Three-dimensional numerical analysis of pulsatile flow and wall shear stress in the carotid artery bifurcation

Software that combines deep learning, 3D reconstruction and CFD to analyze the state of carotid arteries from ultrasound imaging

BACKGROUND

Ultrasound is one of the non-invasive techniques that are used in clinical diagnostics of carotid artery disease.

OBJECTIVE

This paper presents software methodology that can be used in combination with this imaging technique to provide additional information about the state of patient-specific artery.

METHODS

Overall three modules are combined within the proposed methodology. A clinical dataset is used within the deep learning module to extract the contours of the carotid artery. This data is then used within the second module to perform the three-dimensional reconstruction of the geometry of the carotid bifurcation and ultimately this geometry is used within the third module, where the hemodynamic analysis is performed. The obtained distributions of hemodynamic quantities enable a more detailed analysis of the blood flow and state of the arterial wall and could be useful to predict further progress of present abnormalities in the carotid bifurcation.

RESULTS

The performance of the deep learning module was demonstrated through the high values of relevant common classification metric parameters. Also, the accuracy of the proposed methodology was shown through the validation of results for the reconstructed parameters against the clinically measured values.

CONCLUSION

The presented methodology could be used in combination with standard clinical ultrasound examination to quickly provide additional quantitative and qualitative information about the state of the patient's carotid bifurcation and thus ensure a treatment that is more adapted to the specific patient.

Vortical Structures Promote Atheroprotective Wall Shear Stress Distributions in a Carotid Artery Bifurcation Model

Carotid artery diseases, such as atherosclerosis, are a major cause of death in the United States. Wall shear stresses are known to prompt plaque formation, but there is limited understanding of the complex flow structures underlying these stresses and how they differ in a pre-disposed high-risk patient cohort. A 'healthy' and a novel 'pre-disposed' carotid artery bifurcation model was determined based on patient-averaged clinical data, where the 'pre-disposed' model represents a pathological anatomy. Computational fluid dynamic simulations were performed using a physiological flow based on healthy human subjects. A main hairpin vortical structure in the internal carotid artery sinus was observed, which locally increased instantaneous wall shear stress. In the pre-disposed geometry, this vortical structure starts at an earlier instance in the cardiac flow cycle and persists over a much shorter period, where the second half of the cardiac cycle is dominated by perturbed secondary flow structures and vortices. This coincides with weaker favorable axial pressure gradient peaks over the sinus for the 'pre-disposed' geometry. The findings reveal a strong correlation between vortical structures and wall shear stress and imply that an intact internal carotid artery sinus hairpin vortical structure has a physiologically beneficial role by increasing local wall shear stresses. The deterioration of this beneficial vortical structure is expected to play a significant role in atherosclerotic plaque formation.

Shear stress metrics associated with pro-atherogenic high-risk anatomical features in a carotid artery bifurcation model

BACKGROUND

Diseases associated with atherosclerotic plaques in the carotid artery are a major cause of deaths in the United States. Blood-flow-induced shear-stresses are known to trigger plaque formation. Prior literature suggests that the internal carotid artery sinus is prone to atherosclerosis, but there is limited understanding of why only certain patients are predisposed towards plaque formation.

METHODS

We computationally investigate the effect of vessel geometry on wall-shear-stress distribution by comparing flowfields and wall-shear-stress-metrics between a low-risk and a novel predisposed high-risk carotid artery bifurcation anatomy. Both models were developed based on clinical risk estimations and patient-averaged anatomical features. The high-risk geometry has a larger internal carotid artery branching angle and a lower internal-to-carotid-artery-diameter-ratio. A patient-averaged physiological carotid artery inflow waveform is used.

FINDINGS

The high-risk geometry experiences stronger flow separation in the sinus. Furthermore, it experiences a more equal flow split at the bifurcation, thereby reducing internal carotid artery flowrate and increasing atherosclerosis-prone low-velocity areas. Lowest time-averaged-wall-shear-stresses are present at the sinus outer wall, where plaques are often found, for both geometries. The high-risk geometry has significantly high, unfavorable oscillatory-shear-index values not found in the low-risk geometry. High oscillatory-shear-index areas are located at the vessels outside walls distal to the bifurcation and on the sinus wall.

INTERPRETATION

These results highlight the effectiveness of oscillatory-shear-index, to augment classical time-averaged-wall-shear-stress, in evaluating pro-atherogenic geometry features. Furthermore, the flow split at the bifurcation is a promising clinical indicator for atherosclerosis risk as it can be directly accessed using clinical imaging, whereas shear-stress-metrics cannot.

Simulating Multi-Scale Pulmonary Vascular Function by Coupling Computational Fluid Dynamics With an Anatomic Network Model

The function of the pulmonary circulation is truly multi-scale, with blood transported through vessels from centimeter to micron scale. There are scale-dependent mechanisms that govern the flow in the pulmonary vascular system. However, very few computational models of pulmonary hemodynamics capture the physics of pulmonary perfusion across the spatial scales of functional importance in the lung. Here we present a multi-scale model that incorporates the 3-dimensional (3D) complexities of pulmonary blood flow in the major vessels, coupled to an anatomically-based vascular network model incorporating the multiple contributing factors to capillary perfusion, including gravity. Using the model we demonstrate how we can predict the impact of vascular remodeling and occlusion on both macro-scale functional drivers (flow distribution between lungs, and wall shear stress) and micro-scale contributors to gas exchange. The model predicts interactions between 3D and 1D models that lead to a redistribution of blood between postures, both on a macro- and a micro-scale. This allows us to estimate the effect of posture on left and right pulmonary artery wall shear stress, with predictions varying by 0.75-1.35 dyne/cm² between postures.

