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SUPPLEMENT to: Does the instantaneous wave-free ratio (iFR) approximate the
fractional flow reserve (FFR)?
AUTHORS AND AFFILIATIONS: Nils P. Johnson, M.D., M.S.a; Richard L. Kirkeeide, Ph.D.a;
Kaleab N. Asrress, M.A., B.M., B.Ch.b; William F. Fearon, M.D.c; Timothy Lockie, M.B., Ch.B.,
Ph.D.b,d; Koen M. J. Marques, M.D., Ph.D.e; Stylianos A. Pyxaras, M.D.f; M. Cristina Rolandi,
M.Sc.g; Marcel van ’t Veer, M.Sc., Ph.D.h,i; Bernard De Bruyne, M.D., Ph.D.f; Jan J. Piek, M.D.,
Ph.D.d; Nico H. J. Pijls, M.D., Ph.D.h,i; Simon Redwood, M.D.b; Maria Siebes, Ph.D.g; Jos A. E.
Spaan, Ph.D.g; K. Lance Gould, M.D.a
a. Weatherhead PET Center For Preventing and Reversing Atherosclerosis, Division of
Cardiology, Department of Medicine, University of Texas Medical School and Memorial
Hermann Hospital, Houston, Texas.
b. Cardiovascular Division, King's College London BHF Centre of Research Excellence, and
the NIHR Biomedical Research Centre at Guy's and St. Thomas' NHS Foundation Trust,
The Rayne Institute, St. Thomas' Hospital, London, United Kingdom.
c. Division of Cardiovascular Medicine, Stanford University Medical Center, Stanford,
California
d. Department of Cardiology, Academic Medical Center, University of Amsterdam,
Amsterdam, the Netherlands.
e. Department of Cardiology, VU University Medical Center, Amsterdam, the Netherlands.
f.
Cardiovascular Center Aalst, Aalst, Belgium.
g. Department of Biomedical Engineering and Physics, Academic Medical Center, University
of Amsterdam, Amsterdam, the Netherlands.
h. Department of Cardiology, Catharina Hospital, Eindhoven, the Netherlands.
i.
Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven,
the Netherlands.
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This supplement provides complete details regarding the pressure-flow basis for the instantaneous
wave-free ratio (iFR) approximation to the fractional flow reserve (FFR), our Monte Carlo
simulation, multi-center data sources and associated clinical variables, statistical methods, and
additional results.
SUPPLEMENTAL BACKGROUND
Historical Context
Supplement Figure F1 contrasts schematically the fundamental relationship of relative distal
pressure between diastole and the whole cardiac cycle. Under the assumption that aortic pressure
and heart rate are constant, the upper, black line shows relative distal pressure over the entire
cardiac cycle and the lower, red line during the diastolic portion of the cardiac cycle. Such data can
be acquired experimentally during simultaneous pressure and flow measurements beginning
before the start of vasodilator infusion or injection and ending after reaching hyperemia.R1 Below
resting flow the curves are dashed to indicate values that would be observed if resting flow could
be lowered further, for example by administering beta-blockers to decrease metabolic demand.
Above hyperemia the curves are dashed to indicate predicted values if peak flow could be
augmented, for example using a more potent vasodilator (such as papaverine or a large dose of
dipyridamole or adenosine) or beginning intra-aortic balloon pump counterpulsation. Practically,
coronary flow velocity serves as an acceptable surrogate for volumetric flow as regular
intracoronary nitroglycerine dosing keeps the cross-sectional area constant across flow conditions.
Five conceptual points have been proposed as invasive physiologic metrics for stenosis severity,
and are marked in Supplement Figure F1:

Rest gradient, whole cardiac cycle: Even as early as the first report of coronary
angioplasty in 1979,R2 resting gradients across a stenosis before and after PCI were used
as an indicator of procedural success (see its Figures #2 and #3).
2

Hyperemic gradient, whole cardiac cycle: Following the development of papaverine and
adenosine, the ability to produce reliable, sustained, and maximal vasodilation allowed for
the first description of mean hyperemic relative distal pressure in 1993, termed FFR.R3

Hyperemic gradient, diastole: Since coronary flow is typically higher during diastole,
pressure-flow relationships during this portion of the cardiac cycle have long been of
interest. However, it was not until work in 2000 that diastolic FFR (d-FFR) was specifically
proposed.R4 As anticipated by our Supplement Figure F1 and shown in their Table #1, dFFR is lower than FFR, especially in the presence of a significant stenosis. Diastolic
pressure in that report was taken from the peak of diastolic distal coronary pressure minus
diastolic left ventricular pressure up to the sudden drop of the pressure gradient at the time
of myocardial contraction (see its Figures #2 through #4).

Arbitrary flow level, diastole: In an attempt to standardize for varying levels of hyperemic
flow, literature in 2006 introduced the coronary pressure gradient measured from mid-toend diastole (taken from mid-diastole until atrial contraction) at an arbitrary 50 cm/sec,
termed the dpv50.R5 One limitation with this selected flow level is that it may not be
physiologic in all patients.

