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.

Design of experiment approach to identify the dominant geometrical feature of left coronary artery influencing atherosclerosis

Background and Objective. Coronary artery geometry heavily influences local hemodynamics, potentially leading to atherosclerosis. Consequently, the unique geometrical configuration of an individual by birth can be associated with future risk of atherosclerosis. Although current researches focus on exploring the relationship between local hemodynamics and coronary artery geometry, this study aims to identify the order of influence of the geometrical features through systematic experiments, which can reveal the dominant geometrical feature for future risk assessment.Methods. According to Taguchi's method of design of experiment (DoE), the left main stem (LMS) length (lLMS), curvature (kLMS), diameter (dLMS) and the bifurcation angle between left anterior descending (LAD) and left circumflex (LCx) artery (αLAD-LCx) of two reconstructed patient-specific left coronary arteries (LCA) were varied in three levels to create L9 orthogonal array. Computational fluid dynamic (CFD) simulations with physiological boundary conditions were performed on the resulting eighteen LCA models. Average helicity intensity (h2) and relative atheroprone area (RAA) of near-wall hemodynamic descriptors were analyzed.Results. The proximal LAD (LADproximal) was identified to be the most atheroprone region of the left coronary artery due to higherh2,large RAA of time averaged wall shear stress (TAWSS < 0.4 Pa), oscillatory shear index (OSI ∼ 0.5) and relative residence time (RRT > 4.17 Pa-1). In both patient-specific cases, based onh2and TAWSS,dlmsis the dominant geometric parameter while based on OSI and RRT,αLAD-LCxis the dominant one influencing hemodynamic condition in proximal LAD (p< 0.05). Based on RRT, the rank of the geometrical factors is:αLAD-LCx>dLMS>lLMS>kLMS, indicating thatαLAD-LCxis the most dominant geometrical factor affecting hemodynamics at proximal LAD which may influence atherosclerosis.Conclusion. The proposed identification of the rank of geometrical features of LCA and the dominant feature may assist clinicians in predicting the possibility of atherosclerosis, of an individual, long before it will occur. This study can further be translated to be used to rank the influence of several arterial geometrical features at different arterial locations to explore detailed relationships between the arterial geometrical features and local hemodynamics.

Considering the Influence of Coronary Motion on Artery-Specific Biomechanics Using Fluid-Structure Interaction Simulation

The endothelium in the coronary arteries is subject to wall shear stress and vessel wall strain, which influences the biology of the arterial wall. This study presents vessel-specific fluid-structure interaction (FSI) models of three coronary arteries, using directly measured experimental geometries and boundary conditions. FSI models are used to provide a more physiologically complete representation of vessel biomechanics, and have been extended to include coronary bending to investigate its effect on shear and strain. FSI both without- and with-bending resulted in significant changes in all computed shear stress metrics compared to CFD (p = 0.0001). Inclusion of bending within the FSI model produced highly significant changes in Time Averaged Wall Shear Stress (TAWSS) + 9.8% LAD, + 8.8% LCx, - 2.0% RCA; Oscillatory Shear Index (OSI) + 208% LAD, 0% LCx, + 2600% RCA; and transverse wall Shear Stress (tSS) + 180% LAD, + 150% LCx and + 200% RCA (all p < 0.0001). Vessel wall strain was homogenous in all directions without-bending but became highly anisotropic under bending. Changes in median cyclic strain magnitude were seen for all three vessels in every direction. Changes shown in the magnitude and distribution of shear stress and wall strain suggest that bending should be considered on a vessel-specific basis in analyses of coronary artery biomechanics.