Comparative Analysis of Blood-Derived Endothelial Cells for Designing Next-Generation Personalized Organ-on-Chips

Background

Organ‐on‐chip technology has accelerated in vitro preclinical research of the vascular system, and a key strength of this platform is its promise to impact personalized medicine by providing a primary human cell–culture environment where endothelial cells are directly biopsied from individual tissue or differentiated through stem cell biotechniques. However, these methods are difficult to adopt in laboratories, and often result in impurity and heterogeneity of cells. This limits the power of organ‐chips in making accurate physiological predictions. In this study, we report the use of blood‐derived endothelial cells as alternatives to primary and induced pluripotent stem cell–derived endothelial cells.

Methods and Results

Here, the genotype, phenotype, and organ‐chip functional characteristics of blood‐derived outgrowth endothelial cells were compared against commercially available and most used primary endothelial cells and induced pluripotent stem cell–derived endothelial cells. The methods include RNA‐sequencing, as well as criterion standard assays of cell marker expression, growth kinetics, migration potential, and vasculogenesis. Finally, thromboinflammatory responses under shear using vessel‐chips engineered with blood‐derived endothelial cells were assessed. Blood‐derived endothelial cells exhibit the criterion standard hallmarks of typical endothelial cells. There are differences in gene expression profiles between different sources of endothelial cells, but blood‐derived cells are relatively closer to primary cells than induced pluripotent stem cell–derived. Furthermore, blood‐derived endothelial cells are much easier to obtain from individuals and yet, they serve as an equally effective cell source for functional studies and organ‐chips compared with primary cells or induced pluripotent stem cell–derived cells.

Conclusions

Blood‐derived endothelial cells may be used in preclinical research for developing more robust and personalized next‐generation disease models using organ‐on‐chips.

Tripartite collaboration of blood-derived endothelial cells, next generation RNA sequencing and bioengineered vessel-chip may distinguish vasculopathy and thrombosis among sickle cell disease patients

Sickle cell disease (SCD) is the most prevalent inherited blood disorder in the world. But the clinical manifestations of the disease are highly variable. In particular, it is currently difficult to predict the adverse outcomes within patients with SCD, such as, vasculopathy, thrombosis, and stroke. Therefore, for most effective and timely interventions, a predictive analytic strategy is desirable. In this study, we evaluate the endothelial and prothrombotic characteristics of blood outgrowth endothelial cells (BOECs) generated from blood samples of SCD patients with known differences in clinical severity of the disease. We present a method to evaluate patient-specific vaso-occlusive risk by combining novel RNA-seq and organ-on-chip approaches. Through differential gene expression (DGE) and pathway analysis we find that BOECs from SCD patients exhibit an activated state through cell adhesion molecule (CAM) and cytokine signaling pathways among many others. In agreement with clinical symptoms of patients, DGE analyses reveal that patient with severe SCD had a greater extent of endothelial activation compared to patient with milder symptoms. This difference is confirmed by performing qRT-PCR of endothelial adhesion markers like E-selectin, P-selectin, tissue factor, and Von Willebrand factor. Finally, the differential regulation of the proinflammatory phenotype is confirmed through platelet adhesion readouts in our BOEC vessel-chip. Taken together, we hypothesize that these easily blood-derived endothelial cells evaluated through RNA-seq and organ-on-chips may serve as a biotechnique to predict vaso-occlusive episodes in SCD patients and will ultimately allow better therapeutic interventions.

Influence of near-wall PIV data on recirculation hemodynamics in a patient-specific moderate stenosis: Experimental-numerical comparison

BACKGROUND

Recirculation zones within the blood vessels are known to influence the initiation and progression of atherosclerotic lesions. Quantification of recirculation parameters with accuracy remains subjective due to uncertainties in measurement of velocity and derived wall shear stress (WSS).

OBJECTIVE

The primary aim is to determine recirculation height and length from PIV experiments while validating with two different numerical methods: finite-element (FE) and -volume (FV). Secondary aim is to analyze how FE and FV compare within themselves.

METHODS

PIV measurements were performed to obtain velocity profiles at eight cross sections downstream of stenosis at flow rate of 200 ml/min. WSS was obtained by linear/quadratic interpolation of experimental velocity measurements close to wall.

RESULTS

Recirculation length obtained from PIV technique was 1.47 cm and was within 2.2% of previously reported in-vitro measurements. Derived recirculation length from PIV agreed within 6.8% and 8.2% of the FE and FV calculations, respectively. For lower shear rate, linear interpolation with five data points results in least error. For higher shear rate either higher order (quadratic) interpolation with five data points or lower order (linear) with lesser (three) data points leads to better results.

CONCLUSION

Accuracy of the recirculation parameters is dependent on number of near wall PIV data points and the type of interpolation algorithm used.