Rest gradient, diastole: Recent work has proposed iFR,R6 which essentially uses the
diastolic resting relative distal pressure (measured from 25% after the dicrotic notch on the
aortic tracing until 5 ms before systole). As can be seen by the above historical sequence of
points shown in Supplement Figure F1, iFR proposed in 2011 has come “full circle” from the
resting gradients proposed by Andreas Grüntzig and colleagues in 1979, albeit now able to
isolate diastole more easily due to technologic advances.
Qualitative Expectations
Generally, the agreement of iFR and FFR hinges on diastolic resting and mean hyperemic
conditions being similar. Several general hemodynamic situations influencing agreement can be
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anticipated as summarized in Supplement Table T1. Hemodynamics during the diastolic interval of
the cardiac cycle are most similar to the beat average at slow heart rates, distal to a severe
stenosis, with low pulse pressure or high diastolic pressure, and as more of diastole is included
(compare the three portions of “diastole” above considered in prior reports.R4-R6)
Supplement Figure F1 depicts a horizontal dashed line connecting the iFR and FFR points,
indicating the special case when they become equal. Three types of perturbations may prevent this
equality, as shown in Supplement Figure F2. First, the shaping function  (which reflects the
pulsatility of flow and pressure waveforms) may move the iFR curve away from the special case,
as shown in Supplement Figure F2A, due to the result of several changes summarized in
Supplement Table T1. Second, as demonstrated in Supplement Figure F2B, rest flow may be
unexpectedly low or high given the sizable variability in baseline myocardial demand. Third, as
depicted in Supplement Figure F2C, hyperemic peak flow may be unexpectedly low or high due to
a variety of factors. Note that for a mild stenosis, both curves in Supplement Figure F1 are very flat,
as no significant pressure gradient exists regardless of the amount of flow. We subsequently
provide below a rigorous mathematical understanding for the special case when iFR equals FFR.
Qualitative Expectations
Generally, the agreement of iFR and FFR hinges on the similarity between diastolic resting
and mean hyperemic conditions. Several general hemodynamic situations can therefore be
anticipated.
As heart rate decreases, diastole accounts for a growing majority of the cardiac cycle.
Diastole approximates the whole cardiac cycle best at slow heart rates. The iFR curve in
Supplement Figure F1 will move towards the FFR curve as heart rate slows, assuming all other
factors remain constant. Similarly, as coronary flow in diastole falls to the levels seen in systole, the
difference between diastole and the whole cardiac cycle diminishes. Therefore, diastole
approximates the whole cardiac cycle best when its flow is most similar to systolic flow, as seen
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distal to a severe stenosis. The iFR and FFR curves will move towards each other as the
diastolic/systolic flow ratio approaches one, which occurs with increasing stenosis severity (but at
the cost of diastolic pressure moving lower from mean pressure, see Figure 1 of reference #R7).
In cases with a low pulse pressure, the aortic pressure does not vary much between systole
and diastole. If all other factors remain constant, the iFR curve will move towards the FFR curve as
pulse pressure decreases. In extreme cases of non-pulsatile flow (for example, as seen with
certain left ventricular assist devices), the iFR and FFR curves will be identical. Similarly, as
diastolic pressure rises, the pulse pressure has less relative contribution. The iFR curve will move
towards the FFR curve as diastolic pressure increases.
Finally, coronary pressure is high during early diastole and returns to low systolic levels at
end diastole. Measuring only during mid-to-end or even central diastole will be less similar to the
whole cardiac cycle than if all of diastole were included (for example, three portions of “diastole”
were considered in prior reportsR4-R6). Therefore, the iFR curve will move towards the FFR curve as
more of early and end diastole is included.
As shown in Supplement Figure F2B, rest flow may be unexpectedly low or high given the
sizable variability in baseline myocardial demand. If rest flow is unexpectedly low, then iFR will
increase. Conversely, if rest flow is unexpectedly high, then iFR will decrease. As depicted in
Supplement Figure F2C, hyperemic peak flow may be unexpectedly low or high depending on a
variety of factors such as biologic variation, endothelial dysfunction, diffuse atherosclerotic disease,
and medications. FFR will be lower when hyperemic flow – rest flow multiplied by the coronary flow
reserve (CFR) – is higher than the special case. In cases when hyperemic flow is lower, FFR will
increase.
Theoretical Foundations
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We seek to separate the whole cardiac cycle mean pressure gradient (P) and mean flow
(Q) into systolic (Ps and Qs) and diastolic (Pd and Qd) components, weighted by the fractional
duration of systole (Ts) and diastole (1-Ts),
P = Ts * Ps + (1-Ts) * Pd,
(1)
Q = Ts * Qs + (1-Ts) * Qd.
(2)
Begin with the well-known quadratic relationship between flow and the pressure gradient across a
stenosis:
P = Cv * Q + Ce * Q2
(3)
where the constants Cv (linear viscous coefficient) and Ce (quadratic coefficient from inertial losses
due to flow expansion as it exits the stenosis) depend only on stenosis and vessel geometry and
blood properties of density and viscosity.R8 Note that an implicit “pulsatility” factor is associated with
the Q2 term but typically folded into Ce coefficient. The pulsatility factor, which we denote  for
consistency with prior literature, depends on the specific flow waveform and converts between the
time average of the flow squared and the square of the average flow (see Figure 8 and the
appendix of reference #R9 and discussion and equations #5 to #10 of reference #R10).
Prior work suggests that each pressure gradient component can be written in a form similar
to equation (3) but with a modified quadratic term,
Pd = Cv * Qd + d * Ce * Qd2
Ps = Cv * Qs + s * Ce * Qs2
(4)
where the pulsatility parameters d and s depend on the specific diastolic and systolic flow
waveforms, respectively, as discussed above. Denote the ratio of average diastolic to systolic flow
 = Qd / Qs,
(5)
which will depend, in general, on many factors as discussed below. The ratio of average flow to
peak flow can be expressed using equations (2) and (5) as
Q / Qd = Ts/ + (1-Ts) = .
(6)
By combining equations (2) and (6), it can be shown that
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Q = Qd *  = Qs *  * .
(7)
Substitute equations (3) and (4) into equation (1) to show that
Cv * Q + Ce * Q2 = Ts * [Cv * Qs + s * Ce * Qs2] + (1-Ts) * [Cv * Qd + d * Ce * Qd2]
= Cv * [Ts * Qs + (1-Ts) * Qd] + Ce * [Ts * s * Qs2 + (1-Ts) * d * Qd2]
which can be simplified by equations (2), (5), and (6) to yield
Cv * Q + Ce * Q2 = Cv * Q + Ce * [Ts * s * Qs2 + (1-Ts) * d * Qd2]
Q2 = Ts * s * Qs2 + (1-Ts) * d * Qd2
(Q/Qd)2 = Ts * s * (Qs/Qd)2 + (1-Ts) * d
2 = (Ts/2) * s + (1-Ts) * d
(8)
Equation (8) allows an infinite number of solutions for s>0 and d>0 (along the line connecting
s=0 and d=2/(1-Ts) to s=2*2/Ts and d=0), using the convention that the Ce coefficient already
incorporates the pulsatility parameter  for the entire flow waveform. (If instead equation (3) makes
whole cycle pulsatility  explicit as P = Cv * Q +  * Ce * Q2, then equation (8) becomes  * 2 =
(Ts/2) * s + (1-Ts) * d which can be written as 2 = (Ts/2) * (s/) + (1-Ts) * (d/).)
Therefore, the exact choice of s and d will depend on the specific systolic and diastolic
waveforms and will vary among clinical observations including flow changes observed during
vasodilation in a single subject. For subsequent analysis we assume that d =  and s =  * ,
which is one possible solution to equation (8), as these d and s offer convenient mathematical
simplification as shown next. (Making whole cycle pulsatility  explicit, these assumptions equate to
(d/) =  and (s/) =  * . In the supplemental results section, we present empiric data to justify
our particular choice of pulsatility parameters.)
Substituting our choices of d =  and s =  *  into equation (4) demonstrates that in this
case the phasic pressure gradients are proportional to mean pressure gradients by applying
equations (5) and (7)
Pd = Cv * Qd +  * Ce * Qd2 = (Cv / ) * Q + (Ce / ) * Q2 = P / 
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Ps = Cv * Qs +  *  * Ce * Qs2 = (Cv /  / ) * Q + (Ce /  / ) * Q2 = P / (*).
(9)
In summary, we have shown that the whole cycle pressure gradient across a stenosis can be
divided into its weighted systolic and diastolic components. Both systolic and diastolic components
have quadratic shapes, as does whole cycle average pressure, and its coefficients are those of the
stenosis (Cv and Ce) modified by a multiplicative factors, after assuming specific systolic and
diastolic flow waveform pulsatility. In the case of the diastolic pressure gradient (which is of interest
for iFR), the multiplicative factor is 1/. In the case of the systolic pressure gradient (which is not of
interest for iFR or FFR), the multiplicative factor is 1/(*). As noted above, the multiplicative factor
depends on many variables, including the heart rate, aortic pressure profile, and stenosis severity
(as reflected by coefficients Cv and Ce).
Relationship between iFR and FFR
The above equations and assumed systolic and diastolic flow waveform pulsatility allow for
a simple formulation of the relationship between iFR and FFR. Note that FFR can be written as
FFR = 1 - P / Paorta
(10)
where Paorta is the average aortic pressure over the whole cardiac cycle. Similarly iFR can be
written as
iFR = 1 - Pd / Pdaorta
(11)
where Pdaorta is the aortic pressure during diastole. Define a diastolic “shaping function”
 = Paorta / ( * Pdaorta) = (Paorta/Pdaorta) / [(1 - Ts) + Ts/(Qd/Qs)]
(12)
Now equation (11) can be rewritten using equations (9) and (12)
iFR = 1 - (P / ) / Pdaorta = 1 -  * P / Paorta
(13)
which is the same form as equation (10) for FFR apart from the shaping function . For the chosen
flow waveform pulsatility factors d =  and s =  * , the shaping function reduces to a constant.
For alternative values of d and s, however, the shaping function will also depend on mean flow
and therefore be a true “function” instead of a constant factor.
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For iFR to equal FFR, equation (10) at hyperemic flow (Qh) must equal equation (11) at
baseline flow (Qr). Note that coronary flow reserve (CFR) equals
CFR = Qh / Qr
(14)
by definition. Therefore
iFR at Qr = FFR at Qh
 * P(Qr) = P(Qh)
 * [Cv * Qr + Ce * Qr2] = Cv * Qh + Ce * Qh2 = CFR * [Cv * Qr + Ce * CFR * Qr2]
 / CFR = [Cv + Ce * CFR * Qr] / [Cv + Ce * Qr]
(15)
after applying equations (1) and (4). Equation (15) demonstrates the exact balance of stenosis
severity (Cv divided by Ce), rest flow (Qr), hyperemic flow (as reflected by CFR), and the shaping
function (which depends on the pulsatility of pressure and flow waveforms) required for iFR to
equal FFR. If all of these parameters except one are fixed, then equation (15) allows for its
solution. In general, equation (15) does not hold and therefore iFR only approximates FFR.
The relative resting gradient during systole (sFR) – the systolic analogy of iFR – can be
written in a form very similar to equation (13)
sFR = 1 - (P / [*]) / Psbp = 1 -  * P / Paorta
(16)
where the systolic “shaping function”  has a similar form to equation (13) above
 = Paorta / (* * Psbp)
(17)
Note that the ratio of the shaping functions in equations (12) and (17) can be expressed simply
[/] *  = Pdbp / Psbp = [/] * (Qd / Qs)
in terms of systolic and diastolic blood pressures and flows.
Multiplicative Factor Model
The multiplicative factors  and  play key roles in modeling iFR. Equations (5) and (7)
define  as depending on Ts and =Qd/Qs. We now present our models for these two components.
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The fraction of the cardiac cycle spent in systole (Ts) depends on heart rate in a direct fashion.
Supplement Figure F3 plots best-fit equations from two studies:
Ts from reference #R11 = 0.01 * exp{4.14 - (40.74/heart rate)}
Ts from reference #R12 = 1 - [-549 + 2.13*heart rate + 61500/heart rate]/(60000/heart rate).
We model Ts as a weighted average of these two curves such that Ts equals reference #R12 at
50/minute and reference #R11 at 120/minute. The black, dashed line in Supplement Figure F3
shows our model, which varies from Ts=0.287 at 50/minute to Ts=0.562 at 120/minute.
The component  is the ratio of average diastolic to systolic flow (Qd/Qs). We consider its
dependence on two factors. First, some literature exists on the normal diastolic/systolic ratio of the
velocity-time integral (VTId/s) of coronary flow as a function of heart rate.R13,R14 As detailed in
Supplement Figure F4 and Supplement Table T2, two studies report VTId/s at rest and during
pacing. Generally, VTId/s starts out around 4.5 at 50 beats per minute (bpm) and falls to about 2.5
by 100 bpm with little change at higher heart rates. We have chosen to model VTId/s in two parts,
with a linear decrease from 50-100 bpm then flat between 100-120 bpm. Heart rates outside of this
range are rarely encountered in practice while studying intra-coronary physiology.
Second, with increasing stenosis severity, diastolic flow becomes blunted, eventually
equaling systolic flow distal to a severe stenosis (see Figure #1 of reference #R7 or Figure #8 of
reference #R15). Thus we modify the above Qd/Qs so that it starts at a maximal value based on
heart rate alone when achieved CFR equals the normal CFR and falls linearly to Qd/Qs = 1 when
CFR1. For example, at a heart rate of 60 bpm, Qd/Qs = 2.02 when CFR=4.2 which would
decrease in linear fashion to Qd/Qs = 1.0 at CFR=1. Supplement Figure F5 shows how Qd/Qs
depends on heart rate with increasing stenosis severity, assuming the modeled VTId/s in
Supplement Figure F4.
Our model for Qd/Qs incorporating only heart rate and stenosis severity is clearly simplistic.
Literature supports the dependence of Qd/Qs on valvular abnormalities (including aortic
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insufficiencyR16 and aortic stenosisR13), electrical function (including left bundle branch blockR17 and
atrial fibrillationR18), and myocardial hypertrophy (most obvious in hypertrophic cardiomyopathyR19).
SUPPLEMENTAL METHODS
Simulation Model and Parameters
Two previous publications have outlined basicR20 and more advancedR21 versions of the
simulation model. Our basic version agreed with animal data while the more advanced version
matched human data regarding the relationship between FFR and CFR with diffuse and segmental
disease.
The simulation consists of a branching network of arterial segments terminating in
myocardial beds. Each arterial segment has a given length, variable diffuse narrowing, and
superimposed focal percent diameter stenosis. Each myocardial bed consists of a two parts – a
lumped vascular length (representing combined arterial and arteriolar conductance vessels) that
can be affected by diffuse disease, and a myocardial mass which autoregulates its resistance.
Model inputs based on the literature include normal resting flow, normal CFR, arterial lengths, and
myocardial mass. Normal vessel area and diameter in each segment are determined from its distal
myocardial mass using experimental data in humans. Summed distal vessel length and myocardial
mass adhere to the observed, linear relationship. The arterial tree and its branching, length, and
myocardial mass distribution are the same as used in our prior work (see Supplement Figure F1 of
reference #R21). Its design parameters were chosen based on experimental or literature data (see
Supplement Tables T1 and T2 of reference #R21).
The Poiseuille equation calculates viscous pressure loss along each segment. A quadratic
relationship determines the pressure drop across a focal stenosis based on its flow. In the absence
of diffuse or focal disease, each myocardial bed lowers its resistance until normal CFR has been
achieved. Flow to each myocardial bed is altered iteratively in the presence of diffuse and/or focal
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disease until all beds reach their minimum resistance. Flow in each arterial segment preserves flow
continuity through the model network.
Our prior work can be updated to compute iFR as follows. First, incorporate the above
models for Ts and Qd/Qs given their dependence on heart rate and stenosis severity. Second,
modify the computation of pressure drop by incorporating the relationships in equation (9).
Equation #16 of the on-line appendix of reference #R21 applies the pressure drop along each
segment of the tree as
P = inlet P - (R * Q) - (Cv * Q + Ce * Q2)
which now must be modified by a factor such that
P* = inlet P - [(R * Q) + (Cv * Q + Ce * Q2)] / factor
When modeling FFR, set factor=1, set the aortic pressure equal to the weighted average of the
systolic and diastolic pressures (Paorta = Ts * Psbp + (1-Ts) * Pdbp, where sbp = systolic blood
pressure and dbp = diastolic blood pressure), and seek the highest whole cycle flow (hyperemic
Qh). When modeling iFR, set factor= as defined in equation (6), set the aortic pressure equal to
the diastolic pressure (Paorta = Pdbp), and apply resting flow (Qr, a variable model parameter). If
systolic gradients were desired (currently not of clinical interest), set factor=* as defined in
equations (5) and (6), set the aortic pressure equal to the systolic pressure (Paorta = Psbp), and
apply resting flow (Qr).
Independent Simulation Parameters
Parameters of heart rate, blood pressure, severity of focal and diffuse disease, rest flow,
and maximal CFR were varied independently to study their impact on the relative error between
iFR and FFR:

