Characterization and evolution poststenotic flow disturbances

Specification and Evaluation of Plasticizer Migration Simulants for Human Blood Products: A Delphi Study

Potentially toxic plasticizers are commonly added to polyvinyl chloride medical devices for transfusion in order to improve their flexibility and workability. As the plasticizers are not chemically bonded to the PVC, they can be released into labile blood products (LBPs) during storage. Ideally, LBPs would be used in laboratory studies of plasticizer migration from the medical device. However, short supply (i.e., limited stocks of human blood in collection centres) has prompted the development of specific simulants for each type of LBP in the evaluation of new transfusion devices. We performed a Delphi study with a multidisciplinary panel of 24 experts. In the first (qualitative) phase, the panel developed consensus definitions of the specification criteria to be met by each migration simulant. Next, we reviewed the literature on techniques for simulating the migration of plasticizers into LBPs. A questionnaire was elaborated and sent out to the experts, and the replies were synthesized in order to obtain a consensus. The qualitative study established specifications for each biological matrix (whole blood, red blood cell concentrate, plasma, and platelet concentrate) and defined the criteria required for a suitable LBP simulant. Ten criteria were suggested: physical and chemical characteristics, opacity, form, stability, composition, ability to mimic a particular clinical situation, ease and safety of use, a simulant–plastic interaction correlated with blood, and compatibility with analytical methods. The questionnaire data revealed a consensus on the use of natural products (such as pig’s blood) to mimic the four LBPs. Opinions diverged with regard to synthetic products. However, an isotonic solution and a rheological property modifier were considered to be of value in the design of synthetic simulants. Consensus reached by the Delphi group could be used as a database for the development of simulants used to assess the migration of plasticizers from PVC bags into LBPs.

Detecting carotid stenosis from skin vibrations using Laser Doppler Vibrometry - An in vitro proof-of-concept

Early detection of asymptomatic carotid stenosis may help identifying individuals at risk of stroke. We explore a new method based on laser Doppler vibrometry (LDV) which could allow the non-contact detection of stenosis from neck skin vibrations due to stenosis-induced flow disturbances. Experimental fluid dynamical tests were performed with water on a severely stenosed patient-specific carotid bifurcation model. Measurements were taken under various physiological flow regimes both in a compliant and stiff-walled version of the model, at 1 to 4 diameters downstream from the stenosis. An inter-arterial pressure catheter was positioned as reference. Increasing flow led to corresponding increase in power spectral density (PSD) of pressure and LDV recordings in the 0-500 Hz range. The stiff model lead to higher PSD. PSD of the LDV signal was less dependent on the downstream measurement location than pressure. The strength of the association between PSD and flow level, model material and measuring location was highest in the 0-50 Hz range, however useful information was found up to 200 Hz. This proof-of-concept suggests that LDV has the potential to detect stenosis-induced disturbed flow. Further computational and clinical validation studies are ongoing to assess the sensitivity and specificity of the technique for clinical screening.

Characterization and estimation of turbulence-related wall shear stress in patient-specific pulsatile blood flow

Disturbed, turbulent-like blood flow promotes chaotic wall shear stress (WSS) environments, impairing essential endothelial functions and increasing the susceptibility and progression of vascular diseases. These flow characteristics are today frequently detected at various anatomical, lesion and intervention-related sites, while their role as a pathological determinant is less understood. To present-day, numerous WSS-based descriptors have been proposed to characterize the spatiotemporal nature of the WSS disturbances, however, without differentiation between physiological laminar oscillations and turbulence-related WSS (tWSS) fluctuations. Also, much attention has been focused on magnetic resonance (MR) WSS estimations, so far with limited success; promoting the need of a near-wall surrogate marker. In this study, a new approach is explored to characterize the tWSS, by taking advantage of the tensor characteristics of the fluctuating WSS correlations, providing both a magnitude and an anisotropy measure of the disturbances. These parameters were studied in two patient-specific coarctation models (sever and mild), using large eddy simulations, and correlated against near-wall reciprocal Reynolds stress parameters. Collectively, results showed distinct regions of differing tWSS characteristics, features which were sensitive to changes in flow conditions. Generally, the post-stenotic tWSS was governed by near axisymmetric fluctuations, findings that where not consistent with conventional WSS disturbance predictors. At the 2-3 mm wall-offset range, a strong linear correlation was found between tWSS magnitude and near-wall turbulence kinetic energy (TKE), in contrast to the anisotropy indices, suggesting that MR-measured TKE can be used to assess elevated tWSS regions while tWSS anisotropy estimates request well-resolved simulation methods.

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.

The Assessment of Stent Effectiveness Using a Wearable Beamforming MEMS Microphone Array System

Studies involving turbulent flow have been carried out in many parts of the cardiovascular system, and it has been widely reported that turbulence related to stenosis (narrowing) of arteries creates audible sounds, which may be analyzed to yield information about the nature and severity of the blockage. Results so far indicate that the high frequency content of the sounds generally increases with the degree of stenosis. In this paper, we designed and built an MEMs microphone array and a signal acquisition board to improve the detection of coronary occlusions using an approach based on the recording and analysis of isolated diastolic heart sounds associated with turbulent blood flow in occluded coronary arteries. The nonlinear dynamic analysis method based on approximate entropy has been proposed for the analysis of diastolic heart sounds from patients with single coronary occlusions, before and after stent placement procedures. The nonlinear dynamic analysis (approximate entropy) measures of the diastolic heart sounds recorded from eight patients with single coronary occlusions and two normal subjects were estimated. In addition, a spectral analysis based on the fast Fourier transform was used to estimate the energy content of the recorded signals. Results suggest the presence of high nonlinear (approximate entropy) values of diastolic heart sounds associated with coronary artery disease (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$p<0.01$ \end{document}) as well as significant differences in the energy content of the heart sound signals above and below 150 Hz (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$p<0.05$ \end{document}).

