Angiography‐Derived Fractional Flow Reserve: More or Less Physiology?

in favor of analytical solutions based broadly upon the laws of Bernoulli and/or Poiseuille. These simpler physical laws characterize pressure losses attributable to convective acceleration and viscous friction, respectively. They are quick and simple to execute and perform well under steady (nonpulsatile), laminar flow conditions, in straight conduits. Coronary arteries, however, are not straight, and flow is pulsatile. Furthermore, these laws are unable to accurately characterize complex trans-lesional pressure dynamics, particularly poststenosis pressure recovery, which is the basis of FFR. Some stenosis models make empiric assumptions or cor-rections for pressure loss and recovery. On average, these may perform adequately, but cannot represent the potentially complex flow patterns in a specific case. Moreover, they may be particularly vulnerable to inaccuracy in the context of serial lesions and diffuse disease in which 3- dimensional computational fluid dynamics computations more reliably characterize in-terstenosis hemodynamic interaction. The impact this has on accuracy, in all disease patterns, is yet to be fully determined.


SIMPLIFICATION
Methods for computing angiography-derived FFR are software based. Three-dimensional arterial anatomy is reconstructed from paired 2-dimensional angiogram images. Mathematical equations that define hemodynamic laws are then applied to the reconstructed artery to predict the pressure dynamics along the artery, which are displayed as a color-mapped 3-dimensional artery. In an effort to rationalize these models to make them practical and expedient for clinical use, many groups have abandoned complex, numerical, computational fluid dynamics simulation in favor of analytical solutions based broadly upon the laws of Bernoulli and/or Poiseuille. These simpler physical laws characterize pressure losses attributable to convective acceleration and viscous friction, respectively. They are quick and simple to execute and perform well under steady (nonpulsatile), laminar flow conditions, in straight conduits. Coronary arteries, however, are not straight, and flow is pulsatile. Furthermore, these laws are unable to accurately characterize complex translesional pressure dynamics, particularly poststenosis pressure recovery, which is the basis of FFR. Some stenosis models make empiric assumptions or corrections for pressure loss and recovery. On average, these may perform adequately, but cannot represent the potentially complex flow patterns in a specific case. Moreover, they may be particularly vulnerable to inaccuracy in the context of serial lesions and diffuse disease in which 3-dimensional computational fluid dynamics computations more reliably characterize interstenosis hemodynamic interaction. The impact this has on accuracy, in all disease patterns, is yet to be fully determined.

Morris et al
Angiography-Derived FFR: More or Less Physiology?

ASSUMPTIONS
The discordance between angiographic severity and physiological (FFR) significance is well described and affects ≥30% of lesions. Discrepancies occur because, unlike angiography, FFR elegantly and automatically incorporates the combined and inter-related effects of coronary flow and microvascular resistance. It is therefore imperative that computational models of angiography-derived FFR include adequate physiological inputs or "tuning" to represent the maximum blood flow or minimum microvascular resistance; the latter dictates the former, which, in turn, dictates the pressure gradient and FFR. Hemodynamic equations are capable of accurately deriving a variety of physiological parameters, but only if other appropriate physiological inputs, such as flow or microvascular resistance, are included. A sensitivity analysis demonstrated that microvascular resistance was the dominant influence on angiography-derived FFR, above and beyond the severity or anatomy of epicardial disease. 3 Hyperemic flow and minimal microvascular resistance are variable in health and disease and are hard to measure, even with invasive instrumentation. Noninvasive models of angiography-derived FFR therefore rely upon assumptions about these parameters, or predict them from surrogate markers such as arterial diameter. Again, empiric assumptions may be sufficient overall, for many cases, but will be inaccurate in nonaverage cases with discordant anatomy and physiology, that is, the very cases where FFR is superior to angiography. Therefore, unless models have an accurate method for achieving this, on a patient-specific basis, the "physiological" prediction becomes simply a function of stenosis geometry and they cannot be a genuine model of FFR at all ( Figure). As an example, 1 study of angiographically derived FFR observed a significant reduction in diagnostic accuracy in patients with elevated microvascular resistance. 4 Paradoxically, physiologically weak models will appear more feasible relative to angiographic appearance, and a potential danger is that user confidence may therefore be increased with poorer methods. FFR has enabled a great stride forward in terms of physiologically guided revascularization. It would be unfortunate if, in an attempt to increase physiological assessment, we were to take half a step back toward assessment based on epicardial arterial anatomy. Table 2 summarizes major trials of angiography-derived FFR. 4-18

