Experimental measurements of turbulence spectra distal to stenoses

Transition to Turbulence Downstream of a Stenosis for Whole Blood and a Newtonian Analog Under Steady Flow Conditions

Blood, a multiphase fluid comprised of plasma, blood cells, and platelets, is known to exhibit a shear-thinning behavior at low shear rates and near-Newtonian behavior at higher shear rates. However, less is known about the impact of its multiphase nature on the transition to turbulence. In this study, we experimentally determined the critical Reynolds number at which the flow began to transition to turbulence downstream of eccentric stenosis for whole porcine blood and a Newtonian blood analog (water-glycerin mixture). Velocity profiles for both fluids were measured under steady-state flow conditions using an ultrasound Doppler probe placed 12 diameters downstream of eccentric stenosis. Velocity was recorded at 21 locations along the diameter at 11 different flow rates. Normalized turbulent kinetic energy was used to determine the critical Reynolds number for each fluid. Blood rheology was measured before and after each experiment. Tests were conducted on five samples of each fluid inside a temperature-controlled in vitro flow system. The viscosity at a shear rate of 1000 s-1 was used to define the Reynolds number for each fluid. The mean critical Reynolds numbers for blood and water-glycerin were 470 ± 27.5 and 395 ± 10, respectively, indicating a ∼19% delay in transition to turbulence for whole blood compared to the Newtonian fluid. This finding is consistent with a previous report for steady flow in a straight pipe, suggesting some aspect of blood rheology may serve to suppress, or at least delay, the onset of turbulence in vivo.

Fundamentals of turbulent flow spectrum imaging

PURPOSE

To introduce a mathematical framework and in-silico validation of turbulent flow spectrum imaging (TFSI) of stenotic flow using phase-contrast MRI, evaluate systematic errors in quantitative turbulence parameter estimation, and propose a novel method for probing the Lagrangian velocity spectra of turbulent flows.

THEORY AND METHODS

The spectral response of velocity-encoding gradients is derived theoretically and linked to turbulence parameter estimation including the velocity autocorrelation function spectrum. Using a phase-contrast MRI simulation framework, the encoding properties of bipolar gradient waveforms with identical first gradient moments but different duration are investigated on turbulent flow data of defined characteristics as derived from computational fluid dynamics. Based on theoretical insights, an approach using velocity-compensated gradient waveforms is proposed to specifically probe desired ranges of the velocity autocorrelation function spectrum with increased accuracy.

RESULTS

Practical velocity-encoding gradients exhibit limited encoding power of typical turbulent flow spectra, resulting in up to 50% systematic underestimation of intravoxel SD values. Depending on the turbulence level in fluids, the error due to a single encoding gradient spectral response can vary by 20%. When using tailored velocity-compensated gradients, improved quantification of the Lagrangian velocity spectrum on a voxel-by-voxel basis is achieved and used for quantitative correction of intravoxel SD values estimated with velocity-encoding gradients.

CONCLUSION

To address systematic underestimation of turbulence parameters using bipolar velocity-encoding gradients in phase-contrast MRI of stenotic flows with short correlation times, tailored velocity-compensated gradients are proposed to improve quantitative mapping of turbulent blood flow characteristics.

Numerical investigation of wall pressure fluctuations downstream of concentric and eccentric blunt stenosis models

Pressure fluctuations that cause acoustic radiation from vessel models with concentric and eccentric blunt stenoses are investigated. Large eddy simulations of non-pulsatile flow condition are performed using OpenFOAM. Calculated amplitude and spatial-spectral distribution of acoustic pressures at the post-stenotic region are compared with previous experimental and theoretical results. It is found that increasing the Reynolds number does not change the location of the maximum root mean square wall pressure, but causes a general increase in the spectrum level, although the change in the shape of the spectrum is not significant. On the contrary, compared to the concentric model at the same Reynolds number, eccentricity leads to an increase both at the distance of the location of the maximum root mean square wall pressure from the stenosis exit and the spectrum level. This effect becomes more distinct when radial eccentricity of the stenosis increases. Both the flow rate and the eccentricity of the stenosis shape are evaluated to be clinically important parameters in diagnosing stenosis.

