FFR can be derived from coronary CTA image data acquired using standard acquisition protocols without the need for additional imaging, medication, or radiation. FFR_CT analysis uses mathematical models of blood flow derived from patient-specific data extracted from coronary CTA images and solved on high-performance computers. Any mathematical model of blood flow in the circulation includes at least 3 elements: first, a description of the anatomic region of interest; second, the mathematical “governing equations” enumerating the physical laws of blood flow within the region of interest; and third, “boundary conditions” to define physiologic relationships between variables at the boundaries of the region of interest [21]. Although the anatomic region of interest and the boundary conditions are unique to each patient and the specific vascular territory, the governing equations describing velocity and pressure are universal and apply in different patients and other arterial beds. The extraction of the patient-specific anatomic model from image data is performed using image processing algorithms [22, 23]. The basic physiologic principles behind FFR_CT have previously been described in detail [20••]. The first principle is that the total coronary blood flow (which is proportional to the myocardial oxygen demand) at rest can be quantified from the myocardial mass as assessed by CT. The second principle is that the microcirculatory vascular resistance at rest is inversely proportional to the size of the coronary arteries supplying the myocardium, and thus the caliber of both healthy and diseased vessels adapt to the amount of flow they carry. The third principle states that the vasodilatory response of the coronary microcirculation to adenosine infusion is predictable, allowing computational modeling of the maximal hyperemic state. Integration of these patient-specific mathematical models of coronary physiology to 3D computational fluid models enable computation of coronary flow and pressure at each point in the coronary tree under hyperemic conditions. Finally, FFR_CT is calculated from the ratio of coronary pressure to aortic pressure under simulated maximal hyperemic conditions.

The diagnostic performance of FFR_CT in patients with or suspected stable CAD has been tested in 3 prospective multicenter trials, the “Diagnosis of Ischemia-Causing Coronary Stenoses by Noninvasive Fractional Flow Reserve Computed from Coronary Computed Tomographic Angiograms” (DISCOVER-FLOW) study [24] the “Determination of Fractional Flow Reserve by Anatomic Computed Tomographic Angiography” (DeFACTO) study [25••], and the “Analysis of Coronary Blood Flow Using CT Angiography, Next Steps” (NXT) [26••] study, respectively. A total of 609 patients and 1050 vessels have been investigated. An overview of study design, populations, and estimates of FFR_CT diagnostic performance in these 3 trials is presented in Table 1. In all 3 trials, FFR_CT revealed high per-patient and per-vessel discrimination for the presence of ischemia with blinded comparison to measured FFR. Moreover, the diagnostic performance of FFR_CT was consistently superior compared with anatomic interpretation alone. However, in the DeFACTO trial, the prespecified end-point was not met as the FFR_CT accuracy lower limit of the 95 % confidence interval (67 %–78 %) did not exceed 70 % [25••]. Moreover, although superior to coronary CTA, the diagnostic specificity of FFR_CT in the DeFACTO study was rather low (42 % for coronary CTA vs 54 % for FFR_CT). However, FFR_CT demonstrated higher per-patient and per-vessel discrimination of ischemia compared with coronary CTA alone with AUC’s of 0.81 vs 0.68 (P < 0.001) and 0.81 vs 0.75 (P < 0.001), respectively [25••]. Of note, the DeFACTO study was conducted with an early generation FFR_CT analysis algorithm, and use of pre-acquisition beta-blockers and nitroglycerin was not mandated. Thus, in 25 % of the vessels assessed, nitroglycerin was not administered, which may have resulted in underestimation of the coronary artery diameter with a resultant increase in false positive FFR_CT [27•]. Moreover, beta-blockers were not used in almost one-third of patients, potentially adversely affecting CT image quality and increasing discordance between FFR_CT and FFR [27•, 28]. The most recent and largest study, the NXT trial incorporated learnings from the previous 2 trials, including use of the latest generation of FFR_CT analysis software [26••, 29]. In the NXT trial, the per-patient diagnostic accuracy of FFR_CT in predicting lesion-specific ischemia was superior to anatomic assessment by coronary CTA, 81 % vs 53 % (P < 0.001) arising from an increase in specificity from 34 % to 79 % (P < 0.001). Notably, the NXT trial cohort pre-test probability of significant CAD was in the intermediate range, thus representing patients in whom noninvasive imaging is recommended [30]. The improved diagnostic performance of FFR_CT in the NXT trial compared with the DeFACTO trial reflects substantial refinements in FFR_CT technology and physiologic modeling, as well as increased focus on coronary CTA image quality, in particular, regarding heart rate control and the use of nitroglycerin [27•, 29]. Accordingly, preliminary data indicate that employing the “NXT” FFR_CT computation technology and standardized CT image metrics on the DeFACTO CT data set, results in comparable diagnostic performance of FFR_CT as in the NXT trial [31]. In the NXT trial, there was a good direct correlation of FFR_CT to invasively measured FFR (r = 0.82), with a slight underestimation of FFR_CT (mean difference, 0.03) compared with FFR. The reproducibility of repeated FFR_CT calculations are high with a coefficient of variation between 1.4 % and 4.6 % [32]. Patient examples illustrating the clinical utility of FFR_CT in patients with coronary lesions with or without ischemia is shown in Figs. 1 and 2.

