Coronary Flow Rate Adds Predictive Capability for FFR Assessment

A non-invasive risk assessment tool capable of stratifying coronary artery stenosis into high and low risk would reduce the number of patients who undergo invasive FFR, the current gold standard procedure for assessing coronary artery disease. Current statistic-based models that predict if FFR is above or below the threshold for physiological significance rely completely on anatomical parameters, such as percent diameter stenosis (%DS), resulting in models not accurate enough for clinical application. The inclusion of coronary artery flow rate (CFR) was added to an anatomical-only logistic regression model to quantify added predictive value. Initial hypothesis testing on a cohort of 96 coronary artery segments with some degree of stenosis found higher mean CFR in a group with low FFR < 0.8 (μ = 2.37 ml/s) compared to a group with high FFR > 0.8 (μ = 1.85 ml/s) (p-value = 0.046). Logistic regression modeling using both %DS and CFR (AUC = 0.78) outperformed logistic regression models using either only %DS (AUC = 0.71) or only CFR (AUC = 0.62). Including physiological parameters in addition to anatomical parameters are necessary to improve statistical based models for assessing high or low FFR.


Introduction
Fractional ow reserve (FFR) is hailed as the gold standard for assessing the functional severity of a coronary artery stenosis [1]. Despite this, FFR is rarely used in clinical practices. An electronic survey determined that only 57% of cardiologists use FFR in less than one-third of cases, and that 15% of cardiologists never use FFR [2]. The low adoption rate is often accredited to associated costs, time, practicality, and potential patient complications. In response, researchers have investigated less invasive methodologies for assessing the functional severity of a coronary stenosis.
Initially, Morris et al created fully transient computational uid dynamics (CFD) models to estimate invasive FFR with a virtual counterpart (vFFR) using only angiographic images [3]. Although the model by Morris et al had excellent agreement, 96% diagnostic accuracy, it required o ine computation greater than 24 hours. Papafaklis et al. developed the rst protocol that required a reasonable amount of computational time. The protocol used two steady state calculations with given steady out ow boundary conditions of 1 and 3 ml/s and a constant 100 mmHg aortic pressure inlet boundary condition to produce a pressure drop versus ow rate curve. The pressure gradients from the two steady state simulations were used to calculate the Pouiselle and turbulent coe cients in the quadratic stenotic pressure drop equation. The area under the pressure gradient versus ow rate curve for a speci c patient was then divided by a similar curve for an ideal artery to yield an assessment metric that was coined virtual functional assessment index (vFAI). vFAI showed excellent agreement with invasive FFR and resulted in a diagnostic accuracy, sensitivity, speci city, and AUC of 87.8%, 90.4%, 86.2%, and 0.919, respectively [4]. Morris et al. returned to their previous work to produce a less computationally expensive CFD model based on a pseudo-transient protocol that provided virtual FFR assessment in less than 4 minutes. The new pseudo-transient method produced errors less than 1% of the fully transient method that achieved 96% diagnostic accuracy [6]. Tu et al. initially created a CFD protocol for assessing FFR from 3D models generated from QCA. They calculated a volumetric ow rate using TIMI frame count which was used as an inlet boundary condition. The noninvasive assessment was eventually coined as quantitative ow ratio (QFR). The initial iteration of QFR showed good agreement with invasive FFR showing an accuracy, sensitivity, speci city, and AUC of 88%, 78%, 93%, and 0.93, respectively [5]. Some CFD models have been replaced by mathematical models which were also based on uid dynamic principles but could be computed instantaneously. For example, QFR has been replaced with a mathematical formulation that has built upon the initial CFD protocol [7,[9][10]. There are currently three angiography-based software packages, QFR, FFR angio , and CAAS-vFFR, that are cleared by the Food and Drug Administration and commercially available. Of the three packages, QFR has been rigorously validated against invasive FFR with more studies underway [7][8][9][10][11].
Approaches which are not based on uid dynamics have also been investigated. These methods recognize the functional-visual mismatch between FFR and coronary angiography and the factors causing the mismatch [12]. These methods, clinical prediction models, then attempt to use patient characteristics, lesion morphology, and myocardium-at-risk factors to create a scoring tool capable of stratifying the severity of an intermediate lesion. Some of these models, such as the ASLA score created by Ko et al., have used coronary computed-tomography angiography (CCTA) instead of invasive coronary angiography (ICA) with notable performance (AUC = 0.82) [13,14]. However, most models have relied on ICA. Natsumeda et al. formulated an ICA based model which consisted of 5 independent signi cant predictors of FFR ≤ 0.8 which were combined to create a scoring system, STABLE, which had an AUC score of 0.76 [15]. Wong et al created the DILEMMA scoring system which used lesion length, minimum lumen diameter (MLD), and BARI MJI which is a measure of myocardium subtended by the coronary lesion [16]. The DILEMMA scoring system had an AUC of between 0.82 and 0.88 in the derivation and validation cohorts, respectively. The performance of the DILEMMA score was validated by an outside study performed by Michail et al [17].
Clinical prediction models, although not yet typically as accurate as their CFD or mathematical model counterparts, have the bene t of being simple tools that, if fully developed, can be easily adopted by clinicians and may reduce need for pressure wires [18]. Coronary ow rate (CFR) parameters have been generally excluded from these clinical prediction models despite the cornerstone publications of Gould establishing that the functional severity of an intermediate stenosis is highly dependent on the ow rate through the artery [19]. Flow disturbance after the stenosis, which is related to pressure drop and other non-pressure based metrics for severity, is also known to be a function of ow rate [20]. Therefore, it is not known how including CFR affects the performance of a clinical prediction model.
The purpose here was to determine if including CFR added predictive value to clinical prediction models, particularly compared to percent diameter stenosis (%DS), the most used parameter for percutaneous coronary intervention (PCI) decision. This was met through three speci c aims. First, determine if there is a signi cant statistical difference in CFR between low (FFR ≤ 0.8) and high (FFR > 0.8) groups. Second, determine if including CFR in a predictive model improves accuracy, sensitivity, and speci city relative to a model only containing anatomical features such as %DS. Third, provide a causal explanation for the relationship between CFR and FFR by visualizing differences in hemodynamic ow features between low and high patients using CFD.