Effect of sinus size and position on hemodynamics during pulsatile flow in a carotid artery bifurcation

BACKGROUND AND OBJECTIVES

Hemodynamics plays a crucial role in the progression of atherosclerosis and the treatment of arterial diseases. Stroke is one of the arterial diseases and a leading cause of death worldwide. Hemodynamics in the carotid artery plays a vital role in the stroke. The common carotid artery bifurcates into the internal carotid artery and the external carotid artery. Carotid sinus, a slightly dilated area, exists in the internal carotid artery just after the bifurcation and acts as a pressure receptor and regulator. The location and size of the sinus can vary in different people; the change in sinus size and location may affect the hemodynamics. It is necessary to study the shift in hemodynamics due to changes in sinus size and position on atherosclerosis. The change in flow behavior may suggest the probable sites of backflow and low wall shear stress, and therefore the sites prone to atherosclerosis.

METHODS

The model of the carotid artery has been constructed using patient data. Transient computational fluid dynamics simulations have been performed using a finite volume method for the numerical solution in a three-dimensional computational domain using ANSYS Fluent 19.2. Pulsatile flow is specified at the inlet boundary. The coupled scheme is used for the pressure-velocity coupling. The second-order discretization scheme is used for pressure interpolation and second-order upwind scheme is used for the discretisation of momentum equation. The temporal term is discretized using the first-order implicit scheme.

RESULTS

The effect of sinus size and location on the overall flow behavior, wall shear stress, and secondary flow are presented. Results show that the outer wall of bifurcation has low wall shear stress and bigger recirculation as compared with that on the inner wall of bifurcation. Numerical results obtained for varying sinus size and position are shown in graphs and contours, including wall shear stress, secondary flow, and velocity streamlines.

CONCLUSION

Numerical results reveal that sinus away from bifurcation, and larger diameter sinus has more recirculation and low wall shear stress. Therefore, the person having sinus away from bifurcation and larger sinus diameter are more susceptible to plaque formation.

CardioFAN: open source platform for noninvasive assessment of pulse transit time and pulsatile flow in hyperelastic vascular networks

A profound analysis of pressure and flow wave propagation in cardiovascular systems is the key in noninvasive assessment of hemodynamic parameters. Pulse transit time (PTT), which closely relates to the physical properties of the cardiovascular system, can be linked to variations of blood pressure and stroke volume to provide information for patient-specific clinical diagnostics. In this work, we present mathematical and numerical tools, capable of accurately predicting the PTT, local pulse wave velocity, vessel compliance, and pressure/flow waveforms, in a viscous hyperelastic cardiovascular network. A new one-dimensional framework, entitled cardiovascular flow analysis (CardioFAN), is presented to describe the pulsatile fluid-structure interaction in the hyperelastic arteries, where pertaining hyperbolic equations are solved using a high-resolution total variation diminishing Lax-Wendroff method. The computational algorithm is validated against well-known numerical, in vitro and in vivo data for networks of main human arteries with 55, 37 and 26 segments, respectively. PTT prediction is improved by accounting for hyperelastic nonlinear waves between two arbitrary sections of the arterial tree. Consequently, arterial compliance assignments at each segment are improved in a personalized model of the human aorta and supra-aortic branches with 26 segments, where prior in vivo data were available for comparison. This resulted in a 1.5% improvement in overall predictions of the waveforms, or average relative errors of 5.5% in predicting flow, luminal area and pressure waveforms compared to prior in vivo measurements. The open source software, CardioFAN, can be calibrated for arbitrary patient-specific vascular networks to conduct noninvasive diagnostics.

Influence of microvascular sutures on shear strain rate in realistic pulsatile flow

Arterial thrombus formation is directly related to the mechanical shear experienced by platelets within flow. High shear strain rates (SSRs) and large shear gradients cause platelet activation, aggregation and production of thrombus. This study, for the first time, investigates the influence of pulsatile flow on local haemodynamics within sutured microarterial anastomoses. We measured physiological arterial waveform velocities experimentally using Doppler ultrasound velocimetry, and a representative example was applied to a realistic sutured microarterial geometry. Computational geometries were created using measurements taken from sutured chicken femoral arteries. Arterial SSRs were predicted using computational fluid dynamics (CFD) software, to indicate the potential for platelet activation, deposition and thrombus formation. Predictions of steady and sinusoidal inputs were compared to analyse whether the addition of physiological pulse characteristics affects local intravascular flow characteristics. Simulations were designed to evaluate flow in pristine and hand-sutured microarterial anastomoses, each with a steady-state and sinusoidal pulse component. The presence of sutures increased SSR_max in the anastomotic region by factors of 2.1 and 2.3 in steady-state and pulsatile flows respectively, when compared to a pristine vessel. SSR values seen in these simulations are analogous to the presence of moderate arterial stenosis. Steady-state simulations, driven by a constant inflow velocity equal to the peak systolic velocity (PSV) of the measured pulsatile flow, underestimated SSRs by ∼ 9% in pristine, and ∼ 19% in sutured vessels compared with a realistic pulse. Sinusoidal flows, with equivalent frequency and amplitude to a measured arterial waveform, represent a slight improvement on steady-state simulations, but still SSRs are underestimated by 1-2%. We recommend using a measured arterial waveform, of the form presented here, for simulating pulsatile flows in vessels of this nature. Under realistic pulsatile flow, shear gradients across microvascular sutures are high, of the order ∼ 7.9 × 10⁶ m^-1 s^-1, which may also be associated with activation of platelets and formation of aggregates.

