Instantaneous Mean Velocity Research Articles

Echocardiographic Quantification of Superior Vena Cava (SVC) Flow in Neonates: Pilot Study of Modified Technique.

Ultrasound Superior Vena Cava (SVC) flow assessment is a common measure of systemic and cerebral perfusion, although accuracy is limited. The aim of this study was to evaluate whether any improvements in accuracy could be achieved by measuring stroke distance from the instantaneous mean velocity, rather than from peak velocity, and by directly tracing area from images obtained with a high frequency linear probe. Paired phase contrast magnetic resonance imaging (PCMRI) and ultrasound assessments of SVC flow were performed in a pilot cohort of 7 infants. Median postnatal age, corrected gestation and weight at scan were 7 (2–74) days, 34.8 (31.7–37.2) weeks 1870 (970–2660) g. Median interval between PCMRI and ultrasound scans was 0.3 (0.2–0.5) h. The methodology trialed here showed a better agreement with PCMRI (mean bias −8 mL/kg/min, LOA −25–+8 mL/kg/min), compared to both the original method reported by Kluckow et al. (mean bias + 42 mL/kg/min, LOA −53–+137 mL/kg/min), and our own prior adaptation (mean bias + 23 mL/kg/min, LOA −25–+71 mL/kg/min). Ultrasound assessment of SVC flow volume using the modifications described led to enhanced accuracy and decreased variability compared to prior techniques in a small cohort of premature infants.

Study on probabilistic mean features of lower and upper free-surface profiles and velocity fields of a highly fluctuating free jet over a chute

An optic-based method that utilizes the particle-laden images captured during high-speed particle image velocimetry (HSPIV) measurements is presented, aiming to explore the probabilistic mean characteristics of the free surface profiles and velocity fields of a free jet with high-frequency random fluctuations over a chute. The technique based on the gray-level gradients in the smoothed gray level distribution of the contrast-enhanced images is used to determine the probabilistic mean features of the free jet, right beneath and above which the water-air interfaces have I%/(100－I)% intermittent appearance of air/water phase and (100－I)%/I% fitful show-up of water/air phase. Further, the cross-correlation calculation for HSPIV measurements is employed to obtain the instantaneous and probabilistic mean velocity fields of the free jet. A target experiment of the free jet having a mean water-depth of 2.76 cm and a Froude number of 3.92 over a 17° chute model is performed in a re-circulating water channel to demonstrate the application of this method.

Estimating the instantaneous velocity of randomly moving target swarms in a stratified ocean waveguide by Doppler analysis

Doppler analysis has been extensively used in active radar and sonar sensing to estimate the speed and direction of a single target within an imaging system resolution cell following deterministic theory. For target swarms, such as fish and plankton in the ocean, and raindrops, birds and bats in the atmosphere, multiple randomly moving targets typically occupy a single resolution cell, making single-target theory inadequate. Here, a method is developed for simultaneously estimating the instantaneous mean velocity and position of a group of randomly moving targets within a resolution cell, as well as the respective standard deviations across the group by Doppler analysis in free-space and in a stratified ocean waveguide. While the variance of the field scattered from the swarm is shown to typically dominate over the mean in the range-velocity ambiguity function, cross-spectral coherence remains and maintains high Doppler velocity and position resolution even for coherent signal processing algorithms such as the matched filter. For pseudo-random signals, the mean and variance of the swarms' velocity and position can be expressed in terms of the first two moments of the measured range-velocity ambiguity function. This is shown analytically for free-space and with Monte-Carlo simulations for an ocean waveguide.

Unsteady turbulence in plane channel flow

Direct numerical simulations were conducted for oscillating flow with zero time mean (reciprocating flow) in a plane channel subject to a harmonic forcing term of varying amplitude and frequency. The results confirmed the existence of four flow regimes (laminar, “disturbed laminar”, intermittently turbulent, and fully turbulent) depending on the above parameters. The flow behaviour was found to depend on the complex interplay of mean and turbulence quantities, as described by the closed loop formed by the streamwise Reynolds-averaged momentum equation in conjunction with the exact transport equations for the turbulent (Reynolds) stresses. A crucial role in this loop appeared to be played by the different time response of the mean flow to the applied forcing at different cross-stream locations, due to the laminar and turbulent diffusion of momentum from the walls and causing characteristic distortions of the cross-stream mean velocity profiles at different phases (i.e. acceleration vs. deceleration). The intrinsic inertia of turbulence quantities themselves played only a minor role, as confirmed by the fact that, in a broad range of conditions, turbulent stresses were roughly in phase with the respective production and dissipation terms. The structure of turbulence was found to depend largely on the instantaneous mean velocity profile, as confirmed by “frozen velocity” simulations.

