In-vivo flow simulation in coronary arteries based on computed tomography datasets: feasibility and initial results

A CFD-FFT approach to hemoacoustics that enables degree of stenosis prediction from stethoscopic signals

In this paper, we identify a new (acoustic) frequency-stenosis relation whose frequencies lie within the recommended auscultation threshold of stethoscopy (< 120 Hz). We show that this relation can be used to extend the application of phonoangiography (quantifying the degree of stenosis from bruits) to widely accessible stethoscopes. The relation is successfully identified from an analysis restricted to the acoustic signature of the von Karman vortex street, which we automatically single out by means of a metric we propose that is based on an area-weighted average of the Q-criterion for the post-stenotic region. Specifically, we perform CFD simulations on internal flow geometries that represent stenotic blood vessels of different severities. We then extract their emitted acoustic signals using the Ffowcs Williams-Hawkings equation, which we subtract from a clean signal (stenosis free) at the same heart rate. Next, we transform this differential signal to the frequency domain and carefully classify its acoustic signatures per six (stenosis-)invariant flow phases of a cardiac cycle that are newly identified in this paper. We then automatically restrict our acoustic analysis to the sounds emitted by the von Karman vortex street (phase 4) by means of our Q-criterion-based metric. Our analysis of its acoustic signature reveals a strong linear relationship between the degree of stenosis and its dominant frequency, which differs considerably from the break frequency and the heart rate (known dominant frequencies in the literature). Applying our new relation to available stethoscopic data, we find that its predictions are consistent with clinical assessment. Our finding of this linear correlation is also unlike prevalent scaling laws in the literature, which feature a small exponent (i.e., low stenosis percentage sensitivity over much of the clinical range). They hence can only distinguish mild, moderate, and severe cases. Conversely, our linear law can identify variations in the degree of stenosis sensitively and accurately for the full clinical range, thus significantly improving the utility of the relevant scaling laws... Future research will investigate incorporating the vibroacoustic role of adjacent organs to expand the clinical applicability of our findings. Extending our approach to more complex 3D stenotic morphologies and including the vibroacoustic role of surrounding organs will be explored in future research to advance the clinical reach of our findings.

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.

Non-invasive characterization of complex coronary lesions

Conventional invasive diagnostic imaging techniques do not adequately resolve complex Type B and C coronary lesions, which present unique challenges, require personalized treatment and result in worsened patient outcomes. These lesions are often excluded from large-scale non-invasive clinical trials and there does not exist a validated approach to characterize hemodynamic quantities and guide percutaneous intervention for such lesions. This work identifies key biomarkers that differentiate complex Type B and C lesions from simple Type A lesions by introducing and validating a coronary angiography-based computational fluid dynamic (CFD-CA) framework for intracoronary assessment in complex lesions at ultrahigh resolution. Among 14 patients selected in this study, 7 patients with Type B and C lesions were included in the complex lesion group including ostial, bifurcation, serial lesions and lesion where flow was supplied by collateral bed. Simple lesion group included 7 patients with lesions that were discrete, [Formula: see text] long and readily accessible. Intracoronary assessment was performed using CFD-CA framework and validated by comparing to clinically measured pressure-based index, such as FFR. Local pressure, endothelial shear stress (ESS) and velocity profiles were derived for all patients. We validates the accuracy of our CFD-CA framework and report excellent agreement with invasive measurements ([Formula: see text]). Ultra-high resolution achieved by the model enable physiological assessment in complex lesions and quantify hemodynamic metrics in all vessels up to 1mm in diameter. Importantly, we demonstrate that in contrast to traditional pressure-based metrics, there is a significant difference in the intracoronary hemodynamic forces, such as ESS, in complex lesions compared to simple lesions at both resting and hyperemic physiological states [n = 14, [Formula: see text]]. Higher ESS was observed in the complex lesion group ([Formula: see text] Pa) than in simple lesion group ([Formula: see text] Pa). Complex coronary lesions have higher ESS compared to simple lesions, such differential hemodynamic evaluation can provide much the needed insight into the increase in adverse outcomes for such patients and has incremental prognostic value over traditional pressure-based indices, such as FFR.

Computational fluid dynamics simulation of time-resolved blood flow in Budd-Chiari syndrome with inferior vena cava stenosis and its implication for postoperative efficacy assessment

BACKGROUND

This study aimed to adopt computational fluid dynamics to simulate the blood flow dynamics in inferior vena cava stenosis based on time-dependent patient-specific models of Budd-Chiari syndrome as well as a normal model. It could offer valuable references for a retrospective insight into the underlying mechanisms of Budd-Chiari syndrome pathogenesis as well as more accurate evaluation of postoperative efficacy.

METHODS

Three-dimensional inferior vena cava models of Budd-Chiari syndrome patient-specific (preoperative and postoperative) and normal morphology model were reconstructed as per magnetic resonance images using Simpleware. Moreover, computational fluid dynamics of time-resolved inferior vena cava blood flow were simulated using actual patient-specific measurements to reflect time-dependent flow rates.

FINDINGS

The assessment of the preoperative model revealed the dramatic variations of hemodynamic parameters of the stenotic inferior vena cava. Moreover, the comparison of the preoperative and postoperative models with the normal model as benchmark showed that postoperative hemodynamic parameters were markedly ameliorated via stenting, with the attenuation of overall velocity and wall shear stress, and the increase of pressure. However, the comparative analysis of the patient-specific simulations revealed that some postoperative hemodynamic profiles still bore some resemblance to the preoperative ones, indicating potential risks of restenosis.

