Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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. 1 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 3 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 4 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 5 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 6 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 / 7 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. 8 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. 9 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 CFR1. 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 10 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 11 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 13 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 (4.832.48 23 mmHg/[cm/sec]) did not differ significantly from the ADVISE definition (4.842.55 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 SUPPLEMENTAL REFERENCES R1. Siebes M, Verhoeff BJ, Meuwissen M, de Winter RJ, Spaan JA, Piek JJ. Single-wire pressure and flow velocity measurement to quantify coronary stenosis hemodynamics and effects of percutaneous interventions. Circulation. 2004 Feb 17;109(6):756-62. R2. Grüntzig AR, Senning A, Siegenthaler WE. Nonoperative dilatation of coronary-artery stenosis: percutaneous transluminal coronary angioplasty. N Engl J Med. 1979 Jul 12;301(2):61-8. R3. Pijls NH, van Son JA, Kirkeeide RL, De Bruyne B, Gould KL. Experimental basis of determining maximum coronary, myocardial, and collateral blood flow by pressure measurements for assessing functional stenosis severity before and after percutaneous transluminal coronary angioplasty. Circulation. 1993 Apr;87(4):1354-67. R4. Abe M, Tomiyama H, Yoshida H, Doba N. Diastolic fractional flow reserve to assess the functional severity of moderate coronary artery stenoses: comparison with fractional flow reserve and coronary flow velocity reserve. Circulation. 2000 Nov 7;102(19):2365-70. R5. Marques KM, van Eenige MJ, Spruijt HJ, Westerhof N, Twisk J, Visser CA, Visser FC. The diastolic flow velocity-pressure gradient relation and dpv50 to assess the hemodynamic significance of coronary stenoses. Am J Physiol Heart Circ Physiol. 2006 Dec;291(6):H2630-5. R6. Sen S, Escaned J, Malik IS, Mikhail GW, Foale RA, Mila R, Tarkin J, Petraco R, Broyd C, Jabbour R, Sethi A, Baker CS, Bellamy M, Al-Bustami M, Hackett D, Khan M, Lefroy D, Parker KH, Hughes AD, Francis DP, Di Mario C, Mayet J, Davies JE. Development and Validation of a New Adenosine-Independent Index of Stenosis Severity From Coronary Wave-Intensity Analysis 25 Results of the ADVISE (ADenosine Vasodilator Independent Stenosis Evaluation) Study. J Am Coll Cardiol. 2012 Apr 10;59(15):1392-402. R7. Verhoeff BJ, Siebes M, Meuwissen M, Atasever B, Voskuil M, de Winter RJ, Koch KT, Tijssen JG, Spaan JA, Piek JJ. Influence of percutaneous coronary intervention on coronary microvascular resistance index. Circulation. 2005 Jan 4;111(1):76-82. R8. Kirkeeide RL. Coronary obstructions, morphology and physiologic significance. In Quantitative Coronary Arteriography, editors Reiber JHC and Serruys PW. Kluwer Academic Publishers, 1991. Pages 229-244. R9. Young DF, Cholvin NR, Kirkeeide RL, Roth AC. Hemodynamics of arterial stenoses at elevated flow rates. Circ Res. 1977 Jul;41(1):99-107. R10. Young DF, Cholvin NR, Roth AC. Pressure drop across artificially induced stenoses in the femoral arteries of dogs. Circ Res. 1975 Jun;36(6):735-43. R11. Moran D, Epstein Y, Keren G, Laor A, Sherez J, Shapiro Y. Calculation of mean arterial pressure during exercise as a function of heart rate. Appl Human Sci. 1995 Nov;14(6):293-5. R12. Chung CS, Karamanoglu M, Kovács SJ. Duration of diastole and its phases as a function of heart rate during supine bicycle exercise. Am J Physiol Heart Circ Physiol. 2004 Nov;287(5):H2003-8. 