# Performance of a Novel Computational Hyperemic Resistance Index Derived from Cardiac CT in Coronary Chronic Syndromes

Yahia Bellouche, Clement Benic, Sinda Hannachi, Pierre Phillipe Nicol, Christopher Jousse, Florent Le Ven, Jacques Mansourati, Bastien Pasdeloup, Romain Didier

► To cite this version:

Yahia Bellouche, Clement Benic, Sinda Hannachi, Pierre Phillipe Nicol, Christopher Jousse, et al. Performance of a Novel Computational Hyperemic Resistance Index Derived from Cardiac CT in Coronary Chronic Syndromes. Journal of Clinical Medicine, 2025, 14 (20), pp.7270. 10.3390/jcm14207270. hal-05316601

HAL Id: hal-05316601

https://hal.science/hal-05316601v1

Submitted on 15 Oct 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Article

# Performance of a Novel Computational Hyperemic Resistance Index Derived from Cardiac CT in Coronary Chronic Syndromes

Yahia Bellouche <fnref n="1" />,<fnref n="2" />,* , Clement Benic <fnref n="1" />,<fnref n="2" />, Sinda Hannachi <fnref n="1" />, Pierre Phillipe Nicol <fnref n="1" />, Christopher Jousse <fnref n="1" />, Florent Le Ven <fnref n="1" />,<fnref n="2" />, Jacques Mansourati <fnref n="1" />, , Bastien Pasdeloup <fnref n="3" /> and Romain Didier <fnref n="1" />,<fnref n="2" />

## Abstract

**Background/Objectives:** Coronary artery disease (CAD) remains the leading global cause of mortality, underscoring the need for functional assessments that extend beyond anatomic evaluation. The Hyperemic Stenosis Resistance (HSR) index combines invasive pressure and flow parameters to assess stenosis severity but faces limitations due to methodological and standardization challenges. This study aimed to introduce and validate a novel non-invasive computational equivalent of HSR (cHSR), derived from coronary computed tomography angiography (CCTA), and to compare its diagnostic performance with fractional flow reserve derived from computational fluid dynamics (FFR<sub>CFD</sub>) and quantitative flow ratio (QFR). **Methods:** A retrospective analysis was conducted on 64 patients (106 coronary lesions) with suspected chronic coronary syndrome (CCS) who underwent both CCTA and invasive coronary angiography (ICA). Computational simulations incorporated patient-specific boundary conditions based on CCTA-derived left ventricular and aortic flow data. Diagnostic accuracy for predicting revascularization was compared among cHSR, FFR<sub>CFD</sub>, and QFR. **Results:** FFR<sub>CFD</sub> showed a strong correlation with invasive FFR (r = 0.87, *p* < 0.0001). The cHSR index achieved the highest diagnostic accuracy (96.2%) at an optimal cut-off of 0.75 mmHg/cm·s<sup>-1</sup>, outperforming both FFR<sub>CFD</sub> and QFR. No significant correlation was found between cHSR and shear stress parameters, including the Oscillatory Shear Index (OSI) and Time-Averaged Wall Shear Stress (TAWSS), indicating complex hemodynamic interactions beyond simple flow-pressure relationships. **Conclusions:** The computational hyperemic stenosis resistance (cHSR) index represents a promising non-invasive tool for the functional assessment of CAD, demonstrating superior diagnostic performance compared with existing imaging-based indices. Prospective multicenter studies with larger populations are warranted to confirm its clinical applicability and prognostic value in chronic coronary syndrome management.

**Keywords:** computational fluid dynamics (CFD); coronary computed tomography angiography (CCTA); hyperemic stenosis resistance (HSR); fractional flow reserve (FFR); chronic coronary syndrome (CCS); wall shear stress (WSS)

## 1. Introduction

Coronary artery disease (CAD) is the primary global cause of mortality, accounting for 9 million deaths annually, or roughly one in seven deaths worldwide, according to the World Health Organization (WHO). While invasive coronary angiography (ICA) and

<figure><img src="image_2.png" /></figure>

check for
updates

Academic Editors: Andreas
S. Papazoglou and
Athanasios Samaras

Received: 27 September 2025
Revised: 11 October 2025
Accepted: 12 October 2025
Published: 15 October 2025

**Citation:** Bellouche, Y.; Benic, C.; Hannachi, S.; Nicol, P.P.; Jousse, C.; Le Ven, F.; Mansourati, J.; Pasdeloup, B.; Didier, R. Performance of a Novel Computational Hyperemic Resistance Index Derived from Cardiac CT in Coronary Chronic Syndromes. *J. Clin. Med.* **2025**, *14*, 7270. https://doi.org/10.3390/jcm14207270

**Copyright:** © 2025 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license
(https://creativecommons.org/licenses/by/4.0/).

<footnote n="1">1 Cardiology Department, Brest University Hospital, 29200 Brest, France</footnote>

<footnote n="2">2 Inserm UMR 1304 (GETBO), Western Brittany University Brest, 29200 Brest, France</footnote>

<footnote n="3">3 Lab-STICC, UMR CNRS 6285, IMT Atlantique, 29238 Brest, France</footnote>

<footnote>* Correspondence: yahiaphdmd@gmail.com; Tel.: +33-7-54-00-34-33</footnote>
quantitative coronary angiography (QCA) traditionally assess the anatomical severity of stenosis, relying solely on these measures often proves insufficient. In different series, 20–30% of lesions deemed severe by QCA do not induce ischemia during functional testing [1]. This discrepancy highlights the crucial need for integrating functional evaluations into the revascularization decision-making process to improve patient outcomes [2].

Fractional Flow Reserve (FFR) has emerged as the gold standard for functional lesion assessment and is strongly predictive of adverse cardiovascular events [3–5]. Despite its robustness, FFR does not provide information about the microvascular function, with a known discrepancy between FFR and Coronary Flow Reserve (CFR) in up to 20% cases in both normal and altered CFR populations [6]. While FFR assesses pressure gradients across stenosis under hyperemia, microvascular resistance is neutralized by hyperemic agents (adenosine mainly). However, cases of microvascular dysfunction can cause ischemia independently of epicardial stenosis [7,8]. To address these gaps, the Hyperemic Stenosis Resistance (HSR) index was introduced, combining pressure and flow data to offer a more refined physiological assessment [9]. However, the lack of standardized methods for flow measurement has limited its routine clinical use [10]. In a recent study conducted by Boerhout and al., using data from 853 patients and 1107 vessels from the multicentric ILIAS Registry, they aimed to assess HSR’s diagnostic and prognostic value in chronic coronary syndrome (CCS) patients. HSR more accurately identified inducible ischemia compared to FFR and CFR (AUC 0.71 vs. 0.66 and 0.62, respectively; *p* < 0.005). Additionally, abnormal HSR was a strong, independent predictor of target vessel failure at 5-year follow-up (HR 3.80, 95% CI: 2.12–6.73; *p* < 0.005). In cases where revascularization was deferred, HSR showed superior ability in pinpointing vessels that might still benefit from intervention [11].

