Background: Quantification of coronary blood flow is used to evaluate coronary artery disease, but our understanding of flow through branched systems is poor. Murray’s law defines coronary morphometric scaling, the relationship between flow (Q) and vessel diameter (D) and is the basis for minimum lumen area targets when intervening on bifurcation lesions. Murray’s original law (Q α DP) dictates that the exponent (P) is 3.0, whilst constant blood velocity throughout the system would suggest an exponent of 2.0. In human coronary arteries, the value of Murray’s exponent remains unknown. Aim: To establish the exponent in Murray’s power law relationship that best reproduces coronary blood flows (Q) and microvascular resistances (Rmicro) in a bifurcating coronary tree. Methods and Results: We screened 48 cases, and were able to evaluate inlet Q and Rmicro in 27 branched coronary arteries, taken from 20 patients, using a novel computational fluid dynamics (CFD) model which reconstructs 3D coronary anatomy from angiography and uses pressure-wire measurements to compute Q and Rmicro distribution in the main- and side-branches. Outputs were validated against invasive measurements using a Rayflow™ catheter. A Murray’s power law exponent of 2.15 produced the strongest correlation and closest agreement with inlet Q (zero bias, r = 0.47, p = 0.006) and an exponent of 2.38 produced the strongest correlation and closest agreement with Rmicro (zero bias, r = 0.66, p = 0.0001). Conclusions: The optimal power law exponents for Q and Rmicro were not 3.0, as dictated by Murray’s Law, but 2.15 and 2.38 respectively. These data will be useful in assessing patient-specific coronary physiology and tailoring revascularisation decisions.

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Refining Our Understanding of the Flow Through Coronary Artery Branches; Revisiting Murray’s Law in Human Epicardial Coronary Arteries

3D coronary angiography-based vessel fractional flow reserve (vFFR) proved to be an accurate diagnostic alternative to invasively measured pressure wire based fractional flow reserve (FFR). The ability to compute post-PCI vFFR using pre-PCI vFFR virtual stent analysis is unknown. We aimed to assess the feasibility and diagnostic accuracy of pre-PCI vFFR virtual stenting analysis (residual vFFR) with post-PCI FFR as a reference. This is an observational, single-center retrospective cohort study including consecutive patients from the FFR-SEARCH registry. We blindly calculated residual vFFR from pre-PCI angiograms and compared them to invasive pressure-wire based post-PCI FFR. Inclusion criteria involved presentation with either stable or unstable angina or non-ST elevation myocardial infarction (NSTEMI), ≥1 significant stenosis in one of the epicardial coronary arteries (percentage diameter stenosis of >70% by QCA or hemodynamically relevant stenosis with FFR ≤0.80) and pre procedural angiograms eligible for vFFR analysis. Exclusion criteria comprised patients with ST elevation myocardial infarction (STEMI), coronary bypass grafts, cardiogenic shock or severe hemodynamic instability. Eighty-one pre-PCI residual vFFR measurements were compared to post-PCI FFR and post-PCI vFFR measurements. Mean residual vFFR was 0.91 ± 0.06, mean post-PCI FFR 0.91 ± 0.06 and mean post-PCI vFFR was 0.92 ± 0.05. Residual vFFR showed a high linear correlation (r = 0.84) and good agreement (mean difference (95% confidence interval): 0.005 (−0.002–0.012)) with post-PCI FFR, as well as with post-PCI-vFFR (r = 0.77, mean difference −0.007 (−0.015–0.0003)). Residual vFFR showed good accuracy in the identification of lesions with post-PCI FFR < 0.90 (sensitivity 94%, specificity 71%, area under the curve (AUC) 0.93 (95% CI: 0.86–0.99), p < 0.001). Virtual stenting using vFFR provided an accurate estimation of post-PCI FFR and post-PCI vFFR. Further studies are needed to prospectively validate a vFFR-guided PCI strategy.

