Basic Science for Clinicians
`
`Physiological Basis of Clinically Used Coronary
`Hemodynamic Indices
`
`Jos A.E. Spaan, PhD; Jan J. Piek, MD; Julien I.E. Hoffman, MD; Maria Siebes, PhD
`
`Abstract—In deriving clinically used hemodynamic indices such as fractional flow reserve and coronary flow velocity
`reserve, simplified models of the coronary circulation are used. In particular, myocardial resistance is assumed to be
`independent of factors such as heart contraction and driving pressure. These simplifying assumptions are not always
`justified. In this review we focus on distensibility of resistance vessels, the shape of coronary pressure-flow lines, and
`the influence of collateral flow on these lines. We show that (1) the coronary system is intrinsically nonlinear because
`resistance vessels at maximal vasodilation change diameter with pressure and cardiac function; (2) the assumption of
`collateral flow is not needed to explain the difference between pressure-derived and flow-derived fractional flow
`reserve; and (3) collateral flow plays a role only at low distal pressures. We conclude that traditional hemodynamic
`indices are valuable for clinical decision making but that clinical studies of coronary physiology will benefit greatly from
`combined measurements of coronary flow or velocity and pressure. (Circulation. 2006;113:446-455.)
`
`Key Words: blood flow velocity 䡲 blood pressure 䡲 collateral circulation 䡲 coronary disease 䡲 hemodynamics
`
`Coronary physiology has a rich history, founded on
`
`numerous animal and theoretical models, and significant
`milestones were reached as new measuring techniques were
`developed. Recent progress has been made by applying
`techniques to measure intracoronary flow, flow velocity, and
`pressure to aid in clinical decision making, thereby advancing
`our understanding of human coronary physiology beyond
`what could be extrapolated from animal studies. One unre-
`solved issue that has arisen from these studies, however,
`concerns conflicting interpretations of coronary microvascu-
`lar resistance, a quantity with crucial relevance for clinical
`decision making.1– 4
`There are 2 conflicting interpretations of coronary
`pressure-flow lines during hyperemia: (1) coronary pressure-
`flow relations are straight and, in the absence of collateral
`flow, intercept the pressure axis at venous pressure (Pv); or
`(2) coronary pressure-flow relations are straight at physiolog-
`ical pressures and, when linearly extrapolated, intercept the
`pressure axis at a value well above venous pressure (extrap-
`olated zero flow pressure [PzfE]); at lower pressures, how-
`ever, they curve toward the pressure axis, intercepting it at a
`lower pressure (actual zero flow pressure [Pzf]) that is still
`higher than Pv.
`The purpose of this article is to review the physiological
`literature with respect to coronary pressure-flow relations as
`relevant to myocardial microvascular resistance. This key
`issue relates to important assumptions underlying the fre-
`quently used model of myocardial fractional flow reserve
`(FFRmyo). We conclude with a synopsis of physiological
`
`studies demonstrating the curved nature of pressure-flow
`relations and how this shape relates to the pressure depen-
`dence of minimal coronary microvascular resistance.
`This focused review of coronary physiology is intended to
`help the clinical reader to translate the physiological analysis
`of microvascular resistance from bench to bedside and to
`encourage the use and further development of hemodynamic
`indices in the clinical setting.
`
`Coronary Flow Reserve
`The concept of coronary flow reserve (CFR) was developed
`to describe the flow increase available to the heart in response
`to an increase in oxygen demand.5 Because the perfused
`tissue mass cannot always be measured, CFR was expressed
`as the ratio between maximal hyperemic flow and resting
`flow, with the hyperemic condition implicitly assumed as a
`standard value.6,7 A pressure drop across a stenosis causes
`compensatory vasodilation at rest, thereby diminishing the
`ability of the coronary circulation to adapt to an increase in
`oxygen demand. In other words, a stenosis reduces CFR.