Audible Coronary Artery Stenosis

OBJECTIVE

Hemodynamically significant coronary artery stenoses generate turbulent blood flow patterns that manifest as intracoronary murmurs. This study aims to evaluate the performance of modern acoustic detection of these murmurs by acoustic signals captured from patients undergoing gold standard comparative coronary angiography.

METHODS

We prospectively studied 156 patients undergoing elective coronary angiography, excluding those with acute coronary syndrome, prior chest surgery, or significant valvular disease. Acoustic signals were captured before arterial access. Angiographic degree of stenosis in each coronary artery was graded blinded to clinical and acoustic data. Acoustic data were analyzed blinded to clinical and angiographic data, categorizing subjects as "normal," "diseased," or "inconclusive." Of 156 patients examined, 123 generated analyzable data.

RESULTS

Angiographically significant stenosis (≥50%) prevalence was 52% (18%, 23%, 11% with 1-, 2-, 3-vessel disease, respectively). Acoustic detection sensitivity and specificity for stenosis ≥50% in any vessel were 0.70 and 0.80, respectively (negative predictive value, 0.71; positive predictive value, 0.79). Acoustic detection optimally identified stenosis ≥50% with an area under the curve of 0.75. For stenosis ≥50% in major vessels only (left main, proximal-mid left anterior descending, proximal-mid circumflex, proximal-mid right coronary), prevalence was 46%; sensitivity and specificity were 0.72 and 0.76, respectively (negative predictive value, 0.76; positive predictive value, 0.72; area under the curve, 0.76).

CONCLUSIONS

Acoustic signal patterns and modern analysis techniques may be used to identify intracoronary murmurs generated by hemodynamically significant coronary artery stenoses in all major vessels. Further investigation is warranted to compare the clinical performance of this modality with current noninvasive approaches that evaluate patients at risk for atherosclerotic and obstructive coronary artery disease.

Original Research: Sickle cell anemia and pediatric strokes: Computational fluid dynamics analysis in the middle cerebral artery

Children with sickle cell anemia (SCA) have a high incidence of strokes, and transcranial Doppler (TCD) identifies at-risk patients by measuring blood velocities in large intracerebral arteries; time-averaged mean velocities greater than 200 cm/s confer high stroke risk and warrant therapeutic intervention with blood transfusions. Our objective was to use computational fluid dynamics to alter fluid and artery wall properties, to simulate scenarios causative of significantly elevated arterial blood velocities. Two-dimensional simulations were created and increasing percent stenoses were created in silico, with their locations varied among middle cerebral artery (MCA), internal carotid artery (ICA), and anterior cerebral artery (ACA). Stenoses placed in the MCA, ICA, or ACA generated local increases in velocity, but not sufficient to reach magnitudes > 200 cm/s, even up to 75% stenosis. Three-dimensional reconstructions of the MCA, ICA, and ACA from children with SCA were generated from magnetic resonance angiograms. Using finite element method, blood flow was simulated with realistic velocity waveforms to the ICA inlet. Three-dimensional reconstructions revealed an uneven, internal arterial wall surface in children with SCA and higher mean velocities in the MCA up to 145 cm/s compared to non-SCA reconstructions. There were also greater areas of flow recirculation and larger regions of low wall shear stress. Taken together, these bumps on the internal wall of the cerebral arteries could create local flow disturbances that, in aggregate, could elevate blood velocities in SCA. Identifying cellular causes of these microstructures as adhered blood cells or luminal narrowing due to endothelial hyperplasia induced by disturbed flow would provide new targets to treat children with SCA. The preliminary qualitative results provided here point out the critical role of 3D reconstruction of patient-specific vascular geometries and provide qualitative insight to complex interplay between vascular geometry and rheological properties possibly altered by SCA.

ENDOTHELIAL MECHANOTRANSDUCTION MECHANISMS FOR VASCULAR PHYSIOLOGY AND ATHEROSCLEROSIS

Vascular physiology and disease progression, such as atherosclerosis, are mediated by hemodynamic force generated from blood flow. The hemodynamic force exerts on vascular endothelial cells (ECs), which could perceive the mechanical signals and transmit them into cell interior by multiple potential shear sensors, collectively known as mechanotransduction. However, we do not understand completely how these shear-sensitive components orchestrate physiological and atherosclerotic responses to shear stress. In this review, we provide an overview of biomechanical mechanisms underlying vascular physiology and atherosclerotic progression. Additionally, we summarize current evidences to illustrate that atherosclerotic lesions preferentially develop in arterial regions experiencing disturbance in blood flow, during which endothelial dysfunction is the initial event of atherosclerosis, inflammation plays dominant roles in atherosclerotic progression, and angiogenesis emerges as compensatory explanation for atherosclerotic plaque rupture. Especially in the presence of systemic risk factors (e.g., hyperlipidaemia, hypertension and hyperglycemia), the synergy between these systemic risk factors with hemodynamic factors aggravates atherosclerosis by co-stimulating some of these biomechanical events. Given the hemodynamic environment of vasculature, understanding how the rapid shear-mediated signaling, particularly in combination with systemic risk factors, contribute to atherosclerotic progression through endothelial dysfunction, inflammation and angiogenesis helps to elucidate the role for atherogenic shear stress in specifically localizing atherosclerotic lesions in arterial regions with disturbed flow.

