Flow disturbance measurements through a constricted tube at moderate Reynolds numbers

A continuum model for the elongation and orientation of Von Willebrand factor with applications in arterial flow

The blood protein Von Willebrand factor (VWF) is critical in facilitating arterial thrombosis. At pathologically high shear rates, the protein unfolds and binds to the arterial wall, enabling the rapid deposition of platelets from the blood. We present a novel continuum model for VWF dynamics in flow based on a modified viscoelastic fluid model that incorporates a single constitutive relation to describe the propensity of VWF to unfold as a function of the scalar shear rate. Using experimental data of VWF unfolding in pure shear flow, we fix the parameters for VWF's unfolding propensity and the maximum VWF length, so that the protein is half unfolded at a shear rate of approximately 5000 s - 1 . We then use the theoretical model to predict VWF's behaviour in two complex flows where experimental data are challenging to obtain: pure elongational flow and stenotic arterial flow. In pure elongational flow, our model predicts that VWF is 50% unfolded at approximately 2000 s - 1 , matching the established hypothesis that VWF unfolds at lower shear rates in elongational flow than in shear flow. We demonstrate the sensitivity of this elongational flow prediction to the value of maximum VWF length used in the model, which varies significantly across experimental studies, predicting that VWF can unfold between 2000 and 3200 s - 1 depending on the selected value. Finally, we examine VWF dynamics in a range of idealised arterial stenoses, predicting the relative extension of VWF in elongational flow structures in the centre of the artery compared to high shear regions near the arterial walls.

The pulsatile 3D-Hemodynamics in a doubly afflicted human descending abdominal artery with iliac branching

The study of patient-specific human arterial flow dynamics is well known to face challenges like a) apt geometric modelling, b) bifurcation zone meshing, and c) capturing the hemodynamic prone to variations with multiple disease complications. Due to aneurysms and stenosis in the same arterial network, the blood flow dynamics get affected, which needs to be explored. This study develops a new protocol for accurate geometric modelling, bifurcation zone meshing and numerically investigates the arterial network with abdominal aortic aneurysms (AAA) and right internal iliac stenosis (RIIAS). A realistic arterial model is reconstructed from the computed tomography (CT) data of a human subject. To understand the combined effect of the aneurysm and aortoiliac occlusive diseases in a patient, an arterial network with AAA, RIIAS, multiple branches tapering, and curvature has been considered. Clinically significant pulsatile blood flow simulations have been carried out to trace the alteration in the flow dynamics with multiple pathological complications under consideration. The transient blood flow dynamics are investigated via wall shear stress, wall pressure, velocity contour, streamlines, vorticity, and swirling strength. During the systolic deceleration phase, the rhythmic nested rapid secondary oscillatory WSS, adverse pressure gradients, high WSS, and high WP bands are noticed. Also, the above studies will help researchers, clinicians, and doctors understand the influence of morphological changes on hemodynamics in cardiovascular studies.

Investigation of Artery Wall Elasticity Effect on the Prediction of Atherosclerosis by Hemodynamic Factors

Atherosclerosis is a vascular disease in which some parts of the artery undergo stenosis due to the aggregation of fat. The causes and location of stenosis can be determined using fluid mechanics and parameters such as pressure, effective wall shear stress, and oscillatory shear index (OSI). The present study, for the first time, numerically investigates the pulsatile blood flow inside arteries with elastic and rigid walls in simple and double stenosis (80% stenosis) by using $k$ -ω model and physiological pulse. The reason for applying the $k$ -ω model in the present study was to provide more consistent results with clinical results to improve the accuracy in estimating atherosclerosis disease. The investigation of the time-mean wall shear stress indicated that for double stenosis, the difference between the results of the rigid and elastic artery assumptions is greater than the case of simple stenosis, so that this difference percent can be up to 2.5 times. In addition, the results showed that the pressure drop for the first stenosis is greater than the second stenosis, by 810 Pa (for solid artery) and 540 Pa (for elastic artery). The results also revealed that for simple stenosis, the length of the diseases prone zone in the elastic artery is 21% longer than the rigid one which this figure for double stenosis is calculated to be about 40%. Comparing the results of the simple stenosis with double, one affirmed that the artery wall thickness growth for case of double stenosis is greater than that of the single one.

Computational Modeling of Aortic Stenosis With a Reduced Degree-of-Freedom Fluid-Structure Interaction Valve Model

In this study, a novel reduced degree-of-freedom (rDOF) aortic valve model is employed to investigate the fluid-structure interaction (FSI) and hemodynamics associated with aortic stenosis. The dynamics of the valve leaflets are determined by an ordinary differential equation with two parameters and this rDOF model is shown to reproduce key features of more complex valve models. The hemodynamics associated with aortic stenosis is studied for three cases: a healthy case and two stenosed cases. The focus of the study is to correlate the hemodynamic features with the source generation mechanism of systolic murmurs associated with aortic stenosis. In the healthy case, extremely weak flow fluctuations are observed. However, in the stenosed cases, simulations show significant turbulent fluctuations in the ascending aorta, which are responsible for the generation of strong wall pressure fluctuations after the aortic root mostly during the deceleration phase of the systole. The intensity of the murmur generation increases with the severity of the stenosis, and the source locations for the two diseased cases studied here lie around 1.0 inlet duct diameters (Do) downstream of the ascending aorta.

