Blood Flow Modeling in Coronary Arteries: A Review

Physics-informed neural networks for parameter estimation in blood flow models

BACKGROUND

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving inverse problems, especially in cases where no complete information about the system is known and scatter measurements are available. This is especially useful in hemodynamics since the boundary information is often difficult to model, and high-quality blood flow measurements are generally hard to obtain.

METHODS

In this work, we use the PINNs methodology for estimating reduced-order model parameters and the full velocity field from scatter 2D noisy measurements in the aorta. Two different flow regimes, stationary and transient were studied.

RESULTS

We show robust and relatively accurate parameter estimations when using the method with simulated data, while the velocity reconstruction accuracy shows dependence on the measurement quality and the flow pattern complexity. Comparison with a Kalman filter approach shows similar results when the number of parameters to be estimated is low to medium. For a higher number of parameters, only PINNs were capable of achieving good results.

CONCLUSION

The method opens a door to deep-learning-driven methods in the simulations of complex coupled physical systems.

Integrating Computational and Biological Hemodynamic Approaches to Improve Modeling of Atherosclerotic Arteries

Atherosclerosis is the primary cause of cardiovascular disease, resulting in mortality, elevated healthcare costs, diminished productivity, and reduced quality of life for individuals and their communities. This is exacerbated by the limited understanding of its underlying causes and limitations in current therapeutic interventions, highlighting the need for sophisticated models of atherosclerosis. This review critically evaluates the computational and biological models of atherosclerosis, focusing on the study of hemodynamics in atherosclerotic coronary arteries. Computational models account for the geometrical complexities and hemodynamics of the blood vessels and stenoses, but they fail to capture the complex biological processes involved in atherosclerosis. Different in vitro and in vivo biological models can capture aspects of the biological complexity of healthy and stenosed vessels, but rarely mimic the human anatomy and physiological hemodynamics, and require significantly more time, cost, and resources. Therefore, emerging strategies are examined that integrate computational and biological models, and the potential of advances in imaging, biofabrication, and machine learning is explored in developing more effective models of atherosclerosis.

Patient-Specific Numerical Simulations of Coronary Artery Hemodynamics and Biomechanics: A Pathway to Clinical Use

PURPOSE

Numerical models that simulate the behaviors of the coronary arteries have been greatly improved by the addition of fluid-structure interaction (FSI) methods. Although computationally demanding, FSI models account for the movement of the arterial wall and more adequately describe the biomechanical conditions at and within the arterial wall. This offers greater physiological relevance over Computational Fluid Dynamics (CFD) models, which assume the walls do not move or deform. Numerical simulations of patient-specific cases have been greatly bolstered by the use of imaging modalities such as Computed Tomography Angiography (CTA), Magnetic Resonance Imaging (MRI), Optical Coherence Tomography (OCT), and Intravascular Ultrasound (IVUS) to reconstruct accurate 2D and 3D representations of artery geometries. The goal of this study was to conduct a comprehensive review on CFD and FSI models on coronary arteries, and evaluate their translational potential.

METHODS

This paper reviewed recent work on patient-specific numerical simulations of coronary arteries that describe the biomechanical conditions associated with atherosclerosis using CFD and FSI models. Imaging modality for geometry collection and clinical applications were also discussed.

RESULTS

Numerical models using CFD and FSI approaches are commonly used to study biomechanics within the vasculature. At high temporal and spatial resolution (compared to most cardiac imaging modalities), these numerical models can generate large amount of biomechanics data.

CONCLUSIONS

Physiologically relevant FSI models can more accurately describe atherosclerosis pathogenesis, and help to translate biomechanical assessment to clinical evaluation.

Review of cardiac-coronary interaction and insights from mathematical modeling

Cardiac-coronary interaction is fundamental to the function of the heart. As one of the highest metabolic organs in the body, the cardiac oxygen demand is met by blood perfusion through the coronary vasculature. The coronary vasculature is largely embedded within the myocardial tissue which is continually contracting and hence squeezing the blood vessels. The myocardium-coronary vessel interaction is two-ways and complex. Here, we review the different types of cardiac-coronary interactions with a focus on insights gained from mathematical models. Specifically, we will consider the following: (1) myocardial-vessel mechanical interaction; (2) metabolic-flow interaction and regulation; (3) perfusion-contraction matching, and (4) chronic interactions between the myocardium and coronary vasculature. We also provide a discussion of the relevant experimental and clinical studies of different types of cardiac-coronary interactions. Finally, we highlight knowledge gaps, key challenges, and limitations of existing mathematical models along with future research directions to understand the unique myocardium-coronary coupling in the heart. This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Biomedical Engineering Cardiovascular Diseases > Molecular and Cellular Physiology.