INTERPRETATION

Computational fluid dynamics simulation of time-resolved blood flow could reveal the tight correlation between the hemodynamic characteristics and the pathological mechanisms of inferior vena cava stenosis. Furthermore, such time-resolved hemodynamic profiles could provide a quantitative approach to diagnosis, operative regimen and postoperative evaluation of Budd-Chiari syndrome with inferior vena cava stenosis.

Estimation of endothelial shear stress in atherosclerotic lesions detected by intravascular ultrasound using computational fluid dynamics from coronary CT scans with a pulsatile blood flow and an individualized blood viscosity

INTRODUCTION

Endothelial shear stress (ESS) is a local hemodynamic factor that is dependent on vessel geometry and influences the process of atherogenesis. As in vivo measurements of ESS are not possible, it must be calculated using computational fluid dynamics (CFD). In this feasibility study we explore CFD-models generated from coronary CT-angiography (CCTA) using an individualised blood viscosity and a pulsatile flow profile derived from in vivo measurements.

MATERIALS AND METHODS

We retrospectively recruited 25 consecutive patients who received a CCTA followed by a coronary angiography including intravascular ultrasound (IVUS) and generated 3D models of the coronary arteries from the CT-datasets. We then performed CFD-simulations on these models. Hemodynamically non-relevant stenosis were identified in IVUS. They were isolated in the CFD-model and separated longitudinally into a half with atherosclerotic lesion (AL) and one without (NAL). ESS was measured and compared for both halves.

RESULTS

After excluding vessels with no IVUS data or relevant stenosis we isolated 31 hemodynamically non-relevant excentric AL from a total of 14 vessels. AL segments showed consistently significantly lower ESS when compared to their corresponding NAL segments when regarding minimum (0.9 Pa, CI [0.6, 1.2] vs. 1.3 Pa, CI [0.9, 1.8]; p = 0.004), mean (5.0 Pa, CI [3.4, 6.0] vs. 6.7 Pa, CI [5.5, 8.4]; p = 0.008) and maximum ESS values (12.4 Pa, CI [8.6, 14.6] vs. 19.6 Pa, CI [12.4, 21.0]; p = 0.005). Qualitatively ESS was lower on the inside of bifurcations and curvatures.

CONCLUSION

CFD simulations of coronary arteries from CCTA with an individualised flow profile and blood viscosity are feasible and could provide further prognostic information and a better risk stratification in coronary artery disease. Further prospective studies are needed to investigate this claim.

Fractal dimension and directional analysis of elastic and collagen fiber arrangement in unsectioned arterial tissues affected by atherosclerosis and aging

Structural proteins like collagen and elastin are major constituents of the extracellular matrix (ECM). ECM degradation and remodeling in diseases significantly impact the microorganization of these structural proteins. Therefore, tracking the changes of collagen and elastin fiber morphological features within ECM impacted by disease progression could provide valuable insight into pathological processes such as tissue fibrosis and atherosclerosis. Benefiting from its intrinsic high-resolution imaging power and superior biochemical specificity, nonlinear optical microscopy (NLOM) is capable of providing information critical to the understanding of ECM remodeling. In this study, alterations of structural fibrillar proteins such as collagen and elastin in arteries excised from atherosclerotic rabbits were assessed by the combination of NLOM images and textural analysis methods such as fractal dimension (FD) and directional analysis (DA). FD and DA were tested for their performance in tracking the changes of extracellular elastin and fibrillar collagen remodeling resulting from atherosclerosis progression/aging. Although other methods of image analysis to study the organization of elastin and collagen structures have been reported, the simplified calculations of FD and DA presented in this work prove that they are viable strategies for extracting and analyzing fiber-related morphology from disease-impacted tissues. Furthermore, this study also demonstrates the potential utility of FD and DA in studying ECM remodeling caused by other pathological processes such as respiratory diseases, several skin conditions, or even cancer. NEW & NOTEWORTHY Textural analyses such as fractal dimension (FD) and directional analysis (DA) are straightforward and computationally viable strategies to extract fiber-related morphological data from optical images. Therefore, objective, quantitative, and automated characterization of protein fiber morphology in extracellular matrix can be realized by using these methods in combination with digital imaging techniques such as nonlinear optical microscopy (NLOM), a highly effective visualization tool for fibrillar collagen and elastic network. Combining FD and DA with NLOM is an innovative approach to track alterations of structural fibrillar proteins. The results illustrated in this study not only prove the effectiveness of FD and DA methods in extracellular protein characterization but also demonstrate their potential value in clinical and basic biomedical research where protein microstructure characterization is critical.