`Investigators also recognized that flow per gram of tissue
`varied throughout the cardiac muscle and that subendocardial
`perfusion in particular was impeded by forces related to
`cardiac contraction.8 –11 Consequently, CFR varies regionally
`within the myocardium and is first exhausted in the suben-
`docardium, especially at higher heart rates.12 Reduced sub-
`endocardial CFR is a good paradigm to explain why ischemia
`and infarction start predominantly in this vulnerable region.7
`We expect
`that
`the concept of subendocardial CFR will
`
`From the Departments of Cardiology (J.J.P.) and Medical Physics (J.A.E.S., M.S.), Academic Medical Center, University of Amsterdam, Amsterdam,
`the Netherlands; and Department of Pediatrics and Cardiovascular Research Institute, University of California, San Francisco (J.I.E.H.).
`Correspondence to Jos A.E. Spaan, PhD, Department of Medical Physics, Academic Medical Center, University of Amsterdam, Meibergdreef 15, 1105
`AZ Amsterdam, The Netherlands. E-mail j.a.spaan@amc.uva.nl
`© 2006 American Heart Association, Inc.
`Circulation is available at http://www.circulationaha.org
`
`DOI: 10.1161/CIRCULATIONAHA.105.587196
`
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`Spaan et al
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`Coronary Physiological Indices
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`
`by collateral vessels proximal to the capillary bed. Even with
`collaterals, no collateral vessel flow will occur without a
`stenosis because no pressure difference is present across the
`collateral vessels, but collateral flow will occur with a
`stenosis because the distal pressure in the recipient vessel is
`lower than Pa in the donor vessel; the difference between the
`two is the driving pressure for collateral flow.
`Pressure-based FFRmyo is obtained as (Pd⫺Pv)/(Pa⫺Pv),
`where Pa is proximal coronary arterial (⫽aortic) pressure, Pd
`is distal coronary pressure, and Pv is coronary venous
`pressure. A value for FFRmyo ⬍0.75 indicates that dilatation
`of the coronary stenosis is likely to relieve ischemia.
`The physiological derivation for FFRmyo is as follows:
`
`Q Q
`
`N
`
`FFRmyo⫽
`
`(1)
`
`where QN is myocardial flow without stenosis and Q is the
`myocardial flow when the artery is stenotic and represents the
`sum of flow through the stenotic vessel (QS) and collateral
`flow (QC).
`
`(2)
`
`QN⫽
`
`Pa ⫺ Pv
`RminN
`
`and Q⫽
`
`Pd ⫺ Pv
`RminS
`
`,
`
`where RminN and RminS are the minimal resistances for the
`distal microcirculation without and with a stenosis in the
`supplying artery, respectively.
`
`(3)
`
`Pd ⫺ Pv
`RminN
`Pa ⫺ Pv
`RminS
`that FFRmyo⫽(Pd⫺Pv)/(Pa⫺Pv)
`so
`if
`only
`true
`is
`RminN⫽RminS. If this were true, then minimal microvascular
`resistance would be independent of pressure because the
`respective perfusion pressures Pa and Pd are different. If
`RminS were higher than RminN,
`then FFRmyo based on
`pressure measurements would underestimate the myocardial
`flow ratio Q/QN.