Experimental and numerical investigation of pulsed flows in asevere aortic stenosed model

Steady and pulsatile aortic stenotic flows through stenosis tubes were experimentally and numerically investigated. The objective was the understanding of the fluid dynamics in arterial geometries most relevant in the context of atherosclerosis. Axisymmetric phantoms corresponding to significant artery stenosis of 50% in diameter and severe aortic stenosis of 75% were respectively machined from silicon. A water flow circuit was established, a steady flow was provided by gravity and a pulsed flow by a pulsatile pump. At inlet Reynolds numbers in the range of 85 to 1125, flows at the stenosis region were investigated using two-component Particle Image Velocimetry (PIV). For the unsteady flow, three different heartbeats (60, 69 and 90 beats per minute) were considered. The k-ω shear-stress-transport first-order turbulence model in Computational Fluid Dynamics (CFD) commercial software was adopted for simulations. Experimental measurements of the velocity fields show good agreements with CFD for both steady and pulsed flows. Recirculation regions were found near the stenosis in both cases. Reverse flow through the stenosis was also observed in pulsatile flow during the end diastolic phase of the cycle. CFD simulations allowed us to accurately assess wall shear stress in the stenotic region where the optical measurements are very noisy. High values of wall shear stress (with high variations both in space and time), are observed, which are indicators of possible future aortic wall damage.

Spectral Decomposition and Sound Source Localization of Highly Disturbed Flow through a Severe Arterial Stenosis

For the early detection of atherosclerosis, it is imperative to explore the capabilities of new, effective noninvasive diagnosis techniques to significantly reduce the associated treatment costs and mortality rates. In this study, a multifaceted comprehensive approach involving advanced computational fluid dynamics combined with signal processing techniques was exploited to investigate the highly turbulent fluctuating flow through arterial stenosis. The focus was on localizing high-energy mechano-acoustic source potential to transmit to the epidermal surface. The flow analysis results showed the existence of turbulent pressure fluctuations inside the stenosis and in the post-stenotic region. After analyzing the turbulent kinetic energy and pressure fluctuations on the flow centerline and the vessel wall, the point of maximum excitation in the flow was observed around two diameters downstream of the stenosis within the fluctuating zone. It was also found that the concentration of pressure fluctuation closer to the wall was higher inside the stenosis compared to the post-stenotic region. Additionally, the visualization of the most energetic proper orthogonal decomposition (POD) mode and spectral decomposition of the flow indicated that the break frequencies ranged from 80 to 220 Hz and were correlated to the eddies generated within these regions.

Computational Modeling and Analysis of Murmurs Generated by Modeled Aortic Stenoses

In this study, coupled hemodynamic-acoustic simulations are employed to study the generation and propagation of murmurs associated with aortic stenoses where the aorta with a stenosed aortic valve is modeled as a curved pipe with a constriction near the inlet. The hemodynamics of the post-stenotic flow is investigated in detail in our previous numerical study. The temporal history of the pressure on the aortic lumen is recorded during the hemodynamic study and used as the murmur source in the acoustic simulations. The thorax is modeled as an elliptic cylinder and the thoracic tissue is assumed to be homogeneous, linear and viscoelastic. A previously developed high-order numerical method that is capable of dealing with immersed bodies is applied in the acoustic simulations. To mimic the clinical practice of auscultation, the sound signals from the epidermal surface are collected. The simulations show that the source of the aortic stenosis murmur is located at the proximal end of the aortic arch and that the sound intensity pattern on the epidermal surface can predict the source location of the murmurs reasonably well. Spectral analysis of the murmur reveals the disconnect between the break frequency obtained from the flow and from the murmur signal. Finally, it is also demonstrated that the source locations can also be predicted by solving an inverse problem using the free-space Green's function. The implications of these results for cardiac auscultation are discussed.

Targeted Drug Delivery to Upper Airways Using a Pulsed Aerosol Bolus and Inhaled Volume Tracking Method

The pulmonary route presents an attractive delivery pathway for topical treatment of lung diseases. While significant progress has been achieved in understanding the physical underpinnings of aerosol deposition in the lungs, our ability to target or confine the deposition of inhalation aerosols to specific lung regions remains meagre. Here, we present a novel inhalation proof-of-concept in silico for regional targeting in the upper airways, quantitatively supported by computational fluid dynamics (CFD) simulations of inhaled micron-sized particles (i.e. 1-10 μm) using an intubated, anatomically-realistic, multi-generation airway tree model. Our targeting strategy relies on selecting the particle release time, whereby a short-pulsed bolus of aerosols is injected into the airways and the inhaled volume of clean air behind the bolus is tracked to reach a desired inhalation depth (i.e. airway generations). A breath hold maneuver then follows to facilitate deposition, via sedimentation, before exhalation resumes and remaining airborne particles are expelled. Our numerical findings showcase how particles in the range 5-10 μm combined with such inhalation methodology are best suited to deposit in the upper airways, with deposition fractions between 0.68 and unity. In contrast, smaller (< 2 μm) particles are less than optimal due to their slow sedimentation rates. We illustrate further how modulating the volume inhaled behind the pulsed bolus, prior to breath hold, may be leveraged to vary the targeted airway sites. We discuss the feasibility of the proposed inhalation framework and how it may help pave the way for specialized topical lung treatments.