ACCURACY AND ERROR RANGE
Headline validation results report "diagnostic" accuracy. This quantifies how well a method predicts physiological significance or nonsignificance (FFR ≤0.80), relative to invasive FFR, expressed as sensitivity, specificity, positive, and negative predictive values, area under a receiver operating curve, and overall diagnostic accuracy. Diagnostic accuracy is a function of (1) the method's accuracy and (2) the cases included in a particular study. The fewer cases close to the 0.80 threshold, the better the diagnostic accuracy will appear and vice versa. This is nicely illustrated in a study of FFR computed from computed tomography coronary angiography in which the diagnostic accuracy was 82% overall, but only 46% in cases in FFR were 0.70 to 0.80, which is precisely the range where most accuracy is required. 19 The best test of how accurately angiographyderived FFR agrees with invasive FFR is to plot the Figure. Error in angiography-derived FFR. (A) An anatom ically severe circumflex case. In this case, the method applied an assumed value for microvascular resistance based on a population average, which resulted in considerable disagreement between angiography-derived and invasive FFR (0.55 vs 0.82). (B) Bland-Altman plot from a meta-analysis of 13 studies (1842 vessels). There is minimal bias (gray line), but the ±95% limits of agreement were FFR ±0.14. FFR indicates fractional flow reserve. Reprinted from Collet et al 20   differences between predicted and observed FFR values against the mean (ie, a Bland-Altman plot). From this, the mean difference (delta), which quantifies any bias in the angiography-derived method, and the 95% limits of agreement, are calculated. The limits of agreement (±1.96 SDs) comprise 95% of observed differences and are akin to the 95% CI of a computed, angiography-derived FFR result or an error range (Figure). The wider the limits of agreement, the larger the method's error and vice versa. Unlike diagnostic accuracy, the limits of agreement are only a function of how accurate a method is. A recent meta-analysis of 13 studies of angiography-derived FFR demonstrated impressive diagnostic accuracy (sensitivity, 89%; specificity, 90%), but more-sobering agreement, with limits of agreement of FFR ±0.14. 20 This is remarkably similar to FFR computed from computed tomography in the NXT trial (limits of agreement FFR ±0.15). 21 FFR computed from computed tomography, however, is a noninvasive screening tool, best used to reduce unnecessary invasive catheterization. Arguably, the accuracy "bar" should be set far higher for a test in the catheter laboratory, where results directly influence decisions regarding proceeding to percutaneous or surgical intervention. Is FFR ±0.14 accurate enough for interventional decision making? It is likely that noninferiority trials will be used to assess these methods. These should avoid the usual pitfalls and be appropriate in terms of power, significance, analysis protocol, sample size, patient population, and prespecified noninferiority margins. Moreover, it remains to be seen how accurate and reproducible these methods are, beyond academic core laboratories, in the hands of those who will be expected to use these tools (ie, the interventional cardiologist operating in the catheter laboratory).

CONCLUSIONS
Angiography-derived FFR has the potential to change clinical practice for the considerable benefit of patients by providing routine physiological data, together with coronary anatomy, to provide personalized management and improved clinical outcomes. However, deriving physiology from anatomy is challenging and requires assumptions. Model simplification and physiological assumptions, based on extrapolated or averaged data, are likely to work in the majority of patients. However, much of FFR's success lies in its ability to identify those cases where nonstandard microvascular resistance and/or flow result in discordant physiology and anatomy. It is therefore important that models of angiography-derived FFR retain the same patientspecific physiology that separates traditional FFR from angiography, or at least that they highlight which cases require more-reliable assessment. Operators must understand how accuracy and error are defined in all patient groups. Stringent validation is required to prove that models are accurate and physiologically sound, in the hands of those who will be using them. If this can be achieved, clinicians have the potential to achieve what could be a new level of patient-specific medicine.