(Circulation. 2000;101:1840.)
© 2000 American Heart Association, Inc.
Basic Science Reports |
Pressure-Derived Fractional Flow Reserve to Assess Serial Epicardial Stenoses
Theoretical Basis and Animal Validation
From the Cardiovascular Center, Aalst, Belgium; Department of Cardiology, Catharina Hospital and Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, Netherlands; Department of Physiology, University of Louvain, Brussels, Belgium; and the Weatherhead PET Center for Preventing and Reversing Atherosclerosis, Department of Medicine, University of Texas Medical School, Houston.
Correspondence to Bernard De Bruyne, MD, PhD, O.L.V.-Hospital, Cardiovascular Center, 164, Moorselbaan, 9300 Aalst, Belgium. E-mail bernard.de.bruyne{at}olvz-aalst.be
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Abstract |
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 Top Abstract IntroductionMethodsResultsDiscussionAppendix 1References |
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Background—Fractional flow reserve (FFR) is an index of stenosis severity validated for isolated stenoses. This study develops the theoretical basis and experimentally validates equations for predicting FFR of sequential stenoses separately.
Methods and Results—For 2 stenoses in series, equations were derived to predict FFR (FFRpred) of each stenosis separately (ie, as if the other one were removed) from arterial pressure (Pa), pressure between the 2 stenoses (Pm), distal coronary pressure (Pd), and coronary occlusive pressure (Pw). In 5 dogs with 2 stenoses of varying severity in the left circumflex coronary artery, FFRpred was compared with FFRapp (ratio of the pressure just distal to that just proximal to each stenoses) and to FFRtrue (ratio of the pressures distal to proximal to each stenosis but after removal of the other one) in case of fixed distal and varying proximal stenoses (n=15) and in case of fixed proximal and varying distal stenoses (n=20). The overestimation of FFRtrue by FFRapp was larger than that of FFRtrue by FFRpred (0.070±0.007 versus 0.029±0.004, P<0.01 for fixed distal stenoses, and 0.114±0.01 versus 0.036±0.004, P<0.01 for fixed proximal stenoses). This overestimation of FFRtrue by FFRapp was larger for fixed proximal than for fixed distal stenoses.
Conclusions—The interaction between 2 stenoses is such that FFR of each lesion separately cannot be calculated by the equation for isolated stenoses (Pd/Pa during hyperemia) applied to each separately but can be predicted by more complete equations taking into account Pa, Pm, Pd, and Pw.
Key Words: flow reserve • stenosis
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1References |
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Coronary pressure–derived fractional flow reserve (FFR) is a measure of coronary stenosis severity. FFR is the ratio of hyperemic myocardial blood flow in the presence of a stenosis to hyperemic flow in the absence of stenosis. Stated another way, FFR is the fraction of hyperemic flow that is preserved despite the presence of a stenosis in the epicardial coronary artery. This ratio of hyperemic flows with and without a single stenosis can be derived from the ratio of mean distal coronary pressure (Pd) to mean aortic pressure (Pa) recorded simultaneously under conditions of maximum hyperemia.1 2 FFR has been shown to be valid in patients with stable angina pectoris under widely varying hemodynamic conditions3 4 and to be clinically useful for diagnostic and interventional purposes.5 6 7 8 9 10 11 12 13 14
In humans, however, coronary atherosclerosis is diffuse, and coronary arteriograms frequently demonstrate several consecutive stenoses along the same epicardial artery, the severities of which need to be determined separately. In case of 2 consecutive stenoses, the fluid dynamic interaction between the stenoses alters their relative severity and complicates determination of FFR for each stenosis separately from the simple ratio of Pd/Pa for a single stenosis. Consequently, for stenoses in series, FFR determined by this simple ratio for a single stenosis may not predict to what extent a proximal lesion will influence myocardial flow after complete relief of the distal stenosis, and vice versa.
Therefore, in the present study, theoretical equations were developed for 2 serial stenoses to predict the FFR of each stenosis separately as if the other stenosis were absent. In addition, an animal model of sequential stenoses was used to validate these theoretical equations for determining FFR of each of 2 serial stenoses with direct clinical applicability.
