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.     

Low Reynolds number turbulence modeling of blood flow in arterial stenoses.

Moderate and severe arterial stenoses can produce highly disturbed flow regions with transitional and or turbulent flow characteristics. Neither laminar flow modeling nor standard two-equation models such as the kappa-epsilon turbulence ones are suitable for this kind of blood flow. In order to analyze the transitional or turbulent flow distal to an arterial stenosis, authors of this study have used the Wilcox low-Re turbulence model. Flow simulations were carried out on stenoses with 50, 75 and 86% reductions in cross-sectional area over a range of physiologically relevant Reynolds numbers. The results obtained with this low-Re turbulence model were compared with experimental measurements and with the results obtained by the standard kappa-epsilon model in terms of velocity profile, vortex length, wall shear stress, wall static pressure, and turbulence intensity. The comparisons show that results predicted by the low-Re model are in good agreement with the experimental measurements. This model accurately predicts the critical Reynolds number at which blood flow becomes transitional or turbulent distal an arterial stenosis. Most interestingly, over the Re range of laminar flow, the vortex length calculated with the low-Re model also closely matches the vortex length predicted by laminar flow modeling. In conclusion, the study strongly suggests that the proposed model is suitable for blood flow studies in certain areas of the arterial tree where both laminar and transitional/turbulent flows coexist.     

Two-dimensional color-mapping of turbulent shear stress distribution downstream of two aortic bioprosthetic valves in vitro.

Since artificial heart valve related complications such as thrombus formation, hemolysis and calcification are considered related to flow disturbances caused by the inserted valve, a thorough hemodynamic characterization of heart valve prostheses is essential. In a pulsatile flow model, fluid velocities were measured one diameter downstream of a Hancock Porcine (HAPO) and a Ionescu-Shiley Pericardial Standard (ISPS) aortic valve. Hot-film anemometry (HFA) was used for velocity measurements at 41 points in the cross-sectional area of the ascending aorta. Three-dimensional visualization of the velocity profiles, at 100 different instants during one mean pump cycle, was performed. Turbulence analysis was performed as a function of time by calculating the axial turbulence energy within 50 ms overlapping time windows during the systole. The turbulent shear stresses were estimated by using the correlation equation between Reynolds normal stress and turbulent (Reynolds) shear stress. The turbulent shear stress distribution was visualized by two-dimensional color-mapping at different instants during one mean pump cycle. Based on the velocity profiles and the turbulent shear stress distribution, a relative blood damage index (RBDI) was calculated. It has the feature of combining the magnitude and exposure time of the estimated shear stresses in one index, covering the entire cross-sectional area. The HAPO valve showed a skewed jet-type velocity profile with the highest velocities towards the left posterior aortic wall. The ISPS valve revealed a more parabolic-shaped velocity profile during systole. The turbulent shear stresses were highest in areas of high or rapidly changing velocity gradients. For the HAPO valve the maximum estimated turbulent shear stress was 194 N m-2 and for the ISPS valve 154 Nm-2. The RBDI was the same for the two valves. The turbulent shear stresses had magnitudes and exposure times that might cause endothelial damage and sublethal or lethal damage to blood corpuscules. The RBDI makes comparison between different heart valves easier and may prove important when making correlation with clinical observations.     

Application of Taylor''s hypothesis to an unsteady convective field for the spectral analysis of turbulence in the aorta

Two types of unsteadiness must be considered when spectral analysis is applied to unsteady turbulence such as that found in the aorta. Firstly, the statistical properties of the turbulence itself change in time and so the definition of spectral density must be reconsidered. Secondly, the turbulent velocity fluctuations, whether they are steady or unsteady, are carried by an unsteady convective velocity which alters their properties as seen by a stationary observer.

In the present study, unsteadiness of turbulence in the latter sense is discussed by applying Taylor's hypothesis of ‘frozen turbulence’ to turbulence with an unsteady convective velocity. If both a ‘frozen’ pattern of turbulence and a constant convective velocity are assumed, measured frequency spectra can be easily transformed into wavenumber (spatial) spectra, usually as a trivial part of normalisation. In the case of unsteady turbulence, however, the convection velocity is no longer constant and the conventional method can not be used. A new method of estimating the spatial properties of unsteady turbulence is proposed in which the temporal fluctuations of the turbulent velocity are transformed into spatial fluctuations using a nonlinear transformation based upon the unsteady convective velocity. The transformed data are then Fourier analysed to yield a wavenumber spectrum directly.