Impact of cyclic bending on coronary hemodynamics

It remains unknown that the degree of bias in computational fluid dynamics results without considering coronary cyclic bending. This study aims to investigate the influence of different rates of coronary cyclic bending on coronary hemodynamics. To model coronary bending, a multi-ring-controlled fluid-structural interaction model was designed. A coronary artery was simulated with various cyclic bending rates (0.5, 0.75 and 1 s, corresponding to heart rates of 120, 80 and 60 bpm) and compared against a stable model. The simulated results show that the hemodynamic parameters of vortex Q-criterion, temporal wall shear stress (WSS), time-averaged WSS (TaWSS) and oscillatory shear index (OSI) were sensitive to the changes in cyclic rate. A higher heart rate resulted in higher magnitude and larger variance in the hemodynamic parameters. Whereas, the values and distributions of flow velocity and relative residence time (RRT) did not show significant differences between different bending periods. This study suggests that a stable coronary model is not sufficient to represent the hemodynamics in a bending coronary artery. Different heart rate conditions were found to have significant impact on the hemodynamic parameters. Thus, cyclic bending should be considered to mimic the realistic hemodynamics in future patient-specific coronary hemodynamics studies.

Index of microcirculatory resistance: state-of-the-art and potential applications in computational simulation of coronary artery disease

The dysfunction of coronary microcirculation is an important cause of coronary artery disease (CAD). The index of microcirculatory resistance (IMR) is a quantitative evaluation of coronary microcirculatory function, which provides a significant reference for the prediction, diagnosis, treatment, and prognosis of CAD. IMR also plays a key role in investigating the interaction between epicardial and microcirculatory dysfunctions, and is closely associated with coronary hemodynamic parameters such as flow rate, distal coronary pressure, and aortic pressure, which have been widely applied in computational studies of CAD. However, there is currently a lack of consensus across studies on the normal and pathological ranges of IMR. The relationships between IMR and coronary hemodynamic parameters have not been accurately quantified, which limits the application of IMR in computational CAD studies. In this paper, we discuss the research gaps between IMR and its potential applications in the computational simulation of CAD. Computational simulation based on the combination of IMR and other hemodynamic parameters is a promising technology to improve the diagnosis and guide clinical trials of CAD.

The effects of plaque morphological characteristics on the post-stenotic flow in left main coronary artery bifurcation

Local post-stenotic hemodynamics has critical influence in the atherosclerotic plaque progression occurring in susceptible arterial sites, in particular the left main coronary artery (LMCA) bifurcation. Understanding the effects of plaque morphological characteristics: stenosis severity (SS), eccentricity index (EI) and lesion length (LL) on the post-stenotic flow behavior can significantly improve treatment planning. In order to investigate these effects, we have employed computational fluid dynamics (CFD) simulations in twenty computer-generated and five patient-specific LMCA models and the hemodynamic parameters: velocity, pressure (P), wall pressure gradient (WPG), wall shear stress (WSS), time averaged wall shear stress (TAWSS), oscillatory shear index (OSI), relative residence time (RRT) and helicity intensity (h₂) were analyzed. Our results revealed that the effect of stenosis eccentricity varied significantly for different values of stenosis severity and lesion length. Regions with low WSS, low TAWSS and high RRT were more prominent in models having higher stenosis severity. For smaller lesion length, at low and moderate stenosis severity, surface area with low TAWSS and high RRT decreased with increasing eccentricity index, whereas for high stenosis severity models, low TAWSS region and average RRT values increased with eccentricity. However, for models with longer lesion length, regions with high OSI and RRT overall increased gradually with eccentricity. The helicity intensity (h₂) of all models remained very low except at the most eccentric model with longer lesion length. The presence of very high helical flow in this model suggests the possibility of atheroprotective flow. It can be concluded that all plaque morphological characteristics covered under this investigation play an important role in plaque progression.

Haemodynamic mechanism of formation and distribution of coronary atherosclerosis: A lesion-specific model