Recommendations for Simulating Microparticle Deposition at Conditions Similar to the Upper Airways with Two-Equation Turbulence Models

The development of a CFD model, from initial geometry to experimentally validated result with engineering insight, can be a time-consuming process that often requires several iterations of meshing and solver set-up. Applying a set of guidelines in the early stages can help to streamline the process and improve consistency between different models. The objective of this study was to determine both mesh and CFD solution parameters that enable the accurate simulation of microparticle deposition under flow conditions consistent with the upper respiratory airways including turbulent flow. A 90° bend geometry was used as a characteristic model that occurs throughout the airways and for which high-quality experimental aerosol deposition data is available in the transitional and turbulent flow regimes. Four meshes with varying degrees of near-wall resolution were compared, and key solver settings were applied to determine the parameters that minimize sensitivity to the near-wall (NW) mesh. The Low Reynolds number (LRN) k-ω model was used to resolve the turbulence field, which is a numerically efficient two-equation turbulence model, but has recently been considered overly simplistic. Some recent studies have used more complex turbulence models, such as Large Eddy Simulation (LES), to overcome the perceived weaknesses of two-equation models. Therefore, the secondary objective was to determine whether the more computationally efficient LRN k-ω model was capable of providing deposition results that were comparable to LES. Results show how NW mesh sensitivity is reduced through application of the Green-Gauss Node-based gradient discretization scheme and physically realistic near-wall corrections. Using the newly recommended meshing parameters and solution guidelines gives an excellent match to experimental data. Furthermore, deposition data from the LRN k-ω model compares favorably with LES results for the same characteristic geometry. In summary, this study provides a set of meshing and solution guidelines for simulating aerosol deposition in transitional and turbulent flows found in the upper respiratory airways using the numerically efficient LRN k-ω approach.

Towards Additive Manufacture of Functional, Spline-Based Morphometric Models of Healthy and Diseased Coronary Arteries: In Vitro Proof-of-Concept Using a Porcine Template

The aim of this study is to assess the additive manufacture of morphometric models of healthy and diseased coronary arteries. Using a dissected porcine coronary artery, a model was developed with the use of computer aided engineering, with splines used to design arteries in health and disease. The model was altered to demonstrate four cases of stenosis displaying varying severity, based on published morphometric data available. Both an Objet Eden 250 printer and a Solidscape 3Z Pro printer were used in this analysis. A wax printed model was set into a flexible thermoplastic and was valuable for experimental testing with helical flow patterns observed in healthy models, dominating the distal LAD (left anterior descending) and left circumflex arteries. Recirculation zones were detected in all models, but were visibly larger in the stenosed cases. Resin models provide useful analytical tools for understanding the spatial relationships of blood vessels, and could be applied to preoperative planning techniques, but were not suitable for physical testing. In conclusion, it is feasible to develop blood vessel models enabling experimental work; further, through additive manufacture of bio-compatible materials, there is the possibility of manufacturing customized replacement arteries.

Blood Flow in Idealized Vascular Access for Hemodialysis: A Review of Computational Studies

Although our understanding of the failure mechanism of vascular access for hemodialysis has increased substantially, this knowledge has not translated into successful therapies. Despite advances in technology, it is recognized that vascular access is difficult to maintain, due to complications such as intimal hyperplasia. Computational studies have been used to estimate hemodynamic changes induced by vascular access creation. Due to the heterogeneity of patient-specific geometries, and difficulties with obtaining reliable models of access vessels, idealized models were often employed. In this review we analyze the knowledge gained with the use of computational such simplified models. A review of the literature was conducted, considering studies employing a computational fluid dynamics approach to gain insights into the flow field phenotype that develops in idealized models of vascular access. Several important discoveries have originated from idealized model studies, including the detrimental role of disturbed flow and turbulent flow, and the beneficial role of spiral flow in intimal hyperplasia. The general flow phenotype was consistent among studies, but findings were not treated homogeneously since they paralleled achievements in cardiovascular biomechanics which spanned over the last two decades. Computational studies in idealized models are important for studying local blood flow features and evaluating new concepts that may improve the patency of vascular access for hemodialysis. For future studies we strongly recommend numerical modelling targeted at accurately characterizing turbulent flows and multidirectional wall shear disturbances.

Definition of common carotid wall thickness affects risk classification in relation to degree of internal carotid artery stenosis: the Plaque At RISK (PARISK) study

Background

Mean or maximal intima-media thickness (IMT) is commonly used as surrogate endpoint in intervention studies. However, the effect of normalization by surrounding or median IMT or by diameter is unknown. In addition, it is unclear whether IMT inhomogeneity is a useful predictor beyond common wall parameters like maximal wall thickness, either absolute or normalized to IMT or lumen size. We investigated the interrelationship of common carotid artery (CCA) thickness parameters and their association with the ipsilateral internal carotid artery (ICA) stenosis degree.

Methods

CCA thickness parameters were extracted by edge detection applied to ultrasound B-mode recordings of 240 patients. Degree of ICA stenosis was determined from CT angiography.

Results

Normalization of maximal CCA wall thickness to median IMT leads to large variations. Higher CCA thickness parameter values are associated with a higher degree of ipsilateral ICA stenosis (p < 0.001), though IMT inhomogeneity does not provide extra information. When the ratio of wall thickness and diameter instead of absolute maximal wall thickness is used as risk marker for having moderate ipsilateral ICA stenosis (>50%), 55 arteries (15%) are reclassified to another risk category.

Conclusions

It is more reasonable to normalize maximal wall thickness to end-diastolic diameter rather than to IMT, affecting risk classification and suggesting modification of the Mannheim criteria.

Trial registration

Clinical trials.gov NCT01208025.

Laminar-to-turbulence and relaminarization zones detection by simulation of low Reynolds number turbulent blood flow in large stenosed arteries

Laminar, turbulent, transitional, or combine areas of all three types of viscous flow can occur downstream of a stenosis depending upon the Reynolds number and constriction shape parameter. Neither laminar flow solver nor turbulent models for instance the k-ω (k-omega), k-ε (k-epsilon), RANS or LES are opportune for this type of flow. In the present study attention has been focused vigorously on the effect of the constriction in the flow field with a unique way. It means that the laminar solver was employed from entry up to the beginning of the turbulent shear flow. The turbulent model (k-ω SST Transitional Flows) was utilized from starting of turbulence to relaminarization zone while the laminar model was applied again with onset of the relaminarization district. Stenotic flows, with 50 and 75% cross-sectional area, were simulated at Reynolds numbers range from 500 to 2000 employing FLUENT (v6.3.17). The flow was considered to be steady, axisymmetric, and incompressible. Achieving results were reported as axial velocity, disturbance velocity, wall shear stress and the outcomes were compared with previously experimental and CFD computations. The analogy of axial velocity profiles shows that they are in acceptable compliance with the empirical data. As well as disturbance velocity and wall shear stresses anticipated by this new approach, part by part simulation, are reasonably valid with the acceptable experimental studies.