`To test this assumption, Pijls et al19 compared (Pd⫺Pv)/
`(Pa⫺Pv) with the coronary flow ratio QS/QN. Without collat-
`eral flow, the expected relation passes through the origin, as
`indicated by the dashed line in Figure 2. Their results showed
`that with increasing stenosis severity the coronary flow ratio
`progressively underestimated the pressure-based index. They
`assumed that this was because collateral flow was missed by
`measuring coronary flow proximal to the collateral connec-
`tion. However, the magnitude of collateral flow was not
`verified by direct measurement. Moreover, in a PET study in
`humans, actual myocardial flow per gram of tissue was
`measured distal to a stenotic and reference vessel, and the
`myocardial flow ratio was plotted versus FFR.20 In this
`setting, collateral flow was included in the measurements, but
`a similar underestimation was reported. Such underestimation
`would also follow if microvascular resistance increased as
`distal perfusion pressure fell. It is therefore important to
`
`⫽
`
`Q Q
`
`N
`
`Therefore,
`
`⫽
`
`Pd ⫺ Pv
`Pa ⫺ Pv
`
`⫻
`
`RminN
`RminS
`
`Figure 1. Model of the coronary circulation. Top and bottom
`circuits represent equivalent myocardial mass. Without stenosis
`in the bottom, RminS⫽RminN, QC⫽0, QS⫽QN, and Pd⫽Pa. QS
`indicates hyperemic flow with stenosis; QN, hyperemic flow
`without stenosis; and Qc, collateral flow.
`
`become used in clinical diagnosis once new technological
`modalities mature.13
`Coronary flow velocity reserve (CFVR) measured by
`Doppler ultrasound was introduced as a surrogate for CFR
`and was first measured during open heart surgery by applying
`Doppler suction probes to epicardial arteries for stenosis
`evaluation. This pioneering work of Marcus and colleagues14
`is the clinical precursor of the present-day guidewire-based
`measuring techniques. Marcus et al demonstrated that CFVR
`could also be reduced in normal coronary arteries of hearts
`with hypertrophy resulting from valvar stenosis. The devel-
`opment of intracoronary catheters and Doppler velocity
`sensor– equipped guidewires allowed the application of
`CFVR during catheterization procedures.15,16 A threshold
`value of CFVR indicative of reversible ischemia varies
`between 1.7 and 2.17
`An important problem in applying CFVR and CFR is their
`dependence on the level of control resistance, which in turn is
`affected by oxygen demand or impaired autoregulatory ca-
`pacity.18 However, as discussed below, hyperemic microvas-
`cular resistance also depends on hemodynamic conditions.
`
`Model for Hyperemic Perfusion Assuming Linear
`Pressure-Flow Relations
`Pressure sensor– equipped guidewires were introduced, al-
`lowing measurement of pressure beyond a stenosis. It was
`assumed that the ratio between distal pressure (Pd) and aortic
`pressure (Pa) during maximal hyperemia can be translated to
`represent an estimate of relative (fractional) maximal flow.
`Because good pressure measurements are easier to obtain and
`the dependence on baseline conditions was eliminated, this
`ratio became favored to quantify the significance of a
`coronary stenosis. In particular, Pijls et al19 pioneered this
`field and established pressure-derived indices of stenosis
`severity in clinical practice.
`FFRmyo was defined as the ratio of maximal myocardial
`blood flow distal
`to a stenotic artery to the theoretical
`maximal flow in the absence of the stenosis. The principles
`are illustrated by the model in Figure 1, with parallel normal
`and stenotic circuits that in this model are assumed to perfuse
`the same amount of tissue and may or may not be connected
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`Circulation
`
`January 24, 2006
`
`Figure 3. Passive pressure-diameter relations of isolated resis-
`tance arteries. Diameters at 100 mm Hg varied between 0.065
`and 0.260 mm. For details, see Cornelissen et al.21
`
`tance to flow will increase when Pd decreases as a result of
`flow limitation through a stenosis. When the effect of
`pressure changes on the diameter of dilated arterioles and
`other vessels constituting the microcirculation is considered,
`minimal microvascular resistance should decrease substan-
`tially in patients when a stenosis is dilated.
