# Does the Instantaneous Wave-Free Ratio Approximate the Fractional Flow Reserve?

## Author + information

- Received May 8, 2012
- Revision received September 18, 2012
- Accepted September 18, 2012
- Published online April 2, 2013.

## Author Information

- Nils P. Johnson, MD, MS
^{⁎}, - Richard L. Kirkeeide, PhD
^{⁎}, - Kaleab N. Asrress, MA, BM, BCh
^{†}, - William F. Fearon, MD
^{‡}, - Timothy Lockie, MB, ChB, PhD
^{†},^{§}, - Koen M.J. Marques, MD, PhD
^{∥}, - Stylianos A. Pyxaras, MD
^{¶}, - M. Cristina Rolandi, MSc
^{#}, - Marcel van 't Veer, MSc, PhD
^{⁎⁎},^{††}, - Bernard De Bruyne, MD, PhD
^{¶}, - Jan J. Piek, MD, PhD
^{§}, - Nico H.J. Pijls, MD, PhD
^{⁎⁎},^{††}, - Simon Redwood, MD
^{†}, - Maria Siebes, PhD
^{#}, - Jos A.E. Spaan, PhD
^{#}and - K. Lance Gould, MD
^{⁎},^{⁎}(K.Lance.Gould{at}uth.tmc.edu)

- ↵⁎
**Reprint requests and correspondence:**

Dr. K. Lance Gould, Weatherhead PET Center for Preventing and Reversing Atherosclerosis, University of Texas Medical School at Houston, 6431 Fannin Street, Room 4.256 MSB, Houston, Texas 77030

## Abstract

**Objectives** This study sought to examine the clinical performance of and theoretical basis for the instantaneous wave-free ratio (iFR) approximation to the fractional flow reserve (FFR).

**Background** Recent work has proposed iFR as a vasodilation-free alternative to FFR for making mechanical revascularization decisions. Its fundamental basis is the assumption that diastolic resting myocardial resistance equals mean hyperemic resistance.

**Methods** Pressure-only and combined pressure-flow clinical data from several centers were studied both empirically and by using pressure-flow physiology. A Monte Carlo simulation was performed by repeatedly selecting random parameters as if drawing from a cohort of hypothetical patients, using the reported ranges of these physiologic variables.

**Results** We aggregated observations of 1,129 patients, including 120 with combined pressure-flow data. Separately, we performed 1,000 Monte Carlo simulations. Clinical data showed that iFR was +0.09 higher than FFR on average, with ±0.17 limits of agreement. Diastolic resting resistance was 2.5 ± 1.0 times higher than mean hyperemic resistance in patients. Without invoking wave mechanics, classic pressure-flow physiology explained clinical observations well, with a coefficient of determination of >0.9. Nearly identical scatter of iFR versus FFR was seen between simulation and patient observations, thereby supporting our model.

**Conclusions** iFR provides both a biased estimate of FFR, on average, and an uncertain estimate of FFR in individual cases. Diastolic resting myocardial resistance does not equal mean hyperemic resistance, thereby contravening the most basic condition on which iFR depends. Fundamental relationships of coronary pressure and flow explain the iFR approximation without invoking wave mechanics.

- coronary physiology
- fractional flow reserve
- instantaneous wave-free ratio
- Monte Carlo simulation
- myocardial resistance
- vasodilation

Coronary physiology plays an increasingly important role in interventional cardiology (1). Even as the overall volume of percutaneous coronary interventions declines in the United States, the number of fractional flow reserve (FFR) procedures has grown (2). This growth accelerated after the publication of the FAME (Fractional Flow Reserve Versus angiography for multivessel evaluation) trial (3), leading to strong guideline recommendations for physiologic evaluation of an intermediate stenosis lacking definitive functional data.

Measurement of FFR requires an invasive procedure, systemic anticoagulation, instrumentation of the coronary arteries, and pharmacologic vasodilation. In an attempt to avoid the last of these requirements, recent work has proposed the instantaneous wave-free ratio (iFR) (4). While FFR averages the relative distal pressure over the entire cardiac cycle during hyperemia (5), iFR measures the relative distal pressure from mid-to-end diastole at rest. Because coronary flow occurs predominantly in diastole, pressure gradients are higher than during the lower flow period of systole. The fundamental basis of iFR approximation to FFR is the assumption that diastolic resting myocardial resistance equals mean hyperemic resistance (4).