The Computational Fluid Dynamics Analyses on Hemodynamic Characteristics in Stenosed Arterial Models

Arterial stenosis plays an important role in the progressions of thrombosis and stroke. In the present study, a standard axisymmetric tube model of the stenotic artery is introduced and the degree of stenosis η is evaluated by the area ratio of the blockage to the normal vessel. A normal case (η = 0) and four stenotic cases of η = 0.25, 0.5, 0.625, and 0.75 with a constant Reynolds number of 300 are simulated by computational fluid dynamics (CFD), respectively, with the Newtonian and Carreau models for comparison. Results show that for both models, the poststenotic separation vortex length increases exponentially with the growth of stenosis degree. However, the vortex length of the Carreau model is shorter than that of the Newtonian model. The artery narrowing accelerates blood flow, which causes high blood pressure and wall shear stress (WSS). The pressure drop of the η = 0.75 case is nearly 8 times that of the normal value, while the WSS peak at the stenosis region of η = 0.75 case even reaches up to 15 times that of the normal value. The present conclusions are of generality and contribute to the understanding of the dynamic mechanisms of artery stenosis diseases.

Numerical simulation of hemodynamics in membranous obstruction of the suprahepatic inferior vena cava based on a subject-specific Budd-Chiari syndrome model

BACKGROUND

This study was performed to determine the hemodynamic changes of Budd-Chiari syndrome when the inferior vena vein membrane is developing.

METHODS

A patient-specific Budd-Chiari syndrome vascular model was reconstructed based on magnetic resonance images using Mimics software and different degrees (16%, 37%, and 54%) of idealized membrane were built based on the Budd-Chiari syndrome vascular model using Geomagic software. Three membrane obstruction Budd-Chiari syndrome vascular models were established successfully and fluent software was used to simulate hemodynamic parameters, including blood velocity and wall shear stress.

FINDINGS

The simulation results showed that there is low velocity and a low wall shear stress region at the junction of the inferior vena cava and the branches of the hepatic veins, and swirl may occur in this area. As the membrane develops, the size of the low velocity and low wall shear stress regions enlarged and the wall shear stress was increased at the membrane region. There was a significant difference in the mean values of wall shear stress between the different obstruction membrane models (P<0.05).

INTERPRETATION

Hemodynamic parameters play an important role in vascular disease and there may be a correlation between inferior vena cava wall shear force changes and the slow development process of the inferior vena cava membrane.

Fiber-reinforced computational model of the aortic root incorporating thoracic aorta and coronary structures

Cardiovascular diseases are still the leading causes of death in the developed world. The decline in the mortality associated with circulatory system diseases is accredited to development of new diagnostic and prognostic tools. It is well known that there is an inter relationship between the aortic valve impairment and pathologies of the aorta and coronary vessels. However, due to the limitations of the current tools, the possible link is not fully elucidated. Following our previous model of the aortic root including the coronaries, in this study, we have further developed the global aspect of the model by incorporating the anatomical structure of the thoracic aorta. This model is different from all the previous studies in the sense that inclusion of the coronary structures and thoracic aorta into the natural aortic valve introduces the notion of globality into the model enabling us to explore the possible link between the regional pathologies. The developed model was first validated using the available data in the literature under physiological conditions. Then, to provide a support for the possible association between the localized cardiovascular pathologies and global variations in hemodynamic conditions, we simulated the model for two pathological conditions including moderate and severe aortic valve stenoses. The findings revealed that malformations of the aortic valve are associated with development of low wall shear stress regions and helical blood flow in thoracic aorta that are considered major contributors to aortic pathologies.

3D physiological model of the aortic valve incorporating small coronary arteries

The diseases of the coronary arteries and the aortic root are still the leading causes of mortality and morbidity worldwide. In this study, a 3D global fluid-structure interaction of the aortic root with inclusion of anatomically inspired small coronary arteries using the finite element method is presented. This innovative model allows to study the impact and interaction of root biomechanics on coronary hemodynamics and brings a new understanding to small coronary vessels hemodynamics. For the first time, the velocity profiles and shear stresses are reported in distal coronary arteries as a result of the aortic flow conditions in a global fluid-structure interaction model.

Non-Newtonian Blood Flow Simulation of Diastolic Phase in Bileaflet Mechanical Heart Valve Implanted in a Realistic Aortic Root Containing Coronary Arteries

Coronary arteries, which are branched from the sinuses, have tangible effects on the hemodynamic performance of the bileaflet mechanical heart valve (BMHV), especially in the diastolic phase. To better understand this issue, a computer model of ascending aorta including realistic sinus shapes and coronary arteries has been generated in this study in order to investigate the BMHV performance during diastole. Three-dimensional transient numerical analysis is conducted to simulate the diastolic blood flow through the hinges and in coronary arteries under the assumption of non-Newtonian behavior. Results indicate that as blood flows to the coronary arteries mainly during diastole, leakage flow from the hinge and other gaps will change considering the influence of coronary arteries. In addition, BMHV in the case of aortic replacement will increase blood flow rate into the coronary arteries about 100% as the mechanical valve resistance is higher than a native heart valve. Also, it will change the wall shear stress (WSS) distribution and increase coronary artery disease (CAD) potential. It is found out that although less leakage flow reduces the velocity magnitudes through the gaps, the shear stress acting on blood elements with non-Newtonian assumption will be detrimental in the hinge corner at the ventricular side. High WSS of 1800 Pa is observed at beginning of diastole at this region.

Hemodynamics in Transplant Renal Artery Stenosis and its Alteration after Stent Implantation Based on a Patient-specific Computational Fluid Dynamics Model

Background:

Accumulating studies on computational fluid dynamics (CFD) support the involvement of hemodynamic factors in artery stenosis. Based on a patient-specific CFD model, the present study aimed to investigate the hemodynamic characteristics of transplant renal artery stenosis (TRAS) and its alteration after stent treatment.