In the quest for non-invasive diagnostic alternatives, functional imaging techniques like stress SPECT, echocardiography, and cardiac magnetic resonance (CMR) are commonly used to evaluate ischemia [2]. However, their diagnostic accuracy can be limited in high-risk populations, such as patients with left main or three-vessel disease, where anatomical assessment is crucial for risk stratification [12]. In such cases, combining functional and anatomical data is necessary and may provide a more comprehensive evaluation.

Recent advancements in computational modeling, based on Computational Fluid Dynamics (CFD), have enhanced the diagnostic utility of anatomical imaging by simulating coronary flow and pressure [13]. Quantitative Flow Ratio (QFR), based on ICA, and Computed Tomography Fractional Flow Reserve (FFRCT), based on coronary computed tomography angiography (CCTA), both use CFD models to estimate the functional significance of coronary stenoses [14,15]. These techniques have demonstrated improved diagnostic accuracy by offering both anatomical and functional insights with an acceptable cost-effectiveness ratio [16]. However, the performance of a model relies heavily on the defined boundary conditions (BCs). Most available commercial software uses theoretical assumptions and idealized parameters, which can miss the patient-specific setting. When clinical data are accessible, using patient-specific BCs is preferable over generalized or estimated parameters, which produce more realistic flow/pressure curves, particularly near side branches and curvatures where atherosclerotic plaques commonly form [17].

This study proposes a new non-invasive computational equivalent of Hyperemic Stenosis Resistance (*cHSR*) index derived from CCTA to provide a combined flow/pressure-based assessment of coronary lesions. We aim to evaluate its diagnostic performance in predicting revascularization, with $FFR_{CFD}$ and QFR serving as comparators. Furthermore, we explored the relationship between *cHSR* and shear stress parameters, such as Oscillatory Shear Index (*OSI*) and Time-Averaged Wall Shear Stress (TAWSS).
## 2. Methods

### 2.1. Population of Study and Inclusion/Exclusion Criteria

This retrospective observational outcome-blinded study was conducted at Brest University Hospital between January 2021 and September 2024. Patients referred for CCTA due to suspected chronic coronary syndrome (CCS), who subsequently underwent ICA, were included. The local Institutional Ethics Committee approved the study protocol, which was based on Reference Methodology (MR004), as defined by the French Data Protection Authority (CNIL), and patient data were anonymized in compliance with institutional regulations (Figure 1).

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Study flowchart CCTA: Coronary Computed Tomography Angiography; CCS: Chronic-Coronary Syndrome; CABG: Coronary Artery Bypass Grafting; LV: Left Ventricular; CA: Coronary Angiography.</figcaption></figure>

Inclusion criteria were patients aged between 18 and 85 years who underwent both CCTA and ICA, with at least one significant lesion (40–80%) in a coronary artery larger than 2.5 mm in diameter. Patients were excluded if they had a recent acute coronary syndrome (<40 days), a left ventricular ejection fraction (LVEF) < 40%, significant mitral or aortic valve disease, prior coronary artery bypass graft surgery (CABG), heart transplant, or the presence of chronic total occlusion (CTO). Sixty-four patients with 106 coronary lesions were included in the analysis; the final revascularization decision was omitted from the analysts throughout the study protocol.

In our cohort, the decision whether to proceed with revascularization or not was informed by various methods. Invasive fractional flow reserve (FFR) guided 60% (n = 63 lesions) of the revascularization decisions. An additional 30% (n = 32 lesions) of the decisions were based on stress-induced ischemia detected by stress single-photon emission computed tomography (SPECT), while in the remaining 10% (n = 11 lesions) of patients, revascularization was indicated by electrocardiographic changes and the presence of wall motion abnormalities on rest imaging. Clinical coronary disease pretest probability and coronary calcium scores were calculated in accordance with the most recent guidelines [2].
## 2.2. Data Acquisition

CCTA was performed using a 320-slice volumetric CT scanner (Aquilion One, Toshiba, Tochigi City, Japan) with retrospective ECG-gating and tube modulation. Image acquisition parameters included a slice thickness of 0.6 mm, with a non-ionic contrast agent injected at 5 mL/s followed by a saline flush. The images were reconstructed using the open source Slicer 3D software (version 5.3.0); segmentation and meshing of coronary artery geometries were conducted with SimVascular (version may 2023), an open-source cardiovascular modeling platform [18]. For each patient, we calculated total left ventricular myocardial mass and allocated percentages for each artery through visual analysis. Invasive blood pressure waveforms (which can be replaced by non-invasive blood pressure), stroke volume, and systolic ejection time were important input data for the sake of individualized flow and pressure targets in the parameters tuning process (Figure 2).

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Patient data preprocessing: CCTA: Coronary Computed Tomography Angiography; DICOM: Digital Imaging and Communications in Medicine; FFR: Fractional Flow Reserve; Pa: Aortic Pressure; Pd: Distal Coronary Pressure; MRI: Magnetic Resonance Imaging.</figcaption></figure>

In addition, we modeled aortic flow rates using phase contrast cardiac MRI from 15 healthy individuals, adjusted according to each patient's body surface area (BSA). For intramyocardial pressure modeling, we acquired left ventricular pressure measurements from 22 healthy individuals, also scaled by BSA, to simulate patient-specific myocardial loading conditions more accurately.

ICA was performed following standard clinical protocols, and invasive FFR measurements were obtained using the PressureWire X (Abbott Vascular, Santa Clara, CA, USA). Hyperemia was induced using intravenous adenosine at 140 µg/kg/min besides intracoronary nitroglycerin to avoid spastic coronary lesions. For the purpose of internal model validation, we collected pressure waveforms of the 60% of lesions that had invasive FFR measurements. Quantitative Flow Ratio (QFR) was derived from ICA images through QAngio XA 3D software (research edition, version 2.1, Medis, Leiden, The Netherlands).
## 2.3. Simulations Pipeline and Measurements

Our simulation pipeline used a patient-specific model (which consisted of the initial aorta, and the three coronary arteries) obtained from CCTA, with segmentation and meshing performed in SimVascular platform (as detailed in Supplementary Materials) [18]. Aortic inflow boundary conditions were calculated based on CCTA-derived left ventricular volumetric data to produce a patient-specific aortic flow rate curve (which guided scaling of curves obtained in MRI to adapt to each patient’s hemodynamics and body surface area). Invasive aortic and intraventricular pressure measurements taken during the ICA served both to calculate initial resistances and as targets for lumped parameters tuning.