Patient Population
One hundred arteries from ninety patients who underwent invasive coronary angiography and FFR measurements in two a liated hospitals were considered for this study. The inclusion criteria for this study were all patients with stenoses in major epicardial arteries such as RCA, OM, LCX, or LAD. The exclusion criteria were ostial lesions in the left main artery or RCA, bifurcations, and lesions distal to bypass grafts. Following the application of the exclusion criteria, ninety-six patients were suitable for retrospective investigation. The Institutional Review Board at the University of Louisville approved the study protocol used for patient cases and all research was performed in accordance with relevant regulations. As the study was retrospective, and non-interventional in nature with minimal risk to subjects, the IRB granted waiver of informed consent.

3D Rendering and Angiographic Feature Extraction
The CAAS 7.5 QCA-3D workstation (Pie Medical Imaging, Maastricht, The Netherlands) was used to generate 3D renderings given two angiographic images taken 30° apart [4]. Output from the workstation was used to catalog or calculate mean lumen area, minimum lumen area, minimum lumen diameter, and length of arterial segment. Minimum lumen diameter and mean lumen diameter were calculated from minimum lumen area and mean lumen area by assuming a perfect circle equal to the respective areas. Percent diameter stenosis was de ned as the difference between unity and the minimum lumen diameter divided by the maximum lumen diameter of a given arterial segment.

Meshing, CFD, and Coronary Flow Rate Determination
Computational uid dynamics modeling of coronary blood ow was performed with ANSYS Fluent 17.0. The viscous model was set to laminar, and density was set as a constant value of 1045 kg/m^3. A 100% hematocrit value was assumed to have a viscosity equal to 0.008 kg m-1 s-1, and a 0% hematocrit was assumed to have a viscosity equal to 0.001 kg m-1 s-1. Linear interpolation between these two extrema were used to nd the patient viscosity values. Patient viscosities ranged from 0.0035 to 0.0045 kg m-1s-1, and it should be noted that small changes in viscosity did not appreciably affect the calculations. The 3D renderings provided by the CAAS 7.5 QCA-3D workstation were used to create unstructured computational meshes. The unstructured computational meshes consisted of tetrahedral cells with 10 in ation layers. A mesh sensitivity analysis was performed which determined the optimum cell count of 542,000 for an arterial segment with a total lumen volume equal to 4.04 × 10^-8 m^3. The node count was scaled accordingly for arterial segments of different total lumen volumes. CFR through the arterial segment was determined by iteratively varying a volumetric ow rate boundary condition until the virtual FFR value was within 1% of the invasive FFR value.

Statistical Analysis
Continuous variables are reported as means ± one standard deviation (SD) or median (interquartile range, 25th-75th percentile) for abnormal distributions. Categorical variables are represented as percentages. Variables were investigated visually using histograms and quantile-quantile (qq) plots. All parameters were tested for normality using the Shapiro-Wilk test. Scatter plots were created to visualize the relationship between variables of interest and FFR. The strength of the linear relationship was quanti ed using Pearson correlation coe cients. Two sample t-tests and Mann-Whitney U-tests were used to test mean differences between FFR < 0.8 and FFR > 0.8 groups after testing for normality. Logistic regression models from the python package, StatsModels, were used to map input features from ICA and CFD to the binary outcome of FFR ≤ 0.8 or FFR > 0.8. The difference in goodness-of-t between nested logistic regression models was quanti ed using the log-likelihood test for signi cance. The predictive capability of a model was compared to that of others by various metrics including accuracy, sensitivity, speci city, positive predictive value, negative predictive value and area-under-the-curve (AUC) values. Model performance was compared using receiver operator characteristic (ROC) curves. Odds ratios of the model coe cients were used as measures of effect size for the variables of interest.