The proposed method is applied to data obtained in the canine ascending aorta. Spectra calculated by the proposed method differ significantly from those obtained by the conventional method, particularly in the high wavenumber (or frequency) range. This difference is discussed as an ‘aliasing’ phenomenon that has also been known in steady turbulence.     

Spectrum analysis of turbulence in the canine ascending aorta measured with a hot-film anemometer

We measured turbulence velocity in the canine ascending aorta using a hot-film anemometer. Blood flow velocity was measured at various points across the ascending aorta approximately 1.5-2 times the diameter downstream from the aortic valve. The turbulence spectrum was calculated and its characteristics were examined in connection with the mean Reynolds number and/or measuring positions. In the higher wave number range the values of the turbulence spectra were higher at larger mean Reynolds number. In the higher wave number range, the values of the turbulence spectra were higher at points closer to the centerline of the aorta, when the mean Reynolds number was relatively large. The patterns of the turbulence spectra at various points outside the boundary layer on the aortic wall were similar.     

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 parallelled 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.     

Computational simulations of airflow in an in vitro model of the pediatric upper airways

In order to understand mechanisms of gas and aerosol transport in the human respiratory system airflow in the upper airways of a pediatric subject (male aged 5) was calculated using Computational Fluid Dynamic techniques. An in vitro reconstruction of the subject's anatomy was produced from MRI images. Flow fields were solved for steady inhalation at 6.4 and 8 LPM. For validation of the numerical solution, airflow in an adult cadaver based trachea was solved using identical numerical methods. Comparisons were made between experimental results and computational data of the adult model to determine solution validity. It was found that numerical simulations can provide an accurate representation of axial velocities and turbulence intensity. Data on flow resistance, axial velocities, secondary velocity vectors, and turbulent kinetic energy are presented for the pediatric case. Turbulent kinetic energy and axial velocities were heavily dependant on flow rate, whereas turbulence intensity varied less over the flow rates studied. The laryngeal jet from an adult model was compared to the laryngeal jet in the pediatric model based on Tracheal Reynolds number. The pediatric case indicated that children show axial velocities in the laryngeal jet comparable to adults, who have much higher tracheal Reynolds numbers than children due to larger characteristic dimensions. The intensity of turbulence follows a similar trend, with higher turbulent kinetic energy levels in the pediatric model than would be expected from measurements in adults at similar tracheal Reynolds numbers. There was reasonable agreement between the location of flow structures between adults and children, suggesting that an unknown length scale correlation factor could exist that would produce acceptable predictions of pediatric velocimetry based off of adult data sets. A combined scale for turbulent intensity as well may not exist due to the complex nature of turbulence production and dissipation.     

A mathematical model for the dissolution of non-occlusive blood clots in fast tangential blood flow

Our aim was to study the effect of an axially directed blood plasma flow on the dissolution rate of cylindrical non-occlusive blood clots in an in vitro flow system and to derive a mathematical model for the process. The model was based on the hypothesis that clot dissolution dynamics is proportional not only to the biochemical proteolysis of fibrin but also to the power of the flowing blood plasma dissipated along the clot. The predicted rate of thrombolysis is then proportional to the square of the average blood plasma velocity for laminar flow and to the third power of the average velocity for turbulent flow. To verify the model, the time dependence of the clot cross-sectional area was measured by dynamic magnetic resonance microscopy during fast (turbulent) and slow (laminar) flow of plasma through an axially directed channel along the clot. The flowing plasma contained a magnetic resonance imaging contrast agent (Gd-DTPA) and a thrombolytic agent (recombinant tissue-type plasminogen activator). The experimental data fitted well to the model, and confirmed the predicted increase in the dissolution rate when blood flow changed from a laminar to a turbulent flow regime.     