Transthoracic coronary Doppler vibrometry in the evaluation of normal volunteers and patients with coronary artery stenosis

Coronary artery vibrometry is a new transthoracic Doppler ultrasound method for the detection of coronary artery stenosis. It detects audio-frequency vibrations generated by coronary artery luminal diameter reduction. We studied 31 patients with known or suspected stenosis using coronary artery vibrometry and quantitative coronary angiography and 83 normal volunteers. A tissue vibration difference index (TVDI) was calculated from the left anterior descending, circumflex, left main and right coronary arteries. Accuracy for coronary artery stenosis detection using TVDI was assessed. Sensitivity for detecting coronary stenosis equal or greater than 25% diameter reduction was 89% in the left anterior descending coronary artery (16/18, 95% confidence interval [CI] = 64%-98%), 87% in the right coronary artery (13/15, 95% CI = 58%-98%), 83% in the circumflex coronary artery (5/6, 95% CI = 36%-99%) and 100% in the left main artery (3/3, 95% CI = 31%-100%). The median TVDI increased with severity of stenosis, suggesting that this measure might be used to track progression/regression of coronary artery stenosis.

Effect of geometrical assumptions on numerical modeling of coronary blood flow under normal and disease conditions

Shear stress plays a pivotal role in pathogenesis of coronary heart disease. The spatial and temporal variation in hemodynamics of blood flow, especially shear stress, is dominated by the vessel geometry. The goal of the present study was to investigate the effect of 2D and 3D geometries on the numerical modeling of coronary blood flow and shear stress distribution. We developed physiologically realistic 2D and 3D models (with similar geometries) of the human left coronary artery under normal and stenosis conditions (30%, 60%, and 80%) using PROE (WF 3). Transient blood flows in these models were solved using laminar and turbulent (k-ω) models using a computational fluid dynamics solver, FLUENT (v6.3.26). As the stenosis severity increased, both models predicted a similar pattern of increased shear stress at the stenosis throat, and in recirculation zones formed downstream of the stenosis. The 2D model estimated a peak shear stress value of 0.91, 2.58, 5.21, and 10.09 Pa at the throat location under normal, 30%, 60%, and 80% stenosis severity. The peak shear stress values at the same location estimated by the 3D model were 1.41, 2.56, 3.15, and 13.31 Pa, respectively. The 2D model underestimated the shear stress distribution inside the recirculation zone compared with that of 3D model. The shear stress estimation between the models diverged as the stenosis severity increased. Hence, the 2D model could be sufficient for analyzing coronary blood flow under normal conditions, but under disease conditions (especially 80% stenosis) the 3D model was more suitable.

Sickle cell biomechanics

As the predominant cell type in blood, red blood cells (RBCs) and their biomechanical properties largely determine the rheological and hemodynamic behavior of blood in normal and disease states. In sickle cell disease (SCD), mechanically fragile, poorly deformable RBCs contribute to impaired blood flow and other pathophysiological aspects of the disease. The major underlying cause of this altered blood rheology and hemodynamics is hemoglobin S (HbS) polymerization and RBC sickling under deoxygenated conditions. This review discusses the characterization of the biomechanical properties of sickle RBCs and sickle blood as well as their implications toward a better understanding of the pathophysiology of the disease.

Real-time assessment of flow reversal in an eccentric arterial stenotic model

Plaque rupture is the leading cause of acute coronary syndromes and stroke. Plaque formation, otherwise known as stenosis, preferentially occurs in the regions of arterial bifurcation or curvatures. To date, real-time assessment of stenosis-induced flow reversal remains a clinical challenge. By interfacing microelectromechanical system (MEMS) thermal sensors with the high frequency pulsed wave (PW) Doppler ultrasound, we proposed to assess flow reversal in the presence of an eccentric stenosis. We developed a 3-D stenotic model (inner diameter of 6mm, an eccentric stenosis with a height of 2.75 mm, and width of 21 mm) simulating a superficial arterial vessel. We demonstrated that heat transfer from the sensing element (2 x 80 μm²) to the flow field peaked as a function of flow rates at the throat of the stenosis along the center/midline of arterial model, and dropped downstream from the stenosis, where flow reversal was detected by the high frequency ultrasound device at 45 MHz. Computational fluid dynamics (CFD) codes are in agreement with the ultrasound-acquired flow profiles upstream, downstream, and at the throat of the stenosis. Hence, we characterized regions of eccentric stenosis in terms of changes in heat transfer along the midline of vessel and identified points of flow reversal with high spatial and temporal resolution.

Doppler vibrometry: assessment of arterial stenosis by using perivascular tissue vibrations without lumen visualization

PURPOSE

To correlate vibration frequency and duration at Doppler vibrometry with stenosis severity determined at catheter angiography.

MATERIALS AND METHODS

Sixteen patients (eight women) scheduled to undergo abdominal or pelvic angiography were recruited after providing informed consent. An ultrasonography (US) scanner was customized to acquire raw echo data before conventional Doppler processing. Data were acquired from perivascular tissue regions proximal to stenoses, close to the most narrow lumen, and distal to stenoses in the renal, hepatic, common iliac, and superior mesenteric arteries. The data were processed to quantify vibration frequency and duration. The minimum lumen diameter and the pre- and poststenotic lumen diameters were quantified from angiograms. One patient with a hepatic artery stenosis did not yield measurable vibrometry data due to significant bowel gas.

RESULTS

Stenoses (diameter reduction, 43%-91%) were angiographically measured in the six renal arteries, four hepatic arteries, three iliac arteries, and one superior mesenteric artery yielding vibrometry data. Three iliac arteries were normal (<30% diameter reduction at angiography). For these 17 arteries, the vibration frequency was higher with a greater percentage of stenosis [Pearson r = .75; P < .001) and a smaller minimum lumen diameter (r = .72; P < .001). The vibration duration increased with a greater percentage of stenosis (r = .7; P < .001).

CONCLUSIONS

Preliminary results indicate that the vibration frequency and duration can be used to quantitatively estimate stenosis severity. Doppler vibrometry is complementary to duplex US and does not require lumen visualization.