Heart rate: 50 to 120 bpm

Diastolic blood pressure: 50 to 100 mmHg

Pulse pressure: 20 to 100 mmHg
12

Focal stenosis: 0 to 70%

Diffuse disease: 0% to 40% (reduces normal diameter of all segments)

Resting flow: 0.2 to 2.0 cc/min/gm

Normal CFR without disease: 2.0 to 5.0
Each parameter was modeled as independent from all others. All focal stenoses were
placed in the proximal left anterior descending (LAD) artery to enhance comparability. Unless they
were being varied, the focal stenosis was 60% on a background of 20% diffuse disease, heart rate
was 50 bpm, rest flow was 0.7 cc/min/gm, and normal CFR without disease was 4.2. These values
were chosen to reflect typical percent diameter stenosis and observed CFR during FFR
measurement.R21 Results are summarized as the signed relative error computed as (iFRFFR)/FFR*100.
Chosen resting flow values produced greater distal pressure loss than the aortic driving
pressure in a subset of severe parameter combinations. For example, at a blood pressure of
120/80 mmHg, focal stenosis of 80% in addition to background diffuse disease of 20%, and a
normal CFR without disease of 4.2, all heart rates produce greater distal diastolic pressure loss
than aortic diastolic pressure at a rest flow of 0.7 cc/min/gm. Such cases were excluded from our
analysis. An alternative would be to build into the model an empiric relationship between resting
flow and global disease severity so that distal pressure losses would not exceed aortic driving
pressures at rest.
Monte Carlo Simulation
A Monte Carlo simulation was performed by repeatedly selecting random parameters for
the model as if drawing from a cohort of hypothetical patients. Parameters of heart rate, blood
pressure, rest flow, maximal CFR without any disease, focal lesion location and its percent
diameter stenosis, and diffuse disease severity through the coronary tree were selected
independently and randomly. Distributions for model parameters were chosen based on several
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literature sources. Supplement Table T3 lists reported values in human measurements of FFR. As
our model assumes that heart rate and blood pressure remain constant between rest and stress,
values for these parameters were averaged. Parameters in our simulated population were:

Heart rate: We assumed a Gaussian distribution with mean 74 bpm and standard deviation
13 bpm. Values below 50 bpm or above 120 bpm were not allowed.

Blood pressure: We assumed a Gaussian distribution of mean aortic pressure (MAP) with
mean 96 mmHg and standard deviation 16 mmHg. MAP values below 50 mmHg or above
220 mmHg were not allowed. Pulse pressure (PP) was assumed to have a uniform
distribution between 20 and 80 mmHg. Diastolic blood pressure (DBP) was computed as
MAP-PP/3. Systolic blood pressure (SBP) was computed as diastolic blood pressure plus
PP. DBP values below 50 mmHg or above 110 mmHg were not allowed. SBP values below
80 mmHg or above 220 mmHg were not allowed.

Lesion severity: We assumed a uniform distribution from 22% to 83% diameter stenosis
based on the average minimum and maximum values in Supplement Table T3.

Lesion location: All epicardial segments were allowed equally except for the septal
perforator branch of the left anterior descending (LAD) artery, as it is almost never
instrumented or mechanically revascularized.

Diffuse disease: Based on Figure #2 of reference #R21, we assumed a uniform
distribution from 0% to 40%.

Rest flow: We implemented the empiric distribution of average rest flow (cc/min/gm) in the
whole left ventricle from 1,500 PET cases.R22 Its mean is 0.70 with minimum of 0.33 and
maximum of 1.83 cc/min/gm, but its distribution is not Gaussian.

Normal CFR without disease: Based on our prior work in normal volunteers,R23 we
assumed a Gaussian distribution of with mean 4.03 and standard deviation of 0.84. Normal
CFR values <2 were not allowed.
14
For each selection of these model parameters, lesion iFR, FFR, and CFR were solved using the
method described above. The relationship between iFR and FFR was explored after simulation of
1,000 “patients” (repetitions).
Human Clinical Data
Two types of human clinical data were assembled from a variety of sources: pressure-only
data and combined pressure-flow data. Almost all pressure-only data has been published
previously in conjunction with prior papers on iFR.R6,R24 Values of iFR and FFR in the ADVISE
studyR6 were extracted manually from its Figures #6 and #8A as allowed by image resolution and
data overlap. Values of iFR, FFR, and rest Pd/Pa in the VERIFY studyR24 were contributed by its
authors and are presented in its Figures #2A (prospective) and #6A (retrospective). An additional
174 retrospective cases from VERIFY not presented in its manuscript were included in our
analysis. ADVISE used both intracoronary and intravenous adenosine for hyperemia and several
wires for pressure recordings (ComboWire XT or PrimeWire from Volcano Corporation, Radi
PressureWire from St Jude Medical). VERIFY used only intravenous adenosine and a single wire
type for pressure recordings (Certus, St Jude Medical).
Combined pressure-flow data came mainly from three centers and has been partially
published previously as detailed next. All subjects gave informed consent as approved by the local
institutional review board for data acquisition.

Academic Medical Center (AMC) in Amsterdam: Combined measurements were made
using a ComboWire XT (Volcano Corporation, Rancho Cordova, California) guide wire after
standard calibration and distal placement. Intracoronary nitroglycerin 0.1 mg was given at
the beginning and then every 30 minutes throughout the procedure. Data was acquired at
rest and throughout induction and decline of maximum hyperemia after the intracoronary
bolus administration of adenosine (20 to 40 μg). Off-line data conversion sampled at 200
Hz to record aortic and intra-coronary pressure (both mm Hg), single-lead
15
electrocardiogram (unitless), and instantaneous peak Doppler velocity (cm/sec). A subset of
subjects had more than one measurement performed at two different locations along the
same coronary artery. The R-wave peak from the electrocardiogram was used to mark the
onset of systole.

ADVISE study: A single subject had combined, simultaneous pressure and flow
measurements made using a ComboWire XT (Volcano Corporation, Rancho Cordova,
California) guide wire after standard calibration and distal placement, as previously
described and published.R6 Pressure and flow velocity recordings were made at baseline
and during the infusion of adenosine (140 μg/kg/min) via a femoral venous sheath. Aortic
pressure, distal coronary pressure, and coronary peak flow velocity data was exported from
the digital archive saved by the ComboMap acquisition unit. Figure #2 of reference #R6
demonstrates the angiogram and pressure/flow data from this subject, which were
extracted from the high-resolution scalable vector graphic (SVG) code embedded in its
portable document format (PDF) file.

King's College London (KCL): Combined measurements were made using a ComboWire
(Volcano Corporation, Rancho Cordova, California) guide wire after standard calibration
and distal placement. Intracoronary nitroglycerin 0.3 mg was given prior to the
administration of adenosine. Data was acquired at rest and throughout induction and
decline of hyperemia, using either intracoronary adenosine (20 to 60 μg) in the majority or
intravenous adenosine (140 μg/kg/min) in a minority. Off-line data conversion sampled at
200 Hz to record aortic and intra-coronary pressure (both mm Hg), single-lead
electrocardiogram (unitless), and instantaneous peak Doppler velocity (cm/sec).

University of Texas Medical School (UT) in Houston: A single subject had combined,
simultaneous pressure and flow measurements made using a ComboWire XT (Volcano
Corporation, Rancho Cordova, California) guide wire after standard calibration and distal
placement, including intracoronary nitroglycerin. Intravenous adenosine was infused
16
through a 4F femoral venous sheath at a rate of 140 μg/kg/min. Data acquisition began a
few seconds before the start of adenosine infusion and continued for approximately 2
minutes afterwards until peak hyperemia was achieved. Off-line data exportation from the
ComboMap acquisition unit produced readings of aortic and intra-coronary pressure (both
mm Hg, sampled 200 Hz), single-lead electrocardiogram (unitless, sampled 200 Hz), and
instantaneous peak Doppler velocity (cm/sec, sampled 100 Hz). Supplement Figure F6
shows the combined pressure-flow measurements from this case. The angiogram
demonstrates an intermediate lesion in the left circumflex system (panel A). Clinical data
acquired during intravenous adenosine infusion is shown (panel B) in similar arrangement
to Supplement Figure 1 with the associated best fits. Although the lesion was not
hemodynamically significant, fundamental pressure-flow relationships fit the observed data
well.