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.

Aortic flow patterns before and after personalised external aortic root support implantation in Marfan patients

Implantation of a personalised external aortic root support (PEARS) in the Marfan aorta is a new procedure that has emerged recently, but its haemodynamic implication has not been investigated. The objective of this study was to compare the flow characteristics and hemodynamic indices in the aorta before and after insertion of PEARS, using combined cardiovascular magnetic resonance imaging (CMR) and computational fluid dynamics (CFD). Pre- and post-PEARS MR images were acquired from 3 patients and used to build patient-specific models and upstream flow conditions, which were incorporated into the CFD simulations. The results revealed that while the qualitative patterns of the haemodynamics were similar before and after PEARS implantation, the post-PEARS aortas had slightly less disturbed flow at the sinuses, as a result of reduced diameters in the post-PEARS aortic roots. Quantitative differences were observed between the pre- and post-PEARS aortas, in that the mean values of helicity flow index (HFI) varied by -10%, 35% and 20% in post-PEARS aortas of Patients 1, 2 and 3, respectively, but all values were within the range reported for normal aortas. Comparisons with MR measured velocities in the descending aorta of Patient 2 demonstrated that the computational models were able to reproduce the important flow features observed in vivo.

MODELING BLOOD FLOW IN AN ECCENTRIC STENOSED ARTERY USING LARGE EDDY SIMULATION AND PARALLEL COMPUTING

Computational fluid dynamics (CFD) is an excellent computational tool to assess the hemodynamics and detailed blood-flow structure for cardiovascular applications. Modeling turbulence for cardiovascular applications can be achieved (to some extent) using available numerical models such as Reynolds average Navier–Stokes (RANS), the large eddy simulation (LES) and the direct numerical solution (DNS). In order to develop an efficient model which is as accurate as DNS and as quick as RANS, our laboratory's focus is on LES. In this study, we develop an efficient numerical model which is based on LES and structured but non-orthogonal finite volumes. Using the proposed model, the detailed flow structure and turbulent features of the blood stream in a complicated geometry is captured. The aim of this study is to model blood-flow through an eccentric stenosis accurately and quickly. The results are similar to those obtained using DNS but in a fraction of the CPU time. The computational tools implemented in this study are based on a FORTRAN based in-house code coupled with parallel computing using SHARCNET. The developed model is a significant computational tool which can be used to assess the hemodynamic properties for cardiovascular applications, e.g., prosthetic heart valves and atherosclerosis.

Large eddy simulation of transitional flow in an idealized stenotic blood vessel: evaluation of subgrid scale models

In the present study, we performed large eddy simulation (LES) of axisymmetric, and 75% stenosed, eccentric arterial models with steady inflow conditions at a Reynolds number of 1000. The results obtained are compared with the direct numerical simulation (DNS) data (Varghese et al., 2007, "Direct Numerical Simulation of Stenotic Flows. Part 1. Steady Flow," J. Fluid Mech., 582, pp. 253-280). An inhouse code (WenoHemo) employing high-order numerical methods for spatial and temporal terms, along with a 2nd order accurate ghost point immersed boundary method (IBM) (Mark, and Vanwachem, 2008, "Derivation and Validation of a Novel Implicit Second-Order Accurate Immersed Boundary Method," J. Comput. Phys., 227(13), pp. 6660-6680) for enforcing boundary conditions on curved geometries is used for simulations. Three subgrid scale (SGS) models, namely, the classical Smagorinsky model (Smagorinsky, 1963, "General Circulation Experiments With the Primitive Equations," Mon. Weather Rev., 91(10), pp. 99-164), recently developed Vreman model (Vreman, 2004, "An Eddy-Viscosity Subgrid-Scale Model for Turbulent Shear Flow: Algebraic Theory and Applications," Phys. Fluids, 16(10), pp. 3670-3681), and the Sigma model (Nicoud et al., 2011, "Using Singular Values to Build a Subgrid-Scale Model for Large Eddy Simulations," Phys. Fluids, 23(8), 085106) are evaluated in the present study. Evaluation of SGS models suggests that the classical constant coefficient Smagorinsky model gives best agreement with the DNS data, whereas the Vreman and Sigma models predict an early transition to turbulence in the poststenotic region. Supplementary simulations are performed using Open source field operation and manipulation (OpenFOAM) ("OpenFOAM," http://www.openfoam.org/) solver and the results are inline with those obtained with WenoHemo.

Quantifying turbulent wall shear stress in a subject specific human aorta using large eddy simulation

In this study, large-eddy simulation (LES) is employed to calculate the disturbed flow field and the wall shear stress (WSS) in a subject specific human aorta. Velocity and geometry measurements using magnetic resonance imaging (MRI) are taken as input to the model to provide accurate boundary conditions and to assure the physiological relevance. In total, 50 consecutive cardiac cycles were simulated from which a phase average was computed to get a statistically reliable result. A decomposition similar to Reynolds decomposition is introduced, where the WSS signal is divided into a pulsating part (due to the mass flow rate) and a fluctuating part (originating from the disturbed flow). Oscillatory shear index (OSI) is plotted against time-averaged WSS in a novel way, and locations on the aortic wall where elevated values existed could easily be found. In general, high and oscillating WSS values were found in the vicinity of the branches in the aortic arch, while low and oscillating WSS were present in the inner curvature of the descending aorta. The decomposition of WSS into a pulsating and a fluctuating part increases the understanding of how WSS affects the aortic wall, which enables both qualitative and quantitative comparisons.

