FFR represents the ratio of maximal myocardial blood flow in the territory supplied by the coronary stenosis being interrogated to maximal myocardial blood flow in the same territory if the considered coronary artery was normal (no stenosis). Accordingly, FFR is derived from the ratio between mean coronary blood pressure distal to a stenosed segment (Pd) and mean proximal coronary pressure (Pa) during maximum CBF and a state of minimum microvascular resistance. Essentially, FFR is computed as Pd/Pa during hyperemia induced by intravenous infusion of adenosine for 3 minutes (140 $\mu$g/kg/min), or by intravenous bolus regadenoson (400 $\mu$g) [6], or by an adenosine intracoronary bolus injection (100 $\mu$g) in the right or left coronary artery (100 $\mu$g and 200 $\mu$g, respectively) [7], or by a papaverine intracoronary injection in the left or right coronary artery (12 mg and 8 mg, respectively). The correlations between these methods are excellent, but it can be noted that Regadenoson and intracoronary injections are faster methods with fewer side effects, especially flushing [6].

NHPRs obviate the necessity of adenosine administration. iFr (Philips/Volcano) is the first NHPR that have been proposed [8]. The study of the relationship between coronary pressure and coronary flow leads to the determination of a wave-free period which allowed the measurement of the Pd/Pa ratio during an interval in which microcirculatory resistance is constant but not necessarily minimal [9]. This mimics the constant microcirculatory resistance during the hyperaemic state whereby measured pressure is proportional to flow. Several other NHPRs have been developed with variations in the timepoint at which the Pd/Pa ratio is measured such as the resting full-cycle ratio (RFR) (Abbott), the diastolic hyperemia-free ratio (Boston Scientific), and the diastolic pressure ratio (Opsens Medical). It should be noted that NHPRs can be used only with vendor proprietary software. However, all these indexes appear comparable [10].

Even though the severity of the epicardial and microcirculatory damage are not related [11], the status of the microcirculation will influence the FFR measurement [12]. The HSR index is calculated using the formula (Pa - Pd)/average peak velocity (APV) during maximal hyperaemia, and is defined as the resistance provided by the assessed coronary lesion [13]. Although HSR uses flow velocity measurement that depends on epicardial vasculature and microcirculation, it is an index only of epicardial lesions. A HSR value 0.80 mmHg/cm/sec is considered to indicate a significant epicardial stenosis [14].

Advances in computational power have allowed the development of angiography-derived FFR obviating the need for hyperemia and for a pressure wire. Angiography-derived FFR combines two projections to provide a 3D quantitative coronary angiography, which allows the reconstruction of the specific coronary geometry. An analysis using computational fluid dynamic (CFD) techniques or mathematical formulas then provides a rapid estimation of the pressure drop across a lesion. Angiography-derived FFR demonstrated excellent performances for the diagnosis of hemodynamically significant stenoses defined by FFR 0.80 [15]. Several angiography-derived FFR software packages have been developed. Specifically, Quantitative Flow Ratio (QFR), Cardiovascular Angiographic Analysis Systems for vessel Fractional Flow Reserve (CAAS vFFR), and FFRangio system are angiographically derived estimates of FFR with comparable performances [16]. Suboptimal performances of angiography-derived FFR have been shown for lesions located at bifurcations, for ostial lesions, or for lesions of left main coronary artery. Angiography-derived FFR is also dependent on the quality of angiographic images. It is recommended to have a good catheter engagement in order to optimize contrast artery opacification, to have two optimal angiographic projections $>$25${}^{\circ }$, to avoid excessive movement of the X-ray tube, and to use a zoom that cuts parts of the coronary to be analyzed. Like NHPR, the main scientific limitation and challenge in these technologies consists in the unassessed variability of the resistance of the coronary microvascular bed which is not being evaluated.