VU University Medical Center (VUmc) in Amsterdam: As previously described and
published,R5,R25 combined measurements were made using two wires, one for pressure
(Wavewire from Endosonics or Volcano Therapeutics or Radi PressureWire from Radi
Medical Systems) and another for flow (Doppler guidewire from Cardiometrics Incorporated
or Flowire from Volcano Therapeutics) after standard calibration and distal placement,
including intracoronary nitroglycerin administration. Data was acquired from a few seconds
before administration of adenosine to disappearance of the hyperemic response, using
either intracoronary adenosine (20 to 40 μg) in the majority or intravenous adenosine (140
μg/kg/min) in a minority. Off-line data acquisition used custom hardware (Cardiodynamics,
Zoetermeer, Netherlands) sampling at a frequency of 100 Hz (although 200 Hz was
employed in a small minority) to record aortic and intra-coronary pressure (both mm Hg),
single-lead electrocardiogram (unitless), and instantaneous peak Doppler velocity (cm/sec).
A subset of subjects had more than one measurement performed, either in different vessels
or before/after stenosis modification by angioplasty.
17
All tracings were adjusted for pressure drift and pressure-flow phase lag as necessary. Portions of
the tracings without pressure data during intracoronary injection were excluded. Markers were
placed and manually confirmed or adjusted at the onset of systole and diastole for each complete
cardiac cycle, using the upstroke of the aortic pressure tracing (except AMC as noted above) and
the dicrotic notch, respectively. Standard clinical data for each patient included demographics,
cardiac risk factors, medical history, and medication class, with rare missing values. Percent
diameter stenosis from quantitative coronary angiography was available for the majority of cases.
Custom analysis software in R version 2.14.1 (reference #R26) processed each pressureflow case by first reading in aortic and intra-coronary pressures (mm Hg), instantaneous peak
Doppler velocity (cm/sec), and markers of systole and diastole. Average flow velocity per complete
cardiac cycle identified rest and hyperemic periods as the consecutive 3 beats (when using
intracoronary adenosine) or 5 beats (if intravenous adenosine was used) with the lowest or highest
mean flow. Each variable was summarized for all observations, and also within each of its own
tertiles along with the associated iFR relative error. Beat-by-beat pressure gradient (P) and
whole-cycle flow velocity (Q) data as in Supplement Figure 6B were analyzed using the pressureflow relationships in the above equations to compute best-fit parameters Cv, Ce, Paorta, Psbp,
Pdbp, Ts, , , , and .
Heart rate and fraction of the cardiac cycle in systole were computed using the sampling
frequency and provided systolic markers. Flow velocity, aortic pressure, relative distal coronary
pressures (such as iFR, FFR, diastolic FFR), and myocardial resistance (distal coronary pressure
divided by flow velocity) were summarized for the whole cycle, systole, diastole, rest, and
hyperemia. Hyperemic stenosis resistance (HSR) was computed as the pressure gradient (P)
divided by the flow velocity.R1,R27 Hyperemic microvascular resistance (HMR) was computed as the
distal coronary pressure divided by flow velocity over the entire cardiac cycle during hyperemia.R7
Pulse pressure was examined using both the mean systolic pressure minus the mean diastolic
pressure (mean pulse pressure) and the highest continuous 10% of pressures during systole
18
minus the lowest 10% during diastole (peak pulse pressure). Observed pulsatility was computed as
the ratio of the average squared flow velocity to the square of the average flow velocity. R9,R10
For the main analysis, iFR was computed exactly as described in its original publication,
taken from 25% after the dicrotic notch on the aortic tracing until 5 ms before systole.R6 Four
alternative iFR variants were calculated to study the sensitivity of iFR to its timing: all diastole
(dicrotic notch until following systole), peak 50% of flow (consecutive 50% of diastole with highest
average flow velocity as determined for each beat), peak 25% of flow, and peak 10% of flow.
Statistical Methods
Statistical analyses were performed using R version 2.14.1 (reference #R26). Its ROCR
packageR28 computed the area under receiver-operator characteristic (ROC) curves (AUC). The
optimal ROC cutoff was taken where sensitivity equals specificity. Continuous variables are
summarized as mean  standard deviation if normally distributed, or as median (interquartile
range) if not normally distributed. Frequency variables are expressed as number (percentage). The
association between paired, continuous variables is summarized using the Pearson (r) correlation
coefficient. Differences among tertiles were compared using ANOVA. Summary values for the
literature used number of patients as a weighting factor. One-way ANOVA within subjects
assessed changes in iFR among its original definition and 4 variants. If this ANOVA was
significant, then a Tukey all-pair comparison was performed to determine which iFR variant(s) were
different. Bland-Altman plots display differences between two variables against their mean value
along with mean difference and its 95% confidence interval. Applicable tests were two-tailed, and
p<0.05 was considered statistically significant.
LOWESS (locally weighted scatter plot smoothing) regression fit data using default R
parameters (2/3 smoother span and 3 iterations). Depending on the continuous variables under
study, different models were fit using standard regression techniques, including proportional (no
intercept), linear (variable intercept), and quadratic (with intercept set to zero). Errors were
19
propagated by use of partial derivatives. For model fits, the coefficient of determination (R2) was
computed as one minus the ratio of the residual sum of squares to the total sum of squares. Box
plots identify outliers as 1.5 times the interquartile range.
SUPPLEMENTAL RESULTS
Individual Simulation Parameters
Supplement Table T4 shows the signed relative error between iFR and FFR as diastolic
blood pressure, pulse pressure, and heart rate were varied with a focal 60% stenosis on a
background of 20% diffuse disease. When diastolic and pulse pressure were held constant but
heart rate increased from 50 to 120 bpm, the signed relative error between iFR and FFR
decreased by 8.5±1.5%. As diastolic blood pressure increased from 50 to 100 mmHg, the signed
relative error between iFR and FFR increased by 13.1±1.1%. Increasing pulse pressure from 20 to
80 mmHg decreased the signed relative error between iFR and FFR by 3.1±1.0%.
Supplement Table T5 gives the signed relative error between iFR and FFR as focal and
diffuse disease and heart rate were varied. With diffuse and focal disease held constant, increased
heart rate decreased the relative error by a minimum of 0.7% (no disease present) to a maximum
of 22.3% (20% diffuse disease and a 70% focal stenosis).
Rest flow was increased from 0.2 to 2.0 cc/min/gm with fixed 60% lesion in the proximal
LAD on a background of 20% diffuse disease, while adjusting CFR to maintain the same
hyperemic flow. The signed relative error between iFR and FFR decreased from +32% at 0.2
cc/min/gm to -38% at 1.51 cc/min/gm. Rest flows above 1.51 cc/min/gm exceeded hyperemic flow
in at least one myocardial bed and were therefore not allowed. Maximal CFR was increased from
2.0 to 5.0 with a fixed 60% lesion in the proximal LAD on a background of 20% diffuse disease,
while keeping rest flow fixed at 0.7 cc/min/gm. The signed relative error between iFR and FFR
increased from +5% at CFR=2.0 to +27% at CFR=5.0.
20
These simulation results with independent variation of model parameters confirm the
qualitative expectations summarized in Supplement Figure F2 and Supplement Table T1. The
relationship between iFR and FFR is most sensitive to rest flow and stenosis severity, has an
intermediate sensitivity to diastolic blood pressure and CFR, and is least sensitive to heart rate and
pulse pressure. As rest flow, heart rate, and pulse pressure increase, iFR falls relative to FFR.
Conversely, as focal stenosis severity, diastolic blood pressure, and maximal CFR increase, iFR
rises relative to FFR.
Monte Carlo Simulation
