Turbulence in the canine ascending aorta and the blood pressure.

Turbulent velocity fluctuations were measured and analyzed in the canine ascending aorta using a hot-film anemometer. Blood flow rate and temperature were stabilized using a special bypass technique. Blood pressure was elevated by Methoxamine infusion. Turbulence components were extracted from measured data using an ensemble averaging technique. Turbulence intensity correlated best with blood flow rate although the variance was relatively large, especially when the blood flow velocity was high. When pooled data were grouped into subclasses using peak aortic flow velocity as the criteria, turbulence intensity correlated well with aortic systolic blood pressure in each of the subclasses. Spectral bandwidth correlated with aortic pressure in the same manner. In summary, turbulence in the aorta developed when blood pressure was high. Both an increase of turbulence intensity and an widening of turbulence spectra may be ascribed to a stiffening of the aortic wall due to an elevation of blood pressure.     

Shear-layer detection in poststenotic flow by spectrum analysis of Doppler signals

Spectrum analysis of the Doppler signals was performed 0.5 tube diameters downstream from an axisymmetric constriction with an area reduction of 80 percent in steady flow at a jet Reynolds number of 2840. Both pulsed and continuous wave (CW) Doppler spectra showed significant reverse flow components in the separated flow. The pulsed Doppler spectra exhibited sudden changes when the sample volume crossed the shear layer between the center jet and the separated flow. A power spectrum equation was theoretically derived from continuity of flow to define the Doppler shift frequency for the shear layer velocity. The CW Doppler spectrum showed a minimum spectrum density at a frequency which equalled the shear layer Doppler shift frequency derived from the equation. The pulsed spectra exhibited the sudden changes at the same frequency as well.     

Flutter in flow-limited collapsible tubes: a mechanism for generation of wheezes

We studied flutter in collapsible tubes as a possible mechanism for the generation of respiratory wheezes. The pressure-flow relationships and the wall oscillations of thick-walled [wall thickness (h)-to-lumen radius (r) ratio 1:1.7 to 1.3] self-supporting latex and Silastic tubes mounted between rigid pipes were measured. A high-impedance vacuum pump was connected to the downstream end. Upstream and downstream valves were used to control corresponding resistances. We found loud honking sounds and tube wall oscillations that occurred only when the tubes were buckled and flow limiting, i.e., when the flow became constant and independent of downstream driving pressure. The overall range of oscillatory frequencies was 260-750 Hz for airflow, presenting as sharp peaks of power on the frequency spectrum. The oscillatory frequencies (f) were higher at higher fluid velocities (u) and with narrower distance between opposing flattened walls (2b), resulting from increasing downstream suction pressure and the transmural pressure becoming more negative. The effect of u and b on f for a latex tube (h-to-r ratio 1:1.7) were found to be f = 228 + 0.021 (u/b). These relationships were valid throughout the range of oscillations in this tube (283-720 Hz) and with flow rates of 12-64 l/min. The experimental data were compared with predictions of the fluid dynamic flutter theory and the vortex-induced wall vibrations mechanism. We conclude that viscid flutter in soft tubes is the more probable mechanism for the generation of oscillations in the soft tube model and is a possible mechanism for the generation of respiratory wheezes.     

Exploring high frequency temporal fluctuations in the terminal aneurysm of the basilar bifurcation