Flow-induced vibration analysis of constricted artery models with surrounding soft tissue

Arterial stenosis is a vascular pathology which leads to serious cardiovascular diseases. Blood flow through a constriction generates sound and vibration due to fluctuating turbulent pressures. Generated vibro-acoustic waves propagate through surrounding soft tissues and reach the skin surface and may provide valuable insight for noninvasive diagnostic purposes. Motivated by the aforementioned phenomena, vibration of constricted arteries is investigated employing computational models. The flow-induced pressure field in an artery is modeled as broadband harmonic pressure loading based on previous studies in the literature and applied on the inner artery wall. Harmonic analysis is performed for determining radial velocity responses on the outer surface of the models. Results indicate that stenosis severities higher than 70% lead to significant increase in response amplitudes, especially at high frequencies between 250 and 600 Hz. The findings agree well with experimental and theoretical results in the literature considering bending mode frequencies, amplitude scales, and mainly excited frequency ranges. It is seen that artery vibration is sensitive to the phase behavior of pressure loading but its effect becomes less significant with the presence of surrounding tissue. As the surrounding tissue thickness increases, radial velocity response amplitudes decrease but the effect of changes in tissue elastic modulus is more pronounced.

Large-scale CFD simulations of the transitional and turbulent regime for the large human airways during rapid inhalation

The dynamics of unsteady flow in the human large airways during a rapid inhalation were investigated using highly detailed large-scale computational fluid dynamics on a subject-specific geometry. The simulations were performed to resolve all the spatial and temporal scales of the flow, thanks to the use of massive computational resources. A highly parallel finite element code was used, running on two supercomputers, solving the transient incompressible Navier-Stokes equations on unstructured meshes. Given that the finest mesh contained 350 million elements, the study sets a precedent for large-scale simulations of the respiratory system, proposing an analysis strategy for mean flow, fluctuations and wall shear stresses on a rapid and short inhalation (a so-called sniff). The geometry used encompasses the exterior face and the airways from the nasal cavity, through the trachea and up to the third lung bifurcation; it was derived from a contrast-enhanced computed tomography (CT) scan of a 48-year-old male. The transient inflow produces complex flows over a wide range of Reynolds numbers (Re). Thanks to the high fidelity simulations, many features involving the flow transition were observed, with the level of turbulence clearly higher in the throat than in the nose. Spectral analysis revealed turbulent characteristics persisting downstream of the glottis, and were captured even with a medium mesh resolution. However a fine mesh resolution was found necessary in the nasal cavity to observe transitional features. This work indicates the potential of large-scale simulations to further understanding of airway physiological mechanics, which is essential to guide clinical diagnosis; better understanding of the flow also has implications for the design of interventions such as aerosol drug delivery.

Aggregate breakup in a contracting nozzle

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

On intra- and intersubject variabilities of airflow in the human lungs

The effects of intra- and intersubject variabilities in airway geometry on airflow in the human lungs are investigated by large eddy simulation. The airway models of two human subjects consisting of extra- and intrathoracic airways are reconstructed from CT images. For intrasubject study, airflows at two inspiratory flow rates are simulated on the airway geometries of the same subject with four different levels of truncation. These airway models are the original complete geometry and three geometries obtained by truncating the original one at the subglottis, the supraglottis, and the laryngopharynx, respectively. A comparison of the airflows in the complete geometry model shows that the characteristics of the turbulent laryngeal jet in the trachea are similar regardless of Reynolds number in terms of mean velocities, turbulence statistics, coherent structures, and pressure distribution. The truncated airway models, however, do not produce the similar flow structures observed in the complete geometry. An improved inlet boundary condition is then proposed for the airway model truncated at the laryngopharynx to improve the accuracy of solution. The new boundary condition significantly improves the mean flow. The spectral analysis shows that turbulent characteristics are captured downstream away from the glottis. For intersubject study, although the overall flow characteristics are similar, two morphological factors are found to significantly affect the flows between subjects. These are the constriction ratio of the glottis with respect to the trachea and the curvature and shape of the airways.

