasodilatation also needs scrutiny. With profound ischemia there will be decreased myocardial contractility, usually appearing after about 5 s, that can lead to augmented flow during the period of reflow. This is followed by a period of increased contractility, presumably due to catecholamine release. In our studies of isolated blood perfused rat hearts, we found a great increase in contractility peaking about 30 s after release of the coronary occlusion. This was well beyond the peak of the reactive hyperemic flow response and so probably did not influence it. On the other hand, we do not know if other vasoactive agents are liberated earlier to increase or decrease the maximal flow response. Another factor is that the peak responses of subendocardial and subepicardial flow are asynchronous,40 so that reactive hyperemia may never reveal maximal flow. How Do We Interpret a Decrease in CFR Even if we can measure CFR, we need to know how to interpret the results with particular reference to the fact that CFR is lost first in subendocardial muscle.23 Therefore a reduction of CFR from 4 to 2, which might leave the heart adequately perfused if CFR was uniform across the heart, could well coexist with a loss of reserve in part or all of the subendocardium. There appears to be a wide range of reserve within any layer of the heart, as well as within each layer separately.6,7,23 At a mean coronary perfusion pressure of 80 mm Hg, some pieces of myocardium have CFR ratios as low as 2, whereas others may have ratios as high as 20. This implies that reduction of perfusion pressure to 40 mm Hg will exhaust CFR in pieces with a low reserve, and further decreases in perfusion pressure 共or, what is equivalent, increases in myocardial oxygen demand at that same low pressure兲 will produce subendocardial ischemia. Indeed, this has been shown to be true when perfusing pressures are decreased to 25–37 mm Hg in dogs.15,16,23 What this implies is that a modest reduction of CFR ratio from 4 to 3 is unlikely to be associated with regional ischemia, but a ratio of 2 or less could well be associated with commencing ischemia in some regions, especially in the subendocardium. The present limited number of studies of the distribution of coronary flow reserve suggest that when the average CFR decreases to 2, only a small percentage of the myocardium would become ischemic. This is likely to be an underestimate, however, because to date the distribution of CFR has been measured only in relatively large pieces of tissue 共50–150 mg兲. Studies have indicated that the individual units are likely to be much

smaller.62,85,88,108 Therefore the larger pieces used in our previous studies probably included smaller pieces with both lower and higher CFR ratios than we observed, so that perhaps more of the left ventricular myocardium has a relatively low CFR than appears from our data. A second major problem concerning the distribution of CFR is that all studies to date have been done in normal hearts and in anesthetized animals. Our clinical concerns, however, are mostly with abnormal hearts in conscious subjects. There is great need to study the distribution of CFR in hearts with hypertrophy or those with dilatation and a raised left ventricular diastolic pressure. Both of these types of pathology are likely to reduce the average CFR for the whole left ventricle, and may well have a greater effect on the subendocardial muscle. Finally, we need to learn more about how changes in aortic pressure affect the distribution of CFR. It is true that McGinn et al.86 found CFR to be constant in humans for modest changes in aortic pressure. However, their results were for average CFR only. It is unlikely that changes in aortic pressure and the associated changes in intramyocardial pressure have a linear effect on the regional CFRs, increasing or decreasing them all proportionately. A rise in aortic pressure, by distending intramural coronary arteries, will decrease vascular resistance,53 but it is likely that this effect will predominate in the subepicardium with its low tissue pressures. On the other hand, the equivalent rise in subendocardial tissue pressure may lead to either lesser increases or even decreases in subendocardial CFR. The average CFR might then not appear to change, but the distribution will be altered, perhaps in the direction of more tissue pieces with a low CFR. Clearly, with our present lack of knowledge, we should be conservative, and regard a CFR as low as 2.5, or even 3, as potentially damaging to the subendocardium in humans. How Useful Is CFR in Assessing Regional Ischemia? There is a long history of attempts to decide when coronary arterial lesions of intermediate severity are or are not responsible for regional ischemia. In essence, the exercise thallium study makes use of the CFR concept; if a coronary arterial lesion that can supply basal flow cannot supply maximal flow, then it may well be regarded as severe.49,50 Similarly, the exercising or dobutamine echocardiogram may reveal dysfunction in segments that have normal basal function. These are useful and practical applications of the concept of CFR. They have disadvantages, however, in not being able to be applied during cardiac catheterization when an immediate decision about a given procedure is wanted. Furthermore, the functional tests are not directly quantifiable. The need for an immediate decision also argues against the use of positron emission tomography