Pulsatile viscous flow in a curved pipe: Effects of pulsation on the development of secondary flow

This work presents an experimental and numerical study of pulsated Dean flow, three-dimensional pulsatile flow in a curved pipe. The numerical study is performed by CFD code (Fluent 6) in which a pulsated velocity field is imposed as an inlet condition. The experimental setup involves principally a “Scotch-yoke” pulsatile generator and a 90° bend. Laser Doppler Velocimetry (LDV) measurements have shown that the Scotch-yoke generator produces pure sinusoidal instantaneous mean velocities with a mean deviation of 3%. Visualizations by laser-induced fluorescence (LIF) and velocity measurements, coupled with the numerical results, have permitted analysis of the evolution of the swirling secondary flow structures that develop along the bend during the pulsation phase. These measurements were made for a range of stationary Reynolds number ( 300 ⩽ Re st ⩽ 1200 ) , frequency parameter ( 1 ⩽ α = r 0 ( ω / ν ) 1 / 2 < 20 ) , and two velocity components ratios ( β = U max , osc / U st ) . We observe satisfactory agreement between the numerical and experimental results. For high β, the secondary flow structure is modified by a Lyne instability and a siphon effect during the deceleration phase. The intensity of the secondary flow decreases as the parameter α increases during the acceleration phase. During the deceleration phase, under the effect of reverse flow, the secondary flow intensity increases with the appearance of Lyne flow.

Pulsating Flow for Mixing Intensification in a Twisted Curved Pipe

This work concerns the manipulation of a twisted curved-pipe flow for mixing enhancement. Previous works have shown that geometrical perturbations to a curved-pipe flow can increase mixing and heat transfer by chaotic advection. In this work the flow entering the twisted pipe undergoes a pulsatile motion. The flow is studied experimentally and numerically. The numerical study is carried out by a computational fluid dynamics (CFD) code (FLUENT 6) in which a pulsatile velocity field is imposed as an inlet condition. The experimental setup involves principally a “Scotch-yoke” pulsatile generator and a twisted curved pipe. Laser Doppler velocimetry measurements have shown that the Scotch-yoke generator produces pure sinusoidal instantaneous mean velocities with a mean deviation of 3%. Visualizations by laser-induced fluorescence and velocity measurements, coupled with the numerical results, have permitted analysis of the evolution of the swirling secondary flow structures that develop along the bends during the pulsation phase. These measurements were made for a range of steady Reynolds number (300≤Rest≤1200), frequency parameter (1≤α=r0⋅(ω/υ)1/2&lt;20), and two velocity component ratios (β=Umax,osc/Ust). We observe satisfactory agreement between the numerical and experimental results. For high β, the secondary flow structure is modified by a Lyne instability and a siphon effect during the deceleration phase. The intensity of the secondary flow decreases as the parameter α increases during the acceleration phase. During the deceleration phase, under the effect of reverse flow, the secondary flow intensity increases with the appearance of Lyne flow. Experimental results also show that pulsating flow through a twisted curved pipe increases mixing over the steady twisted curved pipe. This mixing enhancement increases with β.

Doppler sonography assessment of blood flow velocity in the ascending aorta. Problems and possible solutions

Irregularities of the transvascular distribution of blood flow within the human ascending aorta have been documented by means of 16 Doppler gates positioned along one scanline of a sector scanner. The velocity profiles recorded from ten healthy adults, ten patients suffering from hypertrophic obstructive cardiomyopathy, ten patients suffering from hypertrophic nonobstructive cardiomyopathy, and ten patients with severe aortic insufficiency exhibited nonuniformities which varied not only from individual to individual but also between the groups and depending on the phase of the cardiac cycle. These variations prevent any local measurement from being representative for the instantaneous mean velocity in all cases. A reliable mean should therefore be determined by simultaneously taking into account all velocities within the vascular cross-section. A computer simulation in order to indicate a potential solution to this problem demonstrates that an annular array transducer can be excited in such a manner that it produces a homogeneous ultrasound beam of a transverse area a hundred times larger than the one obtained in the conventional maximally focussed mode.