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Methods |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1References |
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Mathematical Model
As illustrated in Figure 1
, Pa is the
pressure proximal to the first stenosis,
Pm is the pressure between the two
stenoses, and Pd is the pressure distal
to the second stenosis. For simplicity, it is assumed that the
resistances of the microvasculature are minimal and that the central
venous pressure (Pv) is close to zero.
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Superficially, the apparent FFR of A and B
(FFRapp) can be calculated by dividing the
pressure distal to stenosis A or B by the pressure proximal to
stenosis A or B, respectively, as
follows:
 | (1) |
 | (2) |
 | (3) |
 | (4) |
When stenosis B is actually physically absent, the actual FFR
of stenosis A [FFR(A)true], and when
stenosis A is actually physically absent, the actual FFR of
stenosis B [FFR(B)true] can be
calculated as follows:
 | (5) |
 | (6) |
Animal Instrumentation
After premedication with 0.1 mg fentanyl, 5.0 mg droperidol, and
0.5 mg atropine IM, 5 mongrel dogs (weight 38 to 43 kg) were
anesthetized with 7 mg/kg IV sodium thiopenthal, intubated, and
ventilated with oxygen-enriched air with a respirator (Drager Spiromat
650). General anesthesia was sustained with isoflurane gas
(1.5% to 2 vol%). A left thoracotomy was carried out in the fifth
intercostal space, and the pericardium was incised. The proximal left
circumflex artery was dissected free. A perivascular ring-mounted
20-MHz pulsed-Doppler transducer (Triton) was placed around the
artery, and 2 circular hydraulic cuff occluders (In Vivo Metric) were
implanted just distal to the Doppler probe and 2 to 3 cm more
distal, respectively. The occluders were placed so that there was no
arterial branch between the stenoses. A femoral
artery was dissected free, and a 6F left Amplatz coronary
guiding catheter was introduced into the right femoral artery and
advanced under fluoroscopy into the ostium of the left main
coronary artery. Through this guiding catheter, two 0.014-in
sensor-tipped high-fidelity pressure guidewires (Pressure Wire, Radi
Medical System) were advanced and positioned distal to the locations of
the first and second balloon occluder, respectively. ECG, phasic and
mean coronary flow velocity signal, phasic and mean
arterial pressure (Pa), and phasic
and mean coronary pressures recorded by both pressure
guidewires (Pm and Pd,
respectively) were recorded continuously on an 8-channel
recorder (Gould ES 1000) and stored digitally on a computer system
(Notocord), which allowed offline analysis of all signals.
After completion of the surgical preparation, the animals were allowed
to stabilize for 30 minutes before the study protocol was begun. The
investigations conformed to the guidelines of the committee for animal
research of the Belgian Fonds de la Recherche Scientifique
Médicale.
Experimental Protocol
At first, maximum hyperemia was induced by continuous
intravenous infusion of adenosine, from 150 to 300
µg · kg-1 ·
min-1. After a steady-state hyperemia
had been achieved, a 20-second occlusion of the coronary artery
was performed by inflation of the proximal occluder to determine
coronary wedge pressure (Pw) and to
verify that no additional, postocclusional hyperemia could be
elicited. In 1 dog, no maximum hyperemia could be achieved by
adenosine, and an additional infusion of dobutamine
20 µg · kg-1 ·
min-1 was started to further increase blood flow
until the presence of a steady-state maximum hyperemia was
confirmed as described above. Next, phasic and mean pressures were
recorded by the guiding catheter (Pa) and by
both pressure guidewires (Pm, coronary
pressure between both occluders, and Pd,
coronary pressure distal to the distal occluder). Thereafter,
different degrees of proximal and distal stenosis were induced,
as follows: at first, a mild stenosis was induced by the
proximal occluder (stenosis A in Figure 1
), guided by the
pressure signal. Whereas this proximal stenosis remained
constant, the distal occluder was inflated to create mild, moderate,
severe, and very severe stenoses, respectively, guided by the
pressure signals. It was aimed at inducing the stenosis in such
a way that the classifications mild, moderate, severe, and very severe
corresponded to transstenotic hyperemic gradients
of 
25%, 50%, 75%, and 90% of the pressure gradient as observed
at total coronary occlusion. Stenoses with a pressure
gradient of <5 mm Hg were avoided. Next, all stenoses
were relieved, and after all signals had stabilized again, a moderate
stenosis was induced in the proximal occluder, followed by the
same sequence of distal stenoses as described above. This
sequence of induction of different distal stenoses was repeated
for a severe and finally for a very severe proximal stenosis.