Comparison of LES of steady transitional flow in an idealized stenosed axisymmetric artery model with a RANS transitional model

In this study, two different turbulence methodologies are investigated to predict transitional flow in a 75% stenosed axisymmetric experimental arterial model and in a slightly modified version of the model with an eccentric stenosis. Large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) methods were applied; in the LES simulations eddy viscosity subgrid-scale models were employed (basic and dynamic Smagorinsky) while the RANS method involved the correlation-based transitional version of the hybrid k-ε/k-ω flow model. The RANS simulations used 410,000 and 820,000 element meshes for the axisymmetric and eccentric stenoses, respectively, with y(+) less than 2 viscous wall units for the boundary elements, while the LES used 1,200,000 elements with y(+) less than 1. Implicit filtering was used for LES, giving an overlap between the resolved and modeled eddies, ensuring accurate treatment of near wall turbulence structures. Flow analysis was carried out in terms of vorticity and eddy viscosity magnitudes, velocity, and turbulence intensity profiles and the results were compared both with established experimental data and with available direct numerical simulations (DNSs) from the literature. The simulation results demonstrated that the dynamic Smagorinsky LES and RANS transitional model predicted fairly comparable velocity and turbulence intensity profiles with the experimental data, although the dynamic Smagorinsky model gave the best overall agreement. The present study demonstrated the power of LES methods, although they were computationally more costly, and added further evidence of the promise of the RANS transition model used here, previously tested in pulsatile flow on a similar model. Both dynamic Smagorinsky LES and the RANS model captured the complex transition phenomena under physiological Reynolds numbers in steady flow, including separation and reattachment. In this respect, LES with dynamic Smagorinsky appeared more successful than DNS in replicating the axisymmetric experimental results, although inflow conditions, which are subject to caveats, may have differed. For the eccentric stenosis, LES with Smagorinsky coefficient of 0.13 gave the closest agreement with DNS despite the known shortcomings of fixed coefficients. The relaminarization as the flow escaped the influence of the stenosis was amply demonstrated in the simulations, graphically so in the case of LES.

Analysis of peripheral artery velocity tracing in a porcine model

BACKGROUND

The aim of the study was to trace the peripheral artery velocity with ultrasound in pigs and provide inference on diagnosis of the type, location and severity of vascular diseases.

MATERIALS AND METHODS

Limb tightening, adrenaline administration and arterial wall pinching were performed independently in six pigs, and then the evolution of the external iliac artery or femoral artery velocity tracing were monitored.

RESULTS

With the increase of the extents of hindlimb tightening, peak systolic velocity (PSV) of ipsilateral external iliac artery turned from 36.33±1.77 cm/s to 59.72±2.67 cm/s, minimum post-principal wave velocity (MPV from 13.68±1.11 cm/s to -7.48±0.82 cm/s, peak diastolic velocity (PDV) from 19.31±0.86 cm/s to 8.98±0.45 cm/s, and, end diastolic velocity (EDV) from 13.2±0.45 cm/s to 0. With the increase of the dose of the epinephrine injection, PSV increased from 36.33±1.77 cm/s to 43.97±2.15 cm/s but then decreased to 35.43±3.01 cm/s, and MPV negatively increased to -23.53±0.82 cm/s after decreasing from 13.68±1.11 cm/s to 0. PDV and EDV gradually decreased to zero. With the increase of the stenosis severity in the abdominal aortic wall pinching, PSV was reduced and had a linearly negative correlation with the stenosis severity (R=0.983, R2=0.967). MPV gradually increased, and its direction reversed when the stenosis severity increased, then diminished when the blood flow was occluded by more than 2/3.

CONCLUSIONS

The formation of peripheral artery velocity is the result of concurrent effects of cardiac ejection, vascular resistance, effective circulating blood volume and elastic recoil. Vascular resistance exerts pronounced effects on the diastolic waveform, and the occurrence of backward wave indicates that the downstream circulation resistance significantly increases.

Quantifying turbulent wall shear stress in a stenosed pipe using large eddy simulation

Large eddy simulation was applied for flow of Re=2000 in a stenosed pipe in order to undertake a thorough investigation of the wall shear stress (WSS) in turbulent flow. A decomposition of the WSS into time averaged and fluctuating components is proposed. It was concluded that a scale resolving technique is required to completely describe the WSS pattern in a subject specific vessel model, since the poststenotic region was dominated by large axial and circumferential fluctuations. Three poststenotic regions of different WSS characteristics were identified. The recirculation zone was subject to a time averaged WSS in the retrograde direction and large fluctuations. After reattachment there was an antegrade shear and smaller fluctuations than in the recirculation zone. At the reattachment the fluctuations were the largest, but no direction dominated over time. Due to symmetry the circumferential time average was always zero. Thus, in a blood vessel, the axial fluctuations would affect endothelial cells in a stretched state, whereas the circumferential fluctuations would act in a relaxed direction.

Aggregate breakup in a contracting nozzle

The breakup of dense aggregates in an extensional flow was investigated experimentally. The flow was realized by pumping the suspension containing the aggregates through a contracting nozzle. Variation of the cluster mass distribution during the breakage process was measured by small-angle light scattering. Because of the large size of primary particles and the dense aggregate structure image analysis was used to determine the shape and structure of the produced fragments. It was found, that neither aggregate structure, characterized by a fractal dimension d(f) = 2.7, nor shape, characterized by an average aspect ratio equal to 1.5, was affected by breakage. Several passes through the nozzle were required to reach the steady state. This is explained by the radial variation of the hydrodynamic stresses at the nozzle entrance, characterized through computational fluid dynamics, which implies that only the fraction of aggregates whose strength is smaller than the local hydrodynamic stress is broken during one pass through the nozzle. Scaling of the steady-state aggregate size as a function of the hydrodynamic stress was used to determine the aggregate strength.