Fluid-structure interaction modeling of aneurysmal arteries under steady-state and pulsatile blood flow: a stability analysis

Tortuous aneurysmal arteries are often associated with a higher risk of rupture but the mechanism remains unclear. The goal of this study was to analyze the buckling and post-buckling behaviors of aneurysmal arteries under pulsatile flow. To accomplish this goal, we analyzed the buckling behavior of model carotid and abdominal aorta with aneurysms by utilizing fluid-structure interaction (FSI) method with realistic waveforms boundary conditions. FSI simulations were done under steady-state and pulsatile flow for normal (1.5) and reduced (1.3) axial stretch ratios to investigate the influence of aneurysm, pulsatile lumen pressure and axial tension on stability. Our results indicated that aneurysmal artery buckled at the critical buckling pressure and its deflection nonlinearly increased with increasing lumen pressure. Buckling elevates the peak stress (up to 118%). The maximum aneurysm wall stress at pulsatile FSI flow was (29%) higher than under static pressure at the peak lumen pressure of 130 mmHg. Buckling results show an increase in lumen shear stress at the inner side of the maximum deflection. Vortex flow was dramatically enlarged with increasing lumen pressure and artery diameter. Aneurysmal arteries are more susceptible than normal arteries to mechanical instability which causes high stresses in the aneurysm wall that could lead to aneurysm rupture.

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.

WALL SHEAR STRESS AND OSCILLATORY SHEAR INDEX DISTRIBUTION IN CAROTID ARTERY WITH VARYING DEGREE OF STENOSIS: A HEMODYNAMIC STUDY

A significant proportion of cerebral stroke is a consequence of the arterial stenotic plaque rupture causing local thrombosis or distal embolization. The formation and subsequent rupture of the plaque depends on wall shear stress (WSS) and oscillatory shear index (OSI). The purpose of the present study was to understand the effect of hemodynamics on the spatial and temporal variations of WSS and OSI using realistic models with varying degree of carotid artery stenosis (DOS). Multiple CT volumes were obtained from subjects in the carotid bifurcation zone and the 3D models were generated. A finite volume-based computational fluid dynamics (CFD) method was utilized to understand the hemodynamics in pulsatile flow conditions. It was observed that high stenosis models occupied a large value of normalized WSS in the internal carotid artery (ICA) whereas they had smaller values of normalized WSS in the common carotid artery (CCA). For clinical use, the authors recommend using the spatial average value of oscillatory shear rather than the maximum value for an accurate knowledge about the severity of stenosis. The resultant vorticity changes the direction of spin after the bifurcation zone. Additionally, we propose the use of limiting streamlines as a novel and convenient method to identify the disturbed flow regions that are prone to atherogenesis.

Machine Learning Approach for Predicting Wall Shear Distribution for Abdominal Aortic Aneurysm and Carotid Bifurcation Models

Computer simulations based on the finite element method represent powerful tools for modeling blood flow through arteries. However, due to its computational complexity, this approach may be inappropriate when results are needed quickly. In order to reduce computational time, in this paper, we proposed an alternative machine learning based approach for calculation of wall shear stress (WSS) distribution, which may play an important role in mechanisms related to initiation and development of atherosclerosis. In order to capture relationships between geometric parameters, blood density, dynamic viscosity and velocity, and WSS distribution of geometrically parameterized abdominal aortic aneurysm (AAA) and carotid bifurcation models, we proposed multivariate linear regression, multilayer perceptron neural network and Gaussian conditional random fields (GCRF). Results obtained in this paper show that machine learning approaches can successfully predict WSS distribution at different cardiac cycle time points. Even though all proposed methods showed high potential for WSS prediction, GCRF achieved the highest coefficient of determination (0.930-0.948 for AAA model and 0.946-0.954 for carotid bifurcation model) demonstrating benefits of accounting for spatial correlation. The proposed approach can be used as an alternative method for real time calculation of WSS distribution.

Studies of Blood Flow in Arterial Bifurcations Using Computational Fluid Dynamics

The local blood flow in arteries, especially at bends and bifurcations, is correlated with the distribution of atherosclerotic lesions. The flow is three-dimensional, unsteady and difficult to measure in vivo. In this paper a numerical treatment of blood flow in general three-dimensional arterial bifurcations is presented. The flow is assumed to be laminar and incompressible, the blood non-Newtonian and the vessel wall rigid. The three-dimensional time-dependent Navier-Stokes equations are employed to describe the flow, and a newly developed computational fluid dynamics (CFD) code AST EC based on finite volume methods is used to solve the equations. A comprehensive range of code validations has been carried out. Good agreement between numerical predictions and in vitro model data is demonstrated, but the correlation with in vivo measurements is less satisfactory. Effects of the non-Newtonian viscosity have also been investigated. It is demonstrated that differences between Newtonian and non-Newtonian flows occur mainly in regions of flow separation. With the non-Newtonian fluid, the duration of flow separation is shorter and the reverse flow is weaker. Nevertheless, it does not have significant effects on the basic features of the flow field. As for the magnitude of wall shear stress, the effect of non-Newtonian viscosity might not be negligible.