`In vivo studies have demonstrated this fundamental rela-
`tion between vascular diameters, volume, and resistance by
`investigating relationships between intramural vascular vol-
`ume and resistance and the effect of arterial pressure on these
`relationships.24 Recent results from studies using ultrasound
`contrast showed a decrease of microvascular volume during
`hyperemia of ⬎50% when arterial pressure was lowered from
`80 to 40 mm Hg.25 This corresponds with earlier studies in
`which intramural blood volume was measured in different
`ways.26 Moreover, pressure dependence of coronary resis-
`tance was clearly demonstrated by experiments in which
`coronary flow increased when the arterial-venous pressure
`difference was kept constant by increasing both pressures by
`the same amount, which is only possible when resistance
`decreases with pressure.27 These findings are important be-
`cause they imply that a stenosis not only adds resistance to
`flow in the epicardial arteries but additionally impedes
`myocardial perfusion by increasing microvascular resistance
`via the passive elastic behavior of the microvascular walls at
`vasodilation.
`
`Coronary Pressure-Flow Relations and
`Microvascular Resistance
`To translate results obtained in isolated vessels to an intact
`circulation, we make use of coronary pressure-flow relations
`at maximal vasodilation that are usually presented with
`pressure (independent variable) on the horizontal axis and
`flow (dependent variable) on the vertical axis. Many physi-
`ological studies show that these pressure-flow lines, even in
`the absence of collateral vessels, are straight at physiological
`pressures but follow a convex curve toward the pressure axis
`at lower pressures, and the zero flow intercept on the pressure
`axis Pzf is higher than Pv (solid line in Figure 4). When the
`
`Figure 2. Typical measurement of the relation between FFR,
`QS/QN, and the pressure ratio (Pd⫺Pv)/(Pa⫺Pv). Circles repre-
`sent control; triangles, increased Pa (phenylephrine); squares,
`decreased Pa (nitroprusside). QS indicates hyperemic flow with
`stenosis; QN, hyperemic flow without stenosis. Adapted from
`Pijls et al19 (Figure 6, panel 5). The axes of the original figure
`have been reversed to facilitate comparison with other figures in
`this article.
`
`explore alternative explanations for the deviation between the
`dashed and solid lines in Figure 2.
`
`Distensibility of Resistance Vessels as Rationale for
`Pressure Dependence of Coronary Resistance
`At maximal vasodilation, the state at which FFRmyo is defined,
`diameters of all vessels depend on distending pressure and
`more at lower than higher pressure. This fundamental prop-
`erty has been demonstrated in many studies on isolated and in
`situ vessels without tone. When normalized to the diameter at
`a pressure of 100 mm Hg, the pressure-diameter relations of
`blood vessels are independent of size. A compilation of such
`in vitro data is shown in Figure 3.21 The diameter change
`induced by a 10-mm Hg pressure change amounts to 1% at a
`mean pressure of 80 mm Hg, 4% at 40 mm Hg, and 10% at
`20 mm Hg. These numbers seem small, but because pressure
`drop in tubes is inversely related to the fourth power of the
`diameter (Poiseuille’s law), these diameter changes corre-
`spond to 4%, 16%, and 40% resistance variations for 10-
`mm Hg pressure variations at the different mean pressures.
`The change in vessel diameter corresponding to a pressure
`increase from 50 to 100 mm Hg, as may occur when a
`stenosis is dilated by balloon angioplasty, is ⬇8%, corre-
`sponding to a resistance change of 32%. Direct observations
`of resistance vessels at the subepicardium and subendocar-
`dium demonstrate a similar response to pressure changes of in
`situ vessels with diameter in the order of 100 ␮m.22 During
`hyperemia and at an arterial pressure of 100 mm Hg, ⬇25%
`of total coronary resistance is in venules and veins ⬎200
`␮m.23 These vessels are rather distensible, and their resis-
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`Coronary Physiological Indices
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`flow from epicardial and particularly intramyocardial micro-
`circulation.26,30 This interpretation is strongly supported by
`the observation that coronary venous outflow continues even
`when pressure has decayed to Pzf.31 This venous outflow at
`cessation of inflow has to come from a pool of blood within
`the microcirculation, which also constitutes the intramyocar-
`dial compliance.32 Pzf values above Pv could not be due to
`collateral flow in those experiments because pressure at the
`source of all epicardial vessels was essentially equal at all
`times.
