Numerical simulation and clinical implications of stenosis in coronary blood flow

A Pseudo-Spectral Method for Wall Shear Stress Estimation from Doppler Ultrasound Imaging in Coronary Arteries

PURPOSE

The Wall Shear Stress (WSS) is the component tangential to the boundary of the normal stress tensor in an incompressible fluid, and it has been recognized as a quantity of primary importance in predicting possible adverse events in cardiovascular diseases, in general, and in coronary diseases, in particular. The quantification of the WSS in patient-specific settings can be achieved by performing a Computational Fluid Dynamics (CFD) analysis based on patient geometry, or it can be retrieved by a numerical approximation based on blood flow velocity data, e.g., ultrasound (US) Doppler measurements. This paper presents a novel method for WSS quantification from 2D vector Doppler measurements.

METHODS

Images were obtained through unfocused plane waves and transverse oscillation to acquire both in-plane velocity components. These velocity components were processed using pseudo-spectral differentiation techniques based on Fourier approximations of the derivatives to compute the WSS.

RESULTS

Our Pseudo-Spectral Method (PSM) is tested in two vessel phantoms, straight and stenotic, where a steady flow of 15 mL/min is applied. The method is successfully validated against CFD simulations and compared against current techniques based on the assumption of a parabolic velocity profile. The PSM accurately detected Wall Shear Stress (WSS) variations in geometries differing from straight cylinders, and is less sensitive to measurement noise. In particular, when using synthetic data (noise free, e.g., generated by CFD) on cylindrical geometries, the Poiseuille-based methods and PSM have comparable accuracy; on the contrary, when using the data retrieved from US measures, the average error of the WSS obtained with the PSM turned out to be 3 to 9 times smaller than that obtained by state-of-the-art methods.

CONCLUSION

The pseudo-spectral approach allows controlling the approximation errors in the presence of noisy data. This gives a more accurate alternative to the present standard and a less computationally expensive choice compared to CFD, which also requires high-quality data to reconstruct the vessel geometry.

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.

A novel method for noninvasive quantification of fractional flow reserve based on the custom function

Boundary condition settings are key risk factors for the accuracy of noninvasive quantification of fractional flow reserve (FFR) based on computed tomography angiography (i.e., FFRCT). However, transient numerical simulation-based FFRCT often ignores the three-dimensional (3D) model of coronary artery and clinical statistics of hyperemia state set by boundary conditions, resulting in insufficient computational accuracy and high computational cost. Therefore, it is necessary to develop the custom function that combines the 3D model of the coronary artery and clinical statistics of hyperemia state for boundary condition setting, to accurately and quickly quantify FFRCT under steady-state numerical simulations. The 3D model of the coronary artery was reconstructed by patient computed tomography angiography (CTA), and coronary resting flow was determined from the volume and diameter of the 3D model. Then, we developed the custom function that took into account the interaction of stenotic resistance, microcirculation resistance, inlet aortic pressure, and clinical statistics of resting to hyperemia state due to the effect of adenosine on boundary condition settings, to accurately and rapidly identify coronary blood flow for quantification of FFRCT calculation (FFRU). We tested the diagnostic accuracy of FFRU calculation by comparing it with the existing methods (CTA, coronary angiography (QCA), and diameter-flow method for calculating FFR (FFRD)) based on invasive FFR of 86 vessels in 73 patients. The average computational time for FFRU calculation was greatly reduced from 1-4 h for transient numerical simulations to 5 min per simulation, which was 2-fold less than the FFRD method. According to the results of the Bland-Altman analysis, the consistency between FFRU and invasive FFR of 86 vessels was better than that of FFRD. The area under the receiver operating characteristic curve (AUC) for CTA, QCA, FFRD and FFRU at the lesion level were 0.62 (95% CI: 0.51-0.74), 0.67 (95% CI: 0.56-0.79), 0.85 (95% CI: 0.76-0.94), and 0.93 (95% CI: 0.87-0.98), respectively. At the patient level, the AUC was 0.61 (95% CI: 0.48-0.74) for CTA, 0.65 (95% CI: 0.53-0.77) for QCA, 0.83 (95% CI: 0.74-0.92) for FFRD, and 0.92 (95% CI: 0.89-0.96) for FFRU. The proposed novel method might accurately and rapidly identify coronary blood flow, significantly improve the accuracy of FFRCT calculation, and support its wide application as a diagnostic indicator in clinical practice.