Acoustic radiation from a fluid-filled, subsurface vascular tube with internal turbulent flow due to a constriction

The vibration of a thin-walled cylindrical, compliant viscoelastic tube with internal turbulent flow due to an axisymmetric constriction is studied theoretically and experimentally. Vibration of the tube is considered with internal fluid coupling only, and with coupling to internal-flowing fluid and external stagnant fluid or external tissue-like viscoelastic material. The theoretical analysis includes the adaptation of a model for turbulence in the internal fluid and its vibratory excitation of and interaction with the tube wall and surrounding viscoelastic medium. Analytical predictions are compared with experimental measurements conducted on a flow model system using laser Doppler vibrometry to measure tube vibration and the vibration of the surrounding viscoelastic medium. Fluid pressure within the tube was measured with miniature hydrophones. Discrepancies between theory and experiment, as well as the coupled nature of the fluid-structure interaction, are described. This study is relevant to and may lead to further insight into the patency and mechanisms of vascular failure, as well as diagnostic techniques utilizing noninvasive acoustic measurements.

Characterization of flow emerging from a stenosis using MRI

MRI ultra-fast imaging techniques are used to characterize flow emerging from streamlined and abrupt stenoses inside cylindrical channels. Reattachment lengths of the shear boundary to the channel wall are measured using rotating ultra-fast imaging sequence (RUFIS) in-flow imaging. Velocity profiles of flow are created using velocity (sine and cosine)-encoded RUFIS sequences. The sine-encoded images permit one to identify reverse flow (i.e., eddies) that arise within the region of flow reattachment. The ratios of peak velocities (downstream/upstream of the stenosis) derived from the cosine-encoded images are used to identify the transition from the laminar to the turbulent regimen. Based on these experiments, the transition from the laminar to turbulent regimen occurs at a stenotic Reynolds Number of 350, whereas fully developed turbulence occurs at a stenotic Reynolds Number of 2600. These results are compared with the results from invasive studies.

Characteristics of glottis-induced turbulence in oscillatory flow: an empirical investigation

Turbulence inducement from the glottis was scrutinized by employing an idealized model of the larynx and trachea for oscillatory flow conditions. The characterization of turbulence was achieved with the two-component velocity measurements of split-film probe anemometry and with the flow visualization of a smoke-wire technique. The apertures of two different (triangular and circular) shapes were utilized in the airway model to address the distinct effects of the triangular-shaped glottal aperture on the generation, development, and decay of turbulence. One of the salient turbulence characteristics for the triangular aperture case was found to be the relatively high turbulence levels around the center region (2r/D approximately 0) in conjunction with the asymmetric mean axial velocity across the frontal-rear (A-O-P) plane of the trachea at one tracheal diameter (x/D = 1) downstream from the glottis. The detailed turbulence properties such as the Reynolds shear stresses and turbulence intensities for the triangular aperture case differed significantly from those for the circular aperture case within a few tracheal diameters (x/D < 7) downstream from the apertures. The glottis-induced turbulence was incipient during the acceleration phase of inspiration and convected downstream with the traits of decaying turbulence.

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

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

Bio-acoustic signals from stenotic tube flow: state of the art and perspectives for future methodological development

To study the degree of stenosis from the acoustic signal generated by the turbulent flow in a stenotic vessel, so-called phonoangiography was first suggested over 20 years ago. A reason for the limited use of the technique today may be that, in the early work, the theory of how to relate the spectrum of the acoustic signal to the degree of the stenosis was not clear. However, during the last decade, the theoretical basis for this and other biological tube flow applications has been clarified. Now there is also easy access to computers for frequency analysis. A further explanation for the limited diagnostic use of bio-acoustic techniques for tube flow is the strong competition from ultrasound Doppler techniques. In the future, however, applications may be expected in biological tube flow where the non-invasive, simple and inexpensive bio-acoustic techniques will have a definite role as a diagnostic method.