Outlet boundary conditions of the peripheral arterial system were based on a simple three-element Windkessel model containing resistances ($R_p$ for proximal arteries and $R_d$ for distale and microvascular systems) and a capacitor (aortic compliance) [19]. Coronary outlet boundary conditions were adapted from Mantero et al. [20] and modified to exclude coronary venous microcirculation compliance for computational simplicity while preserving realistic coronary flow and pressure dynamics. This coronary vascular model incorporated arterial resistance ($R_a$) and compliance ($C_a$), arterial microcirculation resistance ($R_{a-micro}$), myocardial compliance ($C_{im}$), venous microcirculation resistance ($R_{v-micro}$), and intramyocardial pressure ($P_{im}$) to achieve patient-specific hemodynamic responses.

To optimize computational accuracy, both models’ lumped parameters were refined using reduced-order simulations, and different conditions (Rest and exercise) were tested according to the methods proposed by kim and al. [21]. Initial values and tuning process are detailed in Supplementary Materials. Tridimensional CFD simulations were executed after that, using the SimVascular gateway [22], solving Navier-Stokes equations to compute hemodynamic parameters, including pressure, velocity, wall shear stress (WSS), and flow at each point of the coronary arteries tree. These simulations were performed under both basal and hyperemic conditions and produced output, allowing for assessment of stenosis severity in relation to functional coronary flow (Figures 3 and 4). $FFR_{CFD}$ was calculated as the ratio of distal coronary pressure $P_{dist}$ to aortic pressure $P_{aortic}$ during hyperemia:

$$FFR_{CFD} = \frac{P_{dist}}{P_{aortic}}$$

Similarly, $cHSR$ was calculated by dividing the pressure gradient across the lesion ($\Delta P$) by the hyperemic average peak velocity (hAPV) as measured at stenosis level through 3D CFD simulation results:

$$cHSR = \frac{\Delta P}{hAPV}$$

Wall shear stress (WSS) quantifies the tangential force exerted by blood flow on the vessel wall and plays a critical role in endothelial function and atherosclerosis progression. Time-Averaged Wall Shear Stress (TAWSS) was computed using the equation:

$$TAWSS = \frac{1}{T} \int_{0}^{T} |\tau(t)| dt$$

where $\tau(t)$ represents the instantaneous WSS at a given point on the arterial wall, and $T$ is the cardiac cycle duration. This provides an overall measure of shear stress magnitude experienced by the vessel wall over the cardiac cycle.
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Simulation process and output: Pa: Aortic Pressure; Pd: Distal Coronary Pressure; FFR: Fractional Flow Reserve; cHSR: Computational Hyperemic Stenosis Resistance; OSI: Oscillatory Shear Index; TAWSS: Time-Averaged Wall Shear Stress; RCR Model: Resistance, Capacitance, and Resistance model (used in Windkessel outflow modeling); Navier-Stokes Equations: Fundamental equations for fluid dynamics, used to model blood flow.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Computational analysis illustrating key parameters: FFR<sub>CFD</sub>: Fractional Flow Reserve via Computational Fluid Dynamics; hAPV: Hyperemic Average Peak Velocity; cHSR: Computational Hemodynamic Stenosis Resistance; Pd: Distal Pressure, Pa: Proximal Pressure; TAWSS: Time-Averaged Wall Shear Stress; OSI: Oscillatory Shear Index; ROI: Region of Interest, 15 mm of vessel length beyond peak stenosis.</figcaption></figure>

The Oscillatory Shear Index (OSI) Quantifies the Directional Variability of WSS and Is Calculated as

$$OSI = \frac{1}{2} \left( 1 - \frac{\int_{0}^{T} \tau(t) dt}{\int_{0}^{T} |\tau(t)| dt} \right)$$
where the numerator accounts for the net directional shear stress over a full cycle, while the denominator represents the total shear magnitude. OSI values close to 0 indicate unidirectional flow, whereas values approaching 0.5 suggest significant oscillations in shear direction. Both TAWSS and OSI were computed from CFD simulations using Navier-Stokes equations under pulsatile flow conditions, with coronary flow profiles extracted from patient-specific CCTA-derived aortic inflow and coronary geometry. These parameters were analyzed at regions of interest (15 mm beyond the peak stenosis) to evaluate their relationship with cHSR and lesion severity.

## 2.4. Statistical Analysis

For statistical analysis in our study, we used R Statistical Software (v4.4.1; R Core Team 2021). Descriptive statistics were used to summarize the baseline characteristics of the study population and coronary lesions. Normally distributed continuous variables were presented as mean and standard deviation (SD), while non-normally distributed variables were expressed as median and interquartile range (IQR). The Shapiro-Wilk test was used to assess normality, and categorical variables were described as counts and percentages.

The agreement between FFR<sub>CFD</sub> and invasive FFR was assessed using a Bland-Altman plot, and their correlation was evaluated using Pearson's correlation coefficient. The optimal cut-off for cHSR was determined using Youden's index. Diagnostic performance of cHSR for predicting revascularization was assessed using ROC curve analysis, with area under the curve (AUC), sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) calculated for each method. All these metrics were compared to those of FFR<sub>CFD</sub> and QFR using the DeLong test.

Correlation between cHSR and wall shear stress parameters (TAWSS, OSI) was evaluated using Pearson's correlation coefficient. Statistical significance was set at *p* < 0.05.

# 3. Results

## 3.1. Patient Population and Lesion Characteristics

A total of 64 patients (mean age 67.8 ± 9.2 years) were included in the study, with a pre-test probability for coronary artery disease (CAD) averaging 24.5 ± 14.8%. The cohort had a sex ratio of 3:1. Among the patients, 62% had hypertension (HTN), 39% had diabetes mellitus (DM), 41% had a history of smoking, and 40% had dyslipidemia. Obesity was noted in 34% of the cohort, and 20% had chronic kidney disease (CKD). The mean coronary artery calcium (CAC) score was 113.1 ± 102.4 Agatston units (Table 1).

In terms of coronary lesions, a total of 106 lesions were analyzed, with a mean stenosis length of 18.0 ± 7.4 mm. The distribution of lesions across different coronary arteries was as follows: 49% in the left anterior descending artery (LAD), 26% in the left circumflex artery (LCx), 22% in the right coronary artery (RCA), and 3% in the left main artery (LM). The mean stenosis percentage, as determined by quantitative coronary angiography (QCA), was 55.3 ± 11.2% (Table 2).