Coronary arterial disease, as the most devastated cardiovascular disease, is caused by the atherosclerosis in the coronary arteries, which blocks the blood flow to the heart, resulting in the deficient supply of oxygen and nutrition to the heart, and eventually leading to heart failure. To date, haemodynamic mechanisms for atherosclerosis development are not fully understood although it is believed that the haemodynamic disturbance at the region of the arterial bifurcation, particular, bifurcation angle, plays an important role in the atherosclerosis development. In this study, two types of computational fluid dynamics models, lesion-specific and idealized models, combined with the computer tomography imaging techniques, are used to explore the mechanism of formation and distribution of the atherosclerosis around the bifurcation of left coronary artery and its association with the bifurcation angle. The lesion-specific model is used to characterize the effect of personalized features on the haemodynamic performance, while the idealized model is focusing on the effect of single factor, bifurcation angle, on the haemodynamic performance. The simulated results from both types of the models, combined with the clinical observation, revealed that the three key areas around the bifurcations are prone to formation of the atherosclerosis. Unlike the idealized models, lesion-specific modelling results did not show the significant correlation between the wall shear stress and bifurcation angle, although the mean value of the wall shear stress in smaller bifurcation angles (less than 90°) is higher than that with larger bifurcation angles (greater than 90°). In conclusion, lesion-specific computational fluid dynamics modelling is an efficient and convenient way to predict the haemodynamic performance around the bifurcation region, allowing the comprehensive information for the clinicians to predict the atherosclerosis development. The idealized models, which only focus on single parameter, may not provide the sufficient and reliable information for the clinical application. A novel multi-parameters modelling technique, therefore, is suggested to be developed in future, allowing the effects of many parameters on the haemodynamic performance to be evaluated.

A comprehensive fluid-structure interaction model of the left coronary artery

A fluid structure interaction model of a left anterior descending (LAD) coronary artery was developed, incorporating transient blood flow, cyclic bending motion of the artery, and myocardial contraction. The 3D geometry was constructed based on a patient's computed tomography angiography data. To simulate disease conditions, a plaque was placed within the LAD to create a 70% stenosis. The bending motion of the blood vessel was prescribed based on the LAD spatial information. The pressure induced by myocardial contraction was applied to the outside of the blood vessel wall. The fluid domain was solved using the Navier-Stokes equations. The arterial wall was defined as a nonlinear elastic, anisotropic, and incompressible material, and the mechanical behavior was described using the modified hyper-elastic Mooney-Rivlin model. The fluid (blood) and solid (vascular wall) domains were fully coupled. The simulation results demonstrated that besides vessel bending/stretching motion, myocardial contraction had a significant effect on local hemodynamics and vascular all stress/strain distribution. It not only transiently increased blood flow velocity and fluid wall shear stress, but also changed shear stress patterns. The presence of the plaque significantly reduced vascular wall tensile strain. Compared to the coronary artery models developed previously, the current model had improved physiological relevance.

Dependence of leukocyte capture on instantaneous pulsatile flow

Atherosclerosis, an artery disease, is currently the leading cause of death in the United States in both men and women. The first step in the development of atherosclerosis involves leukocyte adhesion to the arterial endothelium. It is broadly accepted that blood flow, more specifically wall shear stress (WSS), plays an important role in leukocyte capture and subsequent development of an atherosclerotic plaque. What is less known is how instantaneous WSS, which can vary by up to 5 Pa over one cardiac cycle, influences leukocyte capture. In this paper we use direct numerical simulations (DNS), performed using an in-house code, to illustrate that leukocyte capture is different whether as a function of instantaneous or time-averaged blood flow. Specifically, a stenotic plaque is modeled using a computational fluid dynamics (CFD) solver through fully three-dimensional Navier-Stokes equations and the immersed boundary method. Pulsatile triphasic inflow is used to simulate the cardiac cycle. The CFD is coupled with an agent-based leukocyte capture model to assess the impact of instantaneous hemodynamics on stenosis growth. The computed wall shear stress agrees well with the results obtained with a commercial software, as well as with theoretical results in the healthy region of the artery. The analysis emphasizes the importance of the instantaneous flow conditions in evaluating the leukocyte rate of capture. That is, the capture rate computed from mean flow field is generally underpredicted compared to the actual rate of capture. Thus, in order to obtain a reliable estimate, the flow unsteadiness during a cardiac cycle should be taken into account.

Coronary artery rotation in native and stented porcine coronary arteries

INTRODUCTION

Coronary arteries are exposed to several complex biomechanical forces during the cardiac cycle. These biomechanical forces potentially contribute to both native coronary artery disease, development of atherosclerosis and eventual stent failure. The aim of the present study was to characterize and define coronary artery axial rotation and the effect of stent implantation on this biomechanical factor.