After this first series, Pw as well as the
presence of ongoing maximum hyperemia was checked again, and
the second series of the sequences was started. This time, at first a
mild stenosis was induced by the distal occluder
(stenosis B in Figure 1), after which the proximal
lesion was varied stepwise from mild to moderate to severe and to very
severe. After release of all stenoses, this was repeated for a
fixed moderate, severe, and very severe proximal lesion, respectively.
Figure 2 illustrates these pressure tracings.
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Data Processing and Statistical Analysis
To investigate the influence of a stenosis B on a given
stenosis A, 71 combinations of a fixed stenosis A and a
variable stenosis B were obtained. For each of these
combinations, FFR(A)app and
FFR(A)pred were compared with
FFR(A)true by linear regression analysis.
To investigate the influence of a stenosis A on a given
stenosis B, 84 combinations of a fixed stenosis B and a
variable stenosis A were created. For each of these
combinations, FFR(B)app and
FFR(B)pred were compared with
FFR(B)true by linear regression analysis.
For each comparison, a Bland-Altman plot was given.15
Paired t tests and 
2 tests were
used when appropriate. Values of P>0.05 were considered
nonsignificant.
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Results |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1References |
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Baseline Hemodynamics
Mean aortic pressure was 88±21 mm Hg (range 71 to 125 mm Hg), and heart rate was 71±14 bpm (range 64 to 129 bpm) at rest. Mean blood pressure decreased significantly to 78±19 mm Hg (range 63 to 118 mm Hg) and heart rate increased significantly to 125±26 bpm (range 76 to 158 bpm) during postocclusion hyperemia. Yet, during pharmacologically induced hyperemia, mean pressure and heart rate remained unchanged throughout the experiments in each dog. The ratio of postocclusional to pharmacologically induced hyperemic blood flow velocities was 1.12±0.14 (range 0.98 to 1.25), suggesting that the dosages of adenosine used in each animal induced maximum arteriolar vasodilation.
Relation Between FFRtrue and
FFRapp
A total of 15 distal stenoses (stenoses B) were
created. For each of them, a mean of 4.7 proximal stenoses
(stenoses A) were superimposed to test their influence on the
calculation of FFR on stenosis B. Figure 3A shows, in the 71 combinations
of stenoses (variable stenosis A and fixed
stenosis B) analyzed in all animals, the plots of the
relation between the FFR of lesion B alone
[FFR(B)true] versus the apparent value of FFR
[FFR(B)app] of the same lesion B when a
progressively increasing level of stenosis A is created
upstream. A large scatter is observed in the plot of the relationship
between FFR(B)true and
FFR(B)app. As expected from the theory, the
corresponding Bland-Altman plot (Figure 3B) shows that
FFR(B)app systematically overestimates
FFR(B)true and that there is an inverse
correlation between this overestimation and
FFR(B)true (r=-0.39,
P<0.01).
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Similarly, a total of 20 proximal stenoses (stenoses A)
were created. For each of those, a mean of 4.2 distal stenoses
(stenoses B) were created to test their influence on the
calculation of FFR on stenosis A. Figure 3C shows, in
the 84 combinations of stenoses (fixed stenosis A and
variable stenosis B) analyzed in all animals,
the plots of the relation between the FFR of lesion A alone
[FFR(A)true] versus the apparent value of FFR
[FFR(A)app] of the same lesion A when a
progressively increasing level of stenosis B is created
downstream. The corresponding Bland-Altman plot (Figure 3D) shows that
FFR(A)app significantly overestimates
FFR(A)true and that there is an inverse
correlation between this overestimation and
FFR(A)true (r=-0.62,
P<0.01).