## 3.2. Correlation Between FFR<sub>CFD</sub> and Invasive FFR

A Bland-Altman analysis was used to assess the agreement between FFR<sub>CFD</sub> and invasive FFR, revealing good agreement with a Pearson correlation coefficient of 0.87 (p < 0.0001), indicating strong linear correlation. The plot confirmed minimal bias (mean difference + 0.01), supporting the validity of the computational FFR<sub>CFD</sub> measurements.
<table><caption>**Table 1.** Baseline Characteristics of the Study Population.</caption><thead><tr><th>Characteristic</th><th>Mean +/− (SD) or Percentage (%)</th></tr></thead><tbody><tr><td>Total Patients</td><td>n = 64</td></tr><tr><td>Age (years)</td><td>67.8 ± 9.2</td></tr><tr><td>Sex Ratio</td><td>3 Male:1 Female</td></tr><tr><td>Hypertension (HTN)</td><td>62% (n = 40)</td></tr><tr><td>Diabetes Mellitus (DM)</td><td>39% (n = 25)</td></tr><tr><td>Smoking History</td><td>30% (n = 19)</td></tr><tr><td>Dyslipidemia</td><td>40% (n = 26)</td></tr><tr><td>Obesity</td><td>34% (n = 22)</td></tr><tr><td>Chronic Kidney Disease (CKD)</td><td>20% (n = 13)</td></tr><tr><td>Pre-test Probability</td><td>24.5 ± 14.8</td></tr><tr><td>Calcium Score (CAC) (Agatston)</td><td>113.1 ± 102.4</td></tr></tbody></table>

CAD: Coronary Artery Disease; HTN: Hypertension; DM: Diabetes Mellitus; CKD: Chronic Kidney Disease; CAC: Coronary Artery Calcium score.

<table><caption>**Table 2.** Lesion Characteristics.</caption><thead><tr><th>Lesion Location</th><th>Mean +/− (SD) or Percentage (%)</th></tr></thead><tbody><tr><td>Total lesions</td><td>n = 106</td></tr><tr><td>LAD</td><td>51 (49%)</td></tr><tr><td>LCx</td><td>26 (26%)</td></tr><tr><td>RCA</td><td>23 (22%)</td></tr><tr><td>Left Main (LM)</td><td>3 (3%)</td></tr><tr><td>QCA (% Stenosis)</td><td>55.3 ± 11.2</td></tr><tr><td>Stenosis Length (mm)</td><td>18.0 ± 7.4</td></tr></tbody></table>

LAD: Left Anterior Descending artery; LCx: Left Circumflex artery; RCA: Right Coronary Artery; LM: Left Main artery; QCA: Quantitative Coronary Angiography.

### 3.3. cHSR Cut-Off Determination

The optimal cut-off value for cHSR to predict the need for revascularization was determined through receiver operating characteristic (ROC) curve analysis and the Youden Index. The ideal cHSR cut-off was found to be 0.75 mmHg/cm·s⁻¹, providing the highest overall diagnostic accuracy. At this cut-off, the sensitivity and specificity for predicting revascularization were 96.2% each.

### 3.4. Diagnostic Performance of cHSR, FFR<sub>CFD</sub>, and QFR

The diagnostic performance of cHSR, FFR<sub>CFD</sub>, and QFR for predicting the necessity of revascularization was compared (Figure 5). cHSR demonstrated the best diagnostic accuracy (96.2%) compared to FFR<sub>CFD</sub> (83.0%) and QFR (81.1%). cHSR also showed superior sensitivity and specificity (96.2%) when compared to FFR<sub>CFD</sub> (sensitivity 71.7%, specificity 94.3%) and QFR (sensitivity 75.5%, specificity 86.8%). The positive predictive value (PPV) and negative predictive value (NPV) for cHSR were also both 96.6%, significantly higher than those of FFR<sub>CFD</sub> and QFR (Table 3).
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Receiver operator curves for *cHSR*, *FFRCFD*, and *QFR*: *cHSR*: Computational Hyperemic Stenosis Resistance; *FFRCFD*: Computed Fractional Flow Reserve; *QFR*: Quantitative Flow Ratio; *AUC*: Area Under the Curve; *ROC*: Receiver Operating Characteristic.</figcaption></figure>

<table><caption>**Table 3.** Diagnostic Performance Metrics of *cHSR*, *FFRCFD*, and *QFR*.</caption><thead><tr><th>Metric</th><th>Sensitivity</th><th>Specificity</th><th>Accuracy</th><th>PPV</th><th>NPV</th><th>AUC</th></tr></thead><tbody><tr><td><strong>cHSR</strong></td><td>96.20%</td><td>96.20%</td><td>96.20%</td><td>96.20%</td><td>96.20%</td><td>0.96</td></tr><tr><td><strong>FFR<sub>CFD</sub></strong></td><td>71.70%</td><td>94.30%</td><td>83.00%</td><td>92.70%</td><td>76.90%</td><td>0.93</td></tr><tr><td><strong>QFR</strong></td><td>75.50%</td><td>86.80%</td><td>81.10%</td><td>85.10%</td><td>77.90%</td><td>0.81</td></tr></tbody></table>

*cHSR*: Computational Hyperemic Stenosis Resistance; *FFRCFD*: Fractional Flow Reserve computed from Computational Fluid Dynamics; *QFR*: Quantitative Flow Ratio; *PPV*: Positive Predictive Value; *NPV*: Negative Predictive Value; *AUC*: Area Under the Curve.

### 3.5. DeLong Test Results

The DeLong test was used to statistically compare the areas under the ROC curves (AUCs) of *cHSR*, *FFRCFD*, and *QFR*. The results showed that *cHSR* had a significantly higher AUC compared to both *FFRCFD* (z = 19.27, *p* < 0.001) and *QFR* (z = 16.55, *p* < 0.001), further confirming its superior diagnostic performance in predicting the necessity of revascularization.

### 3.6. Correlation Between *cHSR*, *TAWSS*, and *OSI*

The relationship between *cHSR* and the shear stress parameters *TAWSS* and *OSI* was evaluated. No significant correlation was found between *cHSR* and *TAWSS* (*r* = -0.05, *p* = 0.61), nor between *cHSR* and *OSI* (*r* = 0.14, *p* = 0.16) (Figure 6).
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Scatter plots for HSR vs. TAWSS and HSR vs. OSI: HSR: Hyperemic Stenosis Resistance; TAWSS: Time-Averaged Wall Shear Stress; OSI: Oscillatory Shear Index.</figcaption></figure>

# 4. Discussion

## 4.1. *Study Population*

Our study included a cohort with suspected chronic coronary syndrome (CCS), encompassing a broad range of pretest probabilities and coronary lesion complexities. This diversity underscores the applicability of coronary computed tomography angiography (CCTA) as an initial diagnostic tool across varied patient profiles, aligning with recent guidelines and recommendations [2]. In a metanalysis conducted by Foy and al. [23], although CCTA did not significantly reduce mortality or cardiac hospitalizations, it was associated with a lower incidence of myocardial infarction, alongside an increase in invasive angiography, revascularizations, coronary artery disease diagnoses, and new prescriptions for aspirin and statins, compared to functional stress testing. This finding suggests CCTA's role in identifying a higher burden of clinically significant CAD. Thus, traditional functional imaging—while valuable for ischemia detection—may have limited diagnostic performance in specific populations, such as those with three vessel disease and left main lesions, where anatomical assessment may offer superior guidance [12].