Results And Discussion
Pressure drop through a constriction is expressed as the product of ow rate through the geometry, Q, and the total uidic resistance, R, in the hydraulic resistance equation (Equation 1). Therefore, a stenotic risk model which includes the ow rate and uidic resistance should better predict the pressure drop across the vessel when compared to single parameter models.
To investigate if coronary ow rate, CFR, would improve a risk scoring tool, we began by performing hypothesis testing to determine if there was a signi cant difference in mean CFR between the FFR < 0.8 and FFR > 0.8 groups. A Mann-Whitney U-Test determined that there was a signi cant difference in CFR between FFR < 0.8 (µ=2.37 ml/s) and FFR > 0.8 (µ=1.85 ml/s) groups (p-value=0.046). The statistically signi cant difference in mean coronary artery ow between the two groups indicates that CFR may be an important predictor in coronary artery disease. To highlight the already known importance of %DS, a twosample t-test showed there was a signi cant difference in %DS among FFR < 0.8 (µ=54%) and FFR > 0.8 (µ=46%) groups (p-value= 0.0001).
Conclusions from hypothesis testing is further supported by a box plot which shows the means (denoted by the white dots), medians, and spread of the data ( Figure 1). As expected, the FFR < 0.8 group had a greater mean (54% vs 46%) and median (56% vs 48%) %DS than the FFR > 0.8 group. The novel nding is the difference in CFR between FFR < 0.8 and FFR > 0.8 groups, speci cally that the FFR < 0.8 group had a higher mean (2.37 ml/s vs 1.85 ml/s) and median (1.96 ml/s vs 1.63 ml/s) CFR than the FFR > 0.8 group.
To give a speci c example, two patients whose %DS differed by less than 1% differed in FFR by 0.33. The high FFR patient had a CFR half that of the low FFR patient. Increased CFR through a constriction increases distal Pouiselle frictional losses and turbulent dissipation, increasing the pressure loss, and leading to a lower FFR. While CFR is ordinarily reduced through a stenosed segment because of a severe blockage, low FFR patients may already have had relatively high CFR prior to the formation of the blockage. The correlation between high CFR and low FFR suggests the possibility that already high CFR is causal to the formation of more severe stenoses.
To further investigate the effect of CFR on FFR, logistic regression models were created to study binary classi cation ability. Table 1 summarizes the performance metrics of three different logistic regression models: %DS only model, CFR only model, and a parent model containing both %DS and coronary ow rate as input features. Accuracy, sensitivity, and speci city were 56%, 45%, and 67% in the CFR only model. Although there is a signi cant difference in mean CFR between FFR < 0.8 and FFR > 0.8 groups, CFR by itself is about the same as random chance at predicting functionally signi cant stenoses. %DS by itself was only marginally better at predicting functionally signi cant coronary lesions with an accuracy, sensitivity, and speci city of 62%, 62%, and 63%.  The odds ratio of CFR shows that there is 103% increase in odds of having a functionally signi cant stenosis for every 1 ml/s increase in CFR. The large increase in odds is likely due to the magnitude of the unit increase in coronary ow rate relative to the typical coronary ow rate. The range of coronary ow rates included in this study ranged from less than 1 ml/s to 5 ml/s. Therefore, a 0.25 ml/s increase in even the largest ow rate at a given %DS would amount to an increase of 25.75% in coronary ow rate. Regardless, investigation of the parent model by inspecting odds ratios of the input features adds further evidence that ow rate and %DS are both important for predicting functionally severe lesions. supporting the claim that CFR incrementally improves FFR predictive capability over %DS alone. MLA was included as an angiographic feature that differentiates between cases with similar %DS. A given CFR through a larger MLA but same %DS will not create the same recirculation when exiting the stenosis. Adding minimum lumen area (MLA) to the parent model increased model performance slightly to an AUC value of 0.82.
A scatter plot of FFR versus CFR colored by %DS (Figure 3) quanti es the effect of %DS and CFR on FFR. The black dashed line represents the clinically accepted threshold for stenosis severity (FFR < 0.8). The red line is a line of best t for patients which had an %DS > 60%, and the blue line is a line of best t for patients which had an %DS less than 40%. There is a higher density of less severe stenoses (dark blue dots) above the clinical threshold, and a higher density of high grade stenoses (dark red dots) below the clinical threshold. The negative slopes of the trend lines indicate that increases in CFR will lower the FFR for both low and high %DS. The relative positions and the y-intercepts of the lines indicate FFR is generally higher for lower %DS at a given ow rate. More interestingly, Figure 3 provides explanations for cases which are seemingly unexpected, such as those that have a low %DS and low FFR. These cases generally have a higher CFR. There are also examples of very high %DS patients that have some of the highest FFR values in the entire cohort. The pressure losses through these stenoses are small due to the low hyperemic ow rate, which limits the Pouiselle and turbulent losses. There are a few cases that have FFR < 0.8 values at both mid-to-low %DS and mid-to-low CFR. These patients may have other anatomical features which would lead to lower FFR, such as severely asymmetric stenoses which would increase turbulent losses, diffuse lesions which would increase Pouiselle losses, or microvascular disease The data points with high FFR and high %DS or vice versa seen in Figure 3 support the well-established result that anatomical assessment alone is not su cient to correctly diagnose the clinical signi cance of a stenosis. The importance of CFR in explaining FFR is highlighted when comparing two patients with similarly low %DS, but one with low CFR and one with high CFR (labeled Patient A and Patient B in Figure  3). Patients A and B both have low %DS (44% and 32%), but Patient A has a much lower CFR (1.63 mL/sec) compared to Patient B (4.97 mL/sec). Patient A (low %DS / low CFR) has an FFR = 0.94 (well above the threshold) while Patient B (low %DS / high CFR) has an FFR = 0.73 (well below the threshold).
In terms of Equation 1, the resistance term, R, is similar for both while the ow rate term, Q, for Patient B is 3 times that of Patient A, creating a larger pressure drop and, hence, lower FFR.
The ow features of Patients A and B are visualized in Figure 4 (Patient A) and Figure 5 (Patient B) as vectors of velocity colored by velocity magnitude. Flow distal to stenosis remains well ordered for Patient A. However, the higher ow rate for Patient B creates a region of ow reversal due to the adverse pressure gradient formed by the expansion and acceleration of uid exiting the stenosis (zoomed region of Figure  4). This ow reversal causes the frictional and turbulent energy losses responsible for the larger pressure drop. The ow reversal and recirculation has been quanti ed in terms of higher residence times, which correlate to lower FFR [20].