Ultrasonic Doppler Vibrometry: Novel Method for Detection of Left Ventricular Wall Vibrations Caused by Poststenotic Coronary Flow

BACKGROUND

A diastolic coronary flow murmur has been reported for patients with coronary stenoses, yet is rarely appreciated during routine auscultation. We hypothesized that an ultrasonic Doppler method can detect the epicardial vibrations associated with this murmur. Ultrasonic Doppler vibrometry is a pulsed wave echocardiography phase demodulation technique designed for detecting vibrations. We correlated the vibration characteristics measured using vibrometry with the angiographic severity of coronary artery stenosis.

METHODS

In a prospective pilot study, 49 patients were recruited for an ultrasound examination before coronary arteriography. An ultrasound instrument was customized to acquire the raw pulsed wave Doppler echocardiographic data from a range gate placed on the left ventricular myocardium near the path of the epicardial coronary arteries.

RESULTS

Patients with angiographically minor stenosis (tightest stenosis < 50% by quantitative coronary angiography, N = 25) had lower diastolic vibration energy (computed as the median spectral energy of myocardial wall velocity in the 100 approximately 1000-Hz frequency band normalized by a baseline diastolic value) compared with patients with moderate or severe stenosis (any stenosis > 50%, N = 24) (P < .001, area under the receiver operating characteristics curve = 0.84). The vibration energy increased with increasing stenosis severity for less severe narrowing (<70%) but decreased for severe narrowing (>70%) (R(2) = 0.21, P < .0002).

CONCLUSIONS

Preliminary evidence indicates that diastolic left ventricular wall vibrations measured using ultrasonic Doppler vibrometry are related to the severity of coronary artery stenoses. With further refinement and validation, this noninvasive and low-cost method could lead to an early screening and monitoring test for coronary artery stenosis.

The shear stress of it all: the cell membrane and mechanochemical transduction

As the inner lining of the vessel wall, vascular endothelial cells are poised to act as a signal transduction interface between haemodynamic forces and the underlying vascular smooth-muscle cells. Detailed analyses of fluid mechanics in atherosclerosis-susceptible regions of the vasculature reveal a strong correlation between endothelial cell dysfunction and areas of low mean shear stress and oscillatory flow with flow recirculation. Conversely, steady shear stress stimulates cellular responses that are essential for endothelial cell function and are atheroprotective. The molecular basis of shear-induced mechanochemical signal transduction and the endothelium's ability to discriminate between flow profiles remains largely unclear. Given that fluid shear stress does not involve a traditional receptor/ligand interaction, identification of the molecule(s) responsible for sensing fluid flow and mechanical force discrimination has been difficult. This review will provide an overview of the haemodynamic forces experienced by the vascular endothelium and its role in localizing atherosclerotic lesions within specific regions of the vasculature. Also reviewed are several recent lines of evidence suggesting that both changes in membrane microviscosity linked to heterotrimeric G proteins, and the transmission of tension across the cell membrane to the cell-cell junction where known shear-sensitive proteins are localized, may serve as the primary force-sensing elements of the cell.

A numerical and experimental investigation of transitional pulsatile flow in a stenosed channel

In the present paper, a closely coupled numerical and experimental investigation of pulsatile flow in a prototypical stenotic site is presented. Detailed laser Doppler velocimetry measurements upstream of the stenosis are used to guide the specification of velocity boundary conditions at the inflow plane in a series of direct numerical simulations (DNSs). Comparisons of the velocity statistics between the experiments and DNS in the post-stenotic area demonstrate the great importance of accurate inflow conditions, and the sensitivity of the post-stenotic flow to the disturbance environment upstream. In general, the results highlight a borderline turbulent flow that sequentially undergoes transition to turbulence and relaminarization. Before the peak mass flow rate, the strong confined jet that forms just downstream of the stenosis becomes unstable, forcing a role-up and subsequent breakdown of the shear layer. In addition, the large-scale structures originating from the shear layer are observed to perturb the near wall flow, creating packets of near wall hairpin vortices.

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.

A turbulence model for pulsatile arterial flows

Difficulties in predicting the behavior of some high Reynolds number flows in the circulatory system stem in part from the severe requirements placed on the turbulence model chosen to close the time-averaged equations of fluid motion. In particular, the successful turbulence model is required to (a) correctly capture the "nonequilibrium" effects wrought by the interactions of the organized mean-flow unsteadiness with the random turbulence, (b) correctly reproduce the effects of the laminar-turbulent transitional behavior that occurs at various phases of the cardiac cycle, and (c) yield good predictions of the near-wall flow behavior in conditions where the universal logarithmic law of the wall is known to be not valid. These requirements are not immediately met by standard models of turbulence that have been developed largely with reference to data from steady, fully turbulent flows in approximate local equilibrium. The purpose of this paper is to report on the development of a turbulence model suited for use in arterial flows. The model is of the two-equation eddy-viscosity variety with dependent variables that are zero-valued at a solid wall and vary linearly with distance from it. The effects of transition are introduced by coupling this model to the local value of the intermittency and obtaining the latter from the solution of a modeled transport equation. Comparisons with measurements obtained in oscillatory transitional flows in circular tubes show that the model produces substantial improvements over existing closures. Further pulsatile-flow predictions, driven by a mean-flow wave form obtained in a diseased human carotid artery, indicate that the intermittency-modified model yields much reduced levels of wall shear stress compared to the original, unmodified model. This result, which is attributed to the rapid growth in the thickness of the viscous sublayer arising from the severe acceleration of systole, argues in favor of the use of the model for the prediction of arterial flows.