Forward-viewing estimation of 3D blood flow velocity fields by intravascular ultrasound: Influence of the catheter on velocity estimation in stenoses

Coronary artery disease is the most common type of cardiovascular disease, affecting > 18 million adults, and is responsible for > 365 k deaths per year in the U.S. alone. Wall shear stress (WSS) is an emerging indicator of likelihood of plaque rupture in coronary artery disease, however, non-invasive estimation of 3-D blood flow velocity and WSS is challenging due to the requirement for high spatial resolution at deep penetration depths in the presence of significant cardiac motion. Thus we propose minimally-invasive imaging with a catheter-based, 3-D intravascular forward-viewing ultrasound (FV US) transducer and present experiments to quantify the effect of the catheter on flow disturbance in stenotic vessel phantoms with realistic velocities and luminal diameters for both peripheral (6.33 mm) and coronary (4.74 mm) arteries. An external linear array ultrasound transducer was used to quantify 2-D velocity fields in vessel phantoms under various conditions of catheter geometry, luminal diameter, and position of the catheter relative to the stenosis at a frame rate of 5000 frames per second via a particle imaging velocimetry (PIV) approach. While a solid catheter introduced an underestimation of velocity measurement by > 20% relative to the case without a catheter, the hollow catheter introduced < 10% velocity overestimation, indicating that a hollow catheter design allowing internal blood flow reduces hemodynamic disturbance. In addition, for both peripheral and coronary arteries, the hollow catheter introduced < 3% deviation in flow velocity at the minimum luminal area compared to the control case. Finally, an initial comparison was made between velocity measurements acquired using a low frequency, catheter-based, 3-D intravascular FV US transducer and external linear array measurements, with relative error < 12% throughout the region of interest for a flow rate of 150 mL/min. While further system development is required, results suggest intravascular ultrasound characterization of blood flow velocity fields in stenotic vessels could be feasible with appropriate catheter design.

Blood Flow Modeling in Coronary Arteries: A Review

Atherosclerosis is one of the main causes of cardiovascular events, namely, myocardium infarction and cerebral stroke, responsible for a great number of deaths every year worldwide. This pathology is caused by the progressive accumulation of low-density lipoproteins, cholesterol, and other substances on the arterial wall, narrowing its lumen. To date, many hemodynamic studies have been conducted experimentally and/or numerically; however, this disease is not yet fully understood. For this reason, the research of this pathology is still ongoing, mainly, resorting to computational methods. These have been increasingly used in biomedical research of atherosclerosis because of their high-performance hardware and software. Taking into account the attempts that have been made in computational techniques to simulate realistic conditions of blood flow in both diseased and healthy arteries, the present review aims to give an overview of the most recent numerical studies focused on coronary arteries, by addressing the blood viscosity models, and applied physiological flow conditions. In general, regardless of the boundary conditions, numerical studies have been contributed to a better understanding of the development of this disease, its diagnosis, and its treatment.

An Introductory Overview of Image-Based Computational Modeling in Personalized Cardiovascular Medicine

Cardiovascular diseases account for the number one cause of deaths in the world. Part of the reason for such grim statistics is our limited understanding of the underlying mechanisms causing these devastating pathologies, which is made difficult by the invasiveness of the procedures associated with their diagnosis (e.g., inserting catheters into the coronal artery to measure blood flow to the heart). Likewise, it is also difficult to design and test assistive devices without implanting them in vivo. However, with the recent advancements made in biomedical scanning technologies and computer simulations, image-based modeling (IBM) has arisen as the next logical step in the evolution of non-invasive patient-specific cardiovascular medicine. Yet, due to its novelty, it is still relatively unknown outside of the niche field. Therefore, the goal of this manuscript is to review the current state-of-the-art and the limitations of the methods used in this area of research, as well as their applications to personalized cardiovascular investigations and treatments. Specifically, the modeling of three different physics – electrophysiology, biomechanics and hemodynamics – used in the cardiovascular IBM is discussed in the context of the physiology that each one of them describes and the mechanisms of the underlying cardiac diseases that they can provide insight into. Only the “bare-bones” of the modeling approaches are discussed in order to make this introductory material more accessible to an outside observer. Additionally, the imaging methods, the aspects of the unique cardiac anatomy derived from them, and their relation to the modeling algorithms are reviewed. Finally, conclusions are drawn about the future evolution of these methods and their potential toward revolutionizing the non-invasive diagnosis, virtual design of treatments/assistive devices, and increasing our understanding of these lethal cardiovascular diseases.