Methods:

Computed tomography angiography (CTA) data of kidney transplant recipients in a single transplant center from April 2013 to November 2014 were reviewed. The three-dimensional geometry of transplant renal artery (TRA) was reconstructed from the qualified CTA images and categorized into three groups: the normal, stenotic, and stented groups. Hemodynamic parameters including pressure distribution, velocity, wall shear stress (WSS), and mass flow rate (MFR) were extracted. The data of hemodynamic parameters were expressed as median (interquartile range), and Mann–Whitney U-test was used for analysis.

Results:

Totally, 6 normal, 12 stenotic, and 6 stented TRAs were included in the analysis. TRAS presented nonuniform pressure distribution, adverse pressure gradient across stenosis throat, flow vortex, and a separation zone at downstream stenosis. Stenotic arteries had higher maximal velocity and maximal WSS (2.94 [2.14, 3.30] vs. 1.06 [0.89, 1.15] m/s, 256.5 [149.8, 349.4] vs. 41.7 [37.8, 45.3] Pa at end diastole, P = 0.001; 3.25 [2.67, 3.56] vs. 1.65 [1.18, 1.72] m/s, 281.3 [184.3, 364.7] vs. 65.8 [61.2, 71.9] Pa at peak systole, P = 0.001) and lower minimal WSS and MFRs (0.07 [0.03, 0.13] vs. 0.52 [0.45, 0.67] Pa, 1.5 [1.0, 3.0] vs. 11.0 [8.0, 11.3] g/s at end diastole, P = 0.001; 0.08 [0.03, 0.19] vs. 0.70 [0.60, 0.81] Pa, 2.0 [1.3, 3.3] vs. 16.5 [13.0, 20.3] g/s at peak systole, P = 0.001) as compared to normal arteries. Stent implantation ameliorated all the alterations of the above hemodynamic factors except low WSS.

Conclusions:

Hemodynamic factors were significantly changed in severe TRAS. Stent implantation can restore or ameliorate deleterious change of hemodynamic factors except low WSS at stent regions.

Numerical study to indicate the vulnerability of plaques using an idealized 2D plaque model based on plaque classification in the human coronary artery

Atherosclerosis is one of the leading causes of death in the world. In this study, an idealized 2D plaque model based on plaque classification in the coronary artery is developed. When creating the idealized 2D model for each plaque type (fibrocalcic, FC; fibrofatty, FT; calcified fibroatheroma, CaFA; fibroatheroma, FA; calcified thin-cap fibroatheroma, CaTCFA; thin-cap fibroatheroma, TCFA), the cap thickness and stenosis by diameter were set as variables. In order to establish the correlation between each plaque type and plaque rupture, a numerical simulation was performed and the stress and stress gradient were reviewed to analyze the mechanical behavior. Results show that both the TCFA and CaTCFA plaque types, which have the smallest cap thicknesses of the different types of plaque, showed relatively high stress values in the thin membrane when compared with the FT type. The FT type is considered to be relatively stable since it does not have necrotic core or a thin membrane. With a stenosis rate of 50% and a cap thickness of 60 μm, the TCFA and CaTCFA types showed approximately 11 and 110% higher stress values, respectively, and 679 and 1568% higher negative stress gradient values, respectively. In other words, the plaque types with thin caps, which have weak load-bearing capacities, showed high stress values and high negative stress gradients in the radial direction. It is understood that this result could indicate the possibility of plaque rupture.

Intravascular hemodynamics and coronary artery disease: New insights and clinical implications

Intracoronary hemodynamics play a pivotal role in the initiation and progression of the atherosclerotic process. Low pro-inflammatory endothelial shear stress impacts vascular physiology and leads to the occurrence of coronary artery disease and its implications.

Assessment of endothelial shear stress in patients with mild or intermediate coronary stenoses using coronary computed tomography angiography: comparison with invasive coronary angiography

Characterization of endothelial shear stress (ESS) may allow for prediction of the progression of atherosclerosis. The aim of this investigation was to develop a non-invasive approach for in vivo assessment of ESS by coronary computed tomography angiography (CTA) and to compare it with ESS derived from invasive coronary angiography (ICA). A total of 41 patients with mild or intermediate coronary stenoses who underwent both CTA and ICA were included in the analysis. Two geometrical models of the interrogated vessels were reconstructed separately from CTA and ICA images. Subsequently, computational fluid dynamics were applied to calculate the ESS, from which ESS_CTA and ESS_ICA were derived, respectively. Comparisons between ESS_CTA and ESS_ICA were performed on 163 segments of 57 vessels in the CTA and ICA models. ESS_CTA and ESS_ICA were similar: mean ESS: 4.97 (4.37-5.57) Pascal versus 4.86 (4.27-5.44) Pascal, p = 0.58; minimal ESS: 0.86 (0.67-1.05) Pascal versus 0.79 (0.63-0.95) Pascal, p = 0.37; and maximal ESS: 14.50 (12.62-16.38) Pascal versus 13.76 (11.44-16.08) Pascal, p = 0.44. Good correlations between the ESS_CTA and the ESS_ICA were observed for the mean (r = 0.75, p < 0.001), minimal (r = 0.61, p < 0.001), and maximal (r = 0.62, p < 0.001) ESS values. In conclusion, geometrical reconstruction by CTA yields similar results to ICA in terms of segment-based ESS calculation in patients with low and intermediate stenoses. Thus, it has the potential of allowing combined local hemodynamic and plaque morphologic information for risk stratification in patients with coronary artery disease.