As for the angiography-Derived FFR several steps will be necessary to obtain the FFT CT from the Coronary computed tomography angiography (CCTA) imaging. First step, with CCTA image data set an anatomic model of coronary arteries is performed. Then a physiologic model of coronary circulation is produced. Resting coronary flow is modelled on the basis of myocardial mass, and maximal hyperemia is modelled in agreement with the expected reduction in resistance if adenosine injection would be achieved. Finally, supercomputers use computational fluid dynamics methods to measure FFR CT. The HeartFlow FFR CT software (FFR${}_{\text{CT}}$, HeartFlow Inc, Redwood city, CA, USA) is the most successful technology that has demonstrated its diagnostic performance compared to FFR in 3 significant studies [17, 18, 19]. The diagnostic performance is interesting compared to other non-invasive tests. The PACIFIC trial showed it comparable to PET and superior to SPECT [20]. The use in real life has also been evaluated in a large register prospective multicenter registry [21]. The weakness remains an off-line analysis. FFRCT analysis is only available at a central laboratory in California. CCTA image data set must be sent to post processing which still takes 1 to 4 hours. In addition to the cost of process, the performance also depends strongly on the quality of the image. Motion artifact, severe calcification, and stenting decrease analyzability. For example, in PACIFIC trial, analyzability of FFRCT was only 75% at the patient level [20].

Acetylcholine provides an endothelium-dependent stimulation. In normal individuals, acetylcholine causes the vasodilatation of epicardial and micro vessels. Paradoxical vasoconstriction occurs in patients with endothelial dysfunction or vasospastic angina. Acetylcholine challenges endothelium-dependent microvascular function. Acetylcholine is usually administered by sequential manual infusion at progressive concentrations of 2 $\mu$g, 20 $\mu$g, 100 $\mu$g and 200 $\mu$g over a period of 3 minutes via the diagnostic catheter used for the assessment of the left coronary artery (LCA). The assessment of the right coronary artery is performed when the LCA shows no abnormal result and a dose of 50 $\mu$g is then applied prior to 300 mg of glyceryl trinitrate. Manual infusion should be slow (1–2 mL/min). It is more straightforward but possibly less standardized than mechanical sequential infusion. Indeed, mechanical infusion pump can infuse (1 mL/min for 2 minutes) precise progressive concentration of 0.182, 1.82, and 18.2 $\mu$g/mL (10${}^{-6}$, 10${}^{-5}$, and 10${}^{-4}$ mol/L, respectively). After each dose, an angiogram is performed. Two criteria are used for diagnosing endothelial dysfunction. Following intracoronary injection of any dose of acetylcholine, endothelial-dependent microvascular dysfunction is defined as a change CBF $\le$50% and epicardial endothelial dysfunction is defined as a reduced coronary artery diameter $\ge$20%. The method of CBF and coronary flow reserve (CFR) computation are detailed below. The change in CBF is provided by the equation (peak at Ach CBF-baseline CBF)/(baseline CBF).

Using Doppler data. It is possible to use the bolus thermodilution technique to diagnose endothelial-dependent microvascular dysfunction through the assessment of endothelial coronary flow reserve with acetylcholine (eCFR) 1.5 [22].

Progressive concentrations of acetylcholine may induce epicardial or microcirculatory spasm. VSA and microvascular spasm (MVS) are defined as follows:

VSA: angina symptoms, ischemic ECG modification and $\ge$90% constriction in epicardial artery,

MVS: angina symptoms, ischemic ECG modification ($\ge$1 mm) and constriction in epicardial 90%.

It should be noted that acetylcholine test patients with microvascular spasm or a history of myocardial infarction with nonobstructive coronary arteries (MINOCA) have a higher risk of myocardial infarction and recurrent chest pain requiring hospitalization at follow-up despite appropriate post-test therapy [23].

CFR provides information on both the epicardial and microvascular compartments by quantifying the ratio of hyperemic to resting CBF. Maximal hyperemia is induced by the intravenous infusion of 140 $\mu$g/kg/min of adenosine. The assessment of CFR using thermodilution tends to overestimate values than those measured using Doppler [24]. The absolute cut-off values are 2.0 and 2.5 by thermodilution and Doppler, respectively [25]. CFR reflects the vasodilator capacity of the coronary circulation and does not allow to differentiate the epicardial or microcirculatory involvement. CFR has less reproducibility than FFR due to its dependence on systemic haemodynamics (diastolic time, intramyocardial pressure) and to the high variability of basal flow [26].