METHODS

Intravascular ultrasound (IVUS) images were obtained from porcine coronary arteries and analyzed in ultrasound analysis software used to evaluate myocardial strain and torsion in echocardiography. In this study the software was utilized for a novel application to evaluate coronary artery rotation and time-to-peak (TTP) rotation in porcine coronary arteries. Clockwise (CW) and counterclockwise (CCW) rotation of coronary arteries during the cardiac cycle and (TTP) rotation were measured.

RESULTS

A total of 11 (4 LAD, 4 LCX, 3 RCA) coronary artery segments were independently analyzed pre- and post-stent implantation for a total of 22 IVUS runs. CW and CCW rotation and TTP varied widely within coronary artery segments and between different coronary arteries. Stent implantation impacted degree, direction and TTP of coronary rotation. Measurement reliability was assessed and the intraclass correlation coefficient for maximum average CCW was 0.990 (95% confidence interval 0.980-0.996, P < 0.0001), indicating excellent agreement.

CONCLUSIONS

Coronary arteries display wide spectrum of CW and CCW rotation during the cardiac cycle. Coronary stents impact the degree and direction of coronary artery rotation. The implications of these findings on development of atherosclerosis and stent failure require further investigation.

Healthy and diseased coronary bifurcation geometries influence near-wall and intravascular flow: A computational exploration of the hemodynamic risk

Local hemodynamics has been identified as one main determinant in the onset and progression of atherosclerotic lesions at coronary bifurcations. Starting from the observation that atherosensitive hemodynamic conditions in arterial bifurcation are majorly determined by the underlying anatomy, the aim of the present study is to investigate how peculiar coronary bifurcation anatomical features influence near-wall and intravascular flow patterns. Different bifurcation angles and cardiac curvatures were varied in population-based, idealized models of both stenosed and unstenosed bifurcations, representing the left anterior descending (LAD) coronary artery with its diagonal branch. Local hemodynamics was analyzed in terms of helical flow and exposure to low/oscillatory shear stress by performing computational fluid dynamics simulations. Results show that bifurcation angle impacts lowly hemodynamics in both stenosed and unstenosed cases. Instead, curvature radius influences the generation and transport of helical flow structures, with smaller cardiac curvature radius associated to higher helicity intensity. Stenosed bifurcation models exhibit helicity intensity values one order of magnitude higher than the corresponding unstenosed cases. Cardiac curvature radius moderately affects near-wall hemodynamics of the stenosed cases, with smaller curvature radius leading to higher exposure to low shear stress and lower exposure to oscillatory shear stress. In conclusion, the proposed controlled benchmark allows investigating the effect of various geometrical features on local hemodynamics at the LAD/diagonal bifurcation, highlighting that cardiac curvature influences near wall and intravascular hemodynamics, while bifurcation angle has a minor effect.

Computational fluid dynamics study of common stent models inside idealised curved coronary arteries

The haemodynamic behaviour of blood inside a coronary artery after stenting is greatly affected by individual stent features as well as complex geometrical properties of the artery including tortuosity and curvature. Regions at higher risk of restenosis, as measured by low wall shear stress (WSS < 0.5 Pa), have not yet been studied in detail in curved stented arteries. In this study, three-dimensional computational modelling and computational fluid dynamics methodologies were used to analyse the haemodynamic characteristics in curved stented arteries using several common stent models. Results in this study showed that stent strut thickness was one major factor influencing the distribution of WSS in curved arteries. Regions of low WSS were found behind struts, particularly those oriented at a large angle relative to the streamwise flow direction. These findings were similar to those obtained in studies of straight arteries. An uneven distribution of WSS at the inner and outer bends of curved arteries was observed where the WSS was lower at the inner bend. In this study, it was also shown that stents with a helical configuration generated an extra swirling component of the flow based on the helical direction; however, this extra swirl in the flow field did not cause significant changes on the distribution of WSS under the current setup.