Numerical investigation of LDL nanoparticle collision in coronary artery grafts with porous wall and different implantation angles and two state of inlet velocity

This study aimed to reduce the risk of graft occlusion by evaluating the two-phase flow of blood and LDL nanoparticles in coronary artery grafts. The study considered blood as an incompressible Newtonian fluid, with the addition of LDL nanoparticles, and the artery wall as a porous medium. Two scenarios were compared, with constant inlet velocity (CIV) and other with pulsatile inlet velocity (PIV), with LDL nanoparticles experiencing drag, wall-induced lift, and induced Saffman lift forces, or drag force only. The study also evaluated the concentration polarization of LDLs (CP of LDLs) near the walls, by considering the artery wall with and without permeation. To model LDL nanoparticles, the study randomly injected 100, 500, and 1000 nanoparticles in three release states at each time step, using different geometries. Numerical simulations were performed using COMSOL software, and the results were presented as relative collision of nanoparticles to the walls in tables, diagrams, and shear stress contours. The study found that a graft implantation angle of 15° had the most desirable conditions compared to larger angles, in terms of nanoparticle collision with surfaces and occlusion. The nanoparticle release modes behaved similarly in terms of collision with the surfaces. A difference was observed between CIV and PIV. Saffman lift and wall-induced lift forces having no effect, possibly due to the assumption of a porous artery wall and perpendicular outlet flow. In case of permeable artery walls, relative collision of particles with the graft wall was larger, suggesting the effect of CP of LDLs.

Virtual Hemodynamic Assessment of Coronary Lesions: The Advent of Functional Angiography and Coronary Imaging

The fractional flow reserve (FFR) is well recognized as a gold standard measure for the estimation of functional coronary stenosis. Technological progressions in image processing have empowered the reconstruction of three-dimensional models of the coronary arteries via both non-invasive and invasive imaging modalities. The application of computational fluid dynamics (CFD) techniques to coronary 3D anatomical models allows the virtual evaluation of the hemodynamic significance of a coronary lesion with high diagnostic accuracy.

METHODS

Search of the bibliographic database for articles published from 2011 to 2023 using the following search terms: invasive FFR and non-invasive FFR. Pooled analysis of the sensitivity and specificity, with the corresponding confidence intervals from 32% to 94%. In addition, the summary processing times were determined.

RESULTS

In total, 24 studies published between 2011 and 2023 were included, with a total of 13,591 patients and 3345 vessels. The diagnostic accuracy of the invasive and non-invasive techniques at the per-patient level was 89% (95% CI, 85-92%) and 76% (95% CI, 61-80%), respectively, while on the per-vessel basis, it was 92% (95% CI, 82-88%) and 81% (95% CI, 75-87%), respectively.

CONCLUSION

These opportunities providing hemodynamic information based on anatomy have given rise to a new era of functional angiography and coronary imaging. However, further validations are needed to overcome several scientific and computational challenges before these methods are applied in everyday clinical practice.

A homogenized two-phase computational framework for meso- and macroscale blood flow simulations

BACKGROUND AND OBJECTIVE

Owing to the complexity of physics linked with blood flow and its associated phenomena, appropriate modeling of the multi-constituent rheology of blood is of primary importance. To this effect, various kinds of computational fluid dynamic models have been developed, each with merits and limitations. However, when additional physics like thrombosis and embolization is included within the framework of these models, computationally efficient scalable translation becomes very difficult. Therefore, this paper presents a homogenized two-phase blood flow framework with similar characteristics to a single fluid model but retains the flow resolution of a classical two-fluid model. The presented framework is validated against four different sets of experiments.

METHODS

The two-phase model of blood presented here is based on the classical diffusion-flux framework. Diffusion flux models are known to be less computationally expensive than two-fluid multiphase models since the numerical implementation resembles single-phase flow models. Diffusion flux models typically use empirical slip velocity correlations to resolve the motion between phases. However, such correlations do not exist for blood. Therefore, a modified slip velocity equation is proposed, derived rigorously from the two-fluid governing equations. An additional drag law for red blood cells (RBCs) as a function of volume fraction is evaluated using a previously published cell-resolved solver. A new hematocrit-dependent expression for lift force on RBCs is proposed. The final governing equations are discretized and solved using the open-source software OpenFOAM.