Cerebral aneurysms are a common cause of death and disability. Of all the cardiovascular diseases, aneurysms are perhaps the most strongly linked with the local fluid mechanic environment. Aside from early in vivo clinical work that hinted at the possibility of high-frequency intra-aneurysmal velocity oscillations, flow in cerebral aneurysms is most often assumed to be laminar. This work investigates, through the use of numerical simulations, the potential for disturbed flow to exist in the terminal aneurysm of the basilar bifurcation. The nature of the disturbed flow is explored using a series of four idealized basilar tip models, and the results supported by four patient specific terminal basilar tip aneurysms. All four idealized models demonstrated instability in the inflow jet through high frequency fluctuations in the velocity and the pressure at approximately 120?Hz. The instability arises through a breakdown of the inflow jet, which begins to oscillate upon entering the aneurysm. The wall shear stress undergoes similar high-frequency oscillations in both magnitude and direction. The neck and dome regions of the aneurysm present 180 deg changes in the direction of the wall shear stress, due to the formation of small recirculation zones near the shear layer of the jet (at the frequency of the inflow jet oscillation) and the oscillation of the impingement zone on the dome of the aneurysm, respectively. Similar results were observed in the patient-specific models, which showed high frequency fluctuations at approximately 112 Hz in two of the four models and oscillations in the magnitude and direction of the wall shear stress. These results demonstrate that there is potential for disturbed laminar unsteady flow in the terminal aneurysm of the basilar bifurcation. The instabilities appear similar to the first instability mode of a free round jet.     

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

3D-PTV is a quantitative flow measurement technique that aims to track the Lagrangian paths of a set of particles in three dimensions using stereoscopic recording of image sequences. The basic components, features, constraints and optimization tips of a 3D-PTV topology consisting of a high-speed camera with a four-view splitter are described and discussed in this article. The technique is applied to the intermediate flow field (5 <x/d <25) of a circular jet at Re ≈ 7,000. Lagrangian flow features and turbulence quantities in an Eulerian frame are estimated around ten diameters downstream of the jet origin and at various radial distances from the jet core. Lagrangian properties include trajectory, velocity and acceleration of selected particles as well as curvature of the flow path, which are obtained from the Frenet-Serret equation. Estimation of the 3D velocity and turbulence fields around the jet core axis at a cross-plane located at ten diameters downstream of the jet is compared with literature, and the power spectrum of the large-scale streamwise velocity motions is obtained at various radial distances from the jet core.     

On flow through bends and branchings

Theoretical modelling of bending and branching tube flows at medium-to-high flow rates is described for current industrial and biomedical projects. This mostly uses slender-flow modelling. Much pressure loss occurs in bends, with increased swirl, large variations in velocity components and wall shear stress, skewing of the downstream motion and reduced flow rate, but the flow regime which is established shows sensitive dependence on the imposed pressure drop and entrance conditions. A small side-branch off a mother tube produces most rapid variation in pressure and velocity near the daughter entrance, this variation now being quantifiable. A multiple branching yields large flow rates and nonunique flow patterns, depending on the form of the imposed pressure differences.     

The flow field downstream of an oscillating collapsed tube

A two-component laser Doppler anemometer was used to determine the velocity of aqueous flow in the region from 0.25 to 2.5 diameters downstream of a collapsible tube while the tube was executing vigorous repetitive flow-induced oscillations. The Reynolds number for the time-averaged flow was 10,750. A simultaneous measurement of the pressure at the downstream end of the tube was used to align all the results in time at sixty locations in each of the two principal planes defined by the axes of collapse of the flexible tube upstream. The raw data of seed-particle velocity were used to create a periodic waveform for each measured velocity component at each location by least-squares fitting of a Fourier series. The results are presented as both velocity vectors and interpolated contours, for each of ten salient instants during the cycle of oscillation. In the plane of the collapse major axis, the dominant feature is the jet which emerges from each of the two tube lobes when it collapses, but transient retrograde flow is observed on both the central and lateral edges of this jet. In the orthogonal, minor-axis plane, the dominant feature is the retrograde flow, which during part of the cycle extends over the whole plane. All these features are essentially confined to the first 1.5 diameters of the rigid pipe downstream of the flexible tube. These data map the temporal and spatial extent of the highly three-dimensional reversing flow just downstream of an oscillating collapsed tube.     