A dual-phantom system for validation of velocity measurements in stenosis models under steady flow

A dual-phantom system is developed for validation of velocity measurements in stenosis models. Pairs of phantoms with identical geometry and flow conditions are manufactured, one for ultrasound and one for particle image velocimetry (PIV). The PIV model is made from silicone rubber, and a new PIV fluid is made that matches the refractive index of 1.41 of silicone. Dynamic scaling was performed to correct for the increased viscosity of the PIV fluid compared with that of the ultrasound blood mimic. The degree of stenosis in the models pairs agreed to less than 1%. The velocities in the laminar flow region up to the peak velocity location agreed to within 15%, and the difference could be explained by errors in ultrasound velocity estimation. At low flow rates and in mild stenoses, good agreement was observed in the distal flow fields, excepting the maximum velocities. At high flow rates, there was considerable difference in velocities in the poststenosis flow field (maximum centreline differences of 30%), which would seem to represent real differences in hydrodynamic behavior between the two models. Sources of error included: variation of viscosity because of temperature (random error, which could account for differences of up to 7%); ultrasound velocity estimation errors (systematic errors); and geometry effects in each model, particularly because of imperfect connectors and corners (systematic errors, potentially affecting the inlet length and flow stability). The current system is best placed to investigate measurement errors in the laminar flow region rather than the poststenosis turbulent flow region.

Numerical simulation of pulsatile turbulent flow in tapering stenosed arteries

Purpose

The purpose of this paper is to investigate the geometric effects and pulsatile characteristics during the stenotic flows in tapering arteries.

Design/methodology/approach

The low Reynolds number k − ω turbulence model is applied to describe the stenotic flows in the tapering arteries in this paper. The results are divided into two sections. The first section characterizes the geometric effects on the turbulent flow under steady condition. The second section illustrates the key physiological parameters including the pressure drop and wall stress during the periodic cycle of the pulsatile flow in the arteries.

Findings

The tapering and stenoses severity intensify the turbulent flow and stretch the recirculation zones in the turbulent arterial flow. The wall shear stress, pressure drop and velocity vary most intensively at the peak phase during the periodic cycle of the pulsatile turbulent flow.

Originality/value

This paper provides a comprehensive understanding of the spatial‐temporal fluid dynamics involved in turbulent and transitional arterial flow with stenoses. The low Reynolds number k − ω turbulence model method is applied for the analyses of the geometric effects on the arterial flow and fluid feature during the periodic cycle.

Analysis of Flow Disturbance in a Stenosed Carotid Artery Bifurcation Using Two-Equation Transitional and Turbulence Models

In this study, newly developed two-equation turbulence models and transitional variants are employed for the prediction of blood flow patterns in a diseased carotid artery where the growth, progression, and structure of the plaque at rupture are closely linked to low and oscillating wall shear stresses. Moreover, the laminar-turbulent transition in the poststenotic zone can alter the separation zone length, wall shear stress, and pressure distribution over the plaque, with potential implications for stresses within the plaque. Following the validation with well established experimental measurements and numerical studies, a magnetic-resonance (MR) image-based model of the carotid bifurcation with 70% stenosis was reconstructed and simulated using realistic patient-specific conditions. Laminar flow, a correlation-based transitional version of Menter’s hybrid k‐ϵ∕k‐ω shear stress transport (SST) model and its “scale adaptive simulation” (SAS) variant were implemented in pulsatile simulations from which analyses of velocity profiles, wall shear stress, and turbulence intensity were conducted. In general, the transitional version of SST and its SAS variant are shown to give a better overall agreement than their standard counterparts with experimental data for pulsatile flow in an axisymmetric stenosed tube. For the patient-specific case reported, the wall shear stress analysis showed discernable differences between the laminar flow and SST transitional models but virtually no difference between the SST transitional model and its SAS variant.

Modeling Transition to Turbulence in Eccentric Stenotic Flows

Mean flow predictions obtained from a host of turbulence models were found to be in poor agreement with recent direct numerical simulation results for turbulent flow distal to an idealized eccentric stenosis. Many of the widely used turbulence models, including a large eddy simulation model, were unable to accurately capture the poststenotic transition to turbulence. The results suggest that efforts toward developing more accurate turbulence models for low-Reynolds number, separated transitional flows are necessary before such models can be used confidently under hemodynamic conditions where turbulence may develop.

Quantification of intravoxel velocity standard deviation and turbulence intensity by generalizing phase-contrast MRI

Turbulent flow, characterized by velocity fluctuations, is a contributing factor to the pathogenesis of several cardiovascular diseases. A clinical noninvasive tool for assessing turbulence is lacking, however. It is well known that the occurrence of multiple spin velocities within a voxel during the influence of a magnetic gradient moment causes signal loss in phase-contrast magnetic resonance imaging (PC-MRI). In this paper a mathematical derivation of an expression for computing the standard deviation (SD) of the blood flow velocity distribution within a voxel is presented. The SD is obtained from the magnitude of PC-MRI signals acquired with different first gradient moments. By exploiting the relation between the SD and turbulence intensity (TI), this method allows for quantitative studies of turbulence. For validation, the TI in an in vitro flow phantom was quantified, and the results compared favorably with previously published laser Doppler anemometry (LDA) results. This method has the potential to become an important tool for the noninvasive assessment of turbulence in the arterial tree.