RESULTS

The framework is validated against four sets of experiments: (i) flow through a rectangular microchannel to validate RBC velocity profiles against experimental measurements and compare computed hematocrit distributions against previously reported simulation results (ii) flow through a sudden expansion microchannel for comparing experimentally obtained contours of hematocrit distributions and normalized cell-free region length obtained at different flowrates and inlet hematocrits, (iii) flow through two hyperbolic channels to evaluate model predictions of cell-free layer thickness, and (iv) flow through a microchannel that mimics crevices of a left ventricular assist device to predict hematocrit distributions observed experimentally. The simulation results exhibit good agreement with the results of all four experiments.

CONCLUSION

The computational framework presented in this paper has the advantage of resolving the multiscale physics of blood flow while still leveraging numerical techniques used for solving single-phase flows. Therefore, it becomes an excellent candidate for addressing more complicated problems related to blood flow, such as modeling mechanical entrapment of RBCs within blood clots, predicting thrombus composition, and visualizing clot embolization.

Modelling blood flow in coronary arteries: Newtonian or shear-thinning non-Newtonian rheology?

BACKGROUND

The combination of medical imaging and computational hemodynamics is a promising technology to diagnose/prognose coronary artery disease (CAD). However, the clinical translation of in silico hemodynamic models is still hampered by assumptions/idealizations that must be introduced in model-based strategies and that necessarily imply uncertainty. This study aims to provide a definite answer to the open question of how to properly model blood rheological properties in computational fluid dynamics (CFD) simulations of coronary hemodynamics.

METHODS

The geometry of the right coronary artery (RCA) of 144 hemodynamically stable patients with different stenosis degree were reconstructed from angiography. On them, unsteady-state CFD simulations were carried out. On each reconstructed RCA two different simulation strategies were applied to account for blood rheological properties, implementing (i) a Newtonian (N) and (ii) a shear-thinning non-Newtonian (non-N) rheological model. Their impact was evaluated in terms of wall shear stress (WSS magnitude, multidirectionality, topological skeleton) and helical flow (strength, topology) profiles. Additionally, luminal surface areas (SAs) exposed to shear disturbances were identified and the co-localization of paired N and non-N SAs was quantified in terms of similarity index (SI).

RESULTS

The comparison between paired N vs. shear-thinning non-N simulations revealed remarkably similar profiles of WSS-based and helicity-based quantities, independent of the adopted blood rheology model and of the degree of stenosis of the vessel. Statistically, for each paired N and non-N hemodynamic quantity emerged negligible bias from Bland-Altman plots, and strong positive linear correlation (r > 0.94 for almost all the WSS-based quantities, r > 0.99 for helicity-based quantities). Moreover, a remarkable co-localization of N vs. non-N luminal SAs exposed to disturbed shear clearly emerged (SI distribution 0.95 [0.93, 0.97]). Helical flow topology resulted to be unaffected by blood rheological properties.

CONCLUSIONS

This study, performed on 288 angio-based CFD simulations on 144 RCA models presenting with different degrees of stenosis, suggests that the assumptions on blood rheology have negligible impact both on WSS and helical flow profiles associated with CAD, thus definitively answering to the question "is Newtonian assumption for blood rheology adequate in coronary hemodynamics simulations?".

CFD analysis on blood flow inside a symmetric stenosed artery: Physiology of a coronary artery disease

This research article interprets the computational fluid dynamics analysis on blood flow inside a symmetric stenosed artery. The current problem models the blood flow inside the left coronary artery as having a symmetric stenosis in the central region. A comprehensive physiological examination of coronary artery disease is numerically evaluated by using the computational fluid dynamics toolbox Open-Field Operation And Manipulation. There are no assumptions of mild stenosis taken into account since the considered stenosis has an exactly measured length, height and position, etc. The blood flow problem is modeled for the non-Newtonian Casson fluid with unsteady, laminar, and incompressible flow assumptions. The underlying problem is solved numerically in its dimensional form. A thorough graphical analysis is provided on the blood flow simulations, pressure profile, velocity line graphs, pressure line graphs, and streamlines for the left coronary artery having a symmetric stenosis formation. The considered artery is divided into three sections, i.e. pre-stenosis, post-stenosis, and stenosis region, and the velocity and pressure line graphs are plotted for these considered regions. The graphical illustrations provide a detailed analysis of how the blood flow is affected inside the left coronary artery due to coronary artery disease. These pre- and post-stenosis velocity line graphs reveal two intriguing results: In the pre-stenosis zone, the velocity increases with increasing axial coordinate length, whereas in the post-stenosis region, the velocity decreases with rising axial coordinate length. It is evident that as the flow moves toward the stenosis region, the flow profile rises; yet, after passing through the stenosis zone, the flow profile begins to fall as the flow moves away from the stenosis region.