Direct numerical simulation of transitional flow in a stenosed carotid bifurcation

The blood flow dynamics of a stenosed, subject-specific, carotid bifurcation were numerically simulated using the spectral element method. Pulsatile inlet conditions were based on in vivo color Doppler ultrasound measurements of blood velocity. The results demonstrated the transitional or weakly turbulent state of the blood flow, which featured rapid velocity and pressure fluctuations in the post-stenotic region of the internal carotid artery (ICA) during systole and laminar flow during diastole. High-frequency vortex shedding was greatest downstream of the stenosis during the deceleration phase of systole. Velocity fluctuations had a frequency within the audible range of 100-300Hz. Instantaneous wall shear stress (WSS) within the stenosis was relatively high during systole ( approximately 25-45Pa) compared to that in a healthy carotid. In addition, high spatial gradients of WSS were present due to flow separation on the inner wall. Oscillatory flow reversal and low pressure were observed distal to the stenosis in the ICA. This study predicts the complex flow field, the turbulence levels and the distribution of the biomechanical stresses present in vivo within a stenosed carotid artery.     

Pulsatile flow past aortic valve bioprostheses in a model human aorta

Pulsatile flow development past tissue valve prostheses in a model human aorta has been studied using qualitative flow visualization and quantitative laser-Doppler techniques. Experiments were conducted both in steady and physiological pulsatile flow situations and the measurements included the pressure drop across the valve, the instantaneous flow rate as well as the velocity profiles and turbulent stresses downstream to the valves. Our study shows that the velocity profiles with pericardial valves are closer to those measured past natural aortic valves. The porcine valves with a smaller valve opening area produce a narrower and stronger jet downstream from the valve with relatively larger turbulent axial stresses in the boundary of the jet. Our study suggests that the pericardial valves with turbulent stresses comparable to those of caged ball and tilting disc valves are preferable from a hemodynamic point of view.     

Oscillation characteristics of biofilm streamers in turbulent flowing water as related to drag and pressure drop

Mixed population biofilms consisting of Pseudomonas aeruginosa, P. fluorescens, and Klebsiella pneumoniae were grown in a flow cell under turbulent conditions with a water flow velocity of 18 cm/s (Reynolds number, Re, =1192). After 7 days the biofilms were patchy and consisted of cell clusters and streamers (filamentous structures attached to the downstream edge of the clusters) separated by interstitial channels. The cell clusters ranged in size from 25 to 750 microm in diameter. The largest clusters were approximately 85 microm thick. The streamers, which were up to 3 mm long, oscillated laterally in the flow. The motion of the streamers was recorded at various flow velocities up to 50.5 cm/s (Re 3351) using confocal scanning laser microscopy. The resulting time traces were evaluated by image analysis and fast Fourier transform analysis (FFT). The amplitude of the motion increased with flow velocity in a sigmoidal shaped curve, reaching a plateau at an average fluid flow velocity of approximately 25 cm/s (Re 1656). The motion of the streamers was possibly limited by the flexibility of the biofilm material. FFT indicated that the frequency of oscillation was directly proportional to the average flow velocity (u(ave)) below 9.5 cm/s (Re 629). At u(ave) greater than 9.5 cm/s, oscillation frequencies were above our measurable frequency range (0.12-6.7 Hz). The oscillation frequency was related to the flow velocity by the Strouhal relationship, suggesting that the oscillations were possibly caused by vortex shedding from the upstream biofilm clusters. A loss coefficient (k) was used to assess the influence of biofilm accumulation on pressure drop. The k across the flow cell colonized with biofilm was 2.2 times greater than the k across a clean flow cell.     

Dependence of adhesive behavior of neutrophils on local fluid dynamics in a region with recirculating flow