As with any approximation, prerequisites for the successful substitution of iFR for FFR need to be understood, as must its diagnostic performance. Certain general conditions may exist to explain the situations in which iFR does not approximate FFR well. For such cases, pharmacologic vasodilation remains essential to accurately assess stenosis severity. Furthermore, iFR may offer a biased or uncertain estimate of FFR. In this case, iFR could not be used interchangeably with FFR.

Therefore, we first applied a simulation model to study the relationship between iFR and FFR while varying independent anatomic and hemodynamic parameters. Next, we validated our predictions of the iFR approximation by using a large, multicenter cohort of human data. Finally, we tested the assumption that myocardial “resistance at rest is equivalent to time-averaged resistance during FFR measurements” (4).

## Methods

### Simulation model

Our model applies fundamental principles of coronary and stenosis hemodynamics to a tree network of arterial segments and myocardial beds while allowing for the natural range of normal and abnormal physiology (such as pressure, flow, heart rate, and focal and diffuse atherosclerosis). Full details can be found in the Online Appendix. Our simulation model is not intended to predict iFR or FFR as a diagnostic application but rather to study interactions, physiologic variables, and mechanisms affecting both parameters.

Two general types of simulations were performed. First, parameters such as heart rate, blood pressure, severity of focal and diffuse disease, rest flow, and maximal coronary flow reserve (CFR) in the absence of disease were varied independently to study their relative influences on the iFR/FFR relationship. Results are provided entirely in the Online Appendix. Second, a Monte Carlo simulation was performed. The Monte Carlo method allows for exploration of a complex system when exact mathematical solutions are not feasible because of many parameters whose values are either uncertain or demonstrate innate variability. We repeatedly selected random parameters for the model as if drawing from a cohort of hypothetical patients, using reported ranges of these physiologic variables. The relationship between iFR and FFR was explored after simulation of 1,000 “patients” (repetitions).

### Human clinical data

Two types of analyses were performed using intracoronary human data: first, the relationship between iFR and FFR; and second, empirical observations and application of physiologic principles to combined pressure-flow measurements. Data were aggregated from multiple centers to produce a large and diverse cohort, as detailed in the Online Appendix. Pressure-only and combined pressure-flow data were acquired using standard equipment and techniques, including both intravenous and intracoronary adenosine for hyperemia. Informed consent approved by the local review board was obtained from each human subject at the time of the original data collection. In most cases, original data had already been analyzed and published as part of other research, occasionally unrelated to iFR, especially for combined pressure-flow data.

Empirical observations from pressure-flow data summarize the signed relative error between iFR and FFR, as ([iFR − FFR]/FFR × 100) across tertiles of hemodynamic parameters (e.g., rest flow velocity, heart rate, mean arterial pressure, and so on). Best-fit parameters, as described in the Online Appendix, were used to test the ability of classical pressure-flow physiology to describe iFR. Myocardial resistance was estimated by dividing distal coronary pressure by its flow velocity only for practical comparison with the results of prior work (4). Conceptually, instantaneous or diastolic myocardial resistance is not correct because of large intramyocardial compliance. Additionally, coronary backpressure should be taken into account, although several issues are controversial and are discussed in detail elsewhere (6).

For our primary analysis, we used the exact definition of the diastolic “wave-free” period as originally proposed, namely “beginning 25% of the way into diastole and ending 5 ms before the end of diastole,” where the “onset of diastole was identified from the dicrotic notch” (4). As a secondary analysis, mainly detailed in the Online Appendix, we explored the sensitivities of iFR and myocardial resistance to the exact definition of diastole.

### Statistical methods

Statistical analyses were performed using R version 2.14.1 software (R Foundation for Statistical Computing, Vienna, Austria). We used standard summary statistical tests and least squares regression, as detailed in the Online Appendix. Applicable tests were two-tailed, and a p value of <0.05 was considered statistically significant.

## Results

### iFR/FFR relationship

Figure 1 displays two scatter plots of iFR versus FFR from 1,000 simulations (Fig. 1A) and from observations of 1,129 patients (Fig. 1B). The plots show similar findings: a large cluster in the upper right corner of hemodynamically insignificant lesions; systematically larger iFR values than FFR values in the central portion, with wide scatter in their relationship; and wider scatter with a steeper slope for cases with FFR of less than approximately 0.6.