## 4.2. *FFRCFD and FFR Correlation and Lumped Model Validation*

In our study, $FFR_{CFD}$ demonstrated excellent agreement with invasive FFR, with a Pearson correlation coefficient of 0.87, which is comparable to the results by Nørgaard et al. [24], who reported a correlation coefficient of 0.81, and Faulder et al. [25], who noted values between 0.82 and 0.85 in large, multicentric cohorts. Bland-Altman analysis in our study showed minimal bias, with most differences falling within ±0.10, affirming our model's accuracy (Figure 7).

However, discrepancies between $FFR_{CFD}$ and invasive FFR were observed in four cases, highlighting areas where further refinement of computational models may be beneficial. Two cases involved patients with a silent myocardial infarction (MI) in the territory of the coronary lesion. Prior research has shown that FFR values in post-MI patients can vary depending on the extent of myocardial viability. De Bruyne et al. demonstrated that viable myocardial tissue can maintain vasoreactivity even in infarcted regions, leading to variability in FFR measurements due to altered blood flow dynamics [26]. This suggests that in cases of silent MI, adjustments to computational models may be needed to accurately account for myocardial viability and regional perfusion changes.
<figure><img src="image_9.png" /><figcaption>**Figure 7.** Bland-Altman analysis $FFR_{CFD}$ vs. invasive FFR: computationally derived fractional flow reserve ($FFR_{CFD}$); invasive fractional flow reserve (FFR).</figcaption></figure>

Two other cases involved patients with a high coronary calcium burden, where segmentation challenges affected the precision of CCTA-derived models. High calcium scores can impair the accuracy of CCTA, impacting the segmentation process and introducing potential errors in model creation. Quality CCTA acquisition and advanced segmentation algorithms are critical in such scenarios, while the use of ultrahigh-resolution photon-counting CT may resolve this problem, with resolution levels approaching those of invasive coronary angiography [27].

The model’s high correlation likely benefits from the rigorous tuning of boundary conditions and patient-specific inputs such as flow adjusted to myocardial mass, which further improved alignment with invasive measures in respect to methods described previously [28,29].

### 4.3. cHSR Cutoff

Our analysis identified an optimal cHSR cutoff of 0.75 mmHg/cm·s⁻¹ for predicting the necessity of revascularization, aligning closely with the findings of Meuwissen et al. [9], who proposed a hyperemic stenosis resistance (HSR) threshold of 0.8 mmHg/cm·s⁻¹ in invasive measurements. However, this slight adjustment in cutoff in our study may result from the fidelity of our simulation methods. Despite promising preliminary evidence, larger studies are needed to substantiate this finding, especially to achieve the statistical power required to define an optimal cHSR threshold across diverse populations. Thus, prospective validations are crucial to reinforce the clinical applicability of cHSR as a complementary measure to $FFR_{CFD}$.

### 4.4. Diagnostic Performances of HSR, QFR, and FFRCFD

Both $FFR_{CFD}$ and QFR displayed high diagnostic performance, consistent with prior studies (Table 4) such as Xu et al. [14] and Agatsthi et al. [30], who reported sensitivities and specificities exceeding 80%. In our study, $FFR_{CFD}$ and QFR achieved accuracies of 83% and 81%, respectively. However, cHSR demonstrated superior performance, with an accuracy of 96%, along with higher sensitivity and specificity than both $FFR_{CFD}$ and QFR. This enhanced diagnostic capability of cHSR and aligns with the conclusions of Van de Hoef et al. [31], who noted that combined pressure and flow measurements can provide a more comprehensive understanding of coronary physiology than pressure indices
alone. This combined approach for HSR appears to capture the hemodynamic impact of coronary stenosis more effectively, potentially refining patient selection for revascularization and addressing limitations inherent to pressure-only indices.

### 4.5. HSR and Shear Stress

Our investigation revealed no significant correlation between cHSR and shear stress parameters such as TAWSS and OSI, suggesting rather an intricate relationship between cHSR and shear stress. The literature on this topic is limited, particularly for computational indices, but some studies on invasive measures provide context. For instance, Puri et al. reported that pathological shear stress correlated with plaque vulnerability [32], while Wong et al. found moderate relationships between invasive indices and WSS parameters in specific lesion types [33]. The absence of a significant relationship in our study may indicate that while cHSR captures functional stenosis effects, it may not reflect local shear stress changes that influence plaque morphology and stability. This finding highlights the complexity of hemodynamic interactions, and the insufficient character of the current models to fully understand them.

<table><caption>**Table 4.** Summary of key studies evaluating the diagnostic performance and clinical benefit of computational fluid dynamics (CFD) and imaging-based coronary physiology indices.</caption><thead><tr><td>Study</td><td>Index</td><td>Sample Size</td><td>Modality</td><td>Key Findings</td></tr></thead><tbody><tr><td>Nørgaard et al., 2014 [24]</td><td>FFR_CT</td><td>254</td><td>CCTA</td><td>Demonstrated high diagnostic accuracy of FFR_CT with invasive FFR as reference, sensitivity and specificity >80%.</td></tr><tr><td>Westra et al., 2018 [34]</td><td>QFR</td><td>352</td><td>Angiography</td><td>QFR was highly accurate in predicting ischemia with FFR reference; achieved >85% accuracy.</td></tr><tr><td>Xu et al., 2021 [14] (FAVOR III China)</td><td>QFR</td><td>3825</td><td>Angiography</td><td>Showed significant reduction in MACE over 1 year for QFR-guided PCI vs. standard angiography-guided PCI.</td></tr><tr><td>Song et al., 2022 [35] (2-Year FAVOR III)</td><td>QFR</td><td>3825</td><td>Angiography</td><td>Demonstrated durability of QFR-guided PCI benefits with reduced MACE over 2 years compared to angiography guidance.</td></tr><tr><td>Driessen et al., 2019 [36]</td><td>FFR_CT</td><td>208</td><td>CCTA</td><td>FFRCT showed higher diagnostic performance than standard coronary CTA, SPECT, and PET for vessel-specific ischemia.</td></tr><tr><td>Koo et al., 2011 [37]</td><td>FFR_CT</td><td>103</td><td>CCTA</td><td>Accuracy, sensitivity, specificity, positive predictive value, and negative predictive value were 84.3%, 87.9%, 82.2%, 73.9%, 92.2%, respectively, for FFR_CT.</td></tr></tbody></table>

FFRCT: Fractional Flow Reserve derived from Coronary Computed Tomography Angiography; QFR: Quantitative Flow Ratio; CCTA: Coronary Computed Tomography Angiography; PCI: Percutaneous Coronary Intervention; MACE: Major Adverse Cardiac Events; SPECT: Single Photon Emission Computed Tomography; PET: Positron Emission Tomography.

### 5. Limitations

This study has several limitations. First, the retrospective design introduces potential selection biases, and the relatively small sample size may limit the generalizability of findings to larger populations. Additionally, the computational power and time required for 3D flow simulations pose challenges, as these processes are resource consuming and not yet feasible for routine clinical application. The study relied on retrospective acquisition protocols for CCTA, which increased cumulative radiation exposure for patients. Furthermore, the simulation models assume rigid arterial walls and omit arterial motion,
which may not fully represent the dynamic nature of coronary arteries in vivo. Future work with larger sample sizes and advanced computational models may help overcome these limitations and increase the applicability of computational hyperemic stenosis resistance (*cHSR*) as a reliable diagnostic tool.