Supplement Table T6 presents results from the Monte Carlo simulation. By analogy with
Table 2 of the main manuscript, Supplement Table T7 summarizes Monte Carlo simulation
parameters and results by tertile of each variable and provides the associated iFR relative error.
Most parameters show a significant effect on the iFR relative error, with the exception of systolic
blood pressure and rest flow. The independent parameters in the simulation model lack
homeostatic mechanisms that, in clinical reality, tend to compensate for changes in any one
variable. Therefore, the larger number of significant model parameters in Supplement Table T7
compared to fewer clinical parameters in Table 2 of the main manuscript can be anticipated and
understood.
Human Clinical Data
A total of 1129 clinical observations were compiled from a variety of centers: 674 pressureonly cases from the multicenter retrospective VERIFY studyR24; 206 pressure-only cases from the
multicenter prospective VERIFY studyR24; 129 pressure-only cases from the multicenter ADVISE
studyR6 (extracted manually from the 157 points in its Figures #6 and #8A as allowed by image
resolution and data overlap); and 120 combined pressure-flow cases (from AMC, ADVISE study,
KCL, UT-Houston, and VUmc).
21
Supplement Table T8 summarizes available clinical data for the pressure-only
measurements. These data were taken from Table #1 of the ADVISE studyR6 and Table #1 of the
VERIFY study.R24 Clinical data for the retrospective cases in the VERIFY study are not available.
Supplement Table T9 summarizes clinical data by its source for the 120 observations in 87 unique
subjects with combined pressure-flow measurements. The scatter plot of iFR and FFR in Figure 1B
of the main manuscript combines pressure-only and pressure-flow subjects.
Supplement Figure F7 shows the iFR versus FFR scatter plot from Figure 1B of the main
paper but with colored LOWESS regression lines for each data set (ADVISE, VERIFY prospective
and retrospective, and the combined pressure-flow measurements). The regression lines
demonstrate very similar behavior above FFR=0.6-0.7 then diverge below this range depending on
the exact mix of severe lesions. The curved shape of all LOWESS regression lines demonstrates
that a simple linear model is a suboptimal description of the relationship between iFR and FFR
over the entire range.
Supplement Table T10 summarizes observations from the combined pressure-flow data by
tertile of each variable and provides the associated iFR relative error. As noted above, fewer
clinical observations significantly affect the iFR relative error than simulation model parameters due
to homeostatic, corrective mechanisms present in humans. Not all parameters discussed in
Supplement Figure F2 and Supplement Table T1 proved important for clinical observations in
Table 2 of the main paper, likely due to physiologic interplay among them so that a change in one
produces a compensatory change in another.
Supplement Table T11 summarizes best-fit values for Cv, Ce, Paorta, Psbp, Pdbp, Ts, , ,
, and  and compares them to observed clinical data reproduced from Supplement Table T10.
Classic pressure-flow theory shows an excellent fit to the clinical data, with R2>0.8-0.9 for all
phases of the cardiac cycle. Fitted parameters of aortic pressure, fractional of cardiac cycle in
systole, and flow ratios match observed values. Therefore, our model describes the observed data
well, using reasonable and physiologic values for its parameters. Larger R2 for diastole and the
22
whole-cardiac cycle likely arises from lower signal/noise in systole due to comparatively lower
pressure gradients.
Comparing clinical observations in Supplement Table T10 to best-fit parameters  and  in
Supplement Table T11 supports our assumed diastolic and systolic pulsatility factors within the
limits of biologic variability:
d/ = 1.05/1.14 = 0.92  0.84 ± 0.07 = 
s/ = 1.09/1.14 = 0.96  (0.84±0.07)*(1.81±0.61) = 1.52 ± 0.53 =  * .
Supplement Figure F8 shows boxplots and outliers for iFR, comparing its original definition to 4
variants using different portions of diastole. While a statistically significant difference was found
among all iFR variants (p<0.001), no difference existed between its original definition (25% after
the dicrotic notch on the aortic tracing until 5 ms before systoleR6) and simply using all of diastole
(p>0.99). The original iFR definition produced values which were statistically higher than using
peak diastolic flow (p<0.001 for each of peak 50%, peak 25%, and peak 10% of diastolic flow),
although these differences were not clinically significant (higher by 0.00 (0.00-0.01) compared to
peak 50% of diastolic flow, higher by 0.01 (0.00-0.01) than peak 25%, and higher by 0.00 (-0.010.02) than peak 10%). Therefore, iFR does not depend greatly on the chosen diastolic interval and
would not be expected to show a different relationship with FFR by adjusting its definition.
As summarized in Supplement Table T12, myocardial resistance and its variation was
comparable among the 3 major sites providing pressure/flow data in our collaborative study
independent of their sample size. In the ADVISE study,R6 the standard deviation exceeded the
mean resistance during hyperemia, suggesting a non-normal distribution. Note, the resistance
during resting diastole in the ADVISE studyR6 was more comparable to the resistance during mean
hyperemia from other sites.
For Supplement Tables T10 and T12, as well as Table 2 of the main manuscript, “diastole”
used the ADVISE definition (25% after the dicrotic notch on the aortic tracing until 5 ms before
systoleR6) to facilitate comparison. However, myocardial resistance during all of diastole (4.832.48
23
mmHg/[cm/sec]) did not differ significantly from the ADVISE definition (4.842.55 mmHg/[cm/sec])
by paired t-test (p=0.75), as detailed in Supplement Figure F9. In only 12 of 120 patients (10%) did
resistance differ by 10% or more between these two definitions.
The iFR bias seen in Figure 2 of the main paper can be corrected most simply by
subtracting 0.09 from iFR. A more complex technique corrects iFR using the LOWESS line fit to the
aggregate data as shown in Supplement Figure F7 for each data source. In this case, a BlandAltman analysis comparing FFR to corrected iFR produces a bias of 0.00 with 95% confidence
limits from -0.17 to +0.18. Therefore, the more complex correction also removes the bias but does
not reduce the limits of agreement.
24
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29
SUPPLEMENTAL FIGURE CAPTIONS AND LEGENDS
Supplement Figure F1. Historical context. Relative distal pressure (ratio of distal to aortic
pressure, where P equals aortic minus distal pressure) for the whole cardiac cycle pressure
(upper, black line) and just diastolic pressure (lower, red line) decreases quadratically with
increasing average flow or flow velocity. Five points have been described on these two curves,
including the resting average pressure gradient (Grüntzig), FFR, diastolic FFR (d-FFR), pressure
drop at a diastolic flow velocity of 50 cm/sec (dpv50), and iFR. Each point is shown along with its
year of initial description. Dashed portions of the curves show predicted data outside of the
observed flow range. The thin, horizontal dashed line demonstrates the special case when iFR
equals FFR, which does not hold in general.  = diastolic shaping function (reflects pulsatility of
flow and pressure waveforms).
Supplement Figure F2. Effects which alter iFR approximation. As in Supplement Figure F1,
relative distal pressure is shown as a function of average flow or flow velocity for the whole cardiac
cycle (black) and just diastolic pressure (red). (A) When the shaping function  decreases, iFR
increases (green). When the shaping function  becomes larger, iFR decreases (purple). See
Supplement Table T1 and the text for anatomic and hemodynamic variables that alter the shaping
function. (B) When rest flow decreases, iFR increases (green). When rest flow increases, iFR
decreases (purple). (C) When peak flow increases due to a higher coronary flow reserve (CFR),
FFR decreases (purple). When peak flow decreases due to a lower CFR, FFR increases (green).
Supplement Figure F3. Systolic fraction of cardiac cycle. Two studies provide data on the
fractional duration of systole (Ts): upper lighter lineR12 and lower darker line.R11 The dashed black