Limitations
If the estimated CFR values used in this study differ signi cantly from actual CFR values, then this could affect regression coe cients which would change the odds ratios. However, the CFR used in this study produced a virtual FFR computed within 1% of invasively measured FFR for each case, providing evidence for validity of the results here. Direct measurement of coronary ow, such as by angiographic contrast [22], is feasible, but these techniques are invasive and time consuming. Measuring coronary ow rates in vivo would provide experimental validation of the correlation between FFR and coronary ow rates. Regression and machine learning type methods, when fully developed, could be used to estimate volumetric ow rate from anatomical imaging and other readily available patient data. Future work will address the best strategy to determine inlet volume ow rate.

Conclusion
This study found that including CFR in stenotic risk models results in greater predictive performance than models which only include angiographic parameters. We have shown the theoretical signi cance of CFR through Equation 1, the clinical signi cance of CFR through statistical analysis, and the underlying causal mechanisms for the effect of CFR on FFR through CFD. The greater predictive capability of the %DS-CFR logistic regression model over either the %DS-only or CFR-only model supports the relationship in Equation 1 between stenotic resistance and stenotic ow rate to accurately describe pressure losses.
The large odds ratio of CFR highlights the importance of CFR in predicting FFR. Lastly, the ow disturbance distal to stenoses, which was visualized by uid modeling in Figure 5, provides a causal explanation for the signi cance of CFR in predicting FFR that was rst alluded to by Equation 1 and then validated statistically using logistic regression. We recommend that existing and new clinical prediction models for coronary artery stenosis severity incorporate physiological ow rate that could be obtained from established measurement techniques. Improved predictive capability may result in improved risk strati cation tools for coronary artery disease thereby saving time, cost, and unnecessary intervention. Figure 1 Box plot of %DS and coronary ow rate for FFR < 0.8 and FFR > 0.8 patient groups. Mean CFR for FFR < 0.8 and FFR > 0.8 is 2.37 ml/s and 1.85 ml/s, respectively. Median CFR for for FFR <0.8 and FFR > 0.8 is 1.96 ml/s and1.63 ml/s, respectively. Mean %DS for FFR <0.8 and FFR > 0.8 is 54% and 46%, respectively.
Page 12/15 Figure 2 ROC curves of various predictive models using coronary ow rate and angiographic parameters.  Velocity vector colored by velocity magnitude for Patient A (Low %DS and Low FR). Flow remains well ordered distal to the stenosis.

Figure 5
Velocity vector colored by velocity magnitude for Patient B (Low %DS and High FR). A recirculation region forms distal to the stenosis.