Fractional flow reserve based on computed tomography: an overview

Computed tomography coronary angiography (CTCA) is a technique proved to provide high sensitivity and negative predictive value for the identification of anatomically significant coronary artery disease (CAD) when compared with invasive X-ray coronary angiography. While the CTCA limitation of a ionizing radiation dose delivered to patients is substantially overcome by recent technical innovations, a relevant limitation remains the only anatomical assessment of coronary stenoses in the absence of evaluation of their functional haemodynamic significance. This limitation is highly important for those stenosis graded as intermediate at the anatomical assessment. Recently, non-invasive methods based on computational fluid dynamics were developed to calculate vessel-specific fractional flow reserve (FFR) using data routinely acquired by CTCA [computed tomographic fractional flow reserve (CT-FFR)]. Here we summarize methods for CT-FFR and review the evidence available in the literature up to June 26, 2016, including 16 original articles and one meta-analysis. The perspective of CT-FFR may greatly impact on CAD diagnosis, prognostic evaluation, and treatment decision-making. The aim of this review is to describe technical characteristics and clinical applications of CT-FFR, also in comparison with catheter-based invasive FFR, in order to make a cost-benefit balance in terms of clinical management and patient's health.

Three-dimensional modeling and numerical analysis of fractional flow reserve in human coronary arteries

Introduction

Noninvasive fractional flow reserve (FFR) computed from CT (FFR_CT) is a novel method for determining the physiologic significance of coronary artery disease (CAD). Several clinical trials have been conducted, but its diagnostic performance varied among different trials.

Aim

To determine the cut-off value of FFR_CT and its correlation with the gold standard used to diagnose CAD in clinical practice.

Material and methods

Forty patients with single vessel disease were included in our study. Computed tomography scan and coronary angiography with FFR were conducted for these patients. Three-dimensional geometric reconstruction and numerical analysis based on the computed tomographic angiogram (CTA) of coronary arteries were applied to obtain the values of FFR_CT. The correlation between FFR_CT and the gold standard used in clinical practice was tested.

Results

For FFR_CT, the best cut-off value was 0.76, with the sensitivity, specificity, positive predictive value and negative predictive values of 84.6%, 92.9%, 88% and 73.3%, respectively. The area under the receiver-operator characteristics curve was 0.945 (p < 0.0001). There was a good correlation of FFR_CT values with FFR values (r = 0.94, p < 0.0001), with a slight overestimation of FFR_CT as compared with measured FFR (mean difference 0.01 ±0.11, p < 0.05). For inter-observer agreement, the mean κ value was 0.69 (0.61 to 0.78) and for intra-observer agreement the mean κ value was 0.61 (0.50 to 0.72).

Conclusions

FFR_CT derived from CT of the coronary artery is a reliable non-invasive way providing reliable functional information of coronary artery stenosis.

COMPUTATIONAL MODEL OF PLATELET FLOW IN CAROTID ARTERY BIFURCATION

Atherosclerotic plaque tends to occur and develop in carotid artery sinus, where stenoses and other lesions can cause cerebral disturbances. The hemodynamics and the platelet profiles in the carotid artery are simultaneously simulated in the present study to reveal the mechanism of the atherosclerotic plaque formation. Firstly, an unsteady PISO solver on unstructured tetrahedral grids is developed to simulate the hemodynamics of carotid artery bifurcation. And small platelets are treated as spherical solid particle described by Newtonian motion equation in the simulation, including inertial force, drag force, shear lift force, virtual mass force and pressure gradient force. Secondly, the visualization experiment for the platelet flow in the straight micro-channel is setup to validate the numerical model. Using the present method, the platelet flow in a carotid artery bifurcation is analyzed. The results show that the outer vascular wall near the bifurcation is more vulnerable in carotid artery sinus, which is mainly due to the lower wall shear stress (WSS) and platelets backflow in the region.

Numerical study of purely viscous non-Newtonian flow in an abdominal aortic aneurysm

It is well known that blood has non-Newtonian properties, but it is generally accepted that blood behaves as a Newtonian fluid at shear rates above 100 s-1. However, in transient conditions, there are times and locations where the shear rate is well below 100 s-1, and it is reasonable to infer that non-Newtonian effects could become important. In this study, purely viscous non-Newtonian (generalized Newtonian) properties of blood are incorporated into the simulation-based framework for cardiovascular surgery planning developed by Taylor et al. (1999, "Predictive Medicine: Computational Techniques in Therapeutic Decision Making," Comput. Aided Surg., 4, pp. 231-247; 1998, "Finite Element Modeling of Blood Flow in Arteries," Comput. Methods Appl. Mech. Eng., 158, pp. 155-196). Equations describing blood flow are solved in a patient-based abdominal aortic aneurysm model under steady and physiological flow conditions. Direct numerical simulation (DNS) is used, and the complex flow is found to be constantly transitioning between laminar and turbulent in both the spatial and temporal sense. It is found for the case simulated that using the non-Newtonian viscosity modifies the solution in subtle ways that yield a mesh-independent solution with fewer degrees of freedom than the Newtonian counterpart. It appears that in regions of separated flow, the lower shear rate produces higher viscosity with the non-Newtonian model, which reduces the associated resolution needs. When considering the real case of pulsatile flow, high shear layers lead to greater unsteadiness in the Newtonian case relative to the non-Newtonian case. This, in turn, results in a tendency for the non-Newtonian model to need fewer computational resources even though it has to perform additional calculations for the viscosity. It is also shown that both viscosity models predict comparable wall shear stress distribution. This work suggests that the use of a non-Newtonian viscosity models may be attractive to solve cardiovascular flows since it can provide simulation results that are presumably physically more realistic with at least comparable computational effort for a given level of accuracy.