Comparison of CFD and MRI Flow and Velocities in an In Vitro Large Artery Bypass Graft Model

Bypass graft failures have been attributed to various hemodynamic factors, including flow stasis and low shear stress. Ideally, surgeries would minimize the occurrence of these detrimental flow conditions, but surgeons cannot currently assess this. Numerical simulation techniques have been proposed as one method for predicting changes in flow distributions and patterns from surgical bypass procedures, but comparisons against experimental results are needed to assess their usefulness. Previous in vitro studies compared simulated results against experimentally obtained measurements, but they focused on peripheral arteries, which have lower Reynolds numbers than those found in the larger arteries. In this study, we compared simulation results against measurements obtained using magnetic resonance imaging (MRI) techniques for a phantom model of a stenotic vessel with a bypass graft under conditions suitable for surgical planning purposes and with inlet Reynolds numbers closer to those found inthe larger arteries. Comparisons of flow rate and velocity profiles were performed at maximum and minimum flows at four locations and used simulation results that were temporally and spatially averaged, key postprocessing when comparing against phase contrast MRI measurements. The maximum error in the computed volumetric flow rates was 6% of the measured values, and excellent qualitative agreement was obtained for the through-plane velocity profiles in both magnitude and shape. The in-plane velocities also agreed reasonably well at most locations.

Noninvasive quantitation of blood flow turbulence in patients with aortic valve disease using online digital computer analysis of Doppler velocity data

Previous experimental studies have demonstrated that aortic valve disease is associated with significant downstream turbulence (T). In this study, we developed a noninvasive method on the basis of Doppler velocity recording for quantitating aortic blood flow T in patients with aortic valve disease. The instantaneous blood velocity at a point in the aorta is equal to the sum of a mean periodic velocity component with a random or turbulent velocity component. According to the ensemble average method, time mean absolute T intensity is the root-mean-square value of turbulent velocity averaged over time and T is better quantitated by the relative T intensity (TIr), which is the ratio of absolute T intensity to the ensemble average velocity averaged over time. We computed TIr in 18 patients with mild to severe aortic stenosis and in 13 healthy volunteers from instantaneous modal velocities of 70 cycle length-matched heart beats recorded in the proximal part of the descending aorta by pulsed Doppler using an ultrasound system with an output port for online digital data transfer into a microcomputer. TIr was greater in patients with aortic valve disease (18.4 +/- 5.1%, range 11.2%-28.9%) than in control patients (7.9 +/- 1.9%, range 4.8%-9.8%; P =.0001). In patients with aortic valve disease, TIr was better linearly related to the ratio of postvalvular aorta to valvular orifice cross-sectional areas (r = 0.89, P =.0001) than to other parameters of valve restriction: transvalvular pressure gradient (r = 0.78, P =.0001); valve area (r = -0.56, P =.01); and valve resistance (r = 0.72, P =.0002). Thus, T that can be computed noninvasively from direct digital transfer of Doppler velocity data appears to be linearly related to indices of aortic valve restriction. Our data support the concept of the postvalvular aorta to valvular orifice cross-sectional areas ratio as a new important hemodynamic parameter in patients with aortic valve disease.

Numerical analysis of flow through a severely stenotic carotid artery bifurcation

The results of computational simulations may supplement MR and other in vivo diagnostic techniques to provide an accurate picture of the hemodynamics in particular vessels, which may help demonstrate the risks of embolism or plaque rupture posed by particular plaque deposits. In this study, a model based on an endarterectomy specimen of the plaque in a carotid bifurcation was examined. The flow conditions include steady flow at Reynolds numbers of 300, 600, and 900 as well as unsteady pulsatile flow. Both dynamic pressure and wall shear stress are very high, with shear values up to 70 N/m2, proximal to the stenosis throat in the internal carotid artery, and both vary significantly through the flow cycle. The wall shear stress gradient is also strong along the throat. Vortex shedding is observed downstream of the most severe occlusion. Two turbulence models, the Chien and Goldberg varieties of k-epsilon, are tested and evaluated for their relevance in this geometry. The Chien model better captures phenomena such as vortex shedding. The flow distal to stenosis is likely transitional, so a model that captures both laminar and turbulent behavior is needed.

In vivo ultrasonic measurement of tissue vibration at a stenosis: a case study

It is known that bruits often can be heard downstream from stenoses. They are thought to be produced by disturbed blood flow and vessel wall vibrations. Our understanding of bruits has been limited, though, to analysis of sounds heard at the level of the skin. For direct measurements from the stenosis site, we developed an ultrasonic pulse-echo multigate system using quadrature phase demodulation. The system simultaneously measures tissue displacements and blood velocities at multiple depths. This paper presents a case study of a severe stenosis in a human infrainguinal vein bypass graft. During systole, nearly sinusoidal vessel wall vibrations were detected. Solid tissue vibration amplitudes measured up to 2 microm, with temporal durations of 100 ms and frequencies of roughly 145 Hz and its harmonics. Cross-axial oscillations were also found in the lumen that correlate with the wall vibrations, suggesting coupling between wall vibration and blood velocity oscillation.

Application of large-eddy simulation to the study of pulsatile flow in a modeled arterial stenosis

The technique of large-eddy simulation (LES) has been applied to the study of pulsatile flow through a modeled arterial stenosis. A simple stenosis model has been used that consists of a one-sided 50 percent semicircular constriction in a planar channel. The inlet volume flux is varied sinusoidally in time in a manner similar to the laminar flow simulations of Tutty (1992). LES is used to compute flow at a peak Reynolds number of 2000 and a Strouhal number of 0.024. At this Reynolds number, the flow downstream of the stenosis transitions to turbulence and exhibits all the classic features of post-stenotic flow as described by Khalifa and Giddens (1981) and Lieber and Giddens (1990). These include the periodic shedding of shear layer vortices and transition to turbulence downstream of the stenosis. Computed frequency spectra indicate that the vortex shedding occurs at a distinct high frequency, and the potential implication of this for noninvasive diagnosis of arterial stenoses is discussed. A variety of statistics have been also extracted and a number of other physical features of the flow are described in order to demonstrate the usefulness of LES for the study of post-stenotic flows.