FFR_CT has high diagnostic performance in the presence of coronary calcification (Fig. 1) [33]. In a NXT trial substudy including 214 patients (333 vessels), there was no difference in diagnostic accuracy, sensitivity, or specificity of FFR_CT across Agatston score quartiles, including the highest quartile of patients with Agatston scores ranging between 416 and 3599 [33]. In vessels with the highest Agatston scores, FFR_CT showed significant improved discrimination of ischemia compared with coronary CTA alone (0.91 vs 0.71, P = 0.004), corresponding to 60 % correct reclassification of cases when moving from coronary CTA to FFR_CT. The apparent robustness of FFR_CT in the event of coronary calcification is most likely a result of the FFR_CT computation process, including information on the global coronary and myocardial anatomy [33]. In contrast, coronary CTA stenosis assessment relies on identification of segmental changes with resultant reduction in lumen interpretability and, for this reason, the presence of artifacts may have a greater impact on interpretation.

In a recent substudy from the NXT trial of vessels with serial multiple lesions (n = 18), FFR_CT values were co-registered with measured FFR across the lesions, and trans-lesional differences between FFR_CT and FFR were compared [34]. The mean values of the most distal FFR and FFR_CT in the same regions were 0.72 ± 0.10 and 0.69 ± 0.11, wheeas FFR and FFR_CT were ≤0.80 in 13 and 14 vessels, respectively. The coefficient of correlation between trans-lesional delta FFR and FFR_CT in each segment was excellent (0.92, P < 0.001).

The diagnostic performance of FFR_CT has been studied only in patients suspected of stable CAD, and thus the generalizability of FFR_CT to other patient categories is currently unknown. These patients include those with left ventricular hypertrophy, diabetes, previous myocardial infarction, or patients with coronary stents or by-pass grafts.

Current guidelines recommend noninvasive functional imaging testing (eg, stress echocardiography, single photon emission computed tomography, or cardiac magnetic resonance) as the first line diagnostic strategy in patients suspected of CAD [30]. In meta-analyses, using ICA stenosis severity as the reference standard, noninvasive functional testing has shown high diagnostic performance for detection or exclusion of obstructive CAD [30]. However, when these diagnostic tests are evaluated using measured FFR rather than ICA stenosis as the reference standard, diagnostic performance diminishes [35]. Most published studies utilizing FFR as the reference standard were small and single center-based, and in many of these studies FFR was often not measured in all vessels, with FFR values assigned to vessels (and vascular perfusion territories) on the basis of the angiographic findings in a significant proportion of patients (vessels) [35]. This strategy may lead to misadjudication since patients with stenosis severity >50 % or even >70 % often have FFR values >0.80 [9, 10, 36‐38], whereas patients with <50 % stenosis may have FFR values ≤ 0.80 [36‐39]. Hitherto no studies have compared head-to-head the diagnostic performance of conventional noninvasive functional testing modalities vs FFR_CT using FFR as the reference standard.

In the context of rising global healthcare costs, greater attention is focused on cost-effectiveness of procedures. The field of noninvasive diagnostic testing comprises a bewildering array of test choices often resulting in 2 separate tests for assessment of coronary anatomy and ischemia [30]. Despite the extensive use of noninvasive testing, ICA continues to play a major role in the assessment of patients suspected of CAD. As a result of inaccurate diagnostic discrimination associated with the use of current noninvasive testing modalities, 60 % or more of patients referred for ICA on a suspicion of CAD do not have obstructive disease [40], and the majority of patients having revascularization performed do not have evidence of ischemia [41]. Moreover, patients with a positive ischemia testing result are only slightly more likely to have obstructive CAD at ICA than those who do not undergo testing [42].