Modeling sound generation in stenosed coronary arteries

Acoustic measurements obtained from sensitive microphones placed on the chest are being used in a procedure to noninvasively diagnose coronary artery disease. Utilizing specially developed signal processing techniques, the spectral content of isolated diastolic heart sounds has been estimated and usually shows an increase in high-frequency components in patients with occlusive coronary arteries. In order to establish a theory for the origin of these spectral features, a sound source model has been developed which combines an incremental network model of the left coronary artery tree with a transfer function model describing arterial chamber resonant characteristics. The network model predicts flow in both normal and stenosed coronary arteries. From this flow information, the arterial chamber transfer function model predicts the development of acoustic signals from the chamber resonant characteristics. The transfer function of a segment of coronary artery demonstrates two resonance frequencies. These resonance frequencies depend upon the length and diameter of the chamber segment, as well as upon the distal hydraulic impedance loading the segment. The lower resonance frequency can be excited by the usual flow fluctuations (low frequency) in the coronary artery. In cases of stenosis, the wideband spectral characteristics of the turbulence produced by the stenosis excites both the low and high resonance frequencies. In a small sample of patients, the spectra obtained from isolated diastolic acoustic signals recorded by a chest microphone agree well with those predicted by this theory.

Pulsed Doppler ultrasound system for the measurement of velocity distributions and flow disturbances in arterial prostheses

For the investigation of flow through prosthetic arteries a pulsed Doppler ultrasound system has been characterized. Preliminary in vitro experiments using this system are described; they verify its suitability for making velocity profile and flow disturbance measurements. The output from a frequency tracker is compared with spectral analysis of Doppler signals for both laminar and turbulent flow regimes and the root mean square fluctuations on the tracker output signal are used to identify transition from laminar to turbulent flow. In addition, the turbulent intensity of poststenotic flow is quantified at several axial locations and for different rates of flow. Finally, we present velocity profile measurements which were obtained using a deconvolution technique to account for the finite size of the sample volume.

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.

The effect of unsteadiness on the flow through stenoses and bifurcations

This paper is concerned with the influence of a stenosis or a bifurcation on the flow through a tube. In particular the effect of unsteadiness is investigated using simple pulsatile and physiological type flows (Fig. 1). The experimental investigations reported herein are concerned with velocity measurements and flow visualizations. (see formula in text) These measurements, performed in a 60 degrees bifurcation, have permitted the reconstruction of the three-dimensional velocity profiles. The importance of the secondary flow in the branching is analyzed for various values of the flow parameters. Results of tests show a strong influence of unsteadiness on flow characteristics and then on hemodynamic factors. One conclusion is the following: if hemodynamic factors play an important role in the problems of atherosclerosis, then, for macrocirculation studies, it is necessary to take into account unsteadiness and, in particular, the actual shape of the flow-time forcing function.

A model investigation of the velocity and pressure spectra in vascular murmurs

A physical model consisting of an axisymmetrical jet in a rigid plexiglass pipe was used to study the flow and pressure fluctuations downstream from an aortic stenosis. The fluctuating velocity components, u and v, at several locations in the steady liquid jet were measured using a laser Doppler anemometer system. Simultaneous wall pressure fluctuations were monitored by an array of nine miniature pressure transducers wall mounted in the axial direction. This paper presents the detailed measurements of mean velocity profiles, turbulent intensity distributions and RMS pressure fluctuations. The energy spectra obtained for the pressure fluctuations and the u and v velocity components are compared. Contrary to earlier works, we found that the differences between peak frequencies of the pressure spectra and the characteristic frequencies of the velocity spectra vary with positions downstream from the nozzle. These differences are discussed in light of pseudosound generation by the eddy structures in the stenotic flow field.