We have recently described patterns of adhesion of different types of leukocytes downstream of a backward facing step. Here the predicted fluid dynamics in channels incorporating backward facing steps are described, and related to the measured velocities of flowing cells, patterns of attachment and characteristics of rolling adhesion for neutrophils perfused over P-selectin. Deeper (upstream depth 300 microm, downstream depth 600 microm, maximum wall shear stress approximately 0.1 Pa) and shallower (upstream depth 260 microm, downstream depth 450 microm, maximum wall shear stress approximately 0.3 Pa) channels were compared. Computational fluid dynamics (CFD) predicted the presence of vortices downstream of the steps, distances to reattachment of flow, local wall shear stresses and components of velocity parallel and perpendicular to the wall. Measurements of velocities of perfused neutrophils agreed well with predictions, and suggested that adhesion to P-selectin should be possible in the regions of recirculating flow, but not downstream in re-established flow in the high shear channel. When channels were coated with a P-selectin-Fc chimaera, neutrophils were captured from flow and immobilised. Capture showed local maxima around the reattachment points, but was absent elsewhere in the high shear chamber. In the low shear chamber there was depression of adhesion just beyond the reattachment point because of expansion of flow and depletion of neutrophils near the wall. Inside the recirculation zones, adhesion decreased approaching the step because of an increasing, vertically upward velocity component. When channels were coated with P-selectin, neutrophils rolled in all regions, but lifted off the surface as they rolled backwards into low shear regions near the step. Rolling velocity in the recirculation zone was independent of shear stress, possibly because of the effects of vertical lift. We conclude that while local wall shear stress influences adhesive behavior, delivery of cells to the wall and their behavior after capture also depend on components of flow perpendicular to the wall.     

Cooperative processes in mitochondria: registration by dyanmic phase microscopy

The spectra of phase fluctuations in mitochondria were measured by the method of dynamic phase microscopy. Contrasting components were revealed whose intensity markedly changed at distances of 100-300 nm. Similar frequency components were observed in the spectra of ATP-stimulated fluctuations in liposomes with the incorporated ATPase. The values of the frequency and intensity of contrasting components in spectra of liposomes, mitochondria, and cells are presented. The possibility of determining the position of active enzyme complexes from their characteristic frequencies is discussed.     

Individual features of circulatory power spectra in man

Rhythms of resting fluctuations of circulatory parameters in man reveal a considerable interindividual variability. We posed the question whether these rhythms are long-term individual characteristics. In nine healthy subjects aged 19-23 years the blood pressure and the finger blood flow were recorded by indirect continuous methods, together with cardiac intervals and respiratory movements. These recordings were repeated in each subject after 1 year. The power spectra of all the parameters recorded were calculated for 5-min periods. The shape of spectra and the division of power into four ranges of frequencies were compared to the spectra recorded after 1 year in each subject and the degree of similarity was evaluated by means of correlation analysis. The average measures of similarity (correlation coefficients) were high, cardiac intervals 0.527, systolic pressure 0.782, pulse pressure 0.755, diastolic pressure 0.709, mean blood pressure 0.673, blood flow 0.818 and respiration 0.627. All these values were higher than values obtained by comparison of spectra of two individuals chosen randomly. The differences were statistically significant for cardiac intervals (Wilcoxon test: P less than 0.05), pulse pressure (P less than 0.05) and respiration (P less than 0.01). These results have shown that interindividual variability of circulatory and respiratory spectra was greater than the intraindividual one. The resting circulatory rhythms are very stable individual features.     

Importance of flow division on transition to turbulence within an arteriovenous graft

Transitional blood flow in an arteriovenous graft under various conditions of flow division was examined through direct numerical simulation. This junction consists of an inlet vessel (prosthetic graft) connected to a host vessel (vein) at an acute angle (21.6 degrees ). Inlet Reynolds numbers, based on mean velocity and graft inlet diameter, ranged from 800 to 1400. Various flow divisions between the two ends of the host vessel (i.e., the proximal venous segment, PVS, and distal venous segment, DVS) were considered (PVS:DVS ratios of 100:0, 85:15, 70:30 and 115:(15)). The numerical technique employed the spectral element method which is a high-order discretization ideally suited to the simulation of transitional flows in complex domains. High velocity and pressure fluctuations were observed for the PVS:DVS=70:30 and 85:15 cases and absent from the 100:0 and 115:(15) cases; the results indicate the importance of flow division on the development of turbulence in this junction. Transition to turbulence was observed at Reynolds numbers as low as 1000 and 800 under flow divisions of 85:15 and 70:30, respectively, significantly lower than the critical value of 2100. The frequency spectra of velocity fluctuations indicated a significant intensity within the frequency range of approximately 300Hz downstream of the junction. An adverse pressure gradient developed in the PVS when graft inflow divided into opposite directions in the junction. This pressure gradient had a destabilizing effect on the flow and enhanced transition to turbulence in the PVS. These findings suggest that measurements of in vivo flow rates at the inlet and outlets are critical for the accurate prediction of arteriovenous hemodynamics. A potential clinical application of these results might be to close off the DVS during graft construction to ensure a 100:0 flow division.     