## 6. Conclusions

Our study (Figure 8: Central illustration) demonstrates the promising diagnostic potential of a new computational index (*cHSR*), showing superior performance compared to traditional imaging-based indices. The computational model used in this study produced values of $FFR_{CFD}$ with strong agreement with invasive FFR. These findings support the integration of computational methods into non-invasive imaging to improve decision-making in CCS management. Future advancements in automation and machine learning could enhance its clinical viability, potentially transforming how CCS is assessed and treated.

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Central illustration: CCS: Chronic Coronary Syndrome; CCTA: Coronary Computed Tomography Angiography; ICA: Invasive Coronary Angiography; QFR: Quantitative Flow Ratio; FFR: Fractional Flow Reserve; $FFR_{CFD}$: Fractional Flow Reserve derived from Computational Fluid Dynamics; *cHSR*: Computational Hyperemic Stenosis Resistance; *OSI*: Oscillatory Shear Index; TAWSS: Time-Averaged Wall Shear Stress; CFD: Computational Fluid Dynamics; AUC: Area Under the Curve; PPV: Positive Predictive Value; NPV: Negative Predictive Value.</figcaption></figure>

**Supplementary Materials:** The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/jcm14207270/s1, Refs. [20,21,38–44] are cited in Supplementary Materials.

**Author Contributions:** Methodology, C.B.; Validation, S.H.; Formal analysis, P.P.N., C.J. and J.M.; Data curation, F.L.V.; Writing—original draft, Y.B. and B.P.; Visualization, B.P.; Supervision, R.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.
**Institutional Review Board Statement:** The Brest university hospital ethics board approved the study protocol which was based on Reference Methodology (MR004), as defined by the French Data Protection Authority (CNIL), and patient data were anonymized in compliance with institutional regulations (Approval date: 24 September 2024).

**Informed Consent Statement:** Informed consent was waived for this retrospective study in accordance with Reference Methodology MR004 and approval by the Brest University Hospital ethics board.

**Data Availability Statement:** The datasets used and analyzed during the current study are available from the corresponding author upon reasonable request. Due to patient confidentiality and ethical restrictions imposed by the Institutional Review Board, the raw data cannot be publicly shared. However, de-identified data relevant to the findings of this study may be provided upon request, subject to institutional approval and compliance with data protection regulations.

**Acknowledgments:** We extend our gratitude to the SimVascular Gateway for providing access to high-performance computing resources, which were essential for conducting the complex simulations presented in this study. This support was instrumental in facilitating our research and enabling the detailed analysis necessary for advancing our understanding of computational hyperemic resistance indices. Additionally, we acknowledge the Radiology Department of Brest University Hospital for their invaluable technical assistance in processing the imaging exams. Their expertise and cooperation significantly contributed to the precision and reliability of our results.

**Conflicts of Interest:** The authors declare no conflict of interest.

## References

1. Christou, M.A.C.; Siontis, G.C.M.; Katritsis, D.G.; Ioannidis, J.P.A. Meta-Analysis of Fractional Flow Reserve Versus Quantitative Coronary Angiography and Noninvasive Imaging for Evaluation of Myocardial Ischemia. *Am. J. Cardiol.* **2007**, *99*, 450–456. [CrossRef]

2. Vrints, C.; Andreotti, F.; Koskinas, K.C.; Rossello, X.; Adamo, M.; Ainslie, J.; Banning, A.P.; Budaj, A.; Buechel, R.R.; Chiariello, G.A.; et al. 2024 ESC Guidelines for the management of chronic coronary syndromes. *Eur. Heart J.* **2024**, *45*, 3415–3537. [CrossRef]

3. Tonino, P.A.L.; Bruyne, B.D.; Pijls, N.H.J.; Siebert, U.; Ikeno, F.; van ‘t Veer, M.; Klauss, V.; Manoharan, G.; Engstrøm, T.; Oldroyd, K.G.; et al. Fractional Flow Reserve versus Angiography for Guiding Percutaneous Coronary Intervention. *N. Engl. J. Med.* **2009**, *360*, 213–224. [CrossRef]

4. Bruyne, B.D.; Pijls, N.H.J.; Kalesan, B.; Barbato, E.; Tonino, P.A.L.; Piroth, Z.; Jagic, N.; Möbius-Winkler, S.; Rioufol, G.; Witt, N.; et al. Fractional Flow Reserve–Guided PCI versus Medical Therapy in Stable Coronary Disease. *N. Engl. J. Med.* **2012**, *367*, 991–1001. [CrossRef] [PubMed]

5. Fearon, W.F.; Zimmermann, F.M.; Bruyne, B.D.; Piroth, Z.; van Straten, A.H.M.; Szekely, L.; Davidavičius, G.; Kalinauskas, G.; Mansour, S.; Kharbanda, R.; et al. Fractional Flow Reserve–Guided PCI as Compared with Coronary Bypass Surgery. *N. Engl. J. Med.* **2022**, *386*, 128–137. [CrossRef] [PubMed]

6. Johnson, N.P.; Kirkeeide, R.L.; Gould, K.L. Is Discordance of Coronary Flow Reserve and Fractional Flow Reserve Due to Methodology or Clinically Relevant Coronary Pathophysiology? *JACC Cardiovasc. Imaging* **2012**, *5*, 193–202. [CrossRef]

7. Hong, D.; Shin, D.; Lee, S.H.; Joh, H.S.; Choi, K.H.; Kim, H.K.; Ha, S.J.; Park, T.K.; Yang, J.H.; Song, Y.B.; et al. Prognostic Impact of Coronary Microvascular Dysfunction According to Different Patterns by Invasive Physiologic Indexes in Symptomatic Patients With Intermediate Coronary Stenosis. *Circ. Cardiovasc. Interv.* **2023**, *16*, 12621. [CrossRef]

8. Fearon, W.F.; Aarnoudse, W.; Pijls, N.H.J.; De Bruyne, B.; Balsam, L.B.; Cooke, D.T.; Robbins, R.C.; Fitzgerald, P.J.; Yeung, A.C.; Yock, P.G. Microvascular Resistance Is Not Influenced by Epicardial Coronary Artery Stenosis Severity: Experimental Validation. *Circulation* **2004**, *109*, 2269–2272. [CrossRef]

9. Meuwissen, M.; Siebes, M.; Chamuleau, S.A.J.; Van Eck-Smit, B.L.F.; Koch, K.T.; De Winter, R.J.; Tijssen, J.G.P.; Spaan, J.A.E.; Piek, J.J. Hyperemic Stenosis Resistance Index for Evaluation of Functional Coronary Lesion Severity. *Circulation* **2002**, *106*, 441–446. [CrossRef]