Problems of Coronary Flow Reserve

which otherwise is of great value.31,47,51 Approaches that have been used are predominantly the measurement of CFR by a Doppler-tipped wire,8,9,39,70–73 and calculation of FFR.73,98–102 The earlier studies of Gould and colleagues mentioned above distinguished between stenosis flow reserve and myocardial flow reserve, the latter including the contributions of collateral flow. Although SFR can be estimated from the geometry of the atheroclerotic lesion, and MFR from either PET scanning or the use of Doppler-tipped wires, both methods of estimation have practical limitations. In particular, frequently adequate flow measurements cannot be made by Doppler-tipped wire. For this reason, Pijls and De Bruyne introduced the allied concept of fractional flow reserve that estimates the same two types of reserve 共FFRcor and FFRmyo兲 by using only pressure-tipped catheters that are small enough to pass most coronary lesions.102 The concept has begun to have extensive clinical use at the time of cardiac catheterization of patients with coronary artery disease. The basic formulas are: 共A兲 Fractional flow reserve in the myocardium 共FFRmyo兲 is defined as the maximal flow in the territory s ) divided by the supplied by the stenotic artery (Q m maximal myocardial flow in that region in the absence of N ). These flows include any collateral blood stenosis (Q m flow. FFRmyo is calculated after dilating the coronary vessels maximally from: ( P d ⫺ P v )/( P a ⫺ P v ), where P d is pressure distal to the stenosis, P a is pressure proximal to the stenosis, P v is coronary venous pressure. Although this is not a measure of CFR per se, it is an estimate of the reduction in CFR due to the stenosis. Implicit in this method is the assumption that in the absence of stenosis, the CFR would be normal. Some consequences of this assumption will be discussed below. Note that if there is no stenosis, then P a ⫽ P d , and the ratio is 1. 共B兲 Fractional flow reserve for the coronary artery 共FFRcor兲 is defined as the maximal flow through the stenosis (Q s ) divided by maximal flow in the same artery without stenosis (Q N ). This specifically excludes collateral blood flow (Q c ) that is distal to the stenosis. To calculate FFRcor, dilate the coronary vessels maximally and occlude the stenotic vessel. In practice, this is done only during PTCA. The distal pressure before occlusion is P d , and the pressure after occlusion falls to P w , the wedge pressure. Then calculate FFRcor as ( P d ⫺ P w )/ P a ⫺ P w ). Once again, if there is no stenosis, P a ⫽ P d , and the ratio is 1. Note that flows and resistances do not enter into these equations. Nevertheless, assumptions regarding resistances are integral to the equations. This can be seen from the simple proof for FFRmyo:

891

s N The desired flow ratio for FFRmyo is Q m /Q m . Minimal myocardial vascular resistance R m is about s N ) as without stenosis (R m ): the same with stenosis (R m

Now

s ⫽ Rm

共 P d⫺ P v 兲 s Qm

and N ⫽ Rm

共 P a⫺ P v 兲 N Qm

,

because s N Rm ⫽R m ,

共 P d⫺ P v 兲 s Qm

⫽

共 P a⫺ P v 兲 N Qm

.