`Pzf and the whole pressure-flow line are shifted to the right
`(higher pressures) by left ventricular hypertrophy,33 elevated
`Pv caused by pericardial tamponade, or an increase in right or
`left ventricular diastolic pressures.34,35
`The effect of this shift is to decrease CFR and increase FFR
`independent of any associated stenosis.
`A few studies in humans have examined long diastoles
`induced by intracoronary injections of high doses of adeno-
`sine or ATP and demonstrated the curvature at low pressure,
`although zero flow velocity was never reached.36,37 These
`clinical studies are consistent with the animal studies in that
`PzfE is high (30 to 40 mm Hg) when coronary autoregulation
`is present and ⬍20 mm Hg at full vasodilation. The slope of
`the hyperemic diastolic coronary velocity–aortic pressure
`curve was proposed as an index for stenosis severity.36
`However, interpretation of these diastolic aortic pressure–
`coronary flow relations is hampered by the superimposed
`hemodynamic effects of microcirculation and stenosis that
`can be overcome with modern guidewire technology measuring
`pressure and velocity distal to a stenosis simultaneously.3,38
`
`Back Pressure and Coronary
`Microvascular Resistance
`The calculation of resistance requires knowledge of the
`pressure distal
`to the resistance;
`this is called the back
`pressure. It
`is commonly but erroneously assumed that
`coronary back pressure can be deduced from the arterial
`pressure-flow relation by measuring the intercept of this
`relationship with the pressure axis. Resistance must be
`calculated when blood is flowing, whereas the intercept is
`obtained at zero flow, when the reduced pressure has altered
`diameters in the coronary vascular bed sometimes even to the
`point of collapse.
`Studies on microvascular diameters in subendocardium
`and subepicardium have not found such collapse in the
`presence of flow.39 When the heart is overfilled in diastole,
`pressure in epicardial veins may be uncoupled from and
`higher than right atrial pressure and correlate better with left
`ventricular diastolic pressure.40,41 In the examples discussed
`in relation to Figures 4 and 5, Pv has been taken as back
`pressure, assuming normal diastolic left ventricular filling.
`
`Effect of Cardiac Contraction on Coronary
`Pressure-Flow Relations
`Most studies of pressure-flow relations were done during
`diastole or cardiac arrest, and it is important to know how
`cardiac contraction affects these relations. More than 50 years
`ago, Sabiston and Gregg42 observed an increase in coronary
`flow at constant pressure when the heart was arrested by
`
`Figure 4. Interpretation of measured pressure-flow relations
`without collateral vessels. Solid curve represents a measured
`pressure flow relation. Dashed line indicates pressure-flow line
`when resistance is constant at RminN, and dotted line indicates
`pressure-flow line when resistance is constant at RminS. PzfE
`indicates zero-flow pressure after linear extrapolation of the
`straight part of the pressure-flow curve.
`
`straight part is linearly extrapolated, it intercepts the pressure
`axis at a value (PzfE) that is even higher.
`The shape of the solid curve is consistent with microvas-
`cular resistance gradually increasing with decreasing Pd.28
`This increase in resistance is indicated by the difference in
`slope of the dashed and dotted lines in Figure 4 that both start
`at Pd⫽Pv. The dashed line is defined when Pd⫽Pa and
`flow⫽QN and the inverse of its slope equals RminN. The
`dotted line connects to the pressure-flow relation at a lower
`value of Pd as determined by a given stenosis. Hence, the
`inverse of its slope represents RminS and is higher than
`RminN.
`The similarity between Figure 2 and Figure 4 is better
`appreciated by converting Figure 2 into a pressure-flow plot
`by assuming constant values for QN, Pa, and Pv. Then the
`solid line in Figure 2 represents the pressure-flow relation for
`the given Pa and is similar to the extrapolated solid curve in
`Figure 4. An important difference is that the line in Figure 2
`lacks the curvature found in other studies for lower flow
`levels. However, it is clear that collateral flow is not the only
`explanation for the deviation between the pressure and flow
`ratios depicted in Figure 2.