Relation Between FFRtrue and
FFRpred
In investigating the influence of a varying stenosis A on
a given, fixed, stenosis B, a close correlation was found
between FFR(B)true and
FFR(B)pred
(r2=0.95, Figure 4A). The Bland-Altman plot (Figure 4B) shows a small mean difference (+0.03±0.04) without
systematic overestimation or underestimation of
FFR(B)true by FFR(B)pred.
In investigation of the influence of a varying stenosis B on a
given fixed stenosis A, a close correlation
(r2=0.95) was found between
FFR(A)true and FFR(A)pred
(Figure 4C). The Bland-Altman plot (Figure 4D) indicates
a small overestimation (+0.040±0.066).
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Relation Between Pw and FFRapp Versus
FFRpred
No relationship was found between the level of coronary
occlusive pressure (wedge pressure, Pw) and the
accuracy of FFRapp versus
FFRpred in determining
FFRtrue.
Accuracy of FFRapp and FFRpred in
Determining FFRtrue
Figure 5 depicts the absolute
difference between FFRapp and
FFRtrue and between FFRpred
and FFRtrue in the 2 experimental settings as
described above, ie, fixed stenosis B and varying
stenosis A (left) and fixed stenosis A and varying
stenosis B (right). In both settings, the overestimation or
underestimation of FFRtrue by
FFRpred is significantly smaller than the
corresponding overestimation or underestimation of
FFRtrue by FFRapp. For a
fixed stenosis B, the absolute error in FFR was >0.1 in 22%
of measurements for FFR(B)app and in 5% of
measurements for FFR(B)pred (P<0.01).
For a fixed stenosis A, the absolute error in FFR was >0.1 in
45% of the measurements of FFR(A)app and 9% of
measurements for FFR(A)pred (P<0.01).
The error in calculating FFR for a stenosis by use of the
simple Pd/Pa ratio
(FFRapp) was significantly larger in the presence
of a second more proximal stenosis than for a second more
distal stenosis. The greatest errors in
FFRapp were found for milder downstream
stenoses when the upstream stenosis was more
severe.
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Discussion |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1References |
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For serial epicardial stenoses without intervening arterial branches, the equation of FFR (Pd/Pa, when central venous pressure is neglected) remains valid for determining the hemodynamic consequences of both stenoses together. However, the present study confirms that this simple ratio cannot be applied to predict the FFR of each stenosis separately as if the other were removed. In contrast, the individual FFR of each stenosis separately can be predicted by different equations from Pa, pressure between the 2 stenoses (Pm), Pd, and Pw recorded during maximum hyperemia. The data also suggest that FFR calculated as the Pd/Pa ratio for the stenosis has a greater error in the presence of a second distal stenosis than in the presence of a second proximal lesion.
Importance of Maximum Transstenotic Flow
Pressure-derived FFR is defined as the ratio of hyperemic
flow in a stenotic territory expressed as a fraction of what it
would be in the hypothetical case that the epicardial stenosis
were absent. This ratio of 2 flows can be derived, during maximum
hyperemia, from the ratio of their respective driving
pressures. An essential prerequisite for the calculation of
pressure-derived FFR is the achievement of maximum
transstenotic flow. When only 1 discrete stenosis
is present, pharmacologically induced microvascular vasodilation
will lead to maximum transstenotic flow for a given lesion
in a given patient. For that reason, FFR tells us exactly to what
extent hyperemic flow is limited by the presence of an
epicardial stenosis and, conversely, to what extent
hyperemic flow will increase after the conductance of the
epicardial vessel is restored.
In contrast, when a second stenosis is present along the same epicardial vessel, flow through 1 stenosis will be submaximal because of the second stenosis, even during vasodilation of the microvasculature. The extent to which both stenoses influence each other is unpredictable from the simple ratio of the pressures distal and proximal to each individual stenosis.