Resource utilization and clinical outcome related to the clinical use of FFR_CT in symptomatic patients with suspected CAD have been evaluated in the prospective, multicenter “Prospective Longitudinal Trial of FFR_CT: Outcome and Resource impacts” (PLATFORM) trial [43••]. This study examined the clinical effectiveness impact of a strategy using FFR_CT to guide management compared with the usual testing strategy in 11 European centers. A total of 584 patients (mean age 61 years, 40 % women) with new-onset chest pain, no prior history of CAD, and an intermediate pre-test likelihood of obstructive CAD were enrolled. Patients referred for noninvasive testing were enrolled in a separate stratum than patients referred for invasive testing. Each stratum was further subdivided into usual care or FFR_CT-guided care. The primary endpoint was the rate of finding no obstructive stenosis among those with planned ICA, as defined by ≥50 % in any coronary artery by quantitative coronary angiography (QCA, core laboratory measurement) or invasive FFR < 0.80. Secondary endpoints included clinical outcomes, downstream testing and treatment, resource utilization, and quality of life measures [43••]. Study results showed high rates of finding no obstructive CAD by ICA in both the planned noninvasive and planned ICA groups. In the planned ICA group, 73 % of usual care patients had no obstructive CAD compared with only 12 % of patients guided by FFR_CT, an 83 % reduction (P < 0.0001). Although clinicians in the PLATFORM study were not protocol-driven to utilize FFR_CT test results, in 61 % of patients with planned ICA, the angiogram was cancelled after receiving FFR_CT results. Nonetheless, there was no difference in coronary revascularization rates (32 % in usual care and 29 % in FFR_CT, P = ns) and there was a 90 % increase in the number of patients with both functional and anatomic information prior to revascularization. Among patients intended for noninvasive testing, there was no difference in the rate of finding no obstructive CAD at ICA between usual care (6 %) and FFR_CT (13 %, P = 0.95). There were no adverse clinical events among patients in whom ICA was cancelled on the basis of FFR_CT, and there was no difference in clinical outcome between the usual care and FFR_CT-guided groups at 90 days. The latter findings are in accordance with a recent single-center real-world study comprising 185 consecutive patients with stable CAD and intermediate range coronary lesions showing a favorable 12-month follow-up clinical outcome in patients with FFR_CT > 0.80 (69 % of the study cohort) being deferred from ICA [44•].

Simulation analyses based on historic data indicate that FFR_CT guidance for selection of ICA and decision-making on coronary revascularization may reduce costs in stable CAD [45, 46]. The effects of using FFR_CT instead of usual care on costs and quality of life (QOL) in the PLATFORM study have been recently published [47••]. Total medical costs were derived from the number of diagnostic tests, invasive procedures, hospitalizations, and medications during 90-day follow-up multiplied by summed US cost weights. Changes in QOL were assessed using the Seattle Angina Questionnaire, the EuroQOL, and a visual analog scale. Among patients with planned ICA, mean costs were 32 % lower among the FFR_CT group than among the usual care group ($7343 vs $10,734, P < 0.0001). Among patients with planned noninvasive testing, mean costs were not significantly different between the FFR_CT group and the usual care group ($2679 vs $2137, P = 0.26). Each of the QOL scores improved in the overall study population (P < 0.0001). At 90 days, in the planned noninvasive testing stratum, QOL scores were significantly higher in FFR_CT patients than in usual care patients, whereas in the planned ICA stratum the improvements in QOL were similar in the FFR_CT and usual care patients.