The vasodilatory capacity of whole coronary tree is therefore measured using two distinct methods, i.e., acetylcholine testing in order to monitor changes in CBF or eCFR, and adenosine testing in order to quantify CFR. The potentially complementary nature of both remains to be determined.

The principles of CBF measurement must be known in order to understand how to obtain the coronary microcirculation indexes. The microcirculation is invisible to all imaging techniques, which explains that functional tests are the only methods of analysis. The determination of CBF can be performed according to two methods.

Based on bolus thermodilution modelling, flow can be calculated from the mean time it takes a fixed vascular volume to travel from an injector to a sensor (Tmn). De Bruyne et al. [27] and Pijls et al. [28] conducted the bolus thermodilution technique in animal model and human and found a strong correlation between 1/Tmn and absolute CBF. Absolute CBF assessment is possible using the continuous thermodilution method. It requires a dedicated monorail infusion (RayFlow, Hexacath, Paris, France), an infusion pump, a pressure/temperature wire (PressureWire, Abbott Vascular, Santa Clara, California) and a dedicated software (CoroFlow, Cardiovascular System, Coroventis Research, Uppsala, Sweden). Absolute CBF in mL/min is then given by the equation:

1.08 $\times$ Ti/T $\times$ Qi,

Qi is the infusion rate of saline at room temperature (20 mL/min). T is the temperature of blood (in ${}^{\circ }$C) mixed with saline in the distal part of the vessel. Ti is the temperature (in ${}^{\circ }$C) of the saline as it enters the coronary artery; and the constant 1.08 accounts for the densities and specific heat of blood and saline. Saline infusion with RayFLow induces maximal hyperemia within seconds, which obviates the need for adenosine [29]. It has been shown that absolute CBF and resting resistance can be achieved by continuous thermodilution and a fixed rate of 10 mL/min of saline [30]. This technique reduces the variability of calculated CFR [31].

Hyperemic APV measured using Doppler is used as a surrogate of absolute CBF. Because the Doppler signal provides only flow velocity, quantification of volumetric flow requires exact knowledge of the vessel lumen size, which can be obtained by quantitative coronary angiography (QCA) or intravascular ultrasound (IVUS). The simultaneous measurement of the vessel cross-sectional area and mean velocity (Vmean) allows to CBF in mL/min. Doppler-based wireline systems measure APV. To calculate the mean Vm, a constant coefficient of 0.5 is used, i.e., mean Vm = 0.5 $\times$ APV. However, this coefficient is not valuable in the case of pulsatile flow, which is why this method only gives a surrogate for the absolute CBF.

The index of microcirculatory resistance (IMR) is based also on the bolus thermodilution principle. IMR is calculated by: Pd $\mathrm{\times }$ Tmn. IMR is measured with a pressure/temperature wire (PressureWire, Abbott Vascular, Santa Clara, California). In case of significant epicardial stenosis, the IMR value is corrected using Yong’s formula (Corrected IMR = Pa $\mathrm{\times }$ Tmn $\mathrm{\times }$ ([1.35] $\mathrm{\times }$ Pd/Pa – 0.32) [32]. A clear cut-off for the diagnosis of CMVD is IMR $\ge$25 [33]. The variability of IMR quantification represents a limit. It is due to the fact that the measurement depends upon the operator’s bolus injection technique. However, IMR does not depend upon resting measurements or on myocardial mass.

HMR is measured using a Doppler-equipped guidewire (ComboWire XT; Philips Volcano, San. Diego, CA, USA). It is determined by: Pd/Hyperemic APV. There is no clear cut-off for the diagnosis of CMVD. HMR $>$1.9 or $\ge$2.5 mmHg/cm/s have been proposed [34, 35].