Computational Study of Hemodynamic Field of an Occluded Artery Model with Anastomosis

In this research work, the hemodynamic field of an occluded artery with anastomosis by means of computational simulation has been studied. The main objective of the current study is the investigation of 3D flow field phenomena in the by-pass region and the effect of the bypass graft to stenosis volume flow ratio on their formation. The anastomosis type was end-to-side with a 45° angle, while stenosis imposed a 75% area blockage of the aorta vessel and the total volume flow was 220 lt/h. The computational study of the flow field was utilized via a laminar flow model and three turbulence models (k-ε RNG, standard k-ω, and k-ω SST). Numerical results were compared qualitatively with experimental visualizations carried out under four different flow conditions, varying according to the flow ratio between the stenosis and the anastomotic graft. Comparison between computational results and experimental visualization findings exhibited a good agreement. Results showed that SST k-ω turbulence models reproduce better visually obtained flow patterns. Furthermore, cross-sectional velocity distributions demonstrated two distinct flow patterns down the bypass graft, depending on the flow ratio. Low values of flow ratio are characterized by fluid rolling up, whereas for high values fluid volume twisting was observed. Finally, areas with low wall shear stresses were mapped, as these are more prone to postoperative degradation of the bypass graft due to the development of subendothelial hyperplasia.

Deep Learning for Computational Hemodynamics: A Brief Review of Recent Advances

Computational fluid dynamics (CFD) modeling of blood flow plays an important role in better understanding various medical conditions, designing more effective drug delivery systems, and developing novel diagnostic methods and treatments. However, despite significant advances in computational technology and resources, the expensive computational cost of these simulations still hinders their transformation from a research interest to a clinical tool. This bottleneck is even more severe for image-based, patient-specific CFD simulations with realistic boundary conditions and complex computational domains, which make such simulations excessively expensive. To address this issue, deep learning approaches have been recently explored to accelerate computational hemodynamics simulations. In this study, we review recent efforts to integrate deep learning with CFD and discuss the applications of this approach in solving hemodynamics problems, such as blood flow behavior in aorta and cerebral arteries. We also discuss potential future directions in the field. In this review, we suggest that incorporating physiologic understandings and underlying fluid mechanics laws in deep learning models will soon lead to a paradigm shift in the development novel non-invasive computational medical decisions.

Modelling coronary flows: impact of differently measured inflow boundary conditions on vessel-specific computational hemodynamic profiles

BACKGROUND AND OBJECTIVES

The translation of hemodynamic quantities based on wall shear stress (WSS) or intravascular helical flow into clinical biomarkers of coronary atherosclerotic disease is still hampered by the assumptions/idealizations required by the computational fluid dynamics (CFD) simulations of the coronary hemodynamics. In the resulting budget of uncertainty, inflow boundary conditions (BCs) play a primary role. Accordingly, in this study we investigated the impact of the approach adopted for in vivo coronary artery blood flow rate assessment on personalized CFD simulations where blood flow rate is used as inflow BC.

METHODS

CFD simulations were carried out on coronary angiograms by applying personalized inflow BCs derived from four different techniques assessing in vivo surrogates of flow rate: continuous thermodilution, intravascular Doppler, frame count-based 3D contrast velocity, and diameter-based scaling law. The impact of inflow BCs on coronary hemodynamics was evaluated in terms of WSS- and helicity-based quantities.

RESULTS

As main findings, we report that: (i) coronary flow rate values may differ based on the applied flow derivation technique, as continuous thermodilution provided higher flow rate values than intravascular Doppler and diameter-based scaling law (p = 0.0014 and p = 0.0023, respectively); (ii) such intrasubject differences in flow rate values lead to different surface-averaged values of WSS magnitude and helical blood flow intensity (p<0.0020); (iii) luminal surface areas exposed to low WSS and helical flow topological features showed robustness to the flow rate values.