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%.     

A new theoretical model for noninvasive quantification of mitral regurgitation

The most common objective assessments of mitral regurgitation are limited by their invasive or semiquantitative nature. Recent attempts at correlation with jet size from Doppler flow maps have failed to produce a direct measure of regurgitant volume and are fundamentally limited by the dependence of jet dimensions on factors other than flow volume. The purpose of this paper was to develop an equation, based on the physics of turbulent regurgitant jets, for calculating regurgitant volume from quantities that can be measured by Doppler ultrasound. The result is an equation forw flow rate Q as a function of orifice velocity Uo, a downstream centerline velocity Um and the intervening distance chi: Q = pi U2m chi 2/160Uo. This equation can also be modified to obtain total regurgitant volume in clinical pulsatile flow. The assumptions made demand a free turbulent jet for which momentum is conserved, but should otherwise be physiologically applicable. The advantage of this technique compared to correlations with jet size are its theoretical justification and ability to quantify regurgitant volume directly.     

On the discrimination between band-limited coherent and random apparent stresses in transitional pulsatile flow

A frequency domain approach that incorporates a matched filter was examined for discriminating between ordered velocity fluctuations with band-limited frequency content and random velocity variations in pulsatile disturbed flows. Fluctuations at pseudo-discrete frequencies may yield a significant contribution to the apparent stress tensor computed from the unsteady Navier Stokes equations, and an estimate of the stresses arising from these ordered structures can be obtained once the velocity variations have been decomposed. This type of decomposition permits the estimation of the apparent stresses in turbulent flows, consisting of coherent and random parts, in blood flow applications such as diseased constricted arteries or downstream of artificial heart valves.     

Velocity field of pulsatile flow in a porous tube

This paper describes velocity fields for fully developed periodic laminar flow in a rigid tube with a porous wall. We obtained an analytical solution of the flow by the linear approximation of the Navier-Stokes equation. Unlike the previous works with a constant seepage rate along the axis, we used a wall velocity which contained hydraulic permeation constant Lp. The axial velocity profile shows a local maximum velocity near the wall at a large Womersley number alpha. This suggests that concentration polarization in porous tubular membrane may be reduced at high frequencies if a membrane device is operated under pulsatile flow conditions. The magnitude of wall permeation velocity decreases linearly along the tube axis because the damping of the pressure difference between the inside and the outside of the tube is very small.     

Lateral line nerve fibers do not code bulk water flow direction in turbulent flow

The discharges of anterior and posterior lateral line nerve afferents were recorded while stimulating goldfish, Carassius auratus, with bulk water flow. With increasing flow velocity lateral line afferents increased their discharge rates. However, an increased response to flow rates occurred even if flow direction was reversed. Thus, individual lateral line afferents did not encode the direction of running water. Frequency spectra of the water motions quantified with particle image velocimetry revealed flow fluctuations that increased with increasing flow velocity. Maximal spectral amplitudes of the flow fluctuations were below 5 Hz (bulk flow velocity 4–15 cm s⁻¹). The frequency spectra of the firing rates of lateral line afferents also showed an increase in amplitude when fish were exposed to running water. The maximal spectral amplitudes of the recorded data were in the frequency range 3–8 Hz. This suggests that the lateral line afferents mainly responded to the higher frequency fluctuations that developed under flow conditions, but not to the direct current flow or the lower frequency fluctuations. Although individual lateral line afferents encoded neither flow velocity nor flow direction we suggest that higher order lateral line neurons can do so by monitoring flow fluctuations as they move across the surface of the fish.     

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.