RRR represents the vasodilatory capacity of microvasculature during hyperemia. It is calculated using the following validated equation [36]: RRR = BRI/IMR. The baseline resistance index (BRI) is a measure of the coronary microcirculatory resting tone and is calculated using the formula: Pd Baseline $\mathrm{\times }$ Tmn Baseline [37]. It can be performed with either the bolus or doppler thermodilution techniques. There is no clear cut-off for the diagnosis of CMVD but RRR 2.62 by Doppler was associated with a 1.6-fold higher risk of death in patients with angina or ischemia with NOCAD [38].

The simultaneous acquisition of phasic pressure and flow velocity signals is required to measure IHDVPS. However, this approach is rather complicated in terms of instrumentation. IHDVPS correlates significantly with arteriolar obliteration, capillary density, or arteriolar density [39]. IHDVPS is defined as the slope ($\beta$-coefficient) of the relationship between hyperaemic intracoronary pressure and flow in mid-to end diastole, which is displayed by a single regression line (y = a + $\beta$x) expressed in cm/s/mmHg. IHDVPS provides a combined view of the arteriolar and capillary domains. IHDVPS normal range has not been established.

Pzf is extrapolated from the regression line of the relationship between hyperaemic intracoronary pressure and flow in mid- to end diastole and is defined as the intercept of the regression line with the pressure axis. Pzf represents the distal coronary pressure in the theoretical situation of coronary flow cessation. Pzf measured after percutaneous coronary intervention (PCI) is a better predictor of the extent of myocardial infarction than HMR or IMR [40] but no normal range has been established. In addition, the methodology required for Pzf assessment is complex with important offline postprocessing.

A wave is a change in pressure and flow that propagates along a blood vessel. There are four wave types: forward compression waves (FCW), forward decompression wave (FDW), backward compression wave (BCW), and backward decompression wave (BDW). The units of wave intensity (Watts/m${}^2$ or J/sec/m${}^2$) reflect the rate at which the wave energy passes through a given cross-section of a coronary vessel. BDW originates from the microcirculation and is supposed to quantitatively reflect the re-expansion of the intramyocardial network in early diastole, thereby reflecting in turn capillary density [41]. Here gain a normal range has not been established yet.

The main common problem with the above-described techniques (HMR, IHDVPS, Pzf, WIA) using the Doppler method is that an optimal Doppler signal is obtained in only 69% of the patients [42]. Repositioning and the use of an intracoronary microcatheter to stabilize the position can improve signal quality.

Once again, Ohm’s law with ratio of pressure and flow provides absolute resistance expressed in Wood units. The following parameters may then be computed:

total coronary resistance = Pa/absolute CBF

epicardial resistance = Pa-Pd/absolute CBF

microvascular resistance = Pd/absolute CBF

Absolute CBF and resistance as assessed using continuous thermodilution display high reproducibility and low intraobserver variability [43]. A strong agreement has been observed with [${}^{15}$O] H${}_2$O PET–derived flow and resistance [44] following normalization for the myocardial mass of the perfused territory with different algorithms applied to cardiac CT data [45, 46] or intracoronary physiological data [47]. However, the range of normal absolute resistance values have not been extensively investigated yet. Due to interindividual variability that persisted even after normalization for myocardial mass of the perfused territory, the measures are therefore less well suited for individual clinical decision.

Microvascular resistance reserve (MRR) is a novel index which presents several advantages. Because it uses the continued thermodilution method and since it relies on baseline and hyperemic measurements in the same epicardial territory, MRR is independent of myocardial mass, and operator independent. MRR is obtained as follows:

MRR = Absolute resistance at rest/absolute resistance at hyperemia

Absolute resistance at rest = Pa rest/absolute CBF rest

Absolute resistance at hyperemia = Pd Hyperemia/absolute CBF hyperemia

MRR = (absolute CBF hyperemia/absolute CBF rest) $\mathrm{\times }$ (Pa rest/Pd hyperemia)

MRR = CFR $\mathrm{\times }$ (Pa rest/Pd hyperemia)

If MRR is expressed in terms of CFR and FFR the equation is:

MRR = CFR/FFR $\mathrm{\times }$ (Pa rest/Pa hyperemia).