`
`Diastolic Coronary Pressure-Flow Relations
`Flow and pressure decrease during arrest or a long diastole,
`and flow near the origin of a major epicardial artery reaches
`zero when coronary pressure is ⬇40 mm Hg during autoreg-
`ulation and between 5 and 15 mm Hg during maximal
`vasodilation, ie, Pzf exceeds Pv. The pressure-flow lines can
`be remarkably straight, especially at physiological pres-
`sures.29 An elevated Pzf can be found because of capacitive
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`that this increase in resistance takes place predominantly in
`the subendocardium and is related to diastolic time fraction.44
`Such observations agree well with direct in vivo observations
`of small-vessel diameters with a needle microscope.22,39,45,46
`It is likely that mechanical forces will be altered in dyskinetic
`segments and therefore affect minimal resistance.
`The linear fits through the measurements of Figure 2 and
`through the measurements of the beating heart in Figure 5
`both have a non–zero pressure intercept. According to Figure
`1 and assuming that RminS is constant, this intercept must be
`caused exclusively by collateral flow. However, Figure 5
`clearly demonstrates that such intercept is caused by cardiac
`contraction. The difference in the 2 curves in Figure 5 at
`higher pressures cannot be explained by collateral flow
`because of the absence of pressure gradient. Hence,
`the
`assumption that microvascular resistance is constant, which is
`thought to be supported by Figure 2,19 is not warranted.
`The concept that heart contraction impedes myocardial
`perfusion particularly at
`the subendocardium is of great
`clinical importance. The beneficial effect of a ␤-blocker is
`frequently attributed to the reduction in oxygen consumption
`because of decreased heart rate. However, the induced in-
`crease in diastolic time fraction reduces the average time for
`compression of the subendocardial vasculature, which has a
`stronger effect in maintaining a positive balance between
`supply and demand.47
`
`Collateral Flow and Coronary
`Pressure-Flow Relations
`In the dog, well known for its naturally occurring collateral
`vessels in contrast to the pig, Messina et al48 cannulated the
`left main coronary artery and the left circumflex artery
`separately. Pressure in the left circumflex artery was varied to
`obtain the pressure-flow line, while pressure in the left main
`artery was set at different levels. A typical result is shown in
`Figure 6. When pressures were reduced simultaneously in the
`left circumflex and left anterior descending coronary arteries,
`there was no collateral flow, and the curve indicated by the
`open circles was obtained. When pressure was reduced in
`only 1 of the arteries there was collateral flow, and the curve
`indicated by the open triangles was obtained.
`A deviation between the 2 relationships caused by collat-
`eral vessels appears only at
`low perfusion pressures
`(⬍40 mm Hg). At higher, clinically relevant pressures, the
`pressure-flow relations with and without collateral flow are
`indistinguishable, and the extrapolated pressure-flow relation
`with PzfE (curve 1 in Figure 6) is hardly affected. Although
`well-developed collateral vessels could induce a rightward
`shift in the pressure intercept, as suggested by curve 2 in
`Figure 6, the reason for such a shift should be distinguished
`from other possible effects.49
`
`Wedge Pressure and Other Collateral Flow Indices
`The pressure distal to an occlusion has been defined as
`peripheral coronary pressure. Peripheral coronary pressure
`falls gradually after an occlusion because of the loss of
`microvascular volume via the venous vessels32 and ap-
`proaches a more or less stable pressure, referred to as wedge
`
`450
`
`Circulation
`
`January 24, 2006
`
`Figure 5. Effect of cardiac contraction on the coronary
`pressure-flow line.9 At higher pressure the curves in the beating
`and arrested state run parallel. The slopes indicate that coro-
`nary resistance in the beating state is higher than in the arrested
`state.