Dataset on blood flow and instantaneous wave-free ratio in normal and stenosed coronary arteries

Instantaneous wave-free ratio (iFR) has been proposed as a hemodynamic parameter that can reliably reflect the blood flow in stenosed coronary arteries. Currently, there are few investigations on the quantitative analysis of iFR in the patients regarding the variation of microcirculatory resistance (MR). The data aim to provide geometric (cross-section area of branches) and hemodynamic (flow rate and iFR of branches) parameters of normal and stenosed coronary arteries derived from CFD simulation. The CFD simulation was performed on the three-dimensional artery models reconstructed from computed tomography (CT) images of four subjects. The hemodynamic parameters were obtained in six situations of MR to simulate coronary microvascular dysfunction (CMD). This dataset could be used as the reference to estimate the iFR and flow rate in patients with CMD and stenosis in coronary arteries. The geometric parameters could be used in the modelling of coronary arteries.

Accelerating massively parallel hemodynamic models of coarctation of the aorta using neural networks

Comorbidities such as anemia or hypertension and physiological factors related to exertion can influence a patient’s hemodynamics and increase the severity of many cardiovascular diseases. Observing and quantifying associations between these factors and hemodynamics can be difficult due to the multitude of co-existing conditions and blood flow parameters in real patient data. Machine learning-driven, physics-based simulations provide a means to understand how potentially correlated conditions may affect a particular patient. Here, we use a combination of machine learning and massively parallel computing to predict the effects of physiological factors on hemodynamics in patients with coarctation of the aorta. We first validated blood flow simulations against in vitro measurements in 3D-printed phantoms representing the patient’s vasculature. We then investigated the effects of varying the degree of stenosis, blood flow rate, and viscosity on two diagnostic metrics – pressure gradient across the stenosis (ΔP) and wall shear stress (WSS) - by performing the largest simulation study to date of coarctation of the aorta (over 70 million compute hours). Using machine learning models trained on data from the simulations and validated on two independent datasets, we developed a framework to identify the minimal training set required to build a predictive model on a per-patient basis. We then used this model to accurately predict ΔP (mean absolute error within 1.18 mmHg) and WSS (mean absolute error within 0.99 Pa) for patients with this disease.

The improvement of the shear stress and oscillatory shear index of coronary arteries during Enhanced External Counterpulsation in patients with coronary heart disease

Background

Enhanced External Counterpulsation (EECP) can chronically relieve ischemic chest pain and improve the prognosis of coronary heart disease (CHD). Despite its role in mitigating heart complications, EECP and the mechanisms behind its therapeutic nature, such as its effects on blood flow hemodynamics, are still not fully understood. This study aims to elucidate the effect of EECP on significant hemodynamic parameters in the coronary arterial tree.

Methods

A finite volume method was used in conjunction with the inlet pressure wave (surrogated by the measured aortic pressure) before and during EECP and outlet flow resistance, assuming the blood as newtonian fluid. The time-average wall shear stress (TAWSS) and oscillatory shear index (OSI) were determined from the flow field.

Results

Regardless of the degree of vascular stenosis, hemodynamic conditions and flow patterns could be improved during EECP. In comparison with the original tree, the tree with a severe stenosis (75% area stenosis) demonstrated more significant improvement in hemodynamic conditions and flow patterns during EECP, with surface area ratio of TAWSS risk area (SAR-TAWSS) reduced from 12.3% to 6.7% (vs. SAR-TAWSS reduced from 7.2% to 5.6% in the original tree) and surface area ratio of OSI risk area (SAR-OSI) reduced from 6.8% to 2.5% (vs. SAR-OSI of both 0% before and during EECP in the original tree because of mild stenosis). Moreover, it was also shown that small ratio of diastolic pressure (D) and systolic pressure (S) (D/S) could only improve the hemodynamic condition mildly. The SAR-TAWSS reduction ratio significantly increased as D/S became larger.

Conclusions

A key finding of the study was that the improvement of hemodynamic conditions along the LMCA trees during EECP became more significant with the increase of D/S and the severity degree of stenoses at the bifurcation site. These findings have important implications on EECP as adjuvant therapy before or after percutaneous coronary intervention (PCI) in patients with diffuse atherosclerosis.