By continue thermodilution method: Pa rest = Pa hyper and final equation is:

MRR = CFR/FFR

MRR represents a very promising index since it is specific for the microcirculation, and independent of autoregulation and epicardial resistance [31].

An elegant use of the QFR in hyperemia has allowed to obtain an angiography-derived IMR [48], which is obtained as follows:

IMR = Pd hyperaemia $\mathrm{\times }$ Tmean hyperaemia

IMR = Pa hyperaemia $\mathrm{\times }$ Pd hyperaemia/Pa hyperaemia $\mathrm{\times }$ Tmean hyperaemia

Pd hyperemia/Pa hyperemia ~ QFR

Tmean hyperemia can be expressed as the ratio between the number of frames (Nframes) that the contrast agent travels from the guiding catheter to a distal marker of the pressure wire to the acquisition rate (fps).

Angiography-Derived IMR = Pa hyperemia $\mathrm{\times }$ QFR $\mathrm{\times }$ (Nframes hyperemia/fps)

Data post-processing allows to obtain an angiography-derived IMR value without the need for hyperemia. The initial steps are similar to those used for QFR, a 3D reconstruction of the coronary artery and estimation of QFR was performed using CFD. The estimated hyperemic Pa is calculated according to the mean arterial pressure (MAP) with the following weighting:

MAP $\mathrm{\times }$ 0.2 when MAP $\mathrm{>}$95 mm Hg and MAP $\mathrm{\times }$ 0.15 when MAP 95 mm Hg.

Finally, angiography-derived IMR is computed using the equation:

Angiography-Derived IMR = Pa hyperemia $\mathrm{\times }$ QFR $\mathrm{\times }$ (Nframes hyperemia/fps).

Vdiastole is the resting flow velocity during diastole and is derived of the TIMI frame count method multiplied by K which is the constant to adjust the difference between resting and hyperemic flow velocity. Vessel length is determined by the length of vessel opacified by the contrast from the ostium to the distal part [49]. These data are currently monocentric and additional data are needed.

Coronary physiological assessment now plays a major role in the decision for PCI revascularization. According to the recommendations, a physiological assessment must be performed before revascularization, when the location of ischemia is not documented for 50% and 90% stenosis by visual estimation or in patients with multivessel CAD [50]. FFR and IFR have been shown to be useful in large randomized studies and should be used as a priority. Accordingly, FFR is currently considered the gold standard because its use has been validated in several large randomized studies. The results of the FAME-1 [1] and FAME-2 trials [51, 52] have demonstrated a clinical benefit in using FFR with a cut off $\le$0.8 to guide PCI revascularization. Interestingly, the first major clinical trial using FFR, the DEFER trial, have showed that an FFR-guided PCI strategy is effective and safe in patients $>$15 years-old [53]. A meta-analysis showed the benefit of FFR-guided PCI over medical therapy alone on the combined end point of cardiovascular death and myocardial infarction [54].

The two largest randomized trials showed that iFR-guided PCI was noninferior to FFR-guided PCI in rates of MACE at 12 months [55, 56]. These results prompted the appearance of iFR in the recommendations using a cut off $\le$0.89 [50]. It is regrettable that iFR has less evidence than FFR on long-term results.

Discordance between FFR and iFR appears in an average of 20% of cases. This discordance results from interactions between clinical characteristics, severity or shape of the stenosis [57, 58], variability in coronary physiological responses to rest and hyperemia [59], and location of the stenosis [60]. Indeed, for the localization some studies have shown that lesion of left main (LM) might be associated with a higher discordance between iFR and FFR values (iFR-/FFR+) questioning the use of iFR in this setting. The DEFINE-LM registry shows that deferral or perform revascularization of LM stenosis based on iFR appears to be secure [61].