`
`vagal stimulation, thus demonstrating that cardiac contraction
`impeded coronary perfusion. The classic study of Downey
`and Kirk9 is highly relevant
`to this subject because it
`demonstrates the quantitative effect of cardiac contraction on
`the coronary pressure-flow relation (Figure 5). In their exper-
`iments, the left circumflex artery was perfused at constant
`flow, and the heart was arrested by vagal stimulation at
`different flow levels. Arterial perfusion pressure decreased
`during these periods of cardiac arrest. This pressure drop was
`rather constant at higher flows but decreased at lower flow
`rates, resulting in curved pressure-flow relationships at lower
`pressures. Linear extrapolation of the pressure-flow relations
`in the arrested and beating heart from physiological pressures
`to the pressure axis resulted in a shift of the pressure
`intercept, both above Pv. This shift
`in the extrapolated
`pressure-flow relation between the arrested and beating state
`has nothing to do with collateral flow because it is also
`present at a flow rate at which pressure in the circumflex
`artery equals the Pa and a pressure difference to drive
`collateral flow is absent.43
`The effect of cardiac contraction on coronary resistance
`can be described in a manner similar to the effect of perfusion
`pressure on the resistance in arrested hearts, and the 2 thin
`arrows in Figure 5 demonstrate the increased resistance. The
`slope of the line connecting Pv with the pressure-flow
`relations at the same flow rate is smaller for the beating than
`the arrested state. Hence, minimal coronary resistance has
`increased by contraction of the heart due to compression of
`intramural vessels. Microsphere studies have demonstrated
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`between collateral and wall stress effects on Pw without a
`direct measure of collateral flow.
`
`Effect of Stenosis on Hyperemic Microvascular
`Resistance in Humans
`The question related to constancy of coronary resistance has
`become relevant because conflicting conclusions have been
`published recently. In agreement with the aforementioned
`analysis, Verhoeff et al2 calculated hyperemic microvascular
`resistance as Pd divided by flow velocity. They concluded
`that hyperemic microvascular resistance is elevated distal to a
`stenosis because of the lower perfusion pressure caused by
`the pressure loss across the stenosis and reported that it was
`reduced to a value even lower than in a nondiseased reference
`vessel of the same heart when perfusion pressure was restored
`after the lesion was treated. According to Aarnoudse et al1
`and Fearon et al,4 such a conclusion is the result of an
`“improper” definition of minimal coronary resistance, and the
`effect of collateral flow as derived from Pw should be
`incorporated in the calculation of minimal microvascular
`resistance to render it constant regardless of perfusion
`pressure.
`This argument can be refuted by pointing out that (1) there
`is no proof that Pw reflects collateral flow, as outlined above;
`(2) a constant hyperemic microvascular resistance is highly
`unlikely, as was shown by a large number of physiological
`studies with more direct measurements (eg,
`references
`11,12,22,24,27,28,39,41,44, and 46); and (3) hyperemic mi-
`crovascular resistance distal to a stenosis did not correlate
`with a collateral index, Pw/Pa, in the study of Verhoeff et al.2
`If the assertion of hyperemic microvascular resistance being
`independent of hemodynamic factors were correct, then many
`physiological concepts developed over the course of time
`would not apply in humans.
`From the data of Aarnoudse et al,1 a pressure-flow relation
`can be derived demonstrating similarity with those represent-
`ed in Figures 5 and 6. The 3 data points in Figure 7 are from
`Table 2 in the report of Aarnoudse et al and represent the
`uncorrected average surrogate flow values derived at 3
`different distal pressures. The lowest measured pressure in
`this curve is 40 mm Hg, and, as shown in Figure 6, it was only
`below this pressure that collateral flow was effective in the
`dog study.48 In Figure 7, the extrapolated intercept with the
`pressure axis is ⬇25 mm Hg, which is similar to the studies
`of Messina et al48 (Figure 6) and Downey and Kirk9 (Figure
`5). A curve with an arbitrary shift of 22 mm Hg (assuming a
`mean left ventricular pressure of 44 mm Hg) is included in
`this figure for comparison with Figure 5. This curve reflects
`the theoretical pressure-flow relation at cardiac arrest for this
`patient population. Hence, comparison between Figures 7 and
`5 shows that the extrapolated intercept in Figure 7 may be to
`a large degree due to the effect of cardiac contraction on the
`intramural vessels rather than collateral flow, as discussed
`above.