Two-equation turbulence modeling of pulsatile flow in a stenosed tube

The study of pulsatile flow in stenosed vessels is of particular importance because of its significance in relation to blood flow in human pathophysiology. To date, however, there have been few comprehensive publications detailing systematic numerical simulations of turbulent pulsatile flow through stenotic tubes evaluated against comparable experiments. In this paper, two-equation turbulence modeling has been explored for sinusoidally pulsatile flow in 75% and 90% area reduction stenosed vessels, which undergoes a transition from laminar to turbulent flow as well as relaminarization. Wilcox's standard k-omega model and a transitional variant of the same model are employed for the numerical simulations. Steady flow through the stenosed tubes was considered first to establish the grid resolution and the correct inlet conditions on the basis of comprehensive comparisons of the detailed velocity and turbulence fields to experimental data. Inlet conditions based on Womersley flow were imposed at the inlet for all pulsatile cases and the results were compared to experimental data from the literature. In general, the transitional version of the k-omega model is shown to give a better overall representation of both steady and pulsatile flow. The standard model consistently over predicts turbulence at and downstream of the stenosis, which leads to premature recovery of the flow. While the transitional model often under-predicts the magnitude of the turbulence, the trends are well-described and the velocity field is superior to that predicted using the standard model. On the basis of this study, there appears to be some promise for simulating physiological pulsatile flows using a relatively simple two-equation turbulence model.

Angle-independent estimation of maximum velocity through stenoses using vector Doppler ultrasound

Categorisation for arterial stenoses treatment is determined primarily by the degree of occlusion, which is often estimated ultrasonically from blood velocity measurements. In current single-beam ultrasound (US) systems, this estimate can suffer from gross errors due to angle-dependence. The purpose of this study was to find out if an experimental dual-beam US system could reduce the angle-dependence of the velocity estimates. We compared four dual-beam velocity estimation algorithms on both a string phantom and straight tube wall-less flow phantoms incorporating symmetrical and asymmetrical stenoses from 0% to 91% by area. The estimated maximum velocity varied, on average, by 7.6% for beam-vessel angles from 40 degrees to 80 degrees. The fluctuation in the magnitude estimate was reduced by a factor of 2.6 using a hybrid single-dual-beam algorithm. We conclude that, when the true velocity lies in the scan plane, the dual-beam system reduces the angle-dependence and, thus, has the potential to improve categorisation of patients with arterial stenoses.

Beamformed nearfield imaging of a simulated coronary artery containing a stenosis

This paper is concerned with the potential for the detection and location of an artery containing a partial blockage by exploiting the space-time properties of the shear wave field in the surrounding elastic soft tissue. As a demonstration of feasibility, an array of piezoelectric film vibration sensors is placed on the free surface of a urethane mold that contains a surgical tube. Inside the surgical tube is a nylon constriction that inhibits the water flowing through the tube. A turbulent field develops in and downstream from the blockage, creating a randomly fluctuating pressure on the inner wall of the tube. This force produces shear and compressional wave energy in the urethane. After the array is used to sample the dominant shear wave space-time energy field at low frequencies, a nearfield (i.e., focused) beamforming process then images the energy distribution in the three-dimensional solid. Experiments and numerical simulations are included to demonstrate the potential of this noninvasive procedure for the early identification of vascular blockages-the typical precursor of serious arterial disease in the human heart.

Computational simulation of turbulent signal loss in 2D time-of-flight magnetic resonance angiograms

Time-of-flight magnetic resonance (MR) angiography is currently limited in the evaluation of arterial stenoses by flow-induced signal loss. This signal loss has been attributed to phase dispersion and to phase misregistration. We have developed a fluid mechanics model of 2D time-of-flight MR angiograms to study the amount of signal loss caused by random turbulence. The simulations were created by stochastic analysis of particle pathlines determined by computational fluid dynamics for turbulent flow. The images obtained by the model compare well to actual MR images of flow in stenoses. By selectively removing the random turbulent motion in the simulation, it can be seen that random phase dispersion is the dominant mechanism of signal loss. Phase misregistration and mean flow phase dispersion act as secondary effects. The MR simulation model recreates accurately the variation of signal loss over a range of echo times. The model can be used further to explore and design new pulse sequences. For example, the current study showed that high slew rate gradient waveforms can significantly reduce poststenotic signal loss. In conclusion, computational modeling of MR angiography can be a useful approach for the analysis of MRA signal loss and the design of improved pulse sequences.

Characterization of blood flow turbulence with pulsed-wave and power Doppler ultrasound imaging

Blood turbulence downstream of a concentric 86 percent area reduction stenosis was characterized using absolute and relative Doppler spectral broadening measurements, relative Doppler velocity fluctuation, and Doppler backscattered power. Bidimensional mappings of each Doppler index were obtained using a 10 MHz pulsed-wave Doppler system. Calf red cells suspended in a saline solution were used to scatter ultrasound and were circulated in an in vitro steady flow loop model. Results showed that the absolute spectral broadening was not a good index of turbulence because it was strongly affected by the deceleration of the jet and by the shear layer between the jet and the recirculation zones. Relative Doppler spectral broadening (absolute broadening divided by the frequency shift), velocity fluctuation, and Doppler power indices provided consistent mapping of the centerline axial variation of turbulence evaluated by hot-film anemometry. The best agreement between the hot-film and Doppler ultrasound methods was however obtained with the Doppler back-scattered power. The most consistent bidimensional mapping of the flow characteristics downstream of the stenosis was also observed with the Doppler power index. The relative broadening and the velocity fluctuation produced artifacts in the shear layer and in the recirculation zones. Power Doppler imaging is a new emerging technique that may provide reliable in vivo characterization of blood flow turbulence.