Importance of Collateral Flow
In patients with severe coronary artery disease,
myocardial perfusion depends both on antegrade flow through the
stenotic epicardial artery and on collateral flow. A >2-fold
increase of myocardial perfusion can be provided solely by
collaterals.16 Myocardial FFR takes into account the
contribution of collateral circulation to hyperemic myocardial
flow, because the distal coronary pressure is determined by
aortic pressure and by the extent of collateral circulation in case of
isolated epicardial stenosis. Measurements of
Pw obtained during coronary occlusion
determine the separate contributions of antegrade flow and of
collateral flow to total hyperemic myocardial
perfusion.1 In case of multiple stenoses along the
same coronary artery, collateral flow will influence both
Pw and Pm. The extent to
which collateral flow will influence Pm depends
on the severity of the second stenosis. Therefore, the value of
Pw cannot be neglected and was incorporated into
the equations derived in the Appendix.
Clinical Implications
Because coronary atherosclerosis is
commonly diffuse, the occurrence of 
2 stenoses in 1
epicardial vessel is frequent. Determining the independent contribution
of each stenosis to the total decrease in conductance of the
epicardial vessel may be useful for clinical decision-making. With the
pressure-measuring guidewire,17 18 it is common to measure
a significant residual hyperemic pressure gradient after
optimal stenting of a stenosis. This residual pressure gradient
is commonly a result of another proximal or distal stenosis,
the severity of which was unmasked by elimination of the resistance of
the stented segment. Objective quantification of the functional
significance of a stenosis of undetermined severity at
angiography may help in guiding the intervention. In investigation of 1
stenosis out of several in series by pressure measurements
before an intervention, the worst stenosis, as indicated by the
largest pressure drop during hyperemia, may not occur where it
would have been expected from angiography. In that case, the equations
for FFRpred can be applied to each
stenosis rather than the simple ratio
Pd/Pa being applied to each
stenosis to determine the severity of each. In clinical
practice, the measurements of Pa,
Pm, and Pd can be obtained
during a simple pullback of the pressure sensor from the distal to the
proximal part of the vessel under maximum hyperemia.
Limitations
These experimental data should be extrapolated to humans with
caution. First, the collateral circulation in humans with chronic
coronary artery disease is most likely more developed than in a
canine model. Therefore, in humans, the influence of
Pw is probably more pronounced than in the
present study and must be included in the equations for FFR in case
of serial stenoses.
Second, Pw can be obtained only during balloon coronary occlusion, which constitutes a practical limitation.
Third, when 1 stenosis is very tight, so that the pressure distal to that stenosis is very close to Pw, very small inaccuracies in measuring Pw might induce large errors in FFRpred. However, this limitation is somewhat academic, because a very tight stenosis will be dilated anyway, and the second stenosis will be evaluated after treatment of the first stenosis.
Finally, for the 2 stenosis equations to be applicable, there should be no major arterial branch between the 2 stenoses being investigated. If there is an arterial branch between the 2 stenoses, the nonstenotic low-resistance branch increases flow through the first stenosis, thereby causing a greater pressure drop across the first stenosis than would occur without the intervening arterial branch. With a lower pressure between the stenoses, flow through the distal stenosis would be reduced in the presence of an arterial branch compared with that without the side branch. Thus, the side branch between the stenoses would divert a "steal" flow away from the second stenosis, so that the flow through the second stenosis would not be maximal. The pressure gradient across the second stenosis would therefore be less than it would have been in the absence of the side branch. Because the flow through the second stenosis would be reduced in the presence of a side branch, removal of the distal stenosis would result in only limited increased flow capacity through the first stenosis.
With several serial stenoses and intervening branches, this phenomenon of "branch steal"19 cumulatively along the length of a branching coronary artery may cause a fall in flow at the apex to below normal resting flow after dipyridamole, with resulting ischemia. In diffuse coronary artery disease, this phenomenon is seen as a longitudinal base-to-apex perfusion gradient on dipyridamole PET perfusion imaging.19 For multiple stenoses or diffuse disease with intervening arterial branches, calculation of flow reserve (or FFR) at each branch point becomes complex and requires fully developed fluid dynamics equations accounting for the myocardial mass supplied by each branch as described previously. For these complex branch-stenosis interactions, both pressure and flow velocity measurements may be necessary for assessing the functional severity of multiple stenoses and/or diffuse disease.