`We agree that a measurement of Pw of ⬇40 mm Hg, as
`some data points show in the study of Aarnoudse et al,1 is
`most
`likely related to collateral function. However,
`the
`aforementioned analysis suggests that values of Pw
`⬍25 mm Hg are related to factors determined by compression
`
`Figure 6. Effect of collateral vessel flow on coronary pressure-
`flow lines. Left main stem minus left circumflex artery and left
`circumflex artery were perfused independently. A collateral ves-
`sel pressure gradient is generated when the left main pressure
`is kept constant at 100 mm Hg, while left circumflex artery pres-
`sure is lowered (data from Messina et al48), but collateral vessel
`flow effect is only apparent at left circumflex artery pressure
`⬍40 mm Hg. Line 1 is the extrapolation of measured data; line 2
`represents a possible relation for better-developed collateral
`vessels. Pw0 indicates wedge pressure without collateral ves-
`sels; PwC, wedge pressure with collateral vessels; PzfE, extrap-
`olated zero-flow pressure; PzfC, extrapolated zero-flow pressure
`in the presence of better-developed collateral vessels; and Plcx,
`pressure in the left circumflex artery.
`
`pressure (Pw). In the absence of collateral vessels, Pw will
`fall to a lower level but will still exceed Pv.
`A positive correlation was found between Pw/Pa and
`anterograde coronary flow velocity after coronary occlu-
`sion.50 However, without collateral flow Pw/Pa still equaled
`on average 0.2. Similarly, when collateral flow was scored by
`the degree of blush of contrast arriving in the perfusion area
`of an occluded vessel, a Pw of approximately the same
`amount of 25 mm Hg was found in patients with complete
`absence of any collateral flow.51 Similar values of Pw in the
`absence of detectable collateral flow were measured by our
`own group using a variety of techniques.52,53 These clinical
`studies corroborate the findings from animal studies that a Pw
`⬍25 mm Hg is not
`likely a measure of collateral flow.
`Therefore, using pressure alone as an index of collateral
`flow54 is likely to result in misinterpretation of the collateral
`flow contribution.
`In the determination of Pw, it is important to wait for a
`stable value. In this waiting time the cessation of flow will
`start to affect cardiac function regionally, leading to increased
`diastolic stress levels and thereby higher Pw values.55,56
`Obviously, this change in regional cardiac function is less
`with well-developed collateral vessels, which also results in
`higher values for Pw, and it
`is difficult
`to differentiate
`
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`CATHWORKS EXHIBIT 1007
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`inducible
`the accuracy of this index to predict
`patients,
`ischemia as determined by SPECT was significantly higher
`than that of FFR and CFVR. The prediction was particularly
`better in the subgroup in which CFVR and FFR produced
`discordant results.59 HSR is not completely independent of
`microvascular resistance because of the nonlinear relation-
`ship between pressure drop and flow velocity. However,
`because pressure drop and flow change in the same direction,
`the influence of altered hyperemic microvascular resistance
`on HSR is minimized compared with single-signal indices. It
`is therefore a pity that in the recent literature FFR is used as
`an independent variable, thereby obscuring the role of abso-
`lute pressure on microvascular resistance.
`
`Combined Measurements of Pressure and
`Flow Velocity
`Technical developments have produced a guidewire equipped
`with both a pressure and Doppler velocity sensor that allows
`simultaneous assessment of both stenosis and microvascular
`hemodynamics. In addition to the assessment of HSR as a
`hy