Spiral blood flow in aorta–renal bifurcation models

The presence of a spiral arterial blood flow pattern in humans has been widely accepted. It is believed that this spiral component of the blood flow alters arterial haemodynamics in both positive and negative ways. The purpose of this study was to determine the effect of spiral flow on haemodynamic changes in aorta–renal bifurcations. In this regard, a computational fluid dynamics analysis of pulsatile blood flow was performed in two idealised models of aorta–renal bifurcations with and without flow diverter. The results show that the spirality effect causes a substantial variation in blood velocity distribution, while causing only slight changes in fluid shear stress patterns. The dominant observed effect of spiral flow is on turbulent kinetic energy and flow recirculation zones. As spiral flow intensity increases, the rate of turbulent kinetic energy production decreases, reducing the region of potential damage to red blood cells and endothelial cells. Furthermore, the recirculation zones which form on the cranial sides of the aorta and renal artery shrink in size in the presence of spirality effect; this may lower the rate of atherosclerosis development and progression in the aorta–renal bifurcation. These results indicate that the spiral nature of blood flow has atheroprotective effects in renal arteries and should be taken into consideration in analyses of the aorta and renal arteries.     

基于物理模型实验的光倒刺鲃生态行为学研究

建立了基于天然河道的物理模型,通过控制实验研究水环境因子对鱼类行为的影响。文中选取了金沙江下游2.6 km河段建立物理模型,以南方水系的经济鱼类光倒刺鲃为研究对象,进行了鱼的行为对底质和流速的响应实验。分析得出,光倒刺鲃对砂卵石底质的选择明显大于其它底质且差异极其显著(P<0.01),光倒刺鲃2龄幼鱼期的喜好流速范围为0.3-0.6 m/s;研究同时发现水流紊动强度对光倒刺鲃行为具有重要影响。该研究结果可以为光倒刺鲃栖息地模型提供参考。     

On the interaction of turbulent flow and feeding behaviour of juvenile Atlantic Salmon (Salmo salar)

Anthropogenic activities can dramatically modify the riverine habitat of juvenile Atlantic salmon ( Salmo salar ). In the perspective of protecting and restoring the fluvial habitat, bioenergetic models are often used to estimate fish habitat quality. These models determine the habitat quality as the ratio between the energetic gains (food) and costs (growth, metabolism) of a fish. The energetic costs of swimming in a river are generally estimated using the average flow velocity without consideration of the effect of turbulence. Juvenile Atlantic salmon (JAS) live in rivers characterized by intense velocity fluctuations, which are often described as a succession of high‐ and low‐speed flow regions. These flow structures are likely to affect the JAS activity that consists of long periods of sit‐and‐wait at the top of a protuberant rock interrupted by short bursting motions to capture drifting food particles. To minimize the energetic costs, it is hypothesized that JAS use low‐speed flow regions to initiate and undertake their feeding motions.  To improve bioenergetic modelling, this study aimed at analyzing the relation between turbulent flow structures and the feeding behaviour of JAS in a natural gravel‐bed river. We filmed eight JAS during 30 min with a submersible video camera while simultaneously measuring velocity fluctuations close to the fish in the St. Marguerite River, Quebec, Canada. Our results show that the proportion of time used for feeding motions decreases with increasing turbulent intensity and mean flow velocity; and that JAS do not seem to prefer low‐speed flow regions to initiate their feeding motions.     

Kinetics of the acid precipitation of soya protein in a continuous-flow tubular reactor

The acid precipitation of soya protein was studied in a continuous-flow tubular reactor under conditions of turbulent flow. Preliminary batchwise experiments of a semiquantitative nature were also carried out on a bench-scale reactor to better define the parameters affecting precipitate growth. The experiments indicated the dominant growth mechanism to be the aggregation of primary precipitate particles produced by the contacting of the protein and acid streams. The rate of particle growth was observed to rise with an increase in the protein concentration as well as with greater intensity of turbulence. The final mean particle size decreased with increased intensity of turbulence. A theoretical model was set up to simulate the growth of the precipitate particles.     

Numerical simulations of the pulsating flow of cerebrospinal fluid flow in the cervical spinal canal of a Chiari patient

The flow of cerebrospinal fluid (CSF) in a patient-specific model of the subarachnoid space in a Chiari I patient was investigated using numerical simulations. The pulsating CSF flow was modeled using a time-varying velocity pulse based on peak velocity measurements (diastole and systole) derived from a selection of patients with Chiari I malformation. The present study introduces the general definition of the Reynolds number to provide a measure of CSF flow instability to give an estimate of the possibility of turbulence occurring in CSF flow. This was motivated by the fact that the combination of pulsating flow and the geometric complexity of the spinal canal may result in local Reynolds numbers that are significantly higher than the commonly used global measure such that flow instabilities may develop into turbulent flow in these regions. The local Reynolds number was used in combination with derived statistics to characterize the flow. The results revealed the existence of both local unstable regions and local regions with velocity fluctuations similar in magnitude to what is observed in fully turbulent flows. The results also indicated that the fluctuations were not self-sustained turbulence, but rather flow instabilities that may develop into turbulence. The case considered was therefore believed to represent a CSF flow close to transition.     