Quantitatively, a linear model reasonably describes the relationship between iFR and FFR: a Pearson correlation coefficient (r) of 0.88 (95% confidence interval [CI]: 0.86 to 0.89, p < 0.001) for the simulation and an r value of 0.82 (95% CI: 0.80 to 0.84, p < 0.001) for human data; a linear slope of 0.90 ± 0.02 (p < 0.001) for the simulation and 0.90 ± 0.02 (p < 0.001) for human data; and a linear intercept of 0.15 ± 0.01 (p < 0.001) for the simulation and 0.16 ± 0.01 (p < 0.001) for human data. The area under the receiver-operating characteristic (ROC) curve for iFR to predict FFR <0.8 equals 0.95 for the simulation and 0.86 for human data. The optimal ROC cutoff value occurs at 0.89 for all clinical observations combined, which is higher than the value 0.83 in the original iFR study (4).

Figure 2 displays the Bland-Altman plot for all human data. On average, iFR exceeded FFR by +0.09, with a 95% CI from −0.08 to +0.26. The Bland-Altman analysis confirms the visual impression from Figure 1, namely, iFR systematically overestimates FFR with a large scatter. Even after removing the bias by subtracting +0.09 from iFR, the ±0.17 limits of agreement with FFR would frequently cross the FFR range of 0.75 to 0.80 validated in randomized trials for clinical management (1,3). As detailed in the Online Appendix, a more sophisticated method of correcting iFR does not shrink the CI.

### Diagnostic accuracy

Figure 3 displays the diagnostic accuracy of iFR (Fig. 3A) and its associated trade-off regarding the frequency of adenosine administration (Fig. 3B) necessary to obtain FFR when iFR is discordant. Table 1 provides the percentage of cases that would require adenosine to achieve an arbitrary accuracy. For example, if a 99% diagnostic accuracy were desired (0.5% false positives plus 0.5% false negatives), then the iFR range requiring adenosine would be 0.74 to 0.98 and 76% of cases would need vasodilation. On the other hand, if only a 96% diagnostic accuracy were desired (2% false positive plus 2% false negatives), then the iFR range requiring adenosine would shrink to 0.82 to 0.96, but still 54% of cases would need vasodilation.

### Testing equivalencies of resistance

Figure 4 demonstrates that diastolic “wave-free” resting resistance, computed exactly as in the original iFR report (4), significantly and consistently exceeds mean hyperemic resistance: 4.84 ± 2.55 mm Hg/(cm/s) versus 2.06 ± 0.83 mm Hg/(cm/s) (paired *t* test, p < 0.001). On average, diastolic resting resistance was 2.46 ± 1.03 times higher than mean hyperemic resistance. In only 11 of 120 cases (9%) did resistance decrease by <10% between these 2 conditions, thereby contravening the most basic condition on which iFR depends.

Neither diastolic resting myocardial resistance nor iFR appears sensitive to the diastolic period. Diastolic resting myocardial resistance does not differ between the original iFR definition (25% after the dicrotic notch on the aortic tracing until 5 ms before systole) and use of all of diastole (4.84 ± 2.55 mm Hg/[cm/s] vs. 4.83 ± 2.48 mm Hg/[cm/s], respectively; paired *t* test, p = 0.75). As detailed more extensively in the Online Appendix, iFR also did not differ significantly between these 2 definitions (p = 0.99).

### Relative distal pressure

Superimposed data in Figure 3B from 1,000 patients demonstrate the need for adenosine when using the mean resting relative distal pressure (“rest Pd/Pa”). Both iFR and rest Pd/Pa require similar frequencies of adenosine to achieve a desired accuracy. The area under the ROC curve equals 0.86 for iFR and 0.87 for rest Pd/Pa.

Figure 5 shows the relationship between iFR and the mean resting relative distal pressure in 1,000 patients. These two variables are highly linear (slope: 1.39; intercept: −0.39), with a 95% CI of ±0.06 (Fig. 5, dashed lines). The correlation coefficient (r = 0.97 with r^{2} = 0.95, p < 0.001) implies that resting Pd/Pa accounts for 95% of the variation in iFR.

### Combined pressure-flow data

Table 2 summarizes key empirical observations and associated relative iFR errors by tertile of each parameter. Relative error of iFR varies significantly with lesion FFR and myocardial resistance during hyperemia. However, neither can be determined before vasodilation. Table 3 compares best-fit parameters to clinical observations. An expanded version of this table can be found in the Online Appendix. Overall, fundamental pressure-flow physiology describes the observations well without invoking wave mechanics. Coefficients of determination (R^{2}) were >0.90 for both diastolic data and the entire cardiac cycle.