line describes our model for Ts, which increases continuously between 50-120 bpm.
30
Supplement Figure F4. Diastolic-to-systolic ratio of the velocity-time integral of coronary flow. Two
studies provide data on normal diastole/systole ratios of the velocity-time integral (VTId/s) of
coronary flow.R13,R14 Open and closed circles with error bars denote raw data, as detailed in
Supplement Table T2. The dashed gray line describes our model for VTId/s, which falls linearly
between 50-100 bpm then remains flat between 100-120 bpm.
Supplement Figure F5. Diastolic-to-systolic ratio of coronary flow. Our model of the
diastole/systole ratio of coronary flow – termed  in equation (5) – combines the models in
Supplement Figures F3 and F4. Additionally, the relative CFR reduces  in linear fashion from its
maximal value (upper solid black line for relative CFR = 1.0) for moderate (middle dotted gray line
for relative CFR = 0.7) and severe (bottom dashed light gray line for relative CFR = 0.4) values.
Supplement Figure F6. Sample pressure-flow experimental data. (A) Angiogram showing an
intermediate lesion at the left circumflex bifurcation with a large obtuse marginal branch (green
arrow and label) as seen in a right anterior oblique, caudal view. A combined pressure-flow wire
was placed in the left circumflex beyond the lesion (yellow arrow and label). (B) Combined
pressure-flow velocity data distal to the lesion presented in a format similar to Supplement Figure
F1. Data points (open circles) for each complete cardiac cycle during the acquisition are connected
by lines in temporal sequence during a two-minute intravenous infusion of adenosine. Whole cycle
peak flow velocity (cm/sec, where peak velocity refers to the flow profile under Doppler
interrogation) remains the same for each heart beat, while the relative distal pressure gradients
differ among its whole cycle (black) and diastolic (red) components. Solid and dashed lines
represent best fits.  = diastolic shaping function.
Supplement Figure F7. iFR versus FFR scatter plot. Identical data from Figure 1B of the main
paper but with colored markers and LOWESS regression lines for each data set (ADVISE = blue
31
line and open circles; VERIFY prospective = red; VERIFY retrospective = green; combined
pressure/flow measurements from several centers = purple). Regression lines demonstrate very
similar behavior above FFR=0.6-0.7, then diverge below this range depending on the exact mix of
severe lesions. The curved shape of all regression lines demonstrates that a simple linear model is
a suboptimal description of the relationship between iFR and FFR over the entire range.
Supplement Figure F8. Alternative iFR definitions. Boxplots of iFR values computed using its
original definition (25% after the dicrotic notch on the aortic tracing until 5 ms before systoleR6) and
four alternative iFR variants: all diastole (dicrotic notch until following systole), peak 50% of
diastolic flow (consecutive 50% of diastole with highest average flow velocity as determined for
each beat), peak 25% of flow, and peak 10% of flow. No difference exists between the original
definition and using all of diastole (p>0.99). Using peak diastolic flow produces statistically
significant lower values, but not clinically meaningful lower values (see text for details). Only a
small minority of points (<20%) are outliers (shown as open circles in each box plot). IQR =
interquartile range.
Supplement Figure F9. Resting myocardial resistance by diastolic definition. Distal coronary
pressure (mmHg) divided by coronary flow velocity (cm/sec) serves as an index of myocardial
resistance. Paired values in 120 patients show no significant difference (paired t-test p=0.75) in
resting diastolic resistance between the entire diastolic period (dicrotic notch until following systole)
and the “wave-free” period as proposed in the original iFR manuscriptR6 (25% after the dicrotic
notch on the aortic tracing until 5 ms before systole). Only 12 cases (10%) differ by 10% or more
(shown in blue).
32
SUPPLEMENT FIGURE F1.
33
SUPPLEMENT FIGURE F2.
34
SUPPLEMENT FIGURE F3.
35
SUPPLEMENT FIGURE F4.
36
SUPPLEMENT FIGURE F5.
37
SUPPLEMENT FIGURE F6.
38
SUPPLEMENT FIGURE F7.
39
SUPPLEMENT FIGURE F8.
40
SUPPLEMENT FIGURE F9.
41
SUPPLEMENTAL TABLES
Supplement Table T1. Effect of independent parameters on iFR approximation to FFR.
Parameter
Variation
iFR Increases
Slow
Yes
iFR Decreases
Heart rate
Fast
None/mild
Yes
Both iFR and FFR within normal range
Stenosis severity
Severe
Yes
Low
Yes
Pulse pressure
High
Yes
Low
Yes
Diastolic pressure
High
Yes
Peak diastole
Yes
Included diastole*
All diastole
Yes
Low
Yes
Rest flow
High
Low
Yes
FFR increases
CFR
High
FFR decreases
* = refers to the portion of the diastolic phase that is averaged to compute distal pressure, which
has differed among prior works (see historical context section for details)
CFR = coronary flow reserve
FFR = fractional flow reserve
iFR = instantaneous wave-free ratio
42
Supplement Table T2. Literature data on normal diasystolic/systolic flow ratio and heart rate.
Heart rate (bpm)
VTId/s
Source
679
3.92.4
Reference #R11*
726
3.40.5 Reference #R10**
1036
2.41.7
Reference #R11
1248
2.51.3
Reference #R11
125
2.60.5
Reference #R10
* = from N=16 subjects in Tables 1 (compute heart rate from cycle length) and 2 (compute VTId/s
from VTIs*HR and VTId*HR)
** = from N=9 control subjects in group 3 of Table 2 (heart rate) and section “Ratio of Systolic to
Diastolic CFR Curve Area” (compute VTId/s from inverse of text values which are systolic/diastolic)
bpm = beats per minute; VTId/s = ratio of diastolic/systolic velocity-time integral of coronary flow
43
Supplement Table T3. Literature data on typical hemodynamics during FFR.
Author
De
Bruyne
Pijls
De
Bruyne
Tron
De
Bruyne
Bech
Jeremias
Claeys
Journal
Citation
Heart rate
(bpm)
Rest Stress
N
MAP
(mm Hg)
Rest
Stress
Circulation
1994 Mar;89:1013
22
63±10
87±17
105±18
102±13
Circulation
1995 Dec;92:3183
101±15
93±16
1995 Jul;92:39
68±14
76±9
78±9
74±18
Circulation
AHJ
1995 Oct;130:723
60
23
37
70
Circulation
1996 Oct;94:1842
15
78±8
Circulation
AHJ
CCI
1999 Feb;99:883
2000 Oct;140:651
2001 Dec;54:427
Bech
Heart
2001 Nov;86:547
Matsuo
Aqel
Parham
Ng
Kolyva
Circulation
AJC
Circulation
Circulation
AJPHCP
2002 Mar;105:1060
2004 Feb;93:343
2004 Mar;109:1236
2006 May;113:2054
2008 Nov;295:H2054
60
53
19
24
30
24
10
21
15
11
Weighted average
494
97±14
79±10
%DS
(%)
Mean Range
55±14
22-77
56±15
14-94
95±13
90±13
94±16
87±16
100±16
90±13
95±18
95±26
89±14
57±12
56±24
47±12
42±9
43±10
50±6
50±9
0-95
26-71
40-60
65±13
71±15
69±10
68±13
75±18
76±13
74±3
97±16
92±20
75±23
93±4
17±20
63±13
0-50
71±11
76±15
100±16
93±16
51±14
22-83
bpm = beats per minute; MAP = mean aortic pressure; %DS = percent diameter stenosis
44
Supplement Table T4. Simulation results of signed relative error between iFR and FFR with a
focal 60% lesion in the proximal LAD on a background of 20% diffuse disease.
Heart rate (bpm)
DBP
50
60
70
80
90
100
PP
20
30
40
50
60
70
80
20
30
40
50
60
70
80
20
30
40
50
60
70
80
20
30
40
50
60
70
80
20
30
40
50
60
70
80
20
30
40
50
60
70
80
50
18.7
18.7
18.7
18.7
18.6
18.4
18.3
24.3
24.1
24.0
23.8
23.6
23.3
23.0
27.7
27.4
27.2
26.9
26.6
26.3
26.0
29.7
29.4
29.1
28.8
28.4
28.1
27.7
30.9
30.5
30.2
29.8
29.5
29.1
28.8
31.5
31.1
30.8
30.4
30.0
29.7
29.3
60
17.6
17.6
17.6
17.4
17.2
17.0
16.7
23.3
23.1
22.8
22.5
22.2
21.9
21.6
26.7
26.4
26.1
25.7
25.3
24.9
24.5
28.8
28.4
28.0
27.6
27.2
26.8
26.4
30.0
29.6
29.2
28.8
28.3
27.9
27.5
30.7
30.3
29.8
29.4
29.0
28.5
28.1
70
16.6
16.5
16.4
16.1
15.8
15.5
15.1
22.2
22.0
21.7
21.3
20.9
20.5
20.1
25.8
25.4
25.0
24.5
24.1
23.6
23.1
27.9
27.5
27.0
26.5
26.0
25.6
25.1
29.2
28.7
28.2
27.7
27.2
26.8
26.3
29.9
29.4
28.9
28.4
27.9
27.4
27.0
80
15.5
15.4
15.2
14.8
14.5
14.0
13.6
21.3
20.9
20.5
20.1
19.6
19.1
18.6
24.8
24.4
23.9
23.4
22.9
22.3
21.8
27.1
26.5
26.0
25.5
24.9
24.4
23.8
28.4
27.8
27.3
26.7
26.2
25.6
25.1
29.2
28.6
28.0
27.5
26.9
26.4
25.9
90
14.6
14.4
14.0
13.6
13.2
12.7
12.1
20.4
20.0
19.5
19.0
18.4
17.9
17.3
24.0
23.5
22.9
22.4
21.8
21.2
20.6
26.3
25.7
25.1
24.5
23.9
23.3
22.7
27.7
27.1
26.4
25.8
25.2
24.6
24.0
28.5
27.8
27.2
26.6
26.0
25.4
24.9
100
13.9
13.6
13.2
12.7
12.2
11.6
10.9
19.7
19.2
18.7
18.1
17.5
16.9
16.2
23.4
22.8
22.2
21.5
20.9
20.2
19.5
25.7
25.0
24.4
23.7
23.0
22.4
21.7
27.1
26.4
25.8
25.1
24.4
23.8
23.1
27.9
27.3
26.6
25.9
25.3
24.7
24.0
110
11.9