No current guidelines provide recommendations about the clinical use of FFR_CT testing and its interpretation. As the first line cohort, we recommend FFR_CT testing to be applied in patients with intermediate range lesions in whom coronary CTA interpretation is most challenging [9], and where guidelines recommend additional ischemia testing to be performed [30]. This is in accord with previous trial evidence showing high and superior diagnostic performance of FFR_CT compared with stenosis assessment by coronary CTA in intermediate lesions [24, 25••, 26••, 48]. It is well known that a coronary stenosis with FFR ≤ 0.75 in general causes ischemia, whereas stenoses with FFR > 0.80 are almost never associated with exercise induced ischemia [49]. Accordingly, an FFR interpretation “grey-zone” ranging between 0.75 and 0.80 has been introduced in which measures other than FFR are recommended to be taken into account for decision making on revascularization [49]. Previous studies assessing the diagnostic performance of FFR_CT used a binary outcome based on a threshold of 0.80 [24, 25••, 26••]. However, as for FFR, a “black and white” decision-making based on a specific FFR_CT threshold may not always fit into the reality of clinical practice. Accordingly, in the most recent NXT trial, despite diagnostic superiority compared with coronary CTA stenosis assessment alone, the FFR_CT per-patient specificity and positive predictive value in predicting ischemia was modest (79 % and 65 %, respectively), and thus a substantial rate of false-positive results remained [26••]. In line with these findings, the aforementioned real-world study showed that only 55 % of lesions with FFR_CT ranging between 0.75 and 0.80 caused ischemia using FFR (threshold, 0.80) as the reference standard, whereas ischemia was documented in 92 % of lesions when FFR_CT was ≤0.75 [44•]. On the other hand, prognosis was favorable in patients being deferred from ICA on the basis of a normal FFR_CT result [44•]. Based on our current knowledge regarding FFR_CT diagnostic performance, and the fact that the overall prognosis in contemporary practice of stable CAD is favorable [11••, 43••, 44•], we recommend in patients (vessels) with FFR_CT > 0.80 or ≤0.75 a dichotomous interpretation strategy, whereas in patients with FFR_CT ranging between 0.75 and 0.80, decisions on referral to ICA (and decision-making on coronary revascularization) should be based on all available information, in particular regarding severity of angina, which is the main target of PCI (Table 2). The clinical value and safety of this FFR_CT interpretation approach needs delineation in future studies.

Although no special imaging protocols are required for FFR_CT assessment, significant CT imaging artifacts such as motion, low contrast, or blooming from coronary calcification may impair the diagnostic performance of coronary CTA and thus of FFR_CT. In the DeFACTO and NXT trials, 11 % and 13 % of the patients had nonevaluable coronary CTA images [25••, 26••]. In contrast, in the aforementioned real-world report of consecutive patients having FFR_CT performed, only 2 % of the patients failed to meet the image quality requirements for FFR_CT analysis, and in the total cohort comprising more than 1200 patients referred for coronary CTA, a conclusive CT-based anatomic or anatomic-physiological result was available in >90 % [44•]. Issues of CT uninterpretability can be minimized by adhering to coronary CTA image acquisition guidelines, particularly by administration of heart-rate lowering medication and sublingual nitrates before image acquisition [27•, 28, 44•, 50]. Although it has been shown that FFR_CT seems to provide significant diagnostic improvement compared with coronary CTA even at lower levels of coronary CTA image quality [51], noncompliance with societal guidelines on best coronary CTA acquisition practice [50] is associated with impaired FFR_CT diagnostic performance [27•]. In the DeFACTO trial, administration of a pre-scan beta-blocker increased FFR_CT diagnostic specificity from 51 % to 66 % (P = 0.03), whereas nitroglycerin pretreatment within 30 minutes of CT was associated with improved specificity from 54 % to 75 % (P = 0.01).

Currently, FFR_CT testing requires offsite computer processing requiring 2–6 hours. However, significantly faster FFR_CT-testing processing times resulting from software improvements are expected in the near future. Concerns on the perceived loss of control of local assessment and the current processing time associated with FFR_CT testing have driven renewed interest in past generations of reduced order computational fluid modeling versions that are less computationally intense and when coupled with less comprehensive anatomic modeling enables on-site analysis with reduced analysis times, but an unknown impact on diagnostic performance. Thus, while noninvasive on-site and fast (<1 hour) CT-derived FFR has shown interesting results in small, single-center, retrospective studies [52, 53], further investigations in prospective multicenter trials are needed in order to determine the actual diagnostic performance of this technique [54]. The relative long-term prognosis and cost-efficiency of FFR_CT testing compared with conventional ischemia testing modalities is not known, but studies are ongoing. In the Computed TomogRaphic Evaluation of Atherosclerotic Determinants of Myocardial IsChEmia (CREDENCE) trial (ClinicalTrials.gov Identifier:NCT02173275), which is a prospective, multicenter, cross-sectional study of patients scheduled to undergo clinically indicated nonemergent ICA, the diagnostic performance of FFR_CT vs myocardial imaging perfusion assessment (SPECT, positron emission tomography and magnetic resonance myocardial imaging) is compared using FFR as the reference standard.