CONCLUSIONS

Although the absence of a clinically applicable gold standard approach prevents a general recommendation for one coronary blood flow rate derivation technique, our findings indicate that the inflow BC may impact computational hemodynamic results, suggesting that a standardization would be desirable to provide comparable results among personalized CFD simulations of the coronary hemodynamics.

Fluid Flow and Structural Numerical Analysis of a Cerebral Aneurysm Model

Intracranial aneurysms (IA) are dilations of the cerebral arteries and, in most cases, have no symptoms. However, it is a very serious pathology, with a high mortality rate after rupture. Several studies have been focused only on the hemodynamics of the flow within the IA. However, besides the effect of the flow, the development and rupture of the IA are also associated with a combination of other factors such as the wall mechanical behavior. Thus, the objective of this work was to analyze, in addition to the flow behavior, the biomechanical behavior of the aneurysm wall. For this, CFD simulations were performed for different Reynolds numbers (1, 100, 500 and 1000) and for two different rheological models (Newtonian and Carreau). Subsequently, the pressure values of the fluid simulations were exported to the structural simulations in order to qualitatively observe the deformations, strains, normal stresses and shear stress generated in the channel wall. For the structural simulations, a hyperelastic constitutive model (5-parameter Mooney–Rivlin) was used. The results show that with the increase in the Reynolds number (Re), the recirculation phenomenon is more pronounced, which is not seen for Re = 1. The higher the Re, the higher the strain, displacement, normal and shear stresses values.

Computational Simulations in Advanced Microfluidic Devices: A Review

Numerical simulations have revolutionized research in several engineering areas by contributing to the understanding and improvement of several processes, being biomedical engineering one of them. Due to their potential, computational tools have gained visibility and have been increasingly used by several research groups as a supporting tool for the development of preclinical platforms as they allow studying, in a more detailed and faster way, phenomena that are difficult to study experimentally due to the complexity of biological processes present in these models—namely, heat transfer, shear stresses, diffusion processes, velocity fields, etc. There are several contributions already in the literature, and significant advances have been made in this field of research. This review provides the most recent progress in numerical studies on advanced microfluidic devices, such as organ-on-a-chip (OoC) devices, and how these studies can be helpful in enhancing our insight into the physical processes involved and in developing more effective OoC platforms. In general, it has been noticed that in some cases, the numerical studies performed have limitations that need to be improved, and in the majority of the studies, it is extremely difficult to replicate the data due to the lack of detail around the simulations carried out.

Numerical Study of the Unsteady Flow in Simplified and Realistic Iliac Bifurcation Models

Cardiovascular diseases are a major cause of death and disability worldwide and they are commonly associated with the occurrence of atherosclerotic plaque deposition in the vessel walls, a process denoted as atherosclerosis. This is a chronic and progressive inflammatory disease of large-/medium-sized blood vessels that affects blood flow profiles, with the abdominal aorta and its branches being one of the locations prone to the development of this pathology, due to their curvatures and bifurcations. In this regard, the effect of flow patterns was studied and compared for both a simplified three-dimensional model of aorta bifurcation on the iliac arteries and a realistic model of iliac bifurcation, which was constructed from a computational tomography medical image. The flow patterns were analyzed in terms of velocity and wall shear stress distribution, but a special focus was given to the size and location of the recirculation zone. The simulations were performed using the Computational Fluid Dynamics software, FLUENT, taking into account the cardiac cycle profile at the infrarenal aorta. The shear stress and the velocity distribution observed for both models indicated that higher shear stress occurred along the flow divider wall (inner wall) and low shear stress occurred along the outer walls. In addition, the results demonstrated that the wall shear stress profiles were deeply affected by the transient profile of the cardiac cycle, with the deceleration phase being the most critical phase to the occurrence of backflow.