26 R13. Petropoulakis PN, Kyriakidis MK, Tentolouris CA, Kourouclis CV, Toutouzas PK. Changes in phasic coronary blood flow velocity profile in relation to changes in hemodynamic parameters during stress in patients with aortic valve stenosis. Circulation. 1995 Sep 15;92(6):1437-47. R14. Hongo M, Nakatsuka T, Watanabe N, Takenaka H, Tanaka M, Kinoshita O, Okubo S, Sekiguchi M. Effects of heart rate on phasic coronary blood flow pattern and flow reserve in patients with normal coronary arteries: a study with an intravascular Doppler catheter and spectral analysis. Am Heart J. 1994 Mar;127(3):545-51. R15. Segal J, Kern MJ, Scott NA, King SB 3rd, Doucette JW, Heuser RR, Ofili E, Siegel R. Alterations of phasic coronary artery flow velocity in humans during percutaneous coronary angioplasty. J Am Coll Cardiol. 1992 Aug;20(2):276-86. R16. Feldman RL, Nichols WW, Pepine CJ, Conti CR. Influence of aortic insufficiency on the hemodynamic significance of a coronary artery narrowing. Circulation. 1979 Aug;60(2):259-68. R17. Skalidis EI, Kochiadakis GE, Koukouraki SI, Parthenakis FI, Karkavitsas NS, Vardas PE. Phasic coronary flow pattern and flow reserve in patients with left bundle branch block and normal coronary arteries. J Am Coll Cardiol. 1999 Apr;33(5):1338-46. R18. Kochiadakis GE, Skalidis EI, Kalebubas MD, Igoumenidis NE, Chrysostomakis SI, Kanoupakis EM, Simantirakis EN, Vardas PE. Effect of acute atrial fibrillation on phasic coronary blood flow pattern and flow reserve in humans. Eur Heart J. 2002 May;23(9):734-41. R19. Yang EH, Yeo TC, Higano ST, Nishimura RA, Lerman A. Coronary hemodynamics in patients with symptomatic hypertrophic cardiomyopathy. Am J Cardiol. 2004 Sep 1;94(5):685-7. 27 R20. Gould KL, Kirkeeide R, Johnson NP. Coronary branch steal: experimental validation and clinical implications of interacting stenosis in branching coronary arteries. Circ Cardiovasc Imaging. 2010 Nov;3(6):701-9. R21. Johnson NP, Kirkeeide RL, Gould KL. Is discordance of coronary flow reserve and fractional flow reserve due to methodology or clinically relevant coronary pathophysiology? JACC Cardiovasc Imaging. 2012 Feb;5(2):193-202. R22. Johnson NP, Gould KL. Integrating noninvasive absolute flow, coronary flow reserve, and ischemic thresholds into a comprehensive map of physiological severity. JACC Cardiovasc Imaging. JACC Cardiovasc Imaging. 2012 Apr;5(4):430-40. R23. Sdringola S, Johnson NP, Kirkeeide RL, Cid E, Gould KL. Impact of unexpected factors on quantitative myocardial perfusion and coronary flow reserve in young, asymptomatic volunteers. JACC Cardiovasc Imaging. 2011 Apr;4(4):402-12. R24. Berry C, van ‘t Veer M, Witt N, Kala P, Bocek O, Pyxaras S, McClure JD, Fearon WF, Barbato E, Tonino P, De Bruyne B, Pijls NH, Oldroyd KG. VERIFY (VERification of Instantaneous wave-Free ratio and fractional flow reserve for the assessment of coronary artery stenosis severity in everydaY practice: a multi-center prospective study in consecutive patients. J Am Coll Cardiol 2013;61:1421–7. R25. Marques KM, Spruijt HJ, Boer C, Westerhof N, Visser CA, Visser FC. The diastolic flowpressure gradient relation in coronary stenoses in humans. J Am Coll Cardiol. 2002 May 15;39(10):1630-6. 28 R26. R Development Core Team. 2011. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. Available at: http://www.R-project.org/. Accessed July 31, 2012. R27. Meuwissen M, Siebes M, Chamuleau SA, van Eck-Smit BL, Koch KT, de Winter RJ, Tijssen JG, Spaan JA, Piek JJ. Hyperemic stenosis resistance index for evaluation of functional coronary lesion severity. Circulation. 2002 Jul 23;106(4):441-6. R28. Sing T, Sander O, Beerenwinkel N, Lengauer T. ROCR: visualizing the performance of scoring classifiers. R package version 1.0-4. 2009. Available at: http://cran.rproject.org/web/packages/ROCR/index.html. Accessed July 31, 2012. 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 679 3.92.4 Reference #R11* 726 3.40.5 Reference #R10** 1036 2.41.7 Reference #R11 1248 2.51.3 Reference #R11 125 2.60.5 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