Deceleration vs. acceleration: a haemodynamic parameter in the assessment of vascular reactivity. A preliminary study

The parameter deceleration vs. acceleration ( dc ac ) as derived from the instantaneous peak velocity is obtained by dividing the descending and ascending slopes of plotted velocity curves. Blood velocities were recorded with a specially designed continuous-wave ultrasonic Doppler unit which provides: the instantaneous peak velocity, the instantaneous mean velocity, the acceleration, and an indication of volume flow. A physical meaning to the dc ac parameter is given through an analysis, based on an electrical model, of a small portion of an artery. This gives a simple relationship which only takes account of the assumed vascular resistances. Measurements were performed in 67 male subjects; 39 were normotensive control subjects and 28 had established moderate hypertension. In both groups there was an increase of dc ac in passing from the supine to the erect position, the increase being more accentuated by hypertension. The variation of dc ac with age was significantly different in both groups. The results suggest that this parameter is a sensitive indicator of variations in vascular reactivity and as an indicator of structural changes in the arterial wall.

Statistical bias and variance in blood flow estimation by spectral analysis of Doppler signals

The stochastic nature of the Doppler signal is discussed as a source of variability and bias in estimation of mean blood velocity and flow performed using the Discrete or Fast-Fourier Transform. The estimators studied are those appropriate when the ultrasound beam is assumed to be wide enough to insonate the cross-section of the vessel uniformly, and assumed to be narrow enough to insonate only a diameter. Approximate expressions are derived theoretically for the biases and variances of these statistics when the Doppler power spectrum is uniform. For more complex spectra numerical evaluation is carried out by computer. Results for the double-sided spectra obtained from mixed flow are inferred from the single-sided cases. Typically, an estimate of instantaneous mean velocity has very little bias added (< 1%) but might have a standard error of ∼10% of its mean value, and an estimate of flow in one cardiac cycle a standard error of ∼1% of its mean value.

LaPlace transform analysis of femoral artery doppler signals: The state of the art

A followup study was conducted to validate our previous experience with the LaPlace Transform Analysis (LTA) method for processing Doppler ultrasound signals from the common femoral artery to detect significant stenosis of the aorto-iliac segment. The first phase used the same instantaneous mean velocity signal processor as used in the prior study. A comparison of the Doppler examinations with angiograms in 98 legs yielded a sensitivity = 92% and sensitivity = 94% in the identification of 50% or greater stenosis of the aorta-iliac segment, results almost identical to the last study. Because of theoretical disadvantages of using the instantaneous mean velocity signal we carried out a second phase using a peak velocity detector. In 148 limbs sensitivity = 87% and specificity = 98%. The presence or absence of superficial femoral artery occlusion did not affect the accuracy of the waveform analysis in the detection of proximal disease. The LTA parameter related to distal resistance, G, was not found to have clinical value in the assessment of the femoral-popliteal segment.

Acute effects of acetazolamide on cerebral blood flow in man.

We have followed the time course of the effect of the carbonic anhydrase inhibitor acetazolamide injected i.v. in unanesthetized healthy human beings. The dose administered was 500 mg as a bolus. Cerebral blood flow (CBF) was measured continuously before, during and after the injection, using a pulsed ultrasound doppler system, which measured the instantaneous mean velocity across the lumen of the internal carotid artery, just below its entrance into the skull. Ventilation, heart-rate, end-expiratory PCO2, arterial PCO2, pH and systemic blood pressure was also measured. We found that acetazolamide caused a rise in CBF which could be detected as early as 2 min after the injection. A maximal average response of 75% increase in CBF was seen after 25 min. The half-time of the declining phase of the response was 95 min. There were no systematic differences in the CO2 reactivities, given as delta CBF/delta PACO2 in % of CBF at normocapnia, before and after acetazolamide injection, regardless of the absolute PACO2 level. The present dose of the drug caused no change in ventilation, alveolar and arterial PCO2 or in arterial blood pH indicating that the carbonic anhydrase was not fully inhibited. Our observations show that acetazolamide nevertheless caused a rapid vasodilation in the brain and over a wide range of PCO2's. We suggest that this agent has a local vasodilator effect on the cerebral arterioles, unrelated to its specific effects as a carbonic anhydrase inhibitor.