Link between deviations from Murray's Law and occurrence of low wall shear stress regions in the left coronary artery

Murray developed two laws for the geometry of bifurcations in the circulatory system. Based on the principle of energy minimization, Murray found restrictions for the relation between the diameters and also between the angles of the branches. It is known that bifurcations are prone to the development of atherosclerosis, in regions associated to low wall shear stresses (WSS) and high oscillatory shear index (OSI). These indicators (size of low WSS regions, size of high OSI regions and size of high helicity regions) were evaluated in this work. All of them were normalized by the size of the outflow branches. The relation between Murray's laws and the size of low WSS regions was analysed in detail. It was found that the main factor leading to large regions of low WSS is the so called expansion ratio, a relation between the cross section areas of the outflow branches and the cross section area of the main branch. Large regions of low WSS appear for high expansion ratios. Furthermore, the size of low WSS regions is independent of the ratio between the diameters of the outflow branches. Since the expansion ratio in bifurcations following Murray's law is kept in a small range (1 and 1.25), all of them have regions of low WSS with similar size. However, the expansion ratio is not small enough to completely prevent regions with low WSS values and, therefore, Murray's law does not lead to atherosclerosis minimization. A study on the effect of the angulation of the bifurcation suggests that the Murray's law for the angles does not minimize the size of low WSS regions.

Influence of catheter insertion on the hemodynamic environment in coronary arteries

Intravascular stenting is one of the most commonly used treatments to restore the vascular lumen and flow conditions, while perioperative complications such as thrombosis and restenosis are still nagging for patients. As the catheter with crimped stent and folded balloon is directly advanced through coronary artery during surgery, it is destined to cause interference as well as obstructive effect on blood flow. We wonder how the hemodynamic environment would be disturbed and weather these disturbances cause susceptible factors for those complications. Therefore, a realistic three-dimensional model of left coronary artery was reconstructed and blood flow patterns were numerically simulated at seven different stages in the catheter insertion process. The results revealed that the wall shear stress (WSS) and velocity in left anterior descending (LAD) were both significantly increased after catheter inserted into LAD. Besides, the WSS on the catheter, especially at the ending of the catheter, was also at high level. Compared with the condition before catheter inserted, the endothelial cells of LAD was exposed to high-WSS condition and the risk of platelet aggregation in blood flow was increased. These influences may make coronary arteries more vulnerable for perioperative complications.

Numerical analysis of the effect of turbulence transition on the hemodynamic parameters in human coronary arteries

BACKGROUND

Local hemodynamics plays an important role in atherogenesis and the progression of coronary atherosclerosis disease (CAD). The primary biological effect due to blood turbulence is the change in wall shear stress (WSS) on the endothelial cell membrane, while the local oscillatory nature of the blood flow affects the physiological changes in the coronary artery. In coronary arteries, the blood flow Reynolds number ranges from few tens to several hundreds and hence it is generally assumed to be laminar while calculating the WSS calculations. However, the pulsatile blood flow through coronary arteries under stenotic condition could result in transition from laminar to turbulent flow condition.

METHODS

In the present work, the onset of turbulent transition during pulsatile flow through coronary arteries for varying degree of stenosis (i.e., 0%, 30%, 50% and 70%) is quantitatively analyzed by calculating the turbulent parameters distal to the stenosis. Also, the effect of turbulence transition on hemodynamic parameters such as WSS and oscillatory shear index (OSI) for varying degree of stenosis is quantified. The validated transitional shear stress transport (SST) k-ω model used in the present investigation is the best suited Reynolds averaged Navier-Stokes turbulence model to capture the turbulent transition. The arterial wall is assumed to be rigid and the dynamic curvature effect due to myocardial contraction on the blood flow has been neglected.

RESULTS

Our observations shows that for stenosis 50% and above, the WSSavg, WSSmax and OSI calculated using turbulence model deviates from laminar by more than 10% and the flow disturbances seems to significantly increase only after 70% stenosis. Our model shows reliability and completely validated.

CONCLUSIONS

Blood flow through stenosed coronary arteries seems to be turbulent in nature for area stenosis above 70% and the transition to turbulent flow begins from 50% stenosis.

Hemodynamics in stented vertebral artery ostial stenosis based on computational fluid dynamics simulations

Hemodynamic factors may affect the potential occurrence of in-stent restenosis (ISR) after intervention procedure of vertebral artery ostial stenosis (VAOS). The purpose of the present study is to investigate the influence of stent protrusion length in implantation strategy on the local hemodynamics of the VAOS. CTA images of a 58-year-old female patient with posterior circulation transient ischemic attack were used to perform a 3D reconstruction of the vertebral artery. Five models of the vertebral artery before and after the stent implantation were established. Model 1 was without stent implantation, Model 2-5 was with stent protruding into the subclavian artery for 0, 1, 2, 3 mm, respectively. Computational fluid dynamics simulations based on finite element analysis were employed to mimic the blood flow in arteries and to assess hemodynamic conditions, particularly the blood flow velocity and wall shear stress (WSS). The WSS and the blood flow velocity at the vertebral artery ostium were reduced by 85.33 and 35.36% respectively after stents implantation. The phenomenon of helical flow disappeared. Hemodynamics comparison showed that stent struts that protruded 1 mm into the subclavian artery induced the least decrease in blood speed and WSS. The results suggest that stent implantation can improve the hemodynamics of VAOS, while stent struts that had protruded 1 mm into the subclavian artery would result in less thrombogenesis and neointimal hyperplasia and most likely decrease the risk of ISR.