## Discussion

Our multifaceted study of the iFR approximation to FFR offers several key results. First, iFR offers both a biased estimate of FFR, on average, and an uncertain estimate of FFR for an individual case. As shown in the Bland-Altman analysis of Figure 2, iFR is +0.09 higher than FFR on average. Even after correcting for this bias, iFR has wide limits of agreement with FFR of ±0.17 that would often alter clinical management. Therefore, for an individual patient, iFR should not be used interchangeably with FFR.

Second, no “perfect” iFR cutoff exists; each possible threshold offers a compromise between diagnostic accuracy and the need for vasodilation to measure FFR. Figure 3 and Table 1 quantify the trade-off for practitioners who seek to avoid vasodilation in a subset of cases. Given the relative ease of vasodilation compared to the profound clinical consequences of an inappropriate decision regarding mechanical revascularization, at best a narrow range of iFR would avoid the need for hyperemia in a minority of patients.

Third, diastolic resting myocardial resistance does not equal mean hyperemic resistance. Figure 4 demonstrates that on average, resistance falls with vasodilation. This finding contravenes the “existence of a diastolic interval in which intracoronary resistance at rest is equivalent to time-averaged resistance during FFR measurements” (4) stipulated by iFR. Indeed, our observations in human subjects of 2.5-fold higher resistance under diastolic resting conditions than in mean hyperemia exactly mirrors results from animal experiments during early development of FFR.

Fourth, iFR offers no diagnostic advantage compared to relative distal pressure at rest averaged over the whole cardiac cycle (rest Pd/Pa). Figure 3B and Table 1 show that iFR provides no improvement in diagnostic accuracy. The explanation can be found in Figure 5, which shows that rest Pd/Pa explains 95% of the variation in iFR because the two variables are highly linear.

Fifth, discordance of iFR from FFR can be explained by a host of factors, as detailed in the Online Appendix. The scatter shown in Figure 1A for simulation data implies that general hemodynamic principles and biological variability, not measurement error in either iFR or FFR, produce the same pattern in Figure 1B for clinical data. Clinical observations shown in Table 2 suggest that lesion FFR and myocardial resistance during hyperemia are the most important factors for explaining discordance. For example, the iFR relative error is smallest for the lowest tertile of the rest/stress resistance ratio. However, the change in resistance cannot be predicted before vasodilation, thereby preventing development of a prospective “rule” for when vasodilation is essential for diagnostic accuracy.

Finally, fundamental relationships of coronary pressure and flow explain the iFR approximation without invoking wave mechanics. The visual and quantitative agreement among our Monte Carlo simulation and a large compilation of human data in Figure 1, as well as the success of best-fit parameters when applied to a large set of human pressure-flow data in Table 3, strongly suggest that our model and its underlying theory have captured the essential physiologic parameters. Therefore, the term “instantaneous wave-free” in the iFR abbreviation has, at best, a limited theoretical basis and clinical utility.

### Comparison to existing literature

Presently, only two published studies of iFR exist (4,7). Our observed scatter in Figure 1B exactly mirrors that presented by others as their data has largely been included in the present analysis. Our Bland-Altman findings of a +0.09 bias with ±0.17 limits of agreement agree with their results: a +0.05 bias with ±0.19 limits of agreement overall (4) and +0.09 bias with ±0.18 limits of agreement in the prospective cohort (7).

In contrast to previous work (4), we found that myocardial resistance falls between diastolic resting and mean hyperemic conditions. Two potential explanations for this key discordant result appear unsatisfactory. First, although we had a larger sample size (over 3 times larger than the combined pressure/flow cohort in the original iFR report), estimates of resistance were consistent among all sites regardless of their individual sample sizes, as detailed in the Online Appendix.

Second, our work used intracoronary adenosine in 90% of cases as opposed to 100% intravenous adenosine in prior work (4). However, intravenous adenosine has generally been shown to produce equivalent if not superior hyperemia compared with that produced by intracoronary adenosine. A study comparing paired FFR measurements between these two routes of delivery found suboptimal hyperemia (FFR difference: >0.05) in 5 of 60 lesions and always higher with intracoronary dosing (8). Similarly, paired FFR measurements in 21 patients by using a variety of vasodilators and delivery routes found no significant overall differences between intracoronary and intravenous adenosine, although in a small subset with FFR of 0.70 to 0.86 intravenous adenosine produced lower FFR values (9). Therefore, our estimate of resistance changes provides a lower boundary and would likely have been greater had intravenous adenosine been used for all cases.

