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 � blood pressure � collateral circulation � coronary disease � hemodynamics
Coronary physiology has a rich history, founded onnumerous 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
446
Basic Science for Clinicians
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
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:
(1) FFRmyo� QQN
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 � PvRminS ,
where RminN and RminS are the minimal resistances for the
distal microcirculation without and with a stenosis in the
supplying artery, respectively.
(3)
Therefore,
Q
QN �
Pd � Pv
RminN
Pa � Pv
RminS
�
Pd � Pv
Pa � Pv �
RminN
RminS
so that FFRmyo�(Pd�Pv)/(Pa�Pv) is true only if
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
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.
Spaan et al Coronary Physiological Indices 447
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-
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.
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
448 Circulation January 24, 2006
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
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