Characterization of vortices using pulsed-wave Doppler ultrasound

The detection and characterization of vortices from a Kaman vortex generator by means of a 20 MHz pulsed-wave Doppler ultrasound system were assessed. Measurements were made at different steady flowrates in a 10 mm internal diameter polyurethane tube, 14 mm distal to a circular cylinder of diameter 2 mm, placed across the tube inlet. The results were compared with those obtained with a two-component laser Doppler anemometer system. There was generally good agreement between the two techniques in the measurement of convective flow velocity, frequency of vortex shedding and the circulation velocity of the vortices. It is concluded that pulsed-wave Doppler ultrasound is a suitable technique for investigating vortical flow structures.

Three-dimensional numerical simulations of flow through a stenosed coronary bypass

This work analyzes the flow patterns at the anastomosis of a stenosed coronary bypass. Three-dimensional numerical simulations are performed using a finite elements method. We consider a geometrical model of the host coronary artery with and without a 75% severity stenosis for three different locations from the anastomosis. The flow features - velocity profiles, secondary motions and wall shear stresses - are compared for different configurations of the flow rate and of the distance of the anastomosis from the site of occlusion (called distance of grafting). The combination of the junction flow effects - counter rotating vortices - with the stenosis effects - confined jet flow - is particularly important when the distance of grafting is short. Given that the residual flow issued from the pathologic stenosis being non-negligible after two weeks grafting, models without stenosis cannot predict the evolution of the wall shear stress in the vicinity of the anastomosis.

Influence of stenosis morphology on flow through severely stenotic vessels: implications for plaque rupture

Flow patterns and flow-related stresses contribute to the characterization of health risks, particularly the risk of plaque rupture, posed by a particular atherosclerotic stenosis. Blood flow in the presence of significant plaque deposits is investigated, and the influence of factors such as stenosis morphology and surface irregularity is evaluated. Solutions for three-dimensional, unsteady flow in these stenotic vessels are obtained for an incompressible, Newtonian fluid. The equations of motion are solved numerically using a finite volume formulation. The resulting flow patterns and shear and normal stresses are interpreted with respect to diagnostic implications, including the possibility of plaque rupture. The inadequacy of "percent stenosis" to characterize the risks posed by a particular plaque is demonstrated. Surface irregularity, stenosis aspect ratio, and the shape of the pulsatile waveform all have considerable influence on the flow field and on the stresses on the plaque. A measure of surface irregularity or plaque symmetry, in particular, may complement percent stenosis in diagnosing the risk of plaque rupture.

Experimental and numerical study of pulsatile flows through stenosis: wall shear stress analysis

Different shapes of pulsatile flows through a model of stenosis are experimentally and numerically modeled to validate both methods and to determine the wall shear stress temporal evolution downstream from the stenosis. Two-dimensional velocity measurements are performed in a 75% severity stenosis using a pulsed Doppler ultrasonic velocimeter. Finite element package is employed for the transient numerical simulations. Polynomial method, based on the experimental velocity values, is proposed to determine the wall shear stress temporal evolution. There is a good agreement between the numerical and experimental results. The wall shear stress temporal analysis shows oscillating wall shear stress values during the cycle with high wall shear stress values at the throat of about 120 dyn/cm2, and low values downstream from the stenosis of about - 2.5 dyn/cm2. The key result of the study is that the presence of the stenosis leads the artery to work in a direction which is opposite to the direction of a healthy artery.

Experimental analysis of unsteady flows through a stenosis

In this paper we present a study of the post-stenotic velocity flow field corresponding to oscillatory, pulsatile and physiological flow waveforms. Two-dimensional velocity measurements are performed in a 75% severity stenosis using a pulsed Doppler ultrasonic velocimeter. Emphasis is placed on the analysis of the experimental velocity-profile patterns. It is recognized that, beyond the influence of the flow parameters such as the Reynolds number and the frequency parameter, velocity profiles (hence wall-shear stresses) highly depend on the flow waveform. In addition to this analysis, a model of the stenosis influence length is proposed in the case of oscillatory flow.

Analysis of the axial flow field in stenosed carotid artery bifurcation models--LDA experiments

Laser Doppler anemometer (LDA) experiments were performed to gain quantitative information on the differences between the large-scale flow phenomena in a non-stenosed and a stenosed model of the carotid artery bifurcation. The influence of the presence of the stenosis was compared to the effect of flow pulse variation to evaluate the feasibility of early detection of stenosis in clinical practice. Three-dimensional Plexiglass models of a non-stenosed and a 25% stenosed carotid artery bifurcation were perfused with a Newtonian fluid. The flow conditions approximated physiological flow. The results of the velocity measurements in the non-stenosed model agreed with the results from previous hydrogen-bubble visualization. A shear layer separated the low-velocity area near the non-divider wall from the high-velocity area near the divider wall. In this shear layer, vortex formation occurred during the deceleration phase of the flow pulse. The instability of this shear layer dictated the flow disturbances. The influences of the mild stenosis, located at the non-divider wall, was mainly limited to the stability of the shear layer. No disturbances were found downstream of the stenosis near the non-divider wall. Using a pulse wave with an increased systolic deceleration time, the velocity distribution showed an extended region with reversed flow, a more pronounced shear layer and increased vortex strength. From these measurements it is obvious that the influence of the presence of a mild stenosis, mainly limited to the stability of the shear layer, can hardly be distinguished from the effects of a variation of the flow pulse. From this it can be concluded that methods for detection of mild stenosis, using solely the large-scale flow phenomena, as can be measured by ultrasound or MRI techniques, will hardly have any clinical relevance.

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.

Studies by pulsed Doppler ultrasonography of velocity fields downstream of graded stenoses on the abdominal aorta in pigs

PURPOSE

To investigate local hemodynamics downstream of arterial stenoses, a perivascular five-element Doppler ultrasound transducer was used for registration of one-dimensional velocity profiles and estimation of Reynolds (turbulent) normal stresses downstream of smooth, graded stenoses on the abdominal aorta in six 90 kg pigs.