Automatic Segmentation of Coronary Artery Lumen via Anisotropic Graph-cuts

Coronary fractional flow reserve (FFR) is the ratio of distal to proximal pressure in a stenotic lesion and defines its presence of ischemia (i.e. FFR≤0.8). However, FFR requires pressure to be measured invasively across the lesion, which is barrier to wider use of the methods. Computational fluid dynamics (CFD) applied to computed tomography coronary angiography (CTCA) enable the computation of FFR (i.e. CT-FFR) noninvasively. The accurate coronary artery geometrical model is the prerequisite for CT-FFR. We aimed to develop a method to automatically segment the coronary artery lumen based on anisotrophic graph-cuts. 5 patients with coronary artery disease underwent CTCA. CTCA images were enhanced by Hessian Matrix filter and then to derive vesselness images and vessel directions. Centrelines were extracted using the shortest path algorithm. We modified the edge energy term based on the dissimilarity of neighboring voxels intensities. The inner product of vessel directions of two neighboring voxels was multiplied as well. All cases were automatically segmented successfully with average computational time of 79.5 seconds. Our anisotropic graph-cuts method reduced unnatural bumps on the lumen than classic graph-cuts methods. Our anisotrophic graph-cuts based method improved coronary lumen segmentation and downstream coronary geometry modelling, will play an important role for real-time CT-FFR computation in clinical practice.

Computational Fluid Dynamics of Vascular Disease in Animal Models

Recent applications of computational fluid dynamics (CFD) applied to the cardiovascular system have demonstrated its power in investigating the impact of hemodynamics on disease initiation, progression, and treatment outcomes. Flow metrics such as pressure distributions, wall shear stresses (WSS), and blood velocity profiles can be quantified to provide insight into observed pathologies, assist with surgical planning, or even predict disease progression. While numerous studies have performed simulations on clinical human patient data, it often lacks prediagnosis information and can be subject to large intersubject variability, limiting the generalizability of findings. Thus, animal models are often used to identify and manipulate specific factors contributing to vascular disease because they provide a more controlled environment. In this review, we explore the use of CFD in animal models in recent studies to investigate the initiating mechanisms, progression, and intervention effects of various vascular diseases. The first section provides a brief overview of the CFD theory and tools that are commonly used to study blood flow. The following sections are separated by anatomical region, with the abdominal, thoracic, and cerebral areas specifically highlighted. We discuss the associated benefits and obstacles to performing CFD modeling in each location. Finally, we highlight animal CFD studies focusing on common surgical treatments, including arteriovenous fistulas (AVF) and pulmonary artery grafts. The studies included in this review demonstrate the value of combining CFD with animal imaging and should encourage further research to optimize and expand upon these techniques for the study of vascular disease.

Myocardial bridging of the left anterior descending coronary artery is associated with reduced myocardial perfusion reserve: a 13N-ammonia PET study

Myocardial Bridging (MB) refers to the band of myocardium that abnormally overlies a segment of a coronary artery. This paper quantitatively evaluates the influence of MB of the left anterior descending artery (LAD) on myocardial perfusion of the entire left ventricle. We studied 131 consecutive patients who underwent hybrid rest/stress 13N-ammonia positron emission tomography (PET) and coronary computed tomography angiography (CCTA) due to suspected myocardial ischemia. Patients with previous myocardial infarction and/or significant coronary artery disease (≥ 50% stenosis) were excluded. Myocardial perfusion measurements were compared between patients with and without LAD-MB. Additionally, we evaluated the relationship between anatomical characteristics (length and depth) of LAD-MB and myocardial perfusion measurements. 17 (13%) patients presented a single LAD-MB. Global myocardial perfusion reserve (MPR) was lower in patients with LAD-MB than in patients without LAD-MB (1.9 ± 0.5 vs. 2.3 ± 0.6, p < 0.01). Global stress myocardial blood flow (MBF) was similar in patients with and without LAD-MB (2.2 ± 0.4 vs. 2.3 ± 0.7 ml/g/min, p = 0.40). Global rest MBF was higher in patients with LAD-MB than in patients without LAD-MB (1.2 ± 0.3 vs. 1.0 ± 0.2 ml/g/min, p < 0.01). Global rest MBF, stress MBF, and MPR quantifications were similar in patients with superficial and deep LAD-MB (all p = NS). We did not find any correlation between length and global rest MBF, stress MBF nor MPR (r = - 0.14, p = 0.59; r = 0.44, p = 0.07; and r = 0.45, p = 0.07 respectively). Quantitative myocardial perfusion suggests that LAD-MB may be related to impaired perfusion reserve, an indicator of microvascular dysfunction. Anatomical characteristics of LAD-MB were not related to changes in myocardial perfusion.