Finally, because the discordance between FFR and iFR does not lead to differences in outcomes [59], it is more interesting to discuss of practical use on specific clinical setting. For example, iFR could be an attractive alternative to FFR in patients with multivessel CAD to perform multiple measurements without inducing hyperemia. There may also be a reluctance by many operators to use vasodilators in patients with bradycardia or hypotension. iFR could be an alternative. The value of iFR in cases of abnormal coronary microcirculation is suggested especially in acute coronary syndrome (ACS) and in patients with severe aortic stenosis. However, the evaluation of non-infarct-related arteries in the early phase of ACS creates diagnostic problems for the FFR but also for the IFR. The first is explained to a blunted hyperemia associated to ACS and the second by increased coronary resting flow on territory of remote myocardial infarction with compensatory hyperkinesia [62]. Recently, FLOWER MI trial failed to prove that a complete revascularization that is guided by FFR is superior to an angiography-guided procedure in STEMI patients [63]. If we can evoke the problem of the use of the FFR at the time of primary PCI due to blunted hyperemia associated to ACS [62], these results were more explained to a lack of statistical power due to lower-than-expected incidence of events. Probably future studies will precise the optimal time to use FFR or iFR to evaluate non-infarct-related arteries. In the setting of patient with severe aortic stenosis, conflicting data of evolution of FFR after TAVR implantation create debate with either a decrease in FFR after TAVR implantation [64] or stability [65]. So, further studies are needed in this area to clarified use of iFR and FFR.

To complete, several recent studies on the FFR appear with negative results in patients with multivessel CAD. However, negative results are probably due to reasons other than a questioning of the FFR performance.

The FUTURE trial compared an FFR-guided strategy with a traditional non-FFR strategy in the treatment of multivessel CAD. The trial was stopped prematurely by data safety and monitoring board due to higher all-cause mortality associated with FFR-guided strategy. This observation was not confirmed by the intention-to treat analysis at 1-year follow-up. At follow up, there was no significant difference between both strategies [66]. It is really difficult to conclude given the limited statistical power of the study. The higher all-cause mortality initial was probably due to chance.

The results of the FAME 3 trial are more instructive [67]. FAME 3 was a multicenter, international, noninferiority trial, patients with multivessel CAD were randomly assigned to undergo CABG or FFR-guided PCI with zotarolimus-eluting stents. The composite primary end point was death from any cause, myocardial infarction, stroke, or repeat revascularization at 1 year. FFR-guided PCI was not found to be noninferior to CABG. Probably it is not the performance of FFR that can be questioned. FAME 3 confirms that CABG is the best treatment for multivessel CAD [50]. Indeed, previous randomized clinical trials that assessed use of FFR were performed in patients eligible for PCI. Patients with multivessel CAD presented often long and severe diffuse lesions and PCI tends to be more appropriate for focal disease where the FFR is known to be more efficient [57, 58].

QFR has an advantage over alternative angiography-derived FFR indexes since the publication of the FAVOR III China study results. This prospective study included 3825 patients from China in which the QFR-guided PCI was used with a cut off $\le$0.89 and compared with an angiography-guided PCI. All cause death, MI and ischemia driven revascularization were the composite endpoint and occurred in 5.8% (11/1913) of patients in the QFR group compared to 8.8% (167/1912) in the angiography group (HR 0.65, 95% CI 0.51–0.83, p = 0.004) at 1 year [68]. The results of FAVOR III EJ (NCT03729739) will be more interesting since the study design investigates whether QFR-guided PCI will be non-inferior at 12 months compared to an FFR-guided PCI.

The number of randomized studies is still limited. The PLATFORM trial, which evaluated FFR CT in patients with planned ICA for chronic coronary syndrome. FFR CT was a feasible and safe with a significantly lower rate of NOCAD at ICA. At 1-year follow-up, the FFR CT strategy appeared lower cost than the ICA strategy with an equivalent cardiac event rate and the same level of quality of life [69, 70]. The SYNTAX III trial, in patients with left main or 3-vessel coronary artery disease, showed that CCTA analysis made the same revascularization decision as ICA analysis, and that the use of FFR CT changed the decision in 7% of cases [71]. In FORECAST trial, use of FFR CT reduced ICA, and did not differ significantly from control group in cost or clinical outcomes [72]. However, control group had mainly CCTA (63%) as the initial test. Studies with adequate statistical power to compare the performance of FFR CT with other non-invasive tests in the management of chronic coronary syndrome are expected.