/pdf/diagnostic-accuracy-of-coronary-angiography-based-vessel-308dj20j.pdf

Diagnostic Accuracy of Coronary Angiography-Based Vessel Fractional Flow Reserve (vFFR) Virtual Stenting

Abstract Fractional flow reserve (FFR) is the current gold standard invasive assessment of coronary artery disease (CAD). FFR reports coronary blood flow (CBF) as a fraction of a hypothetical and unknown normal value. Although used routinely to diagnose CAD and guide treatment, how accurately FFR predicts actual CBF changes remains unknown. In this study, we compared fractional CBF with absolute CBF (aCBF, in ml min −1 ), measured with a computational method during standard angiography and pressure wire assessment, on 203 diseased arteries (143 patients). We found a substantial correlation between the two measurements ( r = 0.89 and Cohen’s kappa = 0.71). Concordance between fractional and absolute CBF reduction was high when FFR was &gt;0.80 (91%) but reduced when FFR was ≤0.80 (81%), 0.70–0.80 (68%) and, particularly, 0.75–0.80 (62%). Discordance was associated with coronary microvascular resistance, vessel diameter and mass of myocardium subtended, all factors to which FFR is agnostic. Assessment of aCBF complements FFR and may be valuable to assess CBF, particularly in cases within the FFR ‘gray zone’. 

/pdf/the-complementary-value-of-absolute-coronary-flow-in-the-715o1f59.pdf

The Complementary Value of Absolute Coronary Flow in the Assessment of Patients with Ischaemic Heart Disease (the COMPAC-Flow Study)

Abstract Aims Angiography-derived fractional flow reserve (angio-FFR) permits physiological lesion assessment without the need for an invasive pressure wire or induction of hyperaemia. However, accuracy is limited by assumptions made when defining the distal boundary, namely coronary microvascular resistance (CMVR). We sought to determine whether machine learning (ML) techniques could provide a patient-specific estimate of CMVR and therefore improve the accuracy of angio-FFR. Methods and results Patients with chronic coronary syndromes underwent coronary angiography with FFR assessment. Vessel-specific CMVR was computed using a three-dimensional computational fluid dynamics simulation with invasively measured proximal and distal pressures applied as boundary conditions. Predictive models were created using non-linear autoregressive moving average with exogenous input (NARMAX) modelling with computed CMVR as the dependent variable. Angio-FFR (VIRTUheart™) was computed using previously described methods. Three simulations were run: using a generic CMVR value (Model A); using ML-predicted CMVR based upon simple clinical data (Model B); and using ML-predicted CMVR also incorporating echocardiographic data (Model C). The diagnostic (FFR ≤ or >0.80) and absolute accuracies of these models were compared. Eighty-four patients underwent coronary angiography with FFR assessment in 157 vessels. The mean measured FFR was 0.79 (±0.15). The diagnostic and absolute accuracies of each personalized model were: (A) 73% and ±0.10; (B) 81% and ±0.07; and (C) 89% and ±0.05, P < 0.001. Conclusion The accuracy of angio-FFR was dependent in part upon CMVR estimation. Personalization of CMVR from standard clinical data resulted in a significant reduction in angio-FFR error.

/pdf/incorporating-clinical-parameters-to-improve-the-accuracy-of-18yo74t9.pdf

Incorporating clinical parameters to improve the accuracy of angiography-derived computed fractional flow reserve

Abstract Aims Ischaemic heart disease results from insufficient coronary blood flow. Direct measurement of absolute flow (mL/min) is feasible, but has not entered routine clinical practice in most catheterization laboratories. Interventional cardiologists, therefore, rely on surrogate markers of flow. Recently, we described a computational fluid dynamics (CFD) method for predicting flow that differentiates inlet, side branch, and outlet flows during angiography. In the current study, we evaluate a new method that regionalizes flow along the length of the artery. Methods and results Three-dimensional coronary anatomy was reconstructed from angiograms from 20 patients with chronic coronary syndrome. All flows were computed using CFD by applying the pressure gradient to the reconstructed geometry. Side branch flow was modelled as a porous wall boundary. Side branch flow magnitude was based on morphometric scaling laws with two models: a homogeneous model with flow loss along the entire arterial length; and a regionalized model with flow proportional to local taper. Flow results were validated against invasive measurements of flow by continuous infusion thermodilution (Coroventis™, Abbott). Both methods quantified flow relative to the invasive measures: homogeneous (r 0.47, P 0.006; zero bias; 95% CI −168 to +168 mL/min); regionalized method (r 0.43, P 0.013; zero bias; 95% CI −175 to +175 mL/min). Conclusion During angiography and pressure wire assessment, coronary flow can now be regionalized and differentiated at the inlet, outlet, and side branches. The effect of epicardial disease on agreement suggests the model may be best targeted at cases with a stenosis close to side branches.