METHODS

Blood velocities were registered by a 10 MHz pulsed Doppler velocimeter that used a modified zero-crossing detector with an upper -3 dB cutoff frequency of 200 Hz. Signal analysis included ensemble averaging, turbulence analysis, and dimensional visualization of velocity profiles.

RESULTS

Velocity profiles downstream of minor (< or = 40%) and moderate (40% to 65%) stenoses were skewed with the highest systolic velocities toward the anterior vessel wall and diastolic flow reversal occasionally present at the posterior vessel wall. Immediately downstream of severe (> or = 65%) stenoses a prominent poststenotic jet and systolic recirculation zones were present. Further downstream, vortices and eddies dominated the flow field. Reynolds normal stresses were highest at locations in the velocity field with high-velocity gradients corresponding to the parajet zone.

CONCLUSIONS

The present study demonstrated that pulsed Doppler ultrasonography can provide detailed and quantitative information of flow phenomena such as jetlike flow, vortices, and recirculation zones in a poststenotic flow field in the abdominal aorta.

Noninvasive characterization of the sound pattern caused by coronary artery stenosis using FTF/FAEST zero tracking filters: normal/abnormal study

In this article, a new approach has been proposed to investigate the extraction of useful information from diastolic heart sounds caused by partially occluded coronary arteries. This method, which estimates and tracks the zeros (poles) of the diastolic heart sounds directly, takes advantage of the FTF/FAEST (Fast Transversal Filters/Fast a Posteriori Error Sequential) technique which possesses the fast convergence property of the Recursive Least Square (RLS) method and the computational simplicity of the Least Mean Square (LMS) method. In previous studies, the main assumption was that the diastolic heart sounds were a stationary process. Since the production of the heart sounds were a stationary process. Since the production of the heart sounds is not a stationary process, a new approach that performs well not only for stationary but also for nonstationary processes can be required. This requirement can be satisfied by the adaptive FTF/FAEST zero tracking method which provides fast and stable convergence as well as computational efficiency since the adaptive FTF/FAEST zero tracking method is based on the exact minimization of least squares criteria and the filter weights of this method are optimal at each time instant. The zero trajectories of the diastolic heart sounds were used to diagnose patients as diseased or normal. Results showed that the normal and abnormal records were incorrectly distinguished in only 6 of 35 cases using a blind protocol where analysis was done without knowledge of the actual disease states of the patients. The most discriminant time region of the zero trajectories of the diastolic heart sounds associated with coronary artery disease was between 200 and 300 msec after the second heart sound during the diastolic period.

Accelerometer type cardiac transducer for detection of low-level heart sounds

New applications in phonocardiography require transducers with high sensitivity, low noise, and extended frequency range. This paper compares several different cardiac transducers and describes the development of a low-mass, accelerometer type cardiac transducer which fulfills these objectives. The accelerometer weighs approximately 5 g and has a theoretical sensitivity of 125 mV/g in the frequency range 200-800 Hz. The basic design allows for easy modification of sensitivity and resonant frequency. This transducer has been effective in detecting sounds associated with turbulent blood flow in partially occluded coronary arteries.

Application of adaptive filters to noninvasive acoustical detection of coronary occlusions before and after angioplasty

Previous studies have indicated that coronary stenoses produce sounds due to the turbulent blood flow in these vessels [1]-[10]. Measurement of these signals forms the basis of our noninvasive approach to the detection of coronary artery disease. It is during diastole that coronary blood flow is maximum and the sounds associated with turbulent blood flow through partially occluded coronary arteries would be loudest [1]-[10]. Isolated diastolic heart sounds taken from recordings made at the patient's bedside were modeled using the autoregressive (AR) and autoregressive moving average (ARMA) methods [4], [7] after adaptive line enhancement (ALE). Decisions were made in a blind fashion without prior knowledge of whether a given recording was made before or after angioplasty. Resulting model frequency spectra showed greater high-frequency components (between 400 and 800 Hz) in preangioplasty patients, and a consistent shift in amplitude of the second pole pairs of the AR and ARMA methods with surgery. Blind assessment, based on frequency spectra and poles, correctly classified the diastolic recordings in 18 of 20 cases. These results provide strong evidence supporting our hypothesis that coronary stenoses produce detectable sounds during diastole [1]-[10].

Application of the ARMA method to acoustic detection of coronary artery disease

To further explore the application of advanced signal processing techniques to the noninvasive detection of coronary artery disease, 30 patients (10 angioplasty and 20 normal or abnormal) were tested using autoregressive moving average (ARMA) modelling of the diastolic heart sound data. It is during diastole that coronary blood flow is maximum and sounds associated with turbulent blood flow through partially occluded coronary arteries would be loudest. Model parameters (the power spectral density (PSD) functions and the poles of the ARMA method) were used to separate the normal patients from the abnormal patients in the normal/abnormal study, or to decide whether the recordings were made before or after angioplasty in the angioplasty study. The decisions were made 'blind', without knowledge of the actual disease states of the patients for the normal/abnormal study and without prior knowledge of whether a given recording was made before or after angioplasty for the angioplasty study. Results from the angioplasty and the normal/abnormal studies showed that pre- and post-angioplasty records were correctly distinguished in 8 out of 10 cases, and normal and abnormal records were correctly distinguished in 17 of 20 cases. These results also confirmed that high frequency energy above 400 Hz is probably associated with coronary stenosis.