Computational Assessment of Blood Flow Heterogeneity in Peritoneal Dialysis Patients' Cardiac Ventricles

Dialysis prolongs life but augments cardiovascular mortality. Imaging data suggests that dialysis increases myocardial blood flow (BF) heterogeneity, but its causes remain poorly understood. A biophysical model of human coronary vasculature was used to explain the imaging observations, and highlight causes of coronary BF heterogeneity. Post-dialysis CT images from patients under control, pharmacological stress (adenosine), therapy (cooled dialysate), and adenosine and cooled dialysate conditions were obtained. The data presented disparate phenotypes. To dissect vascular mechanisms, a 3D human vasculature model based on known experimental coronary morphometry and a space filling algorithm was implemented. Steady state simulations were performed to investigate the effects of altered aortic pressure and blood vessel diameters on myocardial BF heterogeneity. Imaging showed that stress and therapy potentially increased mean and total BF, while reducing heterogeneity. BF histograms of one patient showed multi-modality. Using the model, it was found that total coronary BF increased as coronary perfusion pressure was increased. BF heterogeneity was differentially affected by large or small vessel blocking. BF heterogeneity was found to be inversely related to small blood vessel diameters. Simulation of large artery stenosis indicates that BF became heterogeneous (increase relative dispersion) and gave multi-modal histograms. The total transmural BF as well as transmural BF heterogeneity reduced due to large artery stenosis, generating large patches of very low BF regions downstream. Blocking of arteries at various orders showed that blocking larger arteries results in multi-modal BF histograms and large patches of low BF, whereas smaller artery blocking results in augmented relative dispersion and fractal dimension. Transmural heterogeneity was also affected. Finally, the effects of augmented aortic pressure in the presence of blood vessel blocking shows differential effects on BF heterogeneity as well as transmural BF. Improved aortic blood pressure may improve total BF. Stress and therapy may be effective if they dilate small vessels. A potential cause for the observed complex BF distributions (multi-modal BF histograms) may indicate existing large vessel stenosis. The intuitive BF heterogeneity methods used can be readily used in clinical studies. Further development of the model and methods will permit personalized assessment of patient BF status.

Effect of stenosis eccentricity on the functionality of coronary bifurcation lesions-a numerical study

Interventional cardiologists still rely heavily on angiography for the evaluation of coronary lesion severity, despite its poor correlation with the presence of ischemia. In order to improve the accuracy of the current diagnostic procedures, an understanding of the relative influence of geometric characteristics on the induction of ischemia is required. This idea is especially important for coronary bifurcation lesions (CBLs), whose treatment is complex and is associated with high rates of peri- and post-procedural clinical events. Overall, it is unclear which geometric and morphological parameters of CBLs influence the onset of ischemia. More specifically, the effect of stenosis eccentricity is unknown. Computational fluid dynamic simulations, under a geometric multiscale framework, were executed for seven CBL configurations within the left main coronary artery bifurcation. Both concentric and eccentric stenosis profiles of mild to severe constriction were considered. By using a geometric multiscale framework, the fractional flow reserve, which is the gold-standard clinical diagnostic index, could be calculated and was compared between the eccentric and concentric profiles for each case. The results suggested that for configurations where the supplying vessel is stenosed, eccentricity could have a notable effect on and therefore be an important factor that influences configuration functionality.

Hemodynamic analysis of patient-specific coronary artery tree

Local hemodynamic parameters, such as wall shear stress (WSS), oscillatory shear index and relative resident time (RRT), have been linked to coronary plaque initiation and progression. In this study, a left coronary artery tree model was reconstructed from computed tomography angiography images of a patient with multiple stenoses. The geometry of the coronary artery tree model was virtually restored by eliminating the lesions, essentially re-creating the virtually healthy artery anatomy. Using numerical simulations, flow characteristics and hemodynamic parameter distributions in the stenosed and virtually healthy models were investigated. In the virtually healthy artery model, disturbed flows were found at four locations, prone to initialization of plaque formation. Low WSS and high RRT were exhibited in three of the four locations, and high WSS and low RRT were exhibited in the fourth. These findings suggest that coronary plaque is more likely to form in locations with disturbed flow conditions characterized by low WSS and high RRT or high WSS and low RRT. In addition, clinical index of fractional flow reserve was found to significantly correlate with blood flow rate, rather than anatomic parameters, such as diameter stenosis, which implied the importance of hemodynamic environment in stenosis formation.