Turbulence modeling in three-dimensional stenosed arterial bifurcations

Under normal healthy conditions, blood flow in the carotid artery bifurcation is laminar. However, in the presence of a stenosis, the flow can become turbulent at the higher Reynolds numbers during systole. There is growing consensus that the transitional k-omega model is the best suited Reynolds averaged turbulence model for such flows. Further confirmation of this opinion is presented here by a comparison with the RNG k-epsilon model for the flow through a straight, nonbifurcating tube. Unlike similar validation studies elsewhere, no assumptions are made about the inlet profile since the full length of the experimental tube is simulated. Additionally, variations in the inflow turbulence quantities are shown to have no noticeable affect on downstream turbulence intensity, turbulent viscosity, or velocity in the k-epsilon model, whereas the velocity profiles in the transitional k-omega model show some differences due to large variations in the downstream turbulence quantities. Following this validation study, the transitional k-omega model is applied in a three-dimensional parametrically defined computer model of the carotid artery bifurcation in which the sinus bulb is manipulated to produce mild, moderate, and severe stenosis. The parametric geometry definition facilitates a powerful means for investigating the effect of local shape variation while keeping the global shape fixed. While turbulence levels are generally low in all cases considered, the mild stenosis model produces higher levels of turbulent viscosity and this is linked to relatively high values of turbulent kinetic energy and low values of the specific dissipation rate. The severe stenosis model displays stronger recirculation in the flow field with higher values of vorticity, helicity, and negative wall shear stress. The mild and moderate stenosis configurations produce similar lower levels of vorticity and helicity.     

Laminar and turbulent flow in the mammalian aorta: Reynolds number

Laminar to turbulent flow transition in the mammalian aorta is generally characterized by Reynolds number. When dimensional analysis is applied to obtain the Reynolds number in allometric form, it is found that this number is not invariant of body weight but is approximately proportional to body length dimensions. This implies that flow in the aorta of large mammals is turbulent and laminar in smaller mammals during most of ventricular ejection. Since Reynolds number is defined for steady flow through rigid tubes, it may not reflect the actual fluid behavior of pulsatile flow in compliant vessels such as the aorta. In addition, turbulence is frequency dependent. The larger compliance of the aorta and the slower heart rate in larger mammals and the shorter entrance length and higher heart rate in smaller mammals lead to equal prevalence of turbulence. The consequence is that the aortic flow waveforms remain similar in all mammals.     

Continuous measurement of aortic blood velocity,after cardiac surgery,by means of an extractable doppler ultrasound probe

A new method has been developed for the continuous measurement of aortic blood velocity in patients following cardiac surgery. Using an extractable Doppler ultrasound probe placed on the ascending aorta, the changes in aortic velocity were recorded up to 24 h postoperatively, in 14 patients undergoing coronary bypass surgery. Volume flow rate is calculated from the mean velocity, the diameter of the aorta and the angle between the ultrasound beam and the direction of the blood flow, by means of an analogue flow calculator. Estimation of aortic flow showed a correlation of r = 0.79 with cardiac output measured by a thermodilution technique. The main advantage of the system is that it allows continuous monitoring of cardiac output, as well as short and long-term trend analyses, during the early postoperative period.     

Microflow regimes and the distribution of macroinvertebrates around stream boulders