Analysis of the flow in stenosed carotid artery bifurcation models--hydrogen-bubble visualisation

This paper deals with the effect of geometric changes of mild stenoses on large-scale flow disturbances in the carotid artery bifurcation. Hydrogen-bubble visualisation experiments have been performed in Plexiglas models of a non-stenosed and a 25% stenosed carotid artery bifurcation. The flow conditions approximate physiological flow. The experiments show that shortly after the onset of the diastolic phase vortex formation occurs in the plane of symmetry. This vortex formation is found in a shear layer, which is formed in the carotid sinus. The shear layer is located between a region with low shear rates at the non-divider wall and a region with high shear rates at the divider wall. In order to gain insight into the parameters that are important with respect to the stability of the shear layer, experiments have been performed in which the influence of the shape of the flow pulse, the Reynolds number (Re), the Womersley parameter (alpha) and the flow division ratio (gamma) on the flow phenomena is studied. From these experiments it appears that the flow phenomena in the carotid artery bifurcation are significantly influenced by Re, alpha the systolic acceleration (sa) and deceleration (sd) and the duration of the peak-systolic flow (Tmax). With these results a simplified flow pulse is chosen, with which the experiments in the non-stenosed and the 25% stenosed bifurcation are performed. Comparison of the hydrogen-bubble profiles in the 0 and 25% stenosed models with similar flow conditions shows that the geometric change of the 25% stenosis only slightly influences the flow phenomena. The most striking influences are found in the stability of the shear layer. Quantitative experiments by means of laser Doppler anemometry measurements and numerical computations are needed to analyse the influence of the stenosis of the flow field more accurately.

Coarctation of the stapedial artery: an unusual adaptive response to competing functional demands in the middle ear of some eutherians

In primitive eutherians, the stapedial artery is the primary supplier of blood to the nonneural tissues of the head. Beyond a certain body size, the stapedial artery can no longer function as the sole supplier to its original territory because the diameter of its stem is limited by the size of the intercrural foramen of the stapes, which exhibits strong negative allometry. Some eutherians have extended the upper limit that the diameter of the stapedial stem can attain by developing a coarctation (narrowing) at the transcrual portion of the vessel. In the Norway rat (Rattus norvegicus) and the golden hamster (Mesocricetus auratus) the coarctation develops in postnatal life and is evidently caused by a retardation in growth that keeps the diameter of the vessel at infantile dimensions. In the rat, additional reduction in the external diameter is produced by a thinning of the tunica media of the arterial wall. A comfortable gap between the wall of the artery and the sides of the intercrural foramen is maintained that most likely facilitates the attenuation of potentially disruptive low-frequency vibrations produced by the arterial pressure pulse. The only negative side effect of a coarctation in rat-sized animals is that resistance to flow is increased and volume flow rate is concomitantly diminished. The coarctation does not create flow disturbances downstream of the constriction. One possible additional benefit of the coarctation is a flattening out of the arterial pressure pulse. It is speculated that the capacity to develop a coarctation once a certain body size is reached is an ancient trait that dates at least as far back as the Early Cretaceous.

Effects of vibration on steady flow downstream of a stenosis

A physical model was used to test the effects of vibrations on the position of transition to turbulence (zt) downstream of a constriction. Constrictions were inserted in a length of clear plastic (Tygon) tubing and vibrated. Water was the fluid medium and flow was visualized with India ink. The frequency and velocity of vibration were monitored. For a given constriction and flow velocity, there was a band of frequencies which caused zt to move upstream. This band corresponded to frequencies of flow disturbances as measured with a hot-film anemometer without vibration. Both flow-visualization and hot-film frequencies were correlated via a Strouhal number to the Reynolds number and contraction ratio of the flow. Values of zt decreased with increasing vibration amplitude. The critical Reynolds number for turbulence was also decreased by vibration. These results are of importance in the diagnosis of vascular disease and the design of physical models of stenotic flows.

Analysis of break frequencies downstream of a constriction in a cylindrical tube

Experiments were performed to correlate steady-flow power spectra downstream of a stenosis in a cylindrical tube with the flow geometry and velocity. The experiments were motivated by the need to improve quantitative phonoangiography. An objective break frequency (fb) was computed from spectra of velocity fluctuations, as measured with a hot film anemometer. Least squares fits with two independent variables were used to find an empirical relationship between a Strouhal number (S2), the contraction ratio (ds/D) and the Reynolds number (Re). The variables D and ds, are, respectively, the unobstructed tubing diameter and the inner diameter of the stenosis. The relationship found was S2 = Re 0.72(ds/D)0.26 The contraction ratio ds/D, can be found from the empirical relation in terms of known parameters. For the hot wire data the average error between the computed value of ds/D and the known value was 2.3%.

Pulsatile poststenotic flow studies with laser Doppler anemometry

The pulsatile flow field distal to axisymmetric constrictions in a straight tube was studied using laser Doppler anemometry. The upstream centerline velocity waveform was sinusoidal at a frequency parameter of 7.5 and mean Reynolds number of 600. Stenosis models of 25, 50 and 75% area reduction were employed and velocity data were derived by ensemble averaging methods. Extensive measurements of the pulsatile velocity profiles are reported, and wall shear rates were computed from the near wall velocity profile gradients. The experiments indicate that a permanent region of poststenotic flow separation does not exist even for the severest constriction, in contrast to results for steady flow. Values of wall shear stress were greatest near the throat of the constriction and were relatively low in the poststenotic region, including the region of most intense flow disturbance. Turbulence was found only for the 75% stenosis model and was created only during a segment of the cycle. Although much emphasis has been placed upon turbulence in the detection of arterial stenoses, particularly as identified by Doppler ultrasound spectral broadening, the present study implies that identification of flow disturbances of an organized nature may be more fundamental in recognizing mild to moderate disease. Additionally, the relationship of these flow field results to the animal aortic coarctation model often employed in atherogenesis studies is discussed.