/pdf/validation-of-a-novel-numerical-model-to-predict-1srhqtjg.pdf

Validation of a novel numerical model to predict regionalized blood flow in the coronary arteries

Three dimensional (3D) coronary anatomy, reconstructed from coronary angiography (CA), is now being used as the basis to compute ‘virtual’ fractional flow reserve (vFFR), and thereby guide treatment decisions in patients with coronary artery disease (CAD). Reconstruction accuracy is therefore important. Yet the methods required remain poorly validated. Furthermore, the magnitude of vFFR error arising from reconstruction is unkown. We aimed to validate a method for 3D CA reconstruction and determine the effect this had upon the accuracy of vFFR. Clinically realistic coronary phantom models were created comprosing seven standard stenoses in aluminium and 15 patient-based 3D-printed, imaged with CA, three times, according to standard clinical protocols, yielding 66 datasets. Each was reconstructed using epipolar line projection and intersection. All reconstructions were compared against the real phantom models in terms of minimal lumen diameter, centreline and surface similarity. 3D-printed reconstructions (n = 45) and the reference files from which they were printed underwent vFFR computation, and the results were compared. The average error in reconstructing minimum lumen diameter (MLD) was 0.05 (± 0.03 mm) which was < 1% (95% CI 0.13–1.61%) compared with caliper measurement. Overall surface similarity was excellent (Hausdorff distance 0.65 mm). Errors in 3D CA reconstruction accounted for an error in vFFR of ± 0.06 (Bland Altman 95% limits of agreement). Errors arising from the epipolar line projection method used to reconstruct 3D coronary anatomy from CA are small but contribute to clinically relevant errors when used to compute vFFR.

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The importance of three dimensional coronary artery reconstruction accuracy when computing virtual fractional flow reserve from invasive angiography.

The current management of acute coronary syndromes (ACS) is with an invasive strategy to guide treatment. However, identifying the lesions which are physiologically significant can be challenging. Non-invasive imaging is generally not appropriate or timely in the acute setting, so the decision is generally based upon visual assessment of the angiogram, supplemented in a small minority by invasive pressure wire studies using fractional flow reserve (FFR) or related indices. Whilst pressure wire usage is slowly increasing, it is not feasible in many vessels, patients and situations. Limited evidence for the use of FFR in non-ST elevation (NSTE) ACS suggests a 25% change in management, compared with traditional assessment, with a shift from more to less extensive revascularisation. Virtual (computed) FFR (vFFR), which uses a 3D model of the coronary arteries constructed from the invasive angiogram, and application of the physical laws of fluid flow, has the potential to be used more widely in this situation. It is less invasive, fast and can be integrated into catheter laboratory software. For severe lesions, or mild disease, it is probably not required, but it could improve the management of moderate disease in 'real time' for patients with non-ST elevation acute coronary syndromes (NSTE-ACS), and in bystander disease in ST elevation myocardial infarction. Its practicability and impact in the acute setting need to be tested, but the underpinning science and potential benefits for rapid and streamlined decision-making are enticing.

/pdf/virtual-computed-fractional-flow-reserve-future-role-in-2vm3y0r9yi.pdf

Giulia Pederzani

Papers

The importance of three dimensional coronary artery reconstruction accuracy when computing virtual fractional flow reserve from invasive angiography.

Virtual (Computed) Fractional Flow Reserve: Future Role in Acute Coronary Syndromes.