Velocity field studies at surgically imposed arterial stenoses on the abdominal aorta in pigs

In order to describe velocity profiles and the size of deterministic and non-deterministic velocity disturbances at arterial stenoses, symmetrical and asymmetrical stenoses with intended area reductions of 50% ('moderate') and 85% ('severe') were applied on the abdominal aorta in six pigs. Blood velocities were registered by hot-film anemometry in 21 measuring points distributed across the vessel cross-sectional area in one pre-stenotic and three post-stenotic positions. Signal analysis included ensemble averaging, the high-pass filtering technique, and three-dimensional visualization. None of the stenoses affected the pre-stenotic velocity field. Downstream moderate stenoses flow separation and vortex formation were present. Moderate asymmetric stenoses induced turbulence in the post-stenotic velocity field. Immediately downstream of severe stenoses a prominent post-stenotic jet was present. Farther downstream, a multitude of coherent vortices and turbulence dominated the flow field. The transverse distribution of turbulence intensity paralleled with the peak systolic velocity profile, whereas transverse profiles of the relative turbulence intensity (turbulence intensity/mean velocity) revealed peak values in flow field locations with high velocity gradients. Velocity parameters for symmetric and asymmetric severe stenoses were highly comparable. However, the exact degree of stenosis was significantly higher for symmetrical (85%) than for asymmetrical (76%) stenoses. Therefore, recalling that stenosis severity strongly influences the development of velocity disturbances, this indicates that asymmetry of a stenosis is a predictor for blood velocity disturbances.

Effect of compliance mismatch on flow disturbances in a model of an arterial graft replacement

Flow disturbances in a model of an interposition graft in an arterial segment were measured using an ultrasound Doppler velocimeter. The effect of the degree of compliance mismatch between a stiff' graft' and compliant 'arterial' segments was investigated. In steady flow, disturbances were detected when the compliance ratio (stiff to compliant segments) was less than or equal to 0.1 and the Reynolds number greater than or equal to 2200. A recirculation zone just downstream of the distal anastomosis was observed at a Reynolds number greater than or equal to 2400. Disturbances were also measured under pulsatile flow which consisted of a time-varying component superimposed on a steady flow component. The time-varying flow component was either quasiphysiological or sinusoidal in shape. The Reynolds number was 500 but the frequency parameter varied from 4.2 to 8.5. Significant disturbances were observed for conduits with compliance ratio less than or equal to 0.19. The disturbance intensity tended to increase as the compliance ratio decreased and the frequency parameter increased. The magnitude of the disturbance was also greater with the quasiphysiological than the sinusoidal input flow waveform.

Post-stenotic core flow behavior in pulsatile flow and its effects on wall shear stress

Arteries of several species, including man, tend to adjust their diameters such that the mean wall shear stress is in the range of 10-20 dynes cm-2. Additionally, intimal thickening in the human carotid bifurcation correlates well with the reciprocal of wall shear stress as determined in model studies. The correlation indicates that wherever the local mean wall shear stress exceeds approximately 10 dynes cm-2, the artery tends to be spared from intimal thickening. However, it is not known whether mean shear stress, i.e. the time-averaged value, or the instantaneous shear stress is the appropriate correlative variable. Each of these variables suggests different mechanisms for the reaction of the artery wall to its hemodynamic environment. It is therefore important to devise means by which the effects of mean shear and pulsatile shear can be separated in the study of atherogenesis. The present investigation examines the post-stenotic flow field in Plexiglas models under pulsatile conditions approximating those in the aortas of the cynomolgus monkey, an animal often employed in atherogenesis research. Behavior of the core flow and its effects on wall shear stress are studied for stenoses of 75 and 90% area reductions using laser velocimetry. The results show that the post-stenotic field contains regions in which the mean wall shear stress is low, but the pulsatile excursions are large.(ABSTRACT TRUNCATED AT 250 WORDS)

Analysis of flow characteristics in poststenotic regions of the human coronary artery during bypass graft surgery

Poststenotic blood flow velocities were evaluated in nine patients with 75% to 99% stenosis of the left anterior descending coronary artery (LAD) during coronary artery bypass graft surgery. We used the 20 MHz 80-channel pulsed Doppler velocimeter developed in our laboratory. An operator placed a specially designed probe on the native LAD with his fingers. Before induction of extracorporeal circulation, LAD blood velocities were measured at several locations distal to the stenosis. The poststenotic flow velocities were rich in systolic flow component with reduced diastolic component. The velocity configuration in the poststenotic portions was characterized by the presence of reverse flow velocities and/or irregularity of the velocity pattern near the vessel wall, indicating the existence of flow separation and recirculation in the regions. The broadening of the velocity spectrum observed at central axial regions suggested the occurrence of flow disturbances. After grafting, the velocity waveform in the LAD beyond a vein bypass graft changed to a diastolic-predominant pattern with a relatively small systolic component. A transient bypass graft occlusion caused a marked reduction in diastolic flow velocity. The systolic-to-diastolic velocity ratio increased from 0.27 +/- 0.07 to 1.50 +/- 0.50 (p less than .01) by the graft occlusion.

The analysis of blood velocity measurements by autoregressive modelling

Analysis of velocity disturbances arising in poststenotic flow is examined using the technique of autoregressive modeling. The essential elements of this method are described including relevant criteria for selecting the model order. Velocity data employed in the analysis are taken from in vivo measurements in the dog aorta, and the results indicate that the autoregressive method improves the resolution of coherent features in disturbed flow patterns. By applying homomorphic filtering to individual beats, the occurrence of organized structures convected from their origin in the shear layer is readily identified.

In vivo demonstration of flow recirculation and turbulence downstream of graded stenoses in canine arteries

The velocity field around arterial stenoses was investigated using a pulsed doppler velocimeter in vivo. Asymmetric zones of recirculation were identified by systolic flow reversal in the post-stenotic field in carotid and iliac arteries of anesthetised dogs. There was a close correlation between shear intensity and turbulence as estimated by the velocity difference between the jet and the recirculation zone and by maximum spectral width respectively. Under the conditions of these experiments, stenosis grade (% diameter reduction) dominated hemodynamic variables such as Reynolds number, oscillation and pulsatility in determining the intensity of turbulence. The method used does not appear to have sufficient resolution to distinguish between turbulence and discrete oscillating velocities (vorticity) nor to allow determination of wall shear stress though the pattern of change of the latter is similar to that found downstream of axisymmetric stenosis in models using steady flow.