10. Vijayan, S.; Barmby, D.S.; Pearson, I.R.; Davies, A.G.; Wheatcroft, S.B.; Sivananthan, M. Assessing Coronary Blood Flow Physiology in the Cardiac Catheterisation Laboratory. *Curr. Cardiol. Rev.* **2017**, *13*, 232. [CrossRef]

11. Boerhout, C.; Echavarria-Pinto, M.; de Waard, G.A.; Lee, J.M.; Mejía-Rentería, H.; Lee, S.H.; Jung, J.-H.; Hoshino, M.; Matsuo, H.; Madera-Cambero, M.; et al. Impact of Hyperaemic Stenosis Resistance on Long-Term Outcomes of Stable Angina in the ILIAS Registry. *EuroIntervention* **2024**, *20*, e699–e706. [CrossRef]
12. Knuuti, J.; Ballo, H.; Juarez-Orozco, L.E.; Saraste, A.; Kolh, P.; Rutjes, A.W.S.; Jüni, P.; Windecker, S.; Bax, J.J.; Wijns, W. The performance of non-invasive tests to rule-in and rule-out significant coronary artery stenosis in patients with stable angina: A meta-analysis focused on post-test disease probability. *Eur. Heart J.* **2018**, *39*, 3322–3330. [CrossRef]

13. Zhang, J.; Zhong, L.; Su, B.; Wan, M.; Yap, J.S.; Tham, J.P.L.; Chua, L.P.; Ghista, D.N.; Tan, R.S. Perspective on CFD studies of coronary artery disease lesions and hemodynamics: A review. *Numer. Methods Biomed. Eng.* **2014**, *30*, 659–680. [CrossRef] [PubMed]

14. Xu, B.; Tu, S.; Song, L.; Jin, Z.; Yu, B.; Fu, G.; Zhou, Y.; Wang, J.; Chen, Y.; Pu, J.; et al. Angiographic quantitative flow ratio-guided coronary intervention (FAVOR III China): A multicentre, randomised, sham-controlled trial. *Lancet* **2021**, *398*, 2149–2159. [CrossRef] [PubMed]

15. Tu, S.; Westra, J.; Yang, J.; Von Birgelen, C.; Ferrara, A.; Pellicano, M.; Nef, H.; Tebaldi, M.; Murasato, Y.; Lansky, A.; et al. Diagnostic Accuracy of Fast Computational Approaches to Derive Fractional Flow Reserve From Diagnostic Coronary Angiography. *JACC Cardiovasc. Interv.* **2016**, *9*, 2024–2035. [CrossRef] [PubMed]

16. Douglas, P.S.; De Bruyne, B.; Pontone, G.; Patel, M.R.; Norgaard, B.L.; Byrne, R.A.; Curzen, N.; Purcell, I.; Gutberlet, M.; Rioufol, G.; et al. 1-Year Outcomes of FFRCT-Guided Care in Patients With Suspected Coronary Disease. *J. Am. Coll. Cardiol.* **2016**, *68*, 435–445. [CrossRef]

17. Candreva, A.; Nisco, G.D.; Rizzini, M.L.; D'Ascenzo, F.; Ferrari, G.M.D.; Gallo, D.; Morbiducci, U.; Chiastra, C. Current and Future Applications of Computational Fluid Dynamics in Coronary Artery Disease. *Rev. Cardiovasc. Med.* **2022**, *23*, 377. [CrossRef]

18. Updegrove, A.; Wilson, N.M.; Merkow, J.; Lan, H.; Marsden, A.L.; Shadden, S.C. SimVascular: An Open Source Pipeline for Cardiovascular Simulation. *Ann. Biomed. Eng.* **2017**, *45*, 525–541. [CrossRef]

19. Vignon-Clementel, I.E.; Alberto Figueroa, C.; Jansen, K.E.; Taylor, C.A. Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. *Comput. Methods Appl. Mech. Eng.* **2006**, *195*, 3776–3796. [CrossRef]

20. Mantero, S.; Pietrabissa, R.; Fumero, R. The coronary bed and its role in the cardiovascular system: A review and an introductory single-branch model. *J. Biomed. Eng.* **1992**, *14*, 109–116. [CrossRef]

21. Kim, H.J.; Vignon-Clementel, I.E.; Coogan, J.S.; Figueroa, C.A.; Jansen, K.E.; Taylor, C.A. Patient-Specific Modeling of Blood Flow and Pressure in Human Coronary Arteries. *Ann. Biomed. Eng.* **2010**, *38*, 3195–3209. [CrossRef] [PubMed]

22. Wilson, N.M.; Marru, S.; Abeysinghe, E.; Christie, M.A.; Maher, G.D.; Updegrove, A.R.; Pierce, M.; Marsden, A.L. Using a Science Gateway to Deliver SimVascular Software as a Service for Classroom Instruction. In Proceedings of the Practice and Experience on Advanced Research Computing, Pittsburgh, PA, USA, 22–26 July 2018; pp. 1–4.

23. Foy, A.J.; Dhruva, S.S.; Peterson, B.; Mandrola, J.M.; Morgan, D.J.; Redberg, R.F. Coronary Computed Tomography Angiography vs Functional Stress Testing for Patients With Suspected Coronary Artery Disease: A Systematic Review and Meta-analysis. *JAMA Intern. Med.* **2017**, *177*, 1623. [CrossRef] [PubMed]

24. Nørgaard, B.L.; Leipsic, J.; Gaur, S.; Seneviratne, S.; Ko, B.S.; Ito, H.; Jensen, J.M.; Mauri, L.; De Bruyne, B.; Bezerra, H.; et al. Diagnostic performance of noninvasive fractional flow reserve derived from coronary computed tomography angiography in suspected coronary artery disease: The NXT trial (Analysis of Coronary Blood Flow Using CT Angiography: Next Steps). *J. Am. Coll. Cardiol.* **2014**, *63*, 1145–1155. [CrossRef] [PubMed]

25. Faulder, T.I.; Prematunga, K.; Moloi, S.B.; Faulder, L.E.; Jones, R.; Moxon, J.V. Agreement of Fractional Flow Reserve Estimated by Computed Tomography With Invasively Measured Fractional Flow Reserve: A Systematic Review and Meta-Analysis. *J. Am. Heart Assoc.* **2024**, *13*, e034552. [CrossRef]

26. De Bruyne, B.; Pijls, N.H.J.; Bartunek, J.; Kulecki, K.; Bech, J.-W.; De Winter, H.; Van Crombrugge, P.; Heyndrickx, G.R.; Wijns, W. Fractional Flow Reserve in Patients With Prior Myocardial Infarction. *Circulation* **2001**, *104*, 157–162. [CrossRef]