11.5
11.0
10.5
9.8
9.1
8.4
18.0
17.4
16.8
16.1
15.4
14.7
14.0
21.8
21.1
20.5
19.7
19.0
18.3
17.6
24.2
23.5
22.8
22.1
21.4
20.7
19.9
25.8
25.1
24.3
23.6
22.9
22.2
21.5
26.7
26.0
25.3
24.6
23.9
23.2
22.5
120
10.1
9.6
9.0
8.4
7.6
6.9
6.1
16.3
15.7
15.0
14.3
13.5
12.8
12.0
20.3
19.6
18.9
18.1
17.3
16.6
15.8
22.9
22.2
21.4
20.6
19.9
19.1
18.4
24.6
23.8
23.0
22.3
21.5
20.8
20.1
25.6
24.9
24.1
23.3
22.6
21.9
21.2
bpm = beats per minute; DBP = diastolic blood pressure (mmHg); PP = pulse pressure (mmHg)
45
Supplement Table T5. Simulation results of signed relative error between iFR and FFR for a
lesion in the proximal LAD with blood pressure 120/80 mmHg but varying hear rate and focal or
diffuse disease.
DD
0
20
30
40
DS
0
50
60
70
80
0
50
60
70
80
0
50
60
70
80
0
50
60
70
80
Heart rate (bpm)
50
2.0
16.0
33.7
59.3
57
1.9
15.7
33.0
57.6
64
1.9
15.3
32.3
56.0
71
1.8
15.0
31.6
54.4
78
1.7
14.6
30.9
52.9
2.7
16.2
29.1
18.5
2.6
15.8
28.3
16.5
2.5
15.4
27.6
14.5
2.4
15.1
26.9
12.5
2.2
14.8
26.2
10.5
2.4
11.5
15.3
2.3
11.2
14.5
2.2
10.8
13.8
2.0
10.4
13.0
1.9
10.1
12.2
85
1.6
14.3
30.3
51.5
N/A
2.1
14.4
25.5
8.7
N/A
1.8
9.8
11.5
92
1.6
14.0
29.7
50.2
99
1.5
13.8
29.2
49.1
106
1.4
13.5
28.5
47.2
113
1.4
13.1
27.8
45.1
120
1.3
12.8
27.2
43.2
2.0
14.1
24.9
7.1
2.0
13.9
24.4
5.8
1.8
13.4
23.4
2.7
1.7
13.0
22.4
-0.7
1.5
12.5
21.4
-3.9
1.6
9.5
10.9
1.5
9.2
10.4
1.3
8.7
9.2
1.2
8.1
7.8
1.0
7.6
6.5
-0.3
-1.7
-0.4
-2.0
-0.6
-2.7
-0.9 -1.1
N/A
N/A
0.7
0.5
0.5
0.1
0.4
-0.3
0.2
-0.7
0.0
-1.1
-0.1
-1.4
N/A
bpm = beats per minute; DD = diffuse disease (%); DS = focal diameter stenosis (%); N/A = distal
pressure loss exceeds aortic pressure during diastole for rest flow of 0.7 cc/min/gm
46
Supplement Table T6. Monte Carlo simulation results.
Variable
Lesion location
Left main
Left anterior descending system
Left circumflex system
Rest flow (cc/min/gm)
Systolic blood pressure (mmHg)
Pulse pressure (mmHg)
Diastolic blood pressure (mmHg)
Heart rate (bpm)
Lesion severity (% diameter stenosis)
Diffuse disease (%)
Maximal CFR without disease
Value
N = 1,000 total
63 (6%)
468 (47%)
469 (47%)
0.65 (0.56-0.79)
130 ± 18
50 ± 17
80 ± 14
75 ± 12
49 ± 16
19 ± 11
4.08 ± 0.81
Lesion iFR
Lesion FFR
Lesion CFR
0.90 (0.79-0.95)
0.80 (0.66-0.88)
2.38 ± 0.88
bpm = beats per minute
CFR = coronary flow reserve
FFR = fractional flow reserve
iFR = instantaneous wave-free ratio
47
Supplement Table T7. Monte Carlo results and parameters with iFR relative error by tertile.
Variable
Lesion iFR
Lesion FFR
Lesion CFR
Diameter stenosis (%)
Diffuse disease (%)
Diastolic blood pressure (mmHg)
Pulse pressure (mmHg)
Systolic blood pressure (mmHg)
Heart rate (bpm)
Rest flow (cc/min/gm)
Maximal CFR without disease
Associated iFR relative error (%)
Lowest Middle Highest p value
0.90
(0.79-0.95)
0.80
(0.66-0.88)
2.38 ± 0.88
Variable by its own tertile
Lowest
Middle
Highest
0.70
0.90
0.96
(0.56-0.79) (0.87-0.92) (0.95-0.97)
0.58
0.80
0.91
(0.49-0.66) (0.76-0.83) (0.88-0.93)
1.46 ± 0.25 2.27 ± 0.26 3.40 ± 0.55
49 ± 16
19 ± 11
80 ± 14
50 ± 17
130 ± 18
75 ± 12
0.65
(0.56-0.79)
4.08 ± 0.81
31 ± 5
6±4
65 ± 6
30 ± 6
111 ± 10
62 ± 5
0.53
(0.49-0.56)
3.21 ± 0.41
All (N=1,000)
49 ± 5
18 ± 4
81 ± 4
50 ± 6
131 ± 4
74 ± 3
0.66
(0.63-0.69)
4.06 ± 0.21
68 ± 6
32 ± 4
96 ± 6
70 ± 6
151 ± 9
88 ± 7
0.86
(0.79-0.98)
4.96 ± 0.45
12  22
15 ± 12
7±5
<0.001
18 ± 23
11 ± 7
5±3
<0.001
7 ± 20
15 ± 13
12 ± 10
<0.001
5±4
16 ± 18
10 ± 14
13 ± 14
12 ± 13
12 ± 16
11 ± 9
13 ± 15
12 ± 15
12 ± 17
12 ± 17
12 ± 15
18 ± 23
5 ± 11
13 ± 17
10 ± 15
11 ± 16
10 ± 14
<0.001
<0.001
0.018
0.026
0.41
0.06
10 ± 16
13 ± 15
12 ± 15
0.18
6 ± 11
11 ± 14
18 ± 17
<0.001
bpm = beats per minute; CFR = coronary flow reserve; FFR = fractional flow reserve; iFR = instantaneous wave-free ratio
48
Supplement Table T8. Clinical data* for the pressure-only measurements.
VERIFY
Variable
ADVISE
(prospective)
Number of subjects
131
206
Number of lesions
157**
206
Intracoronary adenosine
94 (60%)
0 (0%)
Intravenous adenosine
63 (40%)
206 (100%)
LAD
69 (44%)
133 (64%)
LCx
43 (27%)
28 (14%)
RCA
45 (29%)
45 (22%)
No significant disease
0 (0%)
16 (8%)
Single-vessel disease
108 (69%)
85 (41%)
Multi-vessel disease
49 (31%)
105 (51%)
Demographics and risk factors
63  10
65  10
131 (83%)
146 (71%)
N/A
28  5
Hypertension
88 (56%)
137 (67%)
Dyslipidemia
N/A
127 (62%)
Tobacco
34 (22%)
64 (31%)
Diabetes mellitus
54 (34%)
50 (24%)
N/A
71 (35%)
Age (years)
Male sex
Body-mass index (kg/m 2)
Family history
Clinical history
Ejection fraction (%)
EF<50%
Stable angina
Unstable angina
N/A
56  11
13 (8%)
N/A
151 (96%)
140 (68%)
6 (4%)
46 (22%)
49
Prior MI in culprit artery
N/A
28 (14%)
Medications
Aspirin
N/A
181 (88%)
Additional antiplatelet
N/A
94 (46%)
ACE inhibitor or ARB
N/A
139 (68%)
Beta blocker
N/A
161 (78%)
Statin
N/A
169 (82%)
Calcium antagonist
N/A
49 (24%)
Long-acting nitrate
N/A
45 (22%)
Insulin
N/A
19 (9%)
Oral anti-diabetic medication
N/A
33 (16%)
* = taken from Tables #1 of the ADVISER4 and VERIFYR21 studies
** = Table #1 of the ADVISE study lists n (%) based on number of lesions (not number of subjects)
ACE = angiotensin-converting enzyme; ADVISE = ADenosine Vasodilator Independent Stenosis
EvaluationR4; ARB = angiotensin receptor blockers; EF = left ventricular ejection fraction; LAD =
left anterior descending coronary artery; LCx = left circumflex coronary artery; MI = myocardial
infarction; N/A = not available; RCA = right coronary artery; VERIFY = VERification of
Instantaneous wave-Free ratio and fractional flow reserve for the assessment of coronary artery
stenosis severity in everydaY practiceR21
50
Supplement Table T9. Clinical data for combined pressure-flow measurements
Variable
AMC
KCL
VUmc
Number of subjects
28
19
38
Number of lesions
44
19
55
47  11
33  8
42 (34-54)
44 (100%)
13 (68%)
51 (93%)
0 (0%)
6 (32%)
4 (7%)
LAD system
17 (61%)
6 (32%)
33 (60%)
LCx system
7 (25%)
7 (37%)
11 (20%)
RCA system
4 (14%)
6 (32%)
8 (15%)
Ramus
0 (0%)
0 (0%)
3 (5%)
Unknown
4 (14%)
0 (0%)
0 (0%)
Diameter stenosis (%)
49  17
N/A
37  17
Lesion iFR
0.90 (0.72-0.95)
0.94 (0.91-0.97)
0.97 (0.94-0.99)
Lesion FFR
0.79 (0.55-0.88)
0.89 (0.85-0.92)
0.88 (0.82-0.90)
2.42  0.92
2.44  0.90
3.14  0.77
Number of beats
Intracoronary adenosine
Intravenous adenosine
Lesion CFVR
Demographics and risk factors
57  10
60  10
61  9
20 (71%)
11 (55%)
30 (79%)
28  4
27  5
N/A
Hypertension
8 (28%)
9 (45%)
16 (42%)
Dyslipidemia
18 (64%)
13 (65%)
21 (55%)
Current or prior tobacco
12 (43%)
8 (40%)*
16 (42%)
Diabetes mellitus
3 (11%)
3 (15%)*
11 (29%)
Family history
17 (61%)
8 (40%)*
13 (34%)
5 (25%)
14 (37%)
Age (years)
Male sex
Body-mass index (kg/m 2)
Clinical history
Prior MI
3 (11%)
51
Prior coronary angioplasty
2(7%)
3 (15%)
N/A
CCS class 1 angina
1 (4%)*
N/A
7 (18%)
CCS class 2 angina
7 (26%)
N/A
20 (53%)
CCS class 3 angina
16 (59%)
N/A
11 (29%)
CCS class 4 angina
3 (11%)
N/A
0 (0%)
Medications
Aspirin
27 (96%)
N/A
36 (95%)
Additional antiplatelet
21 (75%)
N/A
N/A
ACE inhibitor or ARB
4 (14%)
N/A
14 (37%)
Beta blocker
24 (86%)
N/A
30 (79%)
Statin
25 (89%)
N/A
26 (68%)
Calcium antagonist
6 (21%)
N/A
13 (34%)
Long-acting nitrate
11 (39%)
N/A
20 (53%)
Insulin
1 (3%)
1 (5%)*
N/A
Oral anti-diabetic medication
1 (3%)
1 (5%)*
N/A
* = percentages calculated after excluding missing data present in <10% of the marked fields
AMC = Academic Medical Center in Amsterdam; CCS = Canadian Cardiovascular Society; CFVR
= coronary flow velocity reserve; FFR = fractional flow reserve; iFR = instantaneous wave-free
ratio; KCL = King’s College London; LAD = left anterior descending coronary artery; LCx = left
circumflex coronary artery; MI = myocardial infarction; N/A = not available; RCA = right coronary
artery; VUmc = VU University Medical Center in Amsterdam
52
Supplement Table T10. Clinical observations overall and by tertile with associated relative iFR error
Variable
iFR (essentially rest, diastole)
FFR (stress, whole cycle)
Rest, systole
Diastolic FFR (stress, diastole)
Stress, systole
Rest, whole cycle (Grüntzig point)
Rest flow velocity (cm/sec)
Rest diastolic flow velocity (cm/sec)
Rest systolic flow velocity (cm/sec)
Stress flow velocity (cm/sec)
Stress diastolic flow velocity (cm/sec)
Stress systolic flow velocity (cm/sec)
CFVR
Heart rate (bpm)
Rest heart rate (bpm)
Stress heart rate (bpm)
Systolic fraction of cardiac cycle (%)
Mean arterial pressure (mmHg)
Systolic blood pressure (mmHg)
Diastolic blood pressure (mmHg)