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.

Noninvasive fractional flow reserve derived from coronary computed tomography angiography: integrated anatomical and functional assessment

Coronary computed tomographic angiography (CCTA) provides anatomic detail of lumen stenosis and information on plaque burden, plaque extent and plaque characteristics. CCTA does not, however, provide insight into the hemodynamic significance of a stenosis, which is essential to allow appropriate revascularization decision-making. This could reduce downstream invasive coronary angiography and nonbeneficial coronary revascularization, particularly with intermediate coronary stenosis. Invasive fractional flow reserve (FFR) is the gold standard for the determination of lesion-specific ischemia and the need for revascularization. Advances in computational technology now permit calculation of FFR using resting CCTA image data, without the need for additional radiation or medication. Early data demonstrate improved accuracy and a discriminatory ability of FFR computed tomography to identify ischemia-producing lesions compared with CCTA alone. This new, combined anatomic-functional assessment has the potential to simplify the noninvasive diagnosis of coronary artery disease with a single study to identify patients with ischemia-causing stenosis who may benefit from revascularization.

A framework for the co-registration of hemodynamic forces and atherosclerotic plaque components

Local hemodynamic forces, such as wall shear stress (WSS), are thought to trigger cellular and molecular mechanisms that determine atherosclerotic plaque vulnerability to rupture. Magnetic resonance imaging has emerged as a powerful tool to characterize human carotid atherosclerotic plaque composition and morphology, and to identify plaque features shown to be key determinants of plaque vulnerability. Image-based computational fluid dynamics has allowed researchers to obtain time-resolved WSS information of atherosclerotic carotid arteries. A deeper understanding of the mechanisms of initiation and progression of atherosclerosis can be obtained through the comparison of WSS and plaque composition and morphology. To date, however, advance in knowledge has been limited greatly due to the lack of a reliable infrastructure to perform such analysis. The aim of this study is to establish a framework that will allow for the co-registration and analysis of the three-dimensional distribution of WSS and plaque components and morphology. The use of this framework will lead to future studies targeted to determining the role of WSS in atherosclerotic plaque progression and vulnerability.

Computed fractional flow reserve (FFTCT) derived from coronary CT angiography

Recent advances in image-based modeling and computational fluid dynamics permit the calculation of coronary artery pressure and flow from typically acquired coronary computed tomography (CT) scans. Computed fractional flow reserve is the ratio of mean coronary artery pressure divided by mean aortic pressure under conditions of simulated maximal coronary hyperemia, thus providing a noninvasive estimate of fractional flow reserve (FFRCT) at every point in the coronary tree. Prospective multicenter clinical trials have shown that computed FFRCT improves diagnostic accuracy and discrimination compared to CT stenosis alone for the diagnosis of hemodynamically significant coronary artery disease (CAD), when compared to invasive FFR as the reference gold standard. This promising new technology provides a combined anatomic and physiologic assessment of CAD in a single noninvasive test that can help select patients for invasive angiography and revascularization or best medical therapy. Further evaluation of the clinical effectiveness and economic implications of noninvasive FFRCT are now being explored.

A novel carotid covered stent design: in vitro evaluation of performance and influence on the blood flow regime at the carotid artery bifurcation

In the present study, a novel carotid covered stent design has been developed. Prototypes of different geometrical design parameters have been fabricated and their performance has been evaluated in vitro under physiological pulsatile flow condition, utilizing flow visualization (dye injection), and particle image velocimetry techniques. These evaluations include the assessment of emboli prevention capability, side-branch flow preservation, and influence on the branch flow pattern and velocity field. The novel covered stents demonstrated significantly higher emboli prevention capability than the corresponding bare metal stent, while preserving more than 83% of the original flow of the external carotid artery (ECA). Flow in the ECA through these covered stents was uniform without evidence of undesirable flow recirculation and reversed flow that might predispose the vessel wall to post-stenting intimal thickening and atherosclerotic plaque formation. This study demonstrated the potential of these novel covered stent designs for the treatment of carotid atherosclerotic stenosis. However, further computational and in vivo investigations of hemodynamics, biological effects, and mechanical performance of this covered stent design is warranted.

Modeling of fractional flow reserve based on coronary CT angiography

Fractional flow reserve (FFR) at the time of invasive coronary angiography is the current gold standard for determination of ischemia. Coronary CT angiography (coronary CTA) has emerged as an effective noninvasive method for direct visualization of coronary artery disease. However, severe stenosis by coronary CTA are only modestly predictive of ischemia. Recent technological innovations enable non-invasive calculation of FFR from CT. FFRCT is superior to anatomic assessment of stenoses in coronary CTA for the diagnosis of ischemia-causing lesions on both a per-patient and a per-vessel basis. FFRCT improves the diagnostic accuracy mostly by reducing the false positive rate of stenosis assessment alone. Furthermore, in patients where CT demonstrates an intermediate stenosis, FFRCT demonstrates significantly higher diagnostic performance than anatomic assessment alone.