A particular strength of the computational methods used to derive FFR_CT lies in the possibility of altering the patient anatomic or physiological model to predict the anticipated benefit of treatments. The potential use of this technology for planning PCI procedures was explored in a pilot study including 44 patients who had coronary CT and FFR_CT before catheterization and measured FFR before and after PCI [55]. FFR_CT was performed in a blinded fashion prior to and after virtual stenting of the lesions treated invasively. The diagnostic accuracy of FFR_CT to predict ischemia (FFR ≤ 0.8) after stenting was 96 %. Further developments in predicting the potential benefit of alternate revascularization strategies are on the horizon.

There are a variety of different biomechanical forces that act on blood vessels arising from internal pressure and flow and external tissue support. These applied forces result in stress acting on the surface or within blood vessels, where stress is defined as force per unit area. In addition to external applied forces, blood vessels have intrinsic, or residual, stresses emanating from growth and remodeling [56]. These residual stresses are present even in the absence of external applied forces. An example of a residual stress manifests when a vessel is transected and retracts or shortens due to the longitudinal tension in the vessel wall. A detailed discussion of all of the intrinsic and extrinsic forces and stresses in blood vessels is beyond the scope of this review, and herein we focus on forces resulting from internal flow and pressure acting on blood vessels and atherosclerotic plaques. Wall shear stress (WSS) is defined as the tangential force per unit area acting on the luminal surface. Axial plaque stress (APS) is defined as the axial component of the hemodynamic stress acting on stenotic lesions [57•]. APS and WSS both result from hemodynamic forces acting on the luminal surface, but have important differences. APS is strongly related to the absolute pressure on the surface of the plaque, whereas WSS is independent of the absolute pressure but closely coupled to flow and the pressure-gradient. APS is much larger than WSS (ie, approximately 40 times larger than the maximum WSS even in tight stenoses and under hyperemic conditions where WSS is maximal [57•]). Both WSS and APS can be derived from the velocity and pressure fields calculated by patient-specific modeling of coronary blood flow derived from CT data. Image-based computational methods have been used to compute wall shear stress noninvasively in the human abdominal aorta [58, 59], the extracranial and intracranial cerebral arteries [60‐63], and the pulmonary arteries [64, 65].

WSS plays a role in maintaining endothelial function and is likely to influence plaque initiation and progression [66‐69]. WSS is the product of the blood viscosity and the gradient of the velocity field at the luminal surface. WSS is sensed by the endothelium and in turn influences normal endothelial function, as well as atherosclerosis localization and progression. Image-based modeling techniques have also been used to evaluate wall shear stress in the human coronary arteries based on invasive data [70‐74], and to a lesser extent using noninvasive data [75, 76]. The future application of image-based modeling derived from CT data holds great promise for understanding the relationship between WSS and CAD.

Whereas the mechanical influence of WSS is confined to a narrow zone of the vessel wall near the endothelium, APS acts throughout the entire thickness of the plaque and, as such, is likely to play a more direct role in plaque rupture. In a recent publication, Choi et al. described the potential role of APS in plaque rupture and its relationship with lesion geometry [57•]. APS was found to uniquely characterize the stenotic segment and differentiate forces acting on upstream and downstream segments of a plaque. While WSS and pressure were consistently higher in upstream than in downstream segments, APS could be higher at the downstream than upstream segment in some lesions, thus potentially explaining why some plaques rupture at the downstream segments. Figure 3 depicts the FFR_CT result and the APS for a patient experiencing a cardiac arrest, and primary percutaneous coronary intervention of an occluded left anterior descending artery lesion occurring 1 year after a coronary CTA examination. Although coronary CTA identified a stenotic lesion, a rubidium-82 rest-stress perfusion study was deemed normal and the patient was treated medically [77]. The FFR_CT and APS analyses were performed retrospectively (but without any knowledge of the patient history) based on the coronary CTA data acquired 1 year prior to the myocardial infarction, indicating a very low FFR_CT result and high APS on the segment upstream of the minimum lumen area [57•]. The utility of FFR_CT and axial plaque stress for predicting plaque rupture are currently being evaluated in the “Exploring the Mechanism of the Plaque Rupture in Acute Myocardial Infarction” (EMERALD) trial (ClinicalTrials.gov ID: NCT02374775).