A Shearing-Stretching Device That Can Apply Physiological Fluid Shear Stress and Cyclic Stretch Concurrently to Endothelial Cells

Endothelial cell (EC) morphology and functions can be highly impacted by the mechanical stresses that the cells experience in vivo. In most areas in the vasculature, ECs are continuously exposed to unsteady blood flow-induced shear stress and vasodilation-contraction-induced tensile stress/strain simultaneously. Investigations on how ECs respond to combined shear stress and tensile strain will help us to better understand how an altered mechanical environment affects EC mechanotransduction, dysfunction, and associated cardiovascular disease development. In the present study, a programmable shearing and stretching device that can apply dynamic fluid shear stress and cyclic tensile strain simultaneously to cultured ECs was developed. Flow and stress/strain conditions in the device were simulated using a fluid structure interaction (FSI) model. To characterize the performance of this device and the effect of combined shear stress-tensile strain on EC morphology, human coronary artery ECs (HCAECs) were exposed to concurrent shear stress and cyclic tensile strain in the device. Changes in EC morphology were evaluated through cell elongation, cell alignment, and cell junctional actin accumulation. Results obtained from the numerical simulation indicated that in the "in-plane" area of the device, both fluid shear stress and biaxial tensile strain were uniform. Results obtained from the in vitro experiments demonstrated that shear stress, alone or combined with cyclic tensile strain, induced significant cell elongation. While biaxial tensile strain alone did not induce any appreciable change in EC elongation. Fluid shear stress and cyclic tensile strain had different effects on EC actin filament alignment and accumulation. By combining various fluid shear stress and cyclic tensile strain conditions, this device can provide a physiologically relevant mechanical environment to study EC responses to physiological and pathological mechanical stimulation.

Focal association between wall shear stress and clinical coronary artery disease progression

Wall shear stress (WSS) has been investigated as a potential prospective marker to identify rapidly progressing coronary artery disease (CAD) and potential for lesions to acquire vulnerable characteristics. Previous investigations, however, are limited by a lack of understanding of the focal association between WSS and CAD progression (i.e., data are notably spatially averaged). Thus, the aim of this investigation was to examine the focal association between WSS and coronary atherosclerosis progression, and compare these results to those determined by spatial averaging. Five patients with CAD underwent baseline and 6-month follow-up angiographic and virtual histology-intravascular ultrasound imaging to quantify CAD progression. Patient-specific computational fluid dynamics models were constructed to compute baseline WSS values, which were either averaged around the entire artery circumference or examined in focal regions (sectors). Analysis of data within each sector (n = 3871) indicated that circumferentially averaged and sector WSS values were statistically different (p < 0.05) and exhibited poor agreement (concordance correlation coefficient = 0.69). Furthermore, differences were observed between the analysis techniques when examining the association of WSS and CAD progression. This investigation highlights the importance of examining spatially heterogeneous variables at a focal level to reduce the affect of data reduction and warrants implementation in a larger clinical study to determine the predictive power in prospectively identifying rapidly progressing and/or vulnerable coronary plaques.

Computation of Hemodynamics in Tortuous Left Coronary Artery: A Morphological Parametric Study

Coronary tortuosity (CT) would alter the local wall shear stress (WSS) and may become a risk factor for atherosclerosis. Here we performed a systematic computational study to relate CT morphological parameters to abnormal WSS, which is a predisposing factor to the formation of atherosclerotic lesions. Several idealized left coronary artery (LCA) models were created to conduct a series of morphological parametric studies, in which we concentrate on three specific morphological parameters, the center line radius (CLR), the bend angle (BA), and the length between two adjust bends (LBB). The time averaged WSS (TAWSS), the oscillatory shear index (OSI), and the time averaged WSS gradient (WSSGnd) were explored by using the computational fluid dynamics (CFD) method, in order to determine susceptible sites for the onset of early atherosclerosis. In addition, two realistic LCA models were reconstructed to further validate the finding's credibility. The CLR and LBB had great impact on the distributions of WSS-derived parameters, while the BA had minor impact on the hemodynamic of the tortuous arteries. Abnormal regions with low TAWSS (TAWSS < 0.5 Pa), high OSI (OSI > 0.1) and high WSSGnd (WSSGnd > 8) were observed at the inner wall of bend sections in the models with small CLR or small LBB. These findings were also confirmed in the realistic models. Severe CT with small CLR or LBB would lead to the formation of abnormal WSS regions at the bend sections and providing these regions with favorable conditions for the onset and/or progression of atherosclerosis.