Rest mean arterial pressure (mmHg)
Rest systolic blood pressure (mmHg)
Rest diastolic blood pressure (mmHg)
Stress mean arterial pressure (mmHg)
Stress systolic blood pressure (mmHg)
Stress diastolic blood pressure (mmHg)
Mean pulse pressure (mmHg)
Peak pulse pressure (mmHg)
Rest mean pulse pressure (mmHg)
Rest peak pulse pressure (mmHg)
Stress mean pulse pressure (mmHg)
Stress peak pulse pressure (mmHg)
Diastolic/systolic flow ratio
Mean/diastolic flow ratio
Rest diastolic/systolic flow ratio
Variable by its own tertile
All
(n = 120)
Low
Middle
High
Observed relative distal pressure gradient
0.95 (0.90-0.98) 0.84 (0.72-0.91) 0.95 (0.94-0.97) 0.98 (0.98-0.99)
0.86 (0.78-0.90) 0.75 (0.52-0.78) 0.86 (0.84-0.88) 0.91 (0.90-0.93)
0.97 (0.95-0.99) 0.94 (0.91-0.96) 0.98 (0.97-0.98) 0.99 (0.99-1.00)
0.82 (0.71-0.87) 0.66 (0.39-0.72) 0.82 (0.80-0.84) 0.89 (0.87-0.90)
0.92 (0.85-0.95) 0.84 (0.72-0.87) 0.92 (0.91-0.93) 0.96 (0.95-0.96)
0.96 (0.93-0.98) 0.90 (0.81-0.93) 0.96 (0.95-0.97) 0.98 (0.98-0.99)
Observed flow velocity
16.4 ± 7.3
9.9 ± 1.7
15.2 ± 2.2
24.3 ± 6.5
20.2 ± 9.3
11.5 ± 2.2
18.7 ± 2.8
30.3 ± 8.3
10.9 ± 5.8
6.1 ± 2.0
10.0 ± 1.2
16.9 ± 6.1
42.8 ± 17.6
25.6 ± 6.3
40.3 ± 3.8
62.4 ± 13.5
50.6 ± 21.9
29.8 ± 7.9
47.5 ± 4.7
75.1 ± 18.1
31.1 ± 13.4
17.9 ± 3.7
29.0 ± 3.1
46.4 ± 10.2
2.77 ± 0.94
1.72 ± 0.36
2.76 ± 0.27
3.83 ± 0.50
Observed heart rate
66 ± 12
54 ± 8
68 ± 3
79 ± 5
65 ± 13
52 ± 8
65 ± 4
79 ± 9
67 ± 13
53 ± 8
68 ± 3
82 ± 5
41 ± 8
33 ± 2
41 ± 3
51 ± 5
Observed blood pressure
95 ± 17
79 ± 7
93 ± 3
113 ± 14
108 ± 20
90 ± 8
107 ± 4
129 ± 16
86 ± 15
72 ± 6
85 ± 3
102 ± 11
97 ± 17
82 ± 7
97 ± 4
116 ± 14
110 ± 20
91 ± 9
109 ± 3
131 ± 16
89 ± 15
75 ± 7
88 ± 4
105 ± 12
94 ± 17
77 ± 8
92 ± 3
112 ± 13
107 ± 20
87 ± 9
107 ± 5
130 ± 15
84 ± 15
69 ± 7
84 ± 3
101 ± 11
22 ± 10
12 ± 2
20 ± 2
34 ± 6
54 ± 19
36 ± 5
51 ± 6
77 ± 11
21 ± 11
10 ± 3
19 ± 3
34 ± 7
57 ± 20
38 ± 5
55 ± 7
81 ± 11
23 ± 10
13 ± 3
22 ± 3
35 ± 6
57 ± 19
38 ± 5
54 ± 7
80 ± 11
Observed flow ratio
1.81 ± 0.61
1.30 ± 0.17
1.71 ± 0.10
2.43 ± 0.66
0.84 ± 0.07
0.77 ± 0.03
0.83 ± 0.01
0.91 ± 0.05
2.19 ± 1.72
1.33 ± 0.20
1.81 ± 0.12
3.46 ± 2.52
53
Associated iFR relative error (%)
Low
Middle
High
p value*
14 ± 20
21 ± 19
15 ± 18
20 ± 19
20 ± 19
16 ± 19
10 ± 7
9±5
9±7
10 ± 6
9±6
9±7
12 ± 7
6±3
11 ± 7
6±3
6±4
11 ± 7
0.35
<0.001
0.13
<0.001
<0.001
0.13
14 ± 16
14 ± 16
13 ± 14
11 ± 18
14 ± 18
10 ± 17
8 ± 14
10 ± 10
9±8
11 ± 13
12 ± 9
10 ± 9
12 ± 10
16 ± 14
12 ± 13
13 ± 14
12 ± 13
13 ± 11
13 ± 11
14 ± 11
12 ± 11
0.52
0.59
0.80
0.40
0.77
0.16
0.23
15 ± 13
15 ± 14
16 ± 14
13 ± 8
11 ± 12
11 ± 12
10 ± 14
12 ± 13
9 ± 14
10 ± 13
11 ± 12
11 ± 17
0.05
0.10
0.06
0.40
12 ± 12
11 ± 13
11 ± 12
12 ± 12
12 ± 14
11 ± 11
11 ± 12
10 ± 13
11 ± 11
12 ± 14
10 ± 10
12 ± 14
10 ± 9
14 ± 16
10 ± 12
11 ± 12
11 ± 14
13 ± 13
11 ± 12
11 ± 13
12 ± 15
13 ± 11
13 ± 14
12 ± 12
14 ± 12
16 ± 15
14 ± 14
15 ± 16
10 ± 9
16 ± 13
14 ± 16
14 ± 13
13 ± 15
13 ± 15
13 ± 13
13 ± 13
13 ± 17
13 ± 14
14 ± 16
11 ± 14
11 ± 15
10 ± 12
11 ± 14
12 ± 14
10 ± 14
0.57
0.43
0.47
0.77
0.86
0.57
0.58
0.42
0.34
0.69
0.75
0.58
0.66
0.52
0.98
16 ± 16
10 ± 14
11 ± 12
12 ± 13
12 ± 12
14 ± 17
8±8
14 ± 14
11 ± 11
0.011
0.11
0.98
Rest mean/diastolic flow ratio
Stress diastolic/systolic flow ratio
Stress mean/diastolic flow ratio
Peak/mean flow ratio
Rest peak/mean flow ratio
Stress peak/mean flow ratio
Pulsatility (unitless)
Rest pulsatility (unitless)
Stress pulsatility (unitless)
Systolic pulsatility (unitless)
Diastolic pulsatility (unitless)
Rest systolic pulsatility (unitless)
Rest diastolic pulsatility (unitless)
Stress systolic pulsatility (unitless)
Stress diastolic pulsatility (unitless)
Rest resistance (mmHg/[cm/sec])
Rest systolic resistance (mmHg/[cm/sec])
Rest diastolic resistance (mmHg/[cm/sec])
Stress resistance (mmHg/[cm/sec])
Resistance ratio** (no units)
Stress systolic resistance (mmHg/[cm/sec])
Stress diastolic resistance (mmHg/[cm/sec])
HSR (mmHg/[cm/sec])
HMR (mmHg/[cm/sec])
0.83 ± 0.08
1.69 ± 0.51
0.86 ± 0.08
1.64 ± 0.19
1.76 ± 0.28
1.51 ± 0.18
1.14 (1.11-1.19)
1.17 (1.12-1.24)
1.10 (1.07-1.13)
1.09 (1.07-1.15)
1.05 (1.03-1.08)
1.14 (1.09-1.26)
1.07 (1.04-1.10)
1.06 (1.04-1.09)
1.10 (1.07-1.13)
6.47 ± 2.86
13.18 ± 12.85
4.84 ± 2.55
2.06 ± 0.83
2.46 ± 1.03
3.53 ± 1.39
1.44 ± 0.63
0.51 ± 0.57
2.06 ± 0.83
0.76 ± 0.05
0.82 ± 0.01
1.21 ± 0.18
1.63 ± 0.10
0.78 ± 0.03
0.84 ± 0.01
1.47 ± 0.07
1.61 ± 0.04
1.53 ± 0.08
1.70 ± 0.04
1.35 ± 0.07
1.50 ± 0.03
Observed pulsatility
1.09 (1.07-1.11) 1.14 (1.13-1.16)
1.11 (1.09-1.12) 1.17 (1.16-1.19)
1.06 (1.04-1.07) 1.10 (1.09-1.11)
1.06 (1.04-1.07) 1.09 (1.08-1.11)
1.03 (1.02-1.04) 1.06 (1.05-1.07)
1.06 (1.05-1.09) 1.14 (1.12-1.17)
1.04 (1.02-1.05) 1.07 (1.07-1.08)
1.03 (1.02-1.04) 1.06 (1.05-1.07)
1.06 (1.04-1.07) 1.10 (1.09-1.11)
Observed resistance
3.73 ± 0.81
6.08 ± 0.73
6.70 ± 1.35
10.05 ± 1.12
2.46 ± 0.68
4.47 ± 0.61
1.28 ± 0.25
1.92 ± 0.19
1.33 ± 0.37
2.41 ± 0.31
2.19 ± 0.51
3.32 ± 0.28
0.88 ± 0.19
1.33 ± 0.13
0.15 ± 0.04
0.29 ± 0.06
1.28 ± 0.25
1.92 ± 0.19
0.91 ± 0.06
2.23 ± 0.48
0.93 ± 0.06
1.87 ± 0.16
2.08 ± 0.26
1.70 ± 0.17
11 ± 13
16 ± 16
8 ± 11
17 ± 14
14 ± 14
19 ± 16
14 ± 17
13 ± 13
12 ± 13
11 ± 14
11 ± 11
10 ± 9
12 ± 12
8±8
16 ± 15
8±9
11 ± 14
8 ± 11
0.84
0.008
0.005
0.003
0.47
<0.001
1.25 (1.20-1.32)
1.28 (1.25-1.42)
1.17 (1.13-1.23)
1.21 (1.15-1.40)
1.10 (1.08-1.11)
1.35 (1.26-1.72)
1.12 (1.10-1.15)
1.11 (1.09-1.20)
1.17 (1.13-1.23)
14 ± 15
13 ± 15
17 ± 16
11 ± 11
14 ± 16
9 ± 12
12 ± 16
15 ± 14
17 ± 16
13 ± 14
13 ± 14
11 ± 11
12 ± 12
9 ± 12
13 ± 11
13 ± 14
11 ± 9
11 ± 11
9 ± 10
11 ± 11
7±9
12 ± 16
13 ± 10
14 ± 16
11 ± 9
10 ± 16
7±9
0.08
0.46
<0.001
0.74
0.52
0.11
0.81
0.08
<0.001
9.60 ± 2.41
22.81 ± 18.78
7.63 ± 2.21
2.97 ± 0.74
3.63 ± 0.55
5.11 ± 1.04
2.11 ± 0.62
1.12 ± 0.68
2.97 ± 0.74
12 ± 14
14 ± 14
12 ± 15
15 ± 12
7 ± 12
15 ± 11
15 ± 15
7±4
15 ± 12
8±8
7±9
9±8
15 ± 14
13 ± 10
13 ± 13
13 ± 12
10 ± 7
15 ± 14
16 ± 15
15 ± 15
15 ± 15
6 ± 12
17 ± 15
8 ± 15
9 ± 11
19 ± 20
6 ± 12
0.26
0.59
0.244
0.004
<0.001
0.026
0.035
<0.001
0.004
* = p<0.05 colored red and p=0.05-0.10 colored green
** = Ratio of diastolic resting resistance to mean hyperemic resistance (as in Figure 4 of main paper)
bpm = beats per minute; CFVR = coronary flow velocity reserve; FFR = fractional flow reserve; HMR = hyperemic microvascular
resistance; HSR = hyperemic stenosis resistance (same as stress resistance); iFR = instantaneous wave-free ratio
54
Supplement Table T11. Comparison of best-fit parameters to clinical observations
Parameter
Best-fit values
Coefficient of viscous loss (Cv in mmHg/[cm/sec])
Clinical observations
19.2 (12.2-33.8)  10-2
N/A
Coefficient of exit loss (Ce in
mmHg/[cm/sec]2)
1.23 (0.00-3.91) 
Mean arterial pressure (mmHg)
Systolic blood pressure (mmHg)
Diastolic blood pressure (mmHg)
Systolic fraction of cardiac cycle (%)
Diastolic/systolic flow ratio ()
Mean/diastolic flow ratio ()
Diastolic shaping function ()
Coefficient of determination (R2) for diastole
Coefficient of determination (R2) for systole
91 ± 17
95 ± 17
118 ± 47
108 ± 20
85 ± 15
86 ± 15
42 ± 17
41 ± 8
1.78 ± 0.68
1.81 ± 0.61
0.83 ± 0.10
0.84 ± 0.07
1.31 ± 0.17
Systolic shaping function ()
Coefficient of determination (R2) for whole cycle
10-3
0.61 ± 0.16
N/A
0.93 (0.76-0.97)
0.93 (0.80-0.97)
0.79 (0.33-0.90)
N/A = not applicable
55
Supplement Table T12. Comparison of myocardial resistances among centers ordered by size
Center
Size
Resting diastole resistance
Mean hyperemia resistance
Rest/stress resistance
(mmHg/[cm/sec])
(mmHg/[cm/sec])
ratio (unitless)
VUmc
N = 55
5.31 ± 2.52
1.89 ± 0.59
2.79 ± 0.85
AMC
N = 44
4.53 ± 2.42
2.33 ± 1.06
2.15 ± 1.07
ADVISE*
N = 39
2.84 ± 1.47
3.02 ± 3.15
0.94  1.10**
KCL
N = 19
3.96 ± 2.74
1.85 ± 0.71
2.17 ± 1.17
* = means and standard deviations were taken from the left column at the bottom on page 1396
under the subsection “Resistance throughout the cardiac cycle at rest and with pharmacologic
vasodilation” of the ADVISE manuscript,R4 although Figure 5A on page 1397 displays means and
standard errors (which are 1/39 times smaller, or only 16% of the standard deviation)
** = although the ratio is not explicitly provided in the ADVISE manuscript,R4 it can be estimated
using the provided values and standard error propagation techniques
ADVISE = ADenosine Vasodilator Independent Stenosis EvaluationR4; AMC = Academic Medical
Center in Amsterdam; KCL = King’s College London; VUmc = VU University Medical Center in
Amsterdam
56