Therefore, s Qm

N⫽ Qm

共 P d⫺ P v 兲 . 共 P a⫺ P v 兲

The sentence in italics shows that resistance enters into the basic assumption. There are two issues to cons N sider. One is the equality of R m and R m during maximal vasodilatation. Even if that peripheral vascular bed is normal, a severe stenosis will decrease distal coronary pressure so much that myocardial vascular resistance will be higher than if measured at higher perfusing pressures with a less severe or even no stenosis.53 The result of this is that the pressure ratio ( P d ⫺ P v )/( P a ⫺ P v ) will be s N /Q m by some unknown higher than the flow ratio Q m amount. The second issue concerns abnormalities of the small peripheral myocardial vessels. What would happen, for example, if with a single coronary arterial lesion, the branches of that artery as compared with the normal arteries were exposed to different cytokines and autocrine influences, or else had more serious small vessel disease, and so had a different minimal resistance to vasodilators? Assume that in the stenotic region the minimal resistance was twice as high as in the remaining regions. Then a simple calculation will show that the FFRmyo will be about two thirds the value that it would have had with equal minimal resistances 共Fig. 2兲. Atherosclerosis is a diffuse disease that involves smaller as well as larger coronary epicardial arterial branches, and the involvement may well be variable in a given subject. Now consider what would happen if the minimal vascular resistance was doubled equally in all the coronary

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FIGURE 2. Model of effect of changes in myocardial vascular resistance on the calculation of FFRmyo. Panel A: With normal myocardial vascular resistance „ R myo… of 4 mm HgÕmlÕ min and stenosis resistance „ R st… of 4 mm HgÕmlÕmin, the pressure drop from the proximal artery „ P a … to the coronary vein „ P v … is 100 mm Hg. This by the hydraulic equivalent of Ohm’s law gives a flow through this artery of 12.5 mlÕmin. The pressure drop across the coronary stenosis is therefore half of the total pressure drop, and is 50 mm Hg. Therefore FFRmyo is „50–0…Õ100–0…Ä0.5. Panel B: With an increased myocardial vascular resistance of 12 mm HgÕmlÕmin, and the same stenosis resistance and total pressure drop, the flow through the artery is reduced to 6.25 mlÕmin. The pressure drop across the coronary stenosis is now only one quarter of the total pressure drop, so that distal coronary arterial pressure is now 75 mm Hg. Therefore, FFRmyo becomes „75–0…Õ„100–0…Ä0.75. By current criteria, the patient in panel A would benefit from angioplasty, whereas the patient in panel B would not need angioplasty.

vascular beds. The net effect of the raised peripheral resistance when added to the stenosis is either to decrease flow more for any given stenosis severity, or else to intensify the effect of a relatively mild stenosis. Put another way, a raised peripheral stenosis will increase P d for any given flow, thereby increasing the value for FFRmyo. The patient might still be helped by removing the stenosis, but the conventional threshold value for FFRmyo would have been exceeded. Therefore we need values for FFRmyo that are not constants, but that vary with whatever the peripheral coronary vascular resistance is. Current studies appear to show that if FFRmyo is under 0.75, there is reversible ischemia that will improve after revascularization 共or perhaps with intensive medical treatment兲. From the discussion above, it would be prudent not to accept that figure without including all the other information available about the patient.

FUTURE WORK The problems addressed above indicate that research is needed in at least three areas. 共1兲 Sophisticated studies are needed to determine what mechanisms govern maximal coronary vasodilatation, and how this can be evaluated and tested in humans.

共2兲 Systematic studies are needed of the distribution of CFR in both normal and abnormal hearts, and how the common factors that can diminish CFR affect regional reserve, especially in small subendocardial regions. 共3兲 Methods need to be devised to measure regional CFR or the consequences of its loss directly in humans. Given that CFR is lost first in very small regions, we need methods with excellent spatial resolution. If flow is to be measured, then we also need good temporal resolution, and at present ultrafast CT is the only method available. Although MRI has good spatial resolution, its long acquisition time because of the need for gating to minimize the effects of cardiac motion make it an unlikely candidate for regional flow measurements. On the other hand, it might be possible to use MRI to examine the consequences of regional ischemia. For example, functional MRI might be able to detect changes in local venous oxygen saturation after a step increase in myocardial work, or various products of ischemia might be detected. This is clearly a direction that might well produce important and clinically relevant information. ACKNOWLEDGMENT This work was supported in part by Program Project No. HL 25847 from the National Institutes of Health.

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