Coronary Computer Tomography Angiography in 2021-Acquisition Protocols, Tips and Tricks and Heading beyond the Possible

Recent technological advances, together with an increasing body of evidence from randomized trials, have placed coronary computer tomography angiography (CCTA) in the center of the diagnostic workup of patients with coronary artery disease. The method was proven reliable in the diagnosis of relevant coronary artery stenosis. Furthermore, it can identify different stages of the atherosclerotic process, including early atherosclerotic changes of the coronary vessel wall, a quality not met by other non-invasive tests. In addition, newer computational software can measure the hemodynamic relevance (fractional flow reserve) of a certain stenosis. In addition, if required, information related to cardiac and valvular function can be provided with specific protocols. Importantly, recent trials have highlighted the prognostic relevance of CCTA in patients with coronary artery disease, which helped establishing CCTA as the first-line method for the diagnostic work-up of such patients in current guidelines. All this can be gathered in one relatively fast examination with minimal discomfort for the patient and, with newer machines, with very low radiation exposure. Herein, we provide an overview of the current technical aspects, indications, pitfalls, and new horizons with CCTA, providing examples from our own clinical practice.

Investigation of Wall Shear Stress in Cardiovascular Research and in Clinical Practice-From Bench to Bedside

In the 1900s, researchers established animal models experimentally to induce atherosclerosis by feeding them with a cholesterol-rich diet. It is now accepted that high circulating cholesterol is one of the main causes of atherosclerosis; however, plaque localization cannot be explained solely by hyperlipidemia. A tremendous amount of studies has demonstrated that hemodynamic forces modify endothelial athero-susceptibility phenotypes. Endothelial cells possess mechanosensors on the apical surface to detect a blood stream-induced force on the vessel wall, known as "wall shear stress (WSS)", and induce cellular and molecular responses. Investigations to elucidate the mechanisms of this process are on-going: on the one hand, hemodynamics in complex vessel systems have been described in detail, owing to the recent progress in imaging and computational techniques. On the other hand, investigations using unique in vitro chamber systems with various flow applications have enhanced the understanding of WSS-induced changes in endothelial cell function and the involvement of the glycocalyx, the apical surface layer of endothelial cells, in this process. In the clinical setting, attempts have been made to measure WSS and/or glycocalyx degradation non-invasively, for the purpose of their diagnostic utilization. An increasing body of evidence shows that WSS, as well as serum glycocalyx components, can serve as a predicting factor for atherosclerosis development and, most importantly, for the rupture of plaques in patients with high risk of coronary heart disease.

The Holistic Coronary Physiology Display: Calculation of the Flow Separation Index in Vessel-Specific Individual Flow Range during Fractional Flow Reserve Measurement Using 3D Coronary Reconstruction

In order to make optimal decisions on the treatment of atherosclerotic coronary heart disease (CHD), appropriate evaluation is necessary, including both the anatomical and physiological assessment of the coronary arteries. According to current guidelines, a fractional flow reserve (FFR)-based clinical decision is recommended, but coronary flow reserve (CFR) measurements and microvascular evaluation should also be considered in special cases for a detailed exploration of the coronary disease state. We aimed to generate an extended physiological evaluation during routine FFR measurement and define a new pathological flow-related prognostic factor. Fluid dynamic equations were applied to calculate CFR on the basis of the three-dimensional (3D) reconstruction of the invasively acquired coronary angiogram and the measured intracoronary pressure data. A new, potentially robust prognostic parameter of a coronary lesion called the "flow separation index" (FS_i), which is thought to detect the pathological flow amount through a stenosis was introduced in a vessel-specific flow range. Correlations between FS_i and the clinically established physiological indices (CFR and FFR) were determined. The FS_i was calculated in 19 vessels of 16 patients, including data from the pre- and post-stent revascularization treatment of 3 patients. There was no significant correlation between the FS_i and the CFR (r = -0.23, p = 0.34); however, there was significant negative correlation between the FS_i and the FFR (r = -0.66, p = 0.002). An even stronger correlation was found between the FS_i and the ratio of the resting pressure ratio and the FFR (r = 0.92, p < 0.0001). The diagnostic power of the FS_i for predicting the FFR value of <0.80, as a gold standard prognostic factor, was tested by receiver operating characteristic analysis. FS_i > 0.022 proved to be the cutoff value of the prediction of a pathologically low FFR with a 0.856 area under the curve (95% confidence interval: 0.620 to 0.972). The present flow-pressure-velocity display provides a comprehensive summary of patient-specific pathophysiology in CHD. The consequences of epicardial stenoses can be evaluated together with their complex relations to microvascular conditions. Based on these values, clinical decision-making concerning both pharmacological therapy and percutaneous or surgical revascularization may be more precisely guided.