Plaque assessment by coronary CT

Coronary CT angiography (CTA) has emerged as a highly reliable and non-invasive modality for the exclusion of coronary artery disease. Recent technological advancements in coronary CTA imaging allow for robust qualitative and quantitative assessment of atherosclerotic plaques. Furthermore, CTA is a promising modality for functional evaluation of coronary lesions. Individual plaque features, the extent and severity of atherosclerotic plaque burden were proposed to improve cardiovascular risk stratification. It has been suggested that total atherosclerotic plaque burden is a stronger predictor of coronary events than total ischemia burden. The quest to noninvasively detect individual vulnerable plaques still remains. In the current review we sought to summarize state-of-the-art coronary artery plaque assessment by CTA.

Obstructions in Vascular Networks: Relation Between Network Morphology and Blood Supply

We relate vascular network structure to hemodynamics after vessel obstructions. We consider tree-like networks with a viscoelastic fluid with the rheological characteristics of blood. We analyze the network hemodynamic response, which is a function of the frequencies involved in the driving, and a measurement of the resistance to flow. This response function allows the study of the hemodynamics of the system, without the knowledge of a particular pressure gradient. We find analytical expressions for the network response, which explicitly show the roles played by the network structure, the degree of obstruction, and the geometrical place in which obstructions occur. Notably, we find that the sequence of resistances of the network without occlusions strongly determines the tendencies that the response function has with the anatomical place where obstructions are located. We identify anatomical sites in a network that are critical for its overall capacity to supply blood to a tissue after obstructions. We demonstrate that relatively small obstructions in such critical sites are able to cause a much larger decrease on flow than larger obstructions placed in non-critical sites. Our results indicate that, to a large extent, the response of the network is determined locally. That is, it depends on the structure that the vasculature has around the place where occlusions are found. This result is manifest in a network that follows Murray’s law, which is in reasonable agreement with several mammalian vasculatures. For this one, occlusions in early generation vessels have a radically different effect than occlusions in late generation vessels occluding the same percentage of area available to flow. This locality implies that whenever there is a tissue irrigated by a tree-like in vivo vasculature, our model is able to interpret how important obstructions are for the irrigation of such tissue.

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.

Coronary computed tomography angiography based assessment of endothelial shear stress and its association with atherosclerotic plaque distribution in-vivo

Purpose

The relationship between low endothelial shear stress (ESS) and coronary atherosclerosis is well established. ESS assessment so far depended on invasive procedures. The aim of this study was to demonstrate the relationship between ESS and coronary atherosclerosis by using non-invasive coronary computed tomography angiography (CTA) for computational fluid dynamics (CFD) simulations.

Methods

A total number of 7 consecutive patients with suspected coronary artery disease who received CTA and invasive angiography with IVUS analysis were included in this study. CTA examinations were performed using a dual-source scanner. These datasets were used to build a 3D mesh model. CFD calculations were performed using a validated CFD solver. The presence of plaque was assumed if the thickness of the intima-media complex exceeded 0.3 mm in IVUS. Plaque composition was derived by IVUS radiofrequency data analysis.

Results

Plaque was present in 32.1% of all analyzed cross-sections. Plaque prevalence was highest in areas of low ESS (49.6%) and high ESS (34.8%). In parts exposed to intermediate-low and intermediate-high ESS few plaques were found (20.0% and 24.0%) (p<0.001). Wall thickness was closely associated with local ESS. Intima-media thickness was 0.43±0.34mm in low and 0.38±0.32mm in high ESS segments. It was significantly lower when the arterial wall was exposed to intermediate ESS (0.25±0.18mm and 0.28 ± 0.20mm) (p<0.001). Fibrofatty tissue was predominately found in areas exposed to low ESS (p≤0.023).

Conclusions

In this study a close association of atherosclerotic plaque distribution and ESS pattern could be demonstrated in-vivo. Adding CFD analysis to coronary CTA offers the possibility to gather morphologic and physiologic data within one non-invasive examination.

Computational fluid dynamics in coronary artery disease

Computational fluid dynamics (CFD) is a widely used method in mechanical engineering to solve complex problems by analysing fluid flow, heat transfer, and associated phenomena by using computer simulations. In recent years, CFD has been increasingly used in biomedical research of coronary artery disease because of its high performance hardware and software. CFD techniques have been applied to study cardiovascular haemodynamics through simulation tools to predict the behaviour of circulatory blood flow in the human body. CFD simulation based on 3D luminal reconstructions can be used to analyse the local flow fields and flow profiling due to changes of coronary artery geometry, thus, identifying risk factors for development and progression of coronary artery disease. This review aims to provide an overview of the CFD applications in coronary artery disease, including biomechanics of atherosclerotic plaques, plaque progression and rupture; regional haemodynamics relative to plaque location and composition. A critical appraisal is given to a more recently developed application, fractional flow reserve based on CFD computation with regard to its diagnostic accuracy in the detection of haemodynamically significant coronary artery disease.