Conclusions
The present study demonstrates for interventionalists that for
multiple stenoses in the same vessel, the
hemodynamic assessment of 1 stenosis and the
potential benefit of angioplasty is significantly influenced by the
presence of the second stenosis. The practical clinical
application of these new concepts for interventional decisions in
patients with multiple stenoses and diffuse disease are now
being studied.
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Acknowledgments |
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The secretarial expertise of Josefa Cano is warmly acknowledged.
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Footnotes |
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Dr K. Lance Gould is the Martin Bucksbaum Distinguished Professor and Director of the Weatherhead PET Center for Preventing and Reversing Atherosclerosis.
Guest Editor for this article was Morton J. Kern, MD, St Louis University Health Sciences Center, St Louis, Mo.
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Appendix 1 |
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TopAbstractIntroductionMethodsResultsDiscussionAppendix 1References |
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In this Appendix, the equations for predicting myocardial FFR of each of 2 sequential stenoses as if the other stenosis were removed will be derived mathematically from the initially measured pressures Pa, Pm, Pd, and Pw. These predicted values of myocardial FFR are called FFR(A)pred and FFR(B)pred for the proximal (A) and distal (B) stenoses, respectively. The terminology is consistent with the original article on the concept of FFR1 and is further clarified in Figure 1
:
Pa, Pm,
Pd, and Pw indicate mean
aortic pressure, coronary pressure between the 2
stenoses, coronary pressure distal to the second
stenosis, and coronary wedge pressure (distal
coronary pressure during total coronary occlusion) at
that particular Pa, all measured at maximum
coronary hyperemia before any intervention.
Pa', Pm',
Pd', and Pw' indicate the
corresponding pressures after 1 of the 2 lesions has been
completely removed.
After the proximal stenosis A has been removed,
Pm' equals Pa', and after
the distal stenosis B has been removed,
Pm' equals Pd'. True
measured FFR of 1 stenosis after physical removal of the other
stenosis in the animal model is indicated by
FFR(A)true and FFR(B)true,
respectively, and is equal to
Pd'/Pa' . 
P(A) and
P(B) indicate the hyperemic pressure gradients across
stenoses A and B, respectively, before any intervention, and
P'(A) and P'(B) represent the same gradients after
elimination of stenoses B and A, respectively.
Qcor and Q'cor indicate maximum coronary blood flow before and after elimination of 1 or both stenoses, and QNcor and QN'cor indicate the normal values of Qcor and Q'cor, respectively (ie, those values if no stenosis were present). FFRcor and FFR'cor indicate FFR of the coronary artery before and after elimination of 1 of the 2 stenoses.
Influence of Removal of Distal Stenosis B on
Hemodynamics of Proximal Stenosis A
Suppose that stenosis B is eliminated. In that case,
Pm'=Pd' and
FFR(A)true equals
Pm'/Pa' or
Pd'/Pa'.
How to predict FFR(A)true from Pa, Pm, Pd, and Pw?
Because all measurements are performed at maximum vasodilation of the
coronary circulation, the resistances are constant, and
therefore
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It has been proved theoretically and validated experimentally1 that Pw/Pa=Pw'/Pa'. Therefore, PwPa'=Pw'Pa, and those terms can be cancelled in the expression above.
By rearrangement of the remaining terms, the following equation is
obtained:
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Division of both the right and left terms by
Pa' gives
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and therefore,
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Note: This emphasizes that even in the absence of collaterals, the distal lesion influences the hemodynamics of the proximal lesion.
(d) Total occlusion of A:
Pm=Pd=Pw.
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Influence of Removal of Proximal Stenosis A on
Hemodynamics of Distal Stenosis B
Suppose again that stenosis A will be completely
eliminated. In that case,
Pm'=Pa' and
FFR(B)true equals
Pd'/Pm'=Pd'/Pa'.
How to predict FFR(B)true from Pa, Pm, Pd, and Pw?
As above, it is proved that
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PmPdPw.
Therefore,
(Pm-Pw)(Pd-Pw),
and as a consequence,
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In that case,
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In that case, FFR(B)pred=1=FFR(B). (c) No collaterals: Pw=0.
In that case,
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In that case,
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Received June 10, 1999; revision received November 5, 1999; accepted November 15, 1999.
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