Flow disturbance measurements through a constricted tube at moderate Reynolds numbers

Instantaneous velocities in the field distal to contoured axisymmetric stenoses were measured with a laser Doppler anemometer. Upstream flow conditions were steady and spanned a range of Reynolds numbers from 500 to 2000. Autocorrelation functions and spectra of the velocity were employed to describe the nature of fluid dynamic disturbances. Depending upon the degree of stenosis and the Reynolds number, the flow field contained disturbances of a discrete oscillation frequency, of a turbulent nature, or both. If turbulence was detected in a given experiment, it was always preceded upstream by velocity oscillations at discrete frequency arising from vortex shedding. For mild degrees of stenosis (50% area reduction or less) the intensity of flow disturbances was relatively low until the Reynolds number exceeded 1000, thus highlighting difficulties to be expected in employing flow disturbance detection as a diagnostic tool in the recognition of early atherosclerosis in major arteries. In view of the relatively high noise levels inherent in noninvasive Doppler ultrasound systems employed clinically, it seems unlikely that detection of stenosis of less than 50% area reduction is feasible unless the Reynolds numbers exceed 1000 or unless pulsatility introduces new unsteady flow features beyond those studied here.

Effects of surrounding tissue on the sound spectrum of arterial bruits in vivo

Turbulent flow distal to arterial stenoses producers bruits with a characteristic sound spectrum, analysis of which has permitted accurate non-invasive assessment of the residual lumen diameter of the stenosis in the case of the human carotid artery. In contrast, investigators working with in vitro elastic models of arteries or with excised vessels have reported finding mainly resonant spectra of bruits recorded distal to stenoses. We have studied the effects of turbulent flow on the sound spectrum produced at the arterial wall and the influence of surrounding tissue on this spectrum. Aortic, carotid, and femoral stenoses were produced in dogs by external banding of the arteries with 5mm wide Teflon bands. Recordings of bruits made directly on the vessel wall had a sound spectrum made up of 2 components, one due to turbulent flow, and the second to a superimposed resonant spectrum from arterial wall vibration. This was true of 3 kinds of vessels studied. The effects of surrounding tissue on the sound spectrum of arterial bruits was shown by comparing the spectra o bruits recorded directly on the vessel wall, on the freshly closed wound and on the healed wound. The sound properties of the artery in situ are very different from those of exposed or excised vessels or elastic tubes. Although intravascular turbulence may be accurately appreciated at the skin surface, arterial wall resonance in the intact animal is extensively damped by the normal coupling of the artery to its surrounding tissue.

Wall shear stress distribution in a model canine artery during steady flow

The wall shear stress pattern was measured in a rigid plastic cast of a canine artery during steady flow by means of an electrochemical technique. The topographic distribution of shear stress is very nonuniform, with regions of high and low shear in close proximity. The steady shear stresses are highest at the leading edge of flow dividers and at the entrance regions to branch vessels. The shapes of the shear stress curves in the celiac branch are primarily a function of the ratio of branch flow to total aortic flow. However, the shapes of the shear stress curves in the adjacent anterior mesenteric branch remain the same for different anterior mesenteric branch flow ratios, although the shear increases with the branch flow ratio. An unstable pattern of flow separation and reattachment is found at the anterior mesenteric flow divider lip and remains localized to that region. A correlation is suggested between sites of high shear stress, extremes in the range of stress, and unstable stress patterns and sites at which atherosclerosis has been shown to develop.

Measurements of disordered flows distal to subtotal vascular stenoses in the thoracic aortas of dogs

Instantaneous blood velocity measurements employing a constant temperature hot film anemometer were obtained in the region distal to externally enforced, subtotal vascular stenoses in the descending thoracic aortas of anesthetized dogs. Our objectives were to determine alterations in velocity waveforms and energy spectra as the degree of stenosis was increased. We paid particular attention to distinguishing features of the flow which were characteristic of turbulence. Our results indicate that, for the vessels studied, disturbances in the velocity waveforms occur for very minor localized constrictions. The energy spectra follow certain similarity parameters within a restricted region of the distal velocity field. For severe stenoses relatively high levels of energy exist in frequency ranges which previously have been found to produce poststenotic dilation. The measurements suggest that velocity waveforms and energy spectra provide a very early clue to the existence of localized occlusive vascular disease in larger vessels and that, within a limited region distal to a stenosis, the degree of constriction may be estimated by similarity analysis of the energy spectra.