27. Hagar, M.T.; Soschynski, M.; Saffar, R.; Rau, A.; Taron, J.; Weiss, J.; Stein, T.; Faby, S.; Von Zur Muehlen, C.; Ruile, P.; et al. Accuracy of Ultrahigh-Resolution Photon-counting CT for Detecting Coronary Artery Disease in a High-Risk Population. *Radiology* **2023**, *307*, e223305. [CrossRef]

28. Mohammadi, H.; Bahramian, F. Boundary Conditions in Simulation of Stenosed Coronary Arteries. *Cardiovasc. Eng.* **2009**, *9*, 83–91. [CrossRef]

29. Taylor, D.J.; Feher, J.; Halliday, I.; Hose, D.R.; Gosling, R.; Aubiniere-Robb, L.; Van 't Veer, M.; Keulards, D.; Tonino, P.A.L.; Rochette, M.; et al. Refining Our Understanding of the Flow Through Coronary Artery Branches; Revisiting Murray's Law in Human Epicardial Coronary Arteries. *Front. Physiol.* **2022**, *13*, 871912. [CrossRef]

30. Agasthi, P.; Kanmanthareddy, A.; Khalil, C.; Egbuche, O.; Yarlagadda, V.; Sachdeva, R.; Arsanjani, R. Comparison of Computed Tomography derived Fractional Flow Reserve to invasive Fractional Flow Reserve in Diagnosis of Functional Coronary Stenosis: A Meta-Analysis. *Sci. Rep.* **2018**, *8*, 11535. [CrossRef]

31. Van De Hoef, T.P.; Siebes, M.; Spaan, J.A.E.; Piek, J.J. Fundamentals in clinical coronary physiology: Why coronary flow is more important than coronary pressure. *Eur. Heart J.* **2015**, *36*, 3312–3319. [CrossRef]
32. Puri, R.; Leong, D.P.; Nicholls, S.J.; Liew, G.Y.L.; Nelson, A.J.; Carbone, A.; Copus, B.; Wong, D.T.; Beltrame, J.F.; Worthley, S.G.; et al. Coronary artery wall shear stress is associated with endothelial dysfunction and expansive arterial remodelling in patients with coronary artery disease. *EuroIntervention* **2015**, *10*, 1440–1448. [CrossRef] [PubMed]

33. Wong, C.C.Y.; Javadzadegan, A.; Ada, C.; Lau, J.K.; Bhindi, R.; Fearon, W.F.; Kritharides, L.; Ng, M.K.C.; Yong, A.S.C. Fractional Flow Reserve and Instantaneous Wave-Free Ratio Predict Pathological Wall Shear Stress in Coronary Arteries: Implications for Understanding the Pathophysiological Impact of Functionally Significant Coronary Stenoses. *J. Am. Heart Assoc.* **2022**, *11*, e023502. [CrossRef] [PubMed]

34. Westra, J.; Andersen, B.K.; Campo, G.; Matsuo, H.; Koltowski, L.; Eftekhari, A.; Liu, T.; Di Serafino, L.; Di Girolamo, D.; Escaned, J.; et al. Diagnostic Performance of In-Procedure Angiography-Derived Quantitative Flow Reserve Compared to Pressure-Derived Fractional Flow Reserve: The FAVOR II Europe-Japan Study. *J. Am. Heart Assoc.* **2018**, *7*, e009603. [CrossRef] [PubMed]

35. Song, L.; Xu, B.; Tu, S.; Guan, C.; Jin, Z.; Yu, B.; Fu, G.; Zhou, Y.; Wang, J.; Chen, Y.; et al. 2-Year Outcomes of Angiographic Quantitative Flow Ratio-Guided Coronary Interventions. *J. Am. Coll. Cardiol.* **2022**, *80*, 2089–2101. [CrossRef]

36. Driessen, R.S.; Danad, I.; Stuijfzand, W.J.; Raijmakers, P.G.; Schumacher, S.P.; Van Diemen, P.A.; Leipsic, J.A.; Knuuti, J.; Underwood, S.R.; Van De Ven, P.M.; et al. Comparison of Coronary Computed Tomography Angiography, Fractional Flow Reserve, and Perfusion Imaging for Ischemia Diagnosis. *J. Am. Coll. Cardiol.* **2019**, *73*, 161–173. [CrossRef]

37. Koo, B.-K.; Erglis, A.; Doh, J.-H.; Daniels, D.V.; Jegere, S.; Kim, H.-S.; Dunning, A.; DeFrance, T.; Lansky, A.; Leipsic, J.; et al. Diagnosis of Ischemia-Causing Coronary Stenoses by Noninvasive Fractional Flow Reserve Computed From Coronary Computed Tomographic Angiograms. *J. Am. Coll. Cardiol.* **2011**, *58*, 1989–1997. [CrossRef]

38. Maher, G.; Parker, D.; Wilson, N.; Marsden, A. Neural Network Vessel Lumen Regression for Automated Lumen Cross-Section Segmentation in Cardiovascular Image-Based Modeling. *Cardiovasc. Eng. Technol.* **2020**, *11*, 621–635. [CrossRef]

39. Choi, J.H.; Kim, E.; Kim, H.Y.; Lee, S.H.; Kim, S.M. Allometric scaling patterns among the human coronary artery tree, myocardial mass, and coronary artery flow. *Physiol. Rep.* **2020**, *8*, e14514. [CrossRef]

40. Kassab, G.; Finet, G. Anatomy and function relation in the coronary tree: From bifurcations to myocardial flow and mass. *EuroIntervention* **2015**, *11*, V13–V17. [CrossRef]

41. Choy, J.S.; Kassab, G.S. Scaling of Myocardial Mass to Flow and Morphometry of Coronary Arteries. *J. Appl. Physiol.* **2008**, *104*, 1281–1286. [CrossRef]

42. Murai, T.; van de Hoef, T.P.; van den Boogert, T.P.; Wijntjens, G.W.; Stegehuis, V.E.; Echavarria-Pinto, M.; Hoshino, M.; Yonetsu, T.; Planken, R.N.; Henriques, J.P.S.; et al. Quantification of Myocardial Mass Subtended by a Coronary Stenosis Using Intracoronary Physiology. *Circ. Cardiovasc. Interv.* **2019**, *12*, e007322. [CrossRef]

43. van Rosendael, S.E.; van Rosendael, A.R.; Kuneman, J.H.; Patel, M.R.; Nørgaard, B.L.; Fairbairn, T.A.; Nieman, K.; Akasaka, T.; Berman, D.S.; Koweek, L.M.H. Coronary Volume to Left Ventricular Mass Ratio in Patients with Hypertension. *Am. J. Cardiol.* **2023**, *199*, 100–109. [CrossRef]

44. Ghorbanniahassankiadeh, A.; Marks, D.S.; LaDisa, J.F., Jr. Correlation of Computational Instantaneous Wave-Free Ratio with Fractional Flow Reserve for Intermediate Multivessel Coronary Disease. *J. Biomech. Eng.* **2021**, *143*, 051011. [CrossRef]

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.