Perspective on CFD studies of coronary artery disease lesions and hemodynamics: a review

Coronary artery disease (CAD) is the most common cardiovascular disease. Early diagnosis of CAD's physiological significance is of utmost importance for guiding individualized risk-tailored treatment strategies. In this paper, we first review the state-of-the-art clinical diagnostic indices to quantify the severity of CAD and the associated invasive and noninvasive imaging technologies in order to quantify the anatomical parameters of diameter stenosis, area stenosis, and hemodynamic indices of coronary flow reserve and fractional flow reserve. With the development of computational technologies and CFD methods, tremendous progress has been made in applying image-based CFD simulation techniques to elucidate the effects of hemodynamics in vascular pathophysiology toward the initialization and progression of CAD. So then, we review the advancements of CFD technologies in patient-specific modeling, involving the development of geometry reconstruction, boundary conditions, and fluid-structure interaction. Next, we review the applications of CFD to stenotic sites, in order to compute their hemodynamic parameters and study the relationship between the hemodynamic conditions and the clinical indices, to thereby assess the amount of viable myocardium and candidacy for percutaneous coronary intervention. Finally, we review the strengths and limitations of current researches of applying CFD to CAD studies.

Comprehensive plaque assessment by coronary CT angiography

Most acute coronary syndromes are caused by sudden luminal thrombosis due to atherosclerotic plaque rupture or erosion. Preventing such an event seems to be the only effective strategy to reduce mortality and morbidity of coronary heart disease. Coronary lesions prone to rupture have a distinct morphology compared with stable plaques, and provide a unique opportunity for noninvasive imaging to identify vulnerable plaques before they lead to clinical events. The submillimeter spatial resolution and excellent image quality of modern computed tomography (CT) scanners allow coronary atherosclerotic lesions to be detected, characterized, and quantified. Large plaque volume, low CT attenuation, napkin-ring sign, positive remodelling, and spotty calcification are all associated with a high risk of acute cardiovascular events in patients. Computation fluid dynamics allow the calculation of lesion-specific endothelial shear stress and fractional flow reserve, which add functional information to plaque assessment using CT. The combination of morphologic and functional characteristics of coronary plaques might enable noninvasive detection of vulnerable plaques in the future.

Endothelial shear stress in the evolution of coronary atherosclerotic plaque and vascular remodelling: current understanding and remaining questions

The heterogeneity of plaque formation, the vascular remodelling response to plaque formation, and the consequent phenotype of plaque instability attest to the extraordinarily complex pathobiology of plaque development and progression, culminating in different clinical coronary syndromes. Atherosclerotic plaques predominantly form in regions of low endothelial shear stress (ESS), whereas regions of moderate/physiological and high ESS are generally protected. Low ESS-induced compensatory expansive remodelling plays an important role in preserving lumen dimensions during plaque progression, but when the expansive remodelling becomes excessive promotes continued influx of lipids into the vessel wall, vulnerable plaque formation and potential precipitation of an acute coronary syndrome. Advanced plaques which start to encroach into the lumen experience high ESS at their most stenotic region, which appears to promote plaque destabilization. This review describes the role of ESS from early atherogenesis to early plaque formation, plaque progression to advanced high-risk stenotic or non-stenotic plaque, and plaque destabilization. The critical implication of the vascular remodelling response to plaque growth is also discussed. Current developments in technology to characterize local ESS and vascular remodelling in vivo may provide a rationale for innovative diagnostic and therapeutic strategies for coronary patients that aim to prevent clinical coronary syndromes.

CT coronary angiography: 256-slice and 320-detector row scanners

Multidetector computed tomography (MDCT) has rapidly evolved from 4-detector row systems in 1998 to 256-slice and 320-detector row CT systems. With smaller detector element size and faster gantry rotation speed, spatial and temporal resolution of the 64-detector MDCT scanners have made coronary artery imaging a reliable clinical test. Wide-area coverage MDCT, such as the 256-slice and 320-detector row MDCT scanners, has enabled volumetric imaging of the entire heart free of stair-step artifacts at a single time point within one cardiac cycle. It is hoped that these improvements will be realized with greater diagnostic accuracy of CT coronary angiography. Such scanners hold promise in performing a rapid high quality "triple rule-out" test without high contrast load, improved myocardial perfusion imaging, and even four-dimensional CT subtraction angiography. These emerging technical advances and novel applications will continue to change the way we study coronary artery disease beyond detecting luminal stenosis.

A patient-specific method for the evaluation of wall shear stress in human coronary arteries

Atherosclerotic plaques form at specific sites of the arterial tree, an observation that has led to the "geometric risk factor" hypothesis for atherogenesis. It is accepted that the location of atherosclerotic plaques is correlated with sites subjected to low abnormal values of wall shear stress (WSS), which is in turn determined by the specific geometry of the arterial segment. In particular, the left coronary artery (LCA) is one of the most important sites of plaque formation and its progression may lead to stroke. However, little is known about hemodynamics and WSS distributions in the LCA. The purpose of this work is to set up a method to evaluate flow patterns and WSS distributions in the human LCA based on real patient-specific geometries reconstructed from medical images.