In vitro and in vivo investigations on the effects of low-density lipoprotein concentration polarization and haemodynamics on atherosclerotic localization in rabbit and zebrafish

Atherosclerosis (AS) commonly occurs in the regions of the arterial tree with haemodynamic peculiarities, including local flow field disturbances, and formation of swirling flow and vortices. The aim of our study was to confirm low-density lipoprotein (LDL) concentration polarization in the vascular system in vitro and in vivo, and investigate the effects of LDL concentration polarization and flow field alterations on atherosclerotic localization. Red fluorescent LDL was injected into optically transparent Flk1: GFP zebrafish embryos, and the LDL distribution in the vascular lumen was investigated in vivo using laser scanning confocal microscopy. LDL concentration at the vascular luminal surface was found to be higher than that in the bulk. The flow field conditions in blood vessel segments were simulated and measured, and obvious flow field disturbances were found in the regions of vascular geometry change. The LDL concentration at the luminal surface of bifurcation was significantly higher than that in the straight segment, possibly owing to the atherogenic effect of disturbed flow. Additionally, a stenosis model of rabbit carotid arteries was generated. Atherosclerotic plaques were found to have occurred in the stenosis group and were more severe in the stenosis group on a high-fat diet. Our findings provide the first ever definite proof that LDL concentration polarization occurs in the vascular system in vivo. Both lipoprotein concentration polarization and flow field changes are involved in the infiltration/accumulation of atherogenic lipids within the location of arterial luminal surface and promote the development of AS.

Effect of head posture on the healthy human carotid bifurcation hemodynamics

Head and neck postures may cause morphology changes to the geometry of the carotid bifurcation (CB) that alter the low and oscillating wall shear stress (WSS) regions previously reported as important in the development of atherosclerosis. Here the right and left CB were imaged by MRI in two healthy subjects in the neutral head posture with the subject in the supine position and in two other head postures with the subject in the prone position: (1) rightward rotation up to 80°, and (2) leftward rotation up to 80°. Image-based computational models were constructed to investigate the effect of posture on arterial geometry and local hemodynamics. The area exposure to unfavorable hemodynamics, based on thresholds set for oscillatory shear index (OSI), WSS and relative residence time, was used to quantify the hemodynamic impact on the wall. Torsion of the head was found to: (1) cause notable changes in the bifurcation and internal carotid artery angles and, in most cases, on cross-sectional area ratios for common, internal and external carotid artery, (2) change the spatial distribution of wall regions exposed to unfavorable hemodynamics, and (3) cause a marked change in the hemodynamic burden on the wall when the OSI was considered. These findings suggest that head posture may be associated with the genesis and development of atherosclerotic disease as well as complications in stenotic and stented vessels.

Hemodynamics of ulcerated plaques: before and after

The hemodynamics and fluid mechanical forces in blood vessels have long been implicated in the deposition and growth of atherosclerotic plaque. Detailed information about the hemodynamics in vessels affected by significant plaque deposits can also provide insight into the mechanisms and likelihood of plaque weakening and rupture. In the current study, the governing equations are solved in their finite volume formulation in several patient-specific stenotic geometries. Of specific interest are the flow patterns and forces near ulcerations in the plaque. The flow patterns and forces in vessels with ulcerated plaques are compared with those in stenotic vessels without evidence of ulceration and to the hemodynamics in the same vessels as they likely appeared prior to ulceration. Hemodynamics "before" and "after" hemorrhage may suggest fluid mechanical and morphological factors of diagnostic and predictive value. Recirculation zones, vortex shedding, and secondary flows are captured by both laminar and turbulent solutions. The forces on vessel walls are shown to correlate with unstable plaque deposits. Performing before and after studies of vessels in long-term radiology studies may illuminate mechanisms of hemorrhage and other vessel remodeling.

Computer simulation of vertebral artery occlusion in endovascular procedures

OBJECTIVE

The aim of this work is to establish a computational pipeline for the simulation of blood flow in vasculatures and apply this pipeline to endovascular interventional scenarios, e.g. angioplasty in vertebral arteries.

METHODS

A patient-specific supra-aortal vasculature is digitized from a 3D CT angiography image. By coupling a reduced formulation of the governing Navier-Stokes equations with a wall constitutive equation we are able to solve the transient flow in elastic vessels. By further incorporating a bifurcation model the blood flow across vascular branches can be evaluated, thus flow in a large vasculature can be modeled. Vascular diseases are simulated by modifying the arterial tree configurations, e.g. the effective diameters, schematic connectivity, etc. Occlusion in an artery is simulated by removing that artery from the arterial tree.

RESULTS

It takes about 2 min per cardiac cycle to compute blood flow in an arterial tree consisting of 38 vessels and 18 bifurcations on a laptop PC. The simulation results show that blood supply in the posterior region is compensated from the contralateral vertebral artery and the anterior cerebral arteries if one of the vertebral arteries is occluded.

CONCLUSION

The computational pipeline is computationally efficient and can capture main flow patterns at any point in the arterial tree. With further improvement it can serve as a powerful tool for the haemodynamic analysis in patient-specific vascular structures.

[Association of blood pressure levels with carotid intima-media thickness and plaques]

OBJECTIVES

The aim of this study was to investigate the association of blood pressure levels with the common carotid artery intima-media thickness (CCA-IMT) and carotid plaques.

METHODS

Data were obtained from 2,635 subjects, aged 50 years and over, who participated in the Community Health Survey (a population-based, cross-sectional study) in Dong-gu, Gwangju city between 2007 and 2008. Participants were categorized into three groups according to blood pressure levels; normotensives (<120/80 mmHg), prehypertensives (120-139/80-89 mmHg), and hypertensives (> or =140/90 mmHg). Prehypertensives were further categorized as low prehypertensives (120-129/80-84 mmHg) and high prehypertensives (130-139/85-89 mmHg). Carotid intima-media thickness and plaques were evaluated with a high-resolution B-mode ultrasound. Statistical analyses were performed using chi-square test, ANOVA, and multiple logistic regression.