Pulsatile entrance flow in a curved pipe

An experimental investitition was made of the entry flow in a curved pipe under conditions wherein a pulsatile component of flow was superimposed on a steady mean flow. Two experiments were conducted, one in a pipe of curvature ratio for αw = 12·5 and κ = 372. Laser-velocimetry measurements of the axial and secondary velocities were made throughout the cross-section at different instants of time within the cycle and at several axial locations downstream from the pipe entrance.The flow in the first experiment was found to be quasisteady, with axial and secondary velocities varying in time at the several axial stations proportionally to the instantaneous mean velocity, but essentially the same in character as low-Dean-number steady entry flow. The flow in the second experiment was more complex, with separation of the axial flow appearing at the inner bend during deceleration, starting downstream and propagating upstream toward the pipe entrance. Helical motions imbedded within the Dean circulation were also observed, and during certain portions of the cycle the secondary motions within the central core took on a jet-like structure.It suggested that the classifications employed by Smith to describe the different regimes of fully-developed pulsatile flow in curved pipes may also be useful to distinguish between different entry-flow regimes.

Changes in cerebral blood flow during hyperventilation and CO2-breathing measured transcutaneously in humans by a bidirectional, pulsed, ultrasound Doppler blood velocitymeter.

We have used a bidirectional pulsed ultrasound doppler system which measures the instantaneous mean velocity across the lumen of a blood vessel in order to determine the relationship between alveolar PCO2 (PACO2) and blood flow in the four arteries supplying the brain in humans. Both high and low PACO2-values were explored. Six subjects, 3 males and 3 females (22-40 years) were studied by use of this non-invasive technique. To increase the PACO2 the subjects were breathing 4, 6 and 8% CO2 in air. PACO2 was reduced by voluntary hyperventilation down to a chosen end-expiratory PCO2 value of about 2.2 kPa. We found a linear relationship between arterial blood flow expressed as a percentage of control level and PACO2 in the range from 3.3 to 7.3 kPa. At the very lowest PACO2 values a levelling off of the response, with flow values of 40 to 45%, was observed. The CO2-reactivities in the 6 persons varied between 28.1 and 30.0%/kPa. The time course and the magnitude of the flow response were similar in all four arteries.

Refreshed display of ultrasonic Doppler spectragrams and measurement of haemodynamic parameters.

An instrument is described that accepts information from a spectrum analyser, stores this in a 40k×8-bit word memory and hence provides a refreshed spectragram display of the most recent few seconds of data. A digital cursor gives the frequency (velocity), time and amplitude at any point on the display. The instantaneous mean velocity for the displayed flow pattern can be automatically computed, and the time-averaged velocity determined using a digital integrator.

Phase-locked loop techniques applied to ultrasonic Doppler signal processing

A new method of measuring blood flow velocity and acceleration using analogue and phase locked loop techniques is described. Instantaneous peak velocity, instantaneous mean velocity and acceleration can be obtained on-line and displayed on simple recording systems.

Frequency-Dependent Friction in Transient Pipe Flow

An equation is derived, which relates the wall shear stress in transient laminar pipe flow to the instantaneous mean velocity and to the weighted past velocity changes. The term is applied to the method of characteristics to calculate water-hammer phenomena in viscous fluids, in which effects of frequency-dependent friction cause distortion of traveling waves. Theoretical results are compared with the experimental pressure fluctuation due to an instantaneous valve closure and show accurate prediction of the response curve.

Boundary-Shear Stress in Unsteady Turbulent Pipe Flow

In laminar flow, instantaneous mean velocity and instantaneous velocity profile are dependent upon history of motivating force or piezometric-pressure gradient; in turbulent flow, strong lateral diffusion of turbulent eddies tends to eliminate dependence of velocity distribution upon history of motion; greater degree of generalization of results appears to be possible for unsteady turbulent flow in pipe than for laminar flow.