3D fusion of intravascular ultrasound and coronary computed tomography for in-vivo wall shear stress analysis: a feasibility study

Wall shear stress, the force per area acting on the lumen wall due to the blood flow, is an important biomechanical parameter in the localization and progression of atherosclerosis. To calculate shear stress and relate it to atherosclerosis, a 3D description of the lumen and vessel wall is required. We present a framework to obtain the 3D reconstruction of human coronary arteries by the fusion of intravascular ultrasound (IVUS) and coronary computed tomography angiography (CT). We imaged 23 patients with IVUS and CT. The images from both modalities were registered for 35 arteries, using bifurcations as landmarks. The IVUS images together with IVUS derived lumen and wall contours were positioned on the 3D centerline, which was derived from CT. The resulting 3D lumen and wall contours were transformed to a surface for calculation of shear stress and plaque thickness. We applied variations in selection of landmarks and investigated whether these variations influenced the relation between shear stress and plaque thickness. Fusion was successfully achieved in 31 of the 35 arteries. The average length of the fused segments was 36.4 ± 15.7 mm. The length in IVUS and CT of the fused parts correlated excellently (R (2) = 0.98). Both for a mildly diseased and a very diseased coronary artery, shear stress was calculated and related to plaque thickness. Variations in the selection of the landmarks for these two arteries did not affect the relationship between shear stress and plaque thickness. This new framework can therefore successfully be applied for shear stress analysis in human coronary arteries.

Visualization of myocardial perfusion derived from coronary anatomy

Visually assessing the effect of the coronary artery anatomy on the perfusion of the heart muscle in patients with coronary artery disease remains a challenging task. We explore the feasibility of visualizing this effect on perfusion using a numerical approach. We perform a computational simulation of the way blood is perfused throughout the myocardium purely based on information from a three-dimensional anatomical tomographic scan. The results are subsequently visualized using both three-dimensional visualizations and bull's eye plots, partially inspired by approaches currently common in medical practice. Our approach results in a comprehensive visualization of the coronary anatomy that compares well to visualizations commonly used for other scanning technologies. We demonstrate techniques giving detailed insight in blood supply, coronary territories and feeding coronary arteries of a selected region. We demonstrate the advantages of our approach through visualizations that show information which commonly cannot be directly observed in scanning data, such as a separate visualization of the supply from each coronary artery. We thus show that the results of a computational simulation can be effectively visualized and facilitate visually correlating these results to for example perfusion data.

Prevalence and morphology of coronary artery ectasia with dual-source CT coronary angiography

To assess the prevalence and morphological characteristics of coronary artery ectasia (CAE) with CT coronary angiography (CTCA) in comparison to conventional catheterangiography (CCA). Dual-source CTCA examinations from 677 consecutive patients (223 women; median age 57 years) were retrospectively evaluated by two blinded observers for the presence of CAE defined as a diameter enlargement > or = 1.5 times the diameter of adjacent normal coronary segments. Vessel diameters and contrast attenuation within and proximal to ectatic segments were measured. CCA was used to compare measurements obtained from CTCA with the coronary flow velocity by using the thrombolysis in myocardial infarction (TIMI) frame count. CTCA identified CAE in 20 of 677 (3%) patients. CCA was performed in ten of these patients. CAE diameter measurements with CTCA (10.0 +/- 5.4 mm) correlated significantly (r = 0.92, p < 0.001) with the CCA measurements (8.8 +/- 4.9 mm), but had higher diameters (levels of agreement: -1.0 to 3.4 mm). Contrast attenuation was significantly lower in the ectatic (343 +/- 63 HU) than in the proximal (394 +/- 60 HU) segments (p < 0.01). The attenuation difference significantly correlated with the CAE ratio (r = 0.67, p < 0.01) and the TIMI frame count (r = 0.58, p < 0.05). The prevalence of CAE in a population examined by CTCA is around 3%. Contrast attenuation measurements with CTCA correlate well with the flow alterations assessed with CCA.

Coronary artery flow measurement using navigator echo gated phase contrast magnetic resonance velocity mapping at 3.0 T

A validation study and early results for non-invasive, in vivo measurement of coronary artery blood flow using phase contrast magnetic resonance imaging (PC-MRI) at 3.0T is presented. Accuracy of coronary artery blood flow measurements by phase contrast MRI is limited by heart and respiratory motion as well as the small size of the coronary arteries. In this study, a navigator echo gated, cine phase velocity mapping technique is described to obtain time-resolved velocity and flow waveforms of small diameter vessels at 3.0T. Phantom experiments using steady, laminar flow are presented to validate the technique and show flow rates measured by 3.0T phase contrast MRI to be accurate within 15% of true flow rates. Subsequently, in vivo scans on healthy volunteers yield velocity measurements for blood flow in the right, left anterior descending, and left circumflex arteries. Measurements of average, cross-sectional velocity were obtainable in 224/243 (92%) of the cardiac phases. Time-averaged, cross-sectional velocity of the blood flow was 6.8+/-4.3cm/s in the LAD, 8.0+/-3.8cm/s in the LCX, and 6.0+/-1.6cm/s in the RCA.