RESULTS

Prehypertensives had significantly greater maximal CCA-IMT values than normotensives, with a multivariate adjusted odds ratio of 1.78 (95% CI=1.36-2.32) for abnormal CCA-IMT (maximal CCA-IMT > or =1.0 mm), and 1.45 (95% CI=1.19-1.77) for carotid plaques. The multivariate adjusted odds ratio of low prehypertensives was 1.64 (95% CI=1.21-2.21) for abnormal CCA-IMT, and 1.30 (95% CI=1.04-1.63) for carotid plaques compared with normotensives. Subject with hypertension had higher frequency of abnormal CCA-IMT (odds ratio, 2.18; 95% CI=1.49-3.18), and carotid plaques (odds ratio, 1.98; 95% CI=1.46-2.67) compared with normotensives after adjustment for other cardiovascular risk factors.

CONCLUSIONS

Our results indicate that there is a significant increase in the prevalence of carotid atherosclerosis in subjects with prehypertension (even in low prehypertensives) compared with normotensive subjects. Further studies are required to confirm the benefits and role of carotid ultrasonography in persons with prehypertension.

Open Problems in Computational Vascular Biomechanics: Hemodynamics and Arterial Wall Mechanics

The vasculature consists of a complex network of vessels ranging from large arteries to arterioles, capillaries, venules, and veins. This network is vital for the supply of oxygen and nutrients to tissues and the removal of carbon dioxide and waste products from tissues. Because of its primary role as a pressure-driven chemomechanical transport system, it should not be surprising that mechanics plays a vital role in the development and maintenance of the normal vasculature as well as in the progression and treatment of vascular disease. This review highlights some past successes of vascular biomechanics, but emphasizes the need for research that synthesizes complementary advances in molecular biology, biomechanics, medical imaging, computational methods, and computing power for purposes of increasing our understanding of vascular physiology and pathophysiology as well as improving the design of medical devices and clinical interventions, including surgical procedures. That is, computational mechanics has great promise to contribute to the continued improvement of vascular health.

Optimization of intravascular shear stress assessment in vivo

The advent of microelectromechanical systems (MEMS) sensors has enabled real-time wall shear stress (WSS) measurements with high spatial and temporal resolution in a 3-D bifurcation model. To optimize intravascular shear stress assessment, we evaluated the feasibility of catheter/coaxial wire-based MEMS sensors in the abdominal aorta of the New Zealand white (NZW) rabbits. Theoretical and computational fluid dynamics (CFD) analyses were performed. Fluoroscope and angiogram provided the geometry of aorta, and the Doppler ultrasound system provided the pulsatile flow velocity for the boundary conditions. The physical parameters governing the shear stress assessment in NZW rabbits included (1) the position and distance from which the MEMS sensors were mounted to the terminal end of coaxial wire or the entrance length, (L(e)), (2) diameter ratios of aorta to the coaxial wire (D(aorta) /D(coaxial wire)=1.5-9.5), and (3) the range of Reynolds numbers (116-1550). At an aortic diameter of 2.4mm and a maximum Reynolds number of 212 (a mean Reynolds number of 64.2), the time-averaged shear stress (tau(ave)) was computed to be 10.06 dyn cm(-2) with a systolic peak at 33.18 dyn cm(-2). In the presence of a coaxial wire (D(aorta)/D(coaxial wire)=6 and L(e)=1.18 cm), the tau(ave) value increased to 15.54 dyn cm(-2) with a systolic peak at 51.25 dyn cm(-2). Real-time intravascular shear stress assessment by the MEMS sensor revealed an tau(ave) value of 11.92 dyn cm(-2) with a systolic peak at 47.04 dyn cm(-2). The difference between CFD and experimental tau(ave) was 18.5%. These findings provided important insights into packaging the MEMS sensors to optimize in vivo shear stress assessment.

Effects of vessel compliance on flow pattern in porcine epicardial right coronary arterial tree

The compliance of the vessel wall affects hemodynamic parameters which may alter the permeability of the vessel wall. Based on experimental measurements, the present study established a finite element (FE) model in the proximal elastic vessel segments of epicardial right coronary arterial (RCA) tree obtained from computed tomography. The motion of elastic vessel wall was measured by an impedance catheter and the inlet boundary condition was measured by an ultrasound flow probe. The Galerkin FE method was used to solve the Navier-Stokes and Continuity equations, where the convective term in the Navier-Stokes equation was changed in the arbitrary Lagrangian-Eulerian (ALE) framework to incorporate the motion due to vessel compliance. Various hemodynamic parameters (e.g., wall shear stress-WSS, WSS spatial gradient-WSSG, oscillatory shear index-OSI) were analyzed in the model. The motion due to vessel compliance affects the time-averaged WSSG more strongly than WSS at bifurcations. The decrease of WSSG at flow divider in elastic bifurcations, as compared to rigid bifurcations, implies that the vessel compliance decreases the permeability of vessel wall and may be atheroprotective. The model can be used to predict coronary flow pattern in subject-specific anatomy as determined by noninvasive imaging.