1. An acoustic doppler velocimeter (ADV) was used to collect velocity data in three dimensions in front of and in the wakes of selected boulders in a riffle, where macroinvertebrates were also sampled. 2. Shear stress was calculated from the covariance of downstream and vertical velocity fluctuations. 3. Velocities, shear stress and turbulence measured at three points above the bed in the front and wake regions of riffle boulders were consistent with predicted patterns of flow around isolated roughness elements. There was a significant difference in mean velocities, but not near-bed velocities between front and wake regions. At 5 mm above the bed, velocities in both front and wake regions were greatly reduced, relative to the mean velocity (at 0.4 × total depth). Flows at the bed were directed upstream as part of the vortex formed at the front of the boulder and as part of the recirculation occurring in the wake. 4. Shear stress was highest in the vertical plane in the wake of the boulders. Turbulence intensity and turbulent kinetic energy were greatest in the wake region, in both the down-stream and cross-stream directions. However, these results were not statistically significant. Large standard errors associated with measurements within wakes indicated that wake flows are highly variable. Further research is needed to determine the most appropriate methods of analysing differences associated with such variable flow regimes. 5. The benthic macroinvertebrate fauna was significantly richer and more abundant in the wakes than at the front of boulders. Classification and ordination revealed the presence of distinct front and wake benthic communities. These differences could not be attributed to velocity differences within the benthic microhabitat, because near-bed velocities were greatly reduced in both the front and wake regions. The fauna may be responding to the highly variable turbulent regime of the wake and associated effects, such as increased deposition of particulate organic matter and exchange of dissolved gases. 6. Despite the complex flow patterns inherent in natural streamflow, a large roughness element (boulder) appears to predominate in determining microflows within in its immediate surroundings. The design of some benthic sampling programs (e.g. for biomonitoring) may need to incorporate hydraulic microhabitat considerations. 7. The fine-scale field measurements obtained with the ADV indicate that experimental determination of the role of turbulence in the ecology of stream benthos is now both possible and desirable.     

Reproductive ecology of cultured fish in the wild

Domestication has been shown to have an effect on morphology and behaviour of Atlantic salmon ( Salmo salar ). We compared swimming costs of three groups of juvenile Atlantic salmon subject to different levels of domestication: (1) wild fish; (2) first generation farmed fish origination from wild genitors; and (2) seventh generation farmed fish originating from Norwegian aquaculture stocks. We assessed swimming costs under two types of turbulent flow (one mean flow velocity of 23 cm s⁻¹ and two standard deviations of flow velocity of 5 and 8 cm s⁻¹). Respirometry experiments were conducted with fish in a mass range of 5–15 g wet at a water temperature of 15° C. Our results confirm (1) that net swimming costs are affected by different levels of turbulence such that, for a given mean flow velocity, fish spent 1·5‐times more energy as turbulence increased, (2) that domesticated fish differed in their morphology (having deeper bodies and smaller fins) and in their net swimming costs (being up to 30·3% higher than for wild fish) and (3) that swimming cost models developed for farmed fish may be also be applied to wild fish in turbulent environments.     

Influence of cardiac flow rate on turbulent shear stress from a prosthetic heart valve

Elevated turbulent shear stresses associated with sufficient exposure times are potentially damaging to blood constituents. Since these conditions can be induced by mechanical heart valves, the objectives of this study were to locate the maximum turbulent shear stress in both space and time and to determine how the maximum turbulent shear stress depends on the cardiac flow rate in a pulsatile flow downstream of a tilting disk valve. Two-component, simultaneous, correlated laser velocimeter measurements were recorded at four different axial locations and three different flow rates in a straight tube model of the aorta. All velocity data were ensemble averaged within a 15 ms time window located at approximately peak systolic flow over more than 300 cycles. Shear stresses as high as 992 dynes/cm2 were found 0.92 tube diameters downstream of the monostrut, disk valve. The maximum turbulent shear stress was found to scale with flow rate to the 0.72 power. A repeatable starting vortex was shed from the disk at the beginning of each cycle.     

Three-dimensional visualization of stationary flow behind artificial heart valves]

The visualization and quantitative analysis of flow offers a possibility for the hydrodynamic characterization of artificial heart valves. Different types of valves can be compared if velocity profile and the turbulent shear stress caused by the prosthesis are known. The tracer technique was selected, since it permits visualization also of turbulent flow through the valve. With the aid of a simple optical device the three-dimensional flow pattern behind the valve is determinable. The main features of the method are: The regions of interest can easily be identified. Velocity profiles can be determined and shear stress and turbulence intensities estimated. The experimental setup is simple, calibration is not necessary, and it can be used for turbulent flows. The method can be used only with transparent fluids and vessels; measurements in blood are not possible. Because of the large number of measuring points required the method is very time-consuming. The use of an automatic picture analyzing system would make it possible to increase the number of pictures processed, and thus increase resolution. The velocity profile of a three-finger-valve, the TAD 29, was established at a distance of 20 mm from the ring, and compared with known profiles from the literature. The valve has an opening angle of 70 degrees. All typical regions for the flow of an artificial heart valve, such as jet, stagnation gone, backflow and turbulence were demonstrated.