While iFR has been proposed only recently, several groups have examined the ability of relative distal pressure at rest (rest Pd/Pa) to predict FFR at hyperemia. For example, in 480 patients the relative distal pressure at rest had an area under the curve value of 0.86 to predict FFR ≤0.80 (10). The authors proposed the range 0.88 to 0.95 of relative distal pressure at rest for selective adenosine, which occurred in 53% of their retrospective cohort and achieved positive and negative predictive values of approximately 95%. By comparison, our subcohort of relative distal pressure at rest had an area under the curve value of 0.87, and the range 0.88 to 0.95 occurred in 46% of cases, producing 2.1% false positives and 4.1% false negatives for an accuracy of 94%. Similarly, in a different study of 123 patients, the relative distal pressure at rest significantly tracked the FFR at hyperemia on average across 3 groupings: 0.93 for an FFR >0.80; 0.88 for an FFR of 0.75 to 0.80; and 0.84 for an FFR <0.75 (11). Therefore, iFR mirrors these prior results and extends them to diastolic resting conditions but without significant diagnostic advantage. Indeed, measurement noise and errors generally render baseline indices more susceptible to measurement uncertainty.

### Study limitations

Our physiologic framework and Monte Carlo simulation do not account for minor factors such as a potential nonzero average for coronary flow momentum over each cycle, energy loss terms because of the angular branching of the coronary tree, homeostatic interactions among simulation parameters that in actuality tend to compensate for changes in any single variable, changing hemodynamic conditions between rest and stress, and the specifics of coronary flow waveforms.

However, despite these simplifications, our model demonstrated high coefficients of determination R^{2} in Table 3 when fitting “real-world” data and our Monte Carlo simulation produced results visually and quantitatively similar to human data, as seen in Figure 1. Therefore, these limitations do not appear to have prevented a fundamental understanding of the iFR approximation and its physiologic basis.

Myocardial resistance was calculated as the ratio of distal coronary pressure to flow velocity, neglecting several important conceptual issues with this definition (6), only to allow comparison to prior publications (4).

## Conclusions

The original paper concluded that iFR “has an excellent diagnostic efficiency in identifying stenoses with an FFR < 0.80” (4). However, and in answer to the question posed in the title of this study, iFR provides a biased estimate FFR on average with significant and unpredictable discordance that limits its widespread application, especially when considering the clinical consequences. Such discordance is fundamental to the physiologic basis for iFR itself. Furthermore, diastolic resting myocardial resistance does not equal mean hyperemic resistance, a stipulated condition in the original iFR report (4).

## Appendix

For an expanded Methods section with full details, as well as supplemental tables and figures, please see the online version of this article.

## Appendix

## Footnotes

Drs. Johnson, Kirkeeide, and Gould received internal funding from the Weatherhead PET Center for Preventing and Reversing Atherosclerosis, University of Texas Medical School. Dr. Asrress is supported by a fellowship from the British Heart Foundation. Dr. Fearon receives institutional grant support from St. Jude Medical, Inc. Ms. Rolandi is supported by a PhD scholarship from the Academic Medical Center, University of Amsterdam. Dr. De Bruyne is a consultant for St. Jude Medical, Inc. Drs. Spaan, Siebes, and Piek are supported by the European Community's Seventh Framework Programme (FP7/2007–2013) under grant agreement 224495 (euHeart Project). Drs. Siebes and Piek received support from the Dutch Heart Foundation (grant 2006B186). Dr. Pijls has received institutional research grants from St. Jude Medical, Inc., Abbott, and Maquet and is a consultant for St. Jude Medical, Inc. All other authors have reported that they have no relationships relevant to the contents of this paper to disclose.

- Abbreviations and Acronyms
- CFR
- coronary flow reserve
- CI
- confidence interval
- iFR
- instantaneous wave-free ratio
- FFR
- fractional flow reserve
- ROC
- receiver-operating characteristic

- Received May 8, 2012.
- Revision received September 18, 2012.
- Accepted September 18, 2012.

- American College of Cardiology Foundation

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