Turbulent wall pressure measurements in a model of aortic stenosis

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.

Experimental and numerical investigation on soft tissue dynamic response due to turbulence-induced arterial vibration

Peripheral arterial occlusive disease is a serious cardiovascular disorder. The arterial occlusion leads to turbulent flow and arterial sound generation on the inner vessel wall. Stenosis-induced vibro-acoustic waves propagate through the surrounding soft tissues and reach the skin surface. In this study, the feasibility of noninvasive acoustic detection of the peripheral arterial stenosis is investigated using the vibration responses by means of experimental and computational models. Latex rubber tube is used to model the artery, and it is surrounded by a tissue mimicking phantom made of bovine gelatin. Vibration responses on phantom surface are measured using laser Doppler vibrometer, and computational results are obtained performing modal analysis. Experimental findings and computational results showed well agreement in terms of spectral content and vibration amplitudes. The effects of various stenosis severities, flow rates, and phantom thicknesses on the vibration responses are investigated from diagnostic perspective. Stenosis severities greater than 70% resulted in a considerable increase in vibration amplitudes. The structural mode shapes of the tissue phantom are dominant between 0 and 100 Hz, suppressing the signals generated by the stenosis. The optimum range of frequency for acoustic stenosis detection is concluded to be between 200 and 500 Hz, particularly around 300 Hz. Graphical abstract .

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.

Development of a CFD urethral model to study flow-generated vortices under different conditions of prostatic obstruction

A novel, non-invasive method to diagnose bladder outlet obstruction involves the recording of noise with a contact microphone pressed against the perineum (between anus and scrotum). This noise results from flow-generated vortices caused by prostatic obstruction. We developed a computational fluid dynamic (CFD) urethral model including urethral geometry to study the relation between generated noise and the degree of obstruction. This model comprised a bladder, bladder neck, prostate and urethra. Calculations were carried out at four bladder pressures, five degrees of obstruction and three obstruction shapes. For each of the sixty simulations, the velocity and pressure distributions along the urethra were calculated including wall shear stresses to localize flow transition from disturbed to normal. Negative pressures at the obstruction outlet induced recirculation of flow. The location of transition was independent of the applied bladder pressure, but it depended primarily on the degree and secondarily on the shape of the obstruction. Based on the presented results, we hypothesize that the location of the maximum amplitude of perineal noise mainly depends on the degree and shape of the prostatic obstruction. Our future aim is to test our hypothesis in male patients and to extend the presented model to 3D with a viscoelastic urethral wall to calculate the fluid-wall interaction.

Ultrasonic vibration dectection with wavelets: preliminary results

Several arterial disorders are known to cause systolic audio vibrations in tissue: they include stenoses, vasospasm, aneurysms, bleeds and arteriovenous fistulas. High-amplitude vibrations can be discovered with conventional Doppler ultrasound (US) instruments; however, differentiating brief, low-amplitude vibrations from other nonstationary echo sources is difficult. Further, characterizing the frequency and amplitude of vibrations is not feasible with conventional Doppler US. The automated detection and estimation of both the frequency and amplitude of vibrations with durations less than 100 ms and amplitudes of a micrometer or less have remained a signal-processing challenge. These vibrations may be associated with both nonstationary colored noise and strong low-frequency clutter. The normalized continuous Morlet wavelet power-spectrum analysis of quadrature Doppler echoes, followed by a binary hypothesis test for noise, results in simulated detection rates above 99.9%, with 0.1% false alarms for signal-on signal-to-noise ratios (SNRs) as low as one. Two clinical examples are included.

Beamformed nearfield imaging of a simulated coronary artery containing a stenosis

This paper is concerned with the potential for the detection and location of an artery containing a partial blockage by exploiting the space-time properties of the shear wave field in the surrounding elastic soft tissue. As a demonstration of feasibility, an array of piezoelectric film vibration sensors is placed on the free surface of a urethane mold that contains a surgical tube. Inside the surgical tube is a nylon constriction that inhibits the water flowing through the tube. A turbulent field develops in and downstream from the blockage, creating a randomly fluctuating pressure on the inner wall of the tube. This force produces shear and compressional wave energy in the urethane. After the array is used to sample the dominant shear wave space-time energy field at low frequencies, a nearfield (i.e., focused) beamforming process then images the energy distribution in the three-dimensional solid. Experiments and numerical simulations are included to demonstrate the potential of this noninvasive procedure for the early identification of vascular blockages-the typical precursor of serious arterial disease in the human heart.

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.

Heterogeneity in smooth muscle cell population accumulating in the neointimas and the media of poststenotic dilatation of the rabbit carotid artery

Rabbit smooth muscles contain at least three types of myosin heavy chain (MHC) isoforms; SM1, SM2 and SMemb (NMHC-B), the expression of which is developmentally regulated. We have recently reported that smooth muscles with the embryonic phenotype accumulate in the neointimas produced by endothelial denudation or high-cholesterol feeding. In this study, we examined MHC isoform expression in the neointimas and the media of poststenotic dilatation of the rabbit carotid artery, and determined the phenotype of the smooth muscle cell in the dilated segment. We report here that neointimal cells in the dilated segment are smooth muscle cells with the embryonic phenotype as previously reported in our ballooning-injury study. The medial smooth muscles, however, are composed of heterogeneous population of smooth muscles which differ in stage of differentiation as determined by the MHC isoform expression. These results indicate that MHC isoforms are useful molecular markers to identify abnormally proliferating smooth muscles in diseased arteries and to understand the process of atherogenesis occurring following vascular injury.

Morphometric analyses of rabbit thoracic aorta after poststenotic dilatation

The aim of this study was to quantify the morphological changes in the arterial wall resulting from poststenotic dilatation (PSD). PSD was produced by placing a split nylon ring around the thoracic aorta of the rabbits at a level of T6-7 during a sterile thoracotomy done under pentobarbital anesthesia. After period of PSD ranging from 1-51 months these rabbits were anesthetized, as were the control animals, and the descending thoracic aorta from the fourth to the eleventh ribs was removed following perfusion fixation with Karnovsky's solution at a constant pressure of 80 mm Hg. The extent of PSD development was variable even though the stenotic ring was the same size in all rabbits. Ultrastructural findings showed degenerative changes of the wall components in the PSD region and were more prominent in the aortas with greater dilatation. Morphometric measurements showed that the PSD was accompanied by a decrease in volume density of both smooth muscle cells (SMCs) and elastin and an increase in collagen and ground substance. These changes were well correlated with degree of dilatation and ratio of internal radius to wall thickness (hence, mean wall stress) but not with duration of PSD. While the number of SMCs per unit volume in the PSD aortas was significantly less than normal (p less than 0.05), there was no significant change in mean cell volume. Although the reduced muscle mass might be expected to lower the capacity of the vessel to maintain tone, previous results show that this does not occur.

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.

Measurement and calculations of laminar flow in a ninety degree bifurcation

Measurements and numericaL calculations of laminar flow in a plane 90 degrees bifurcation are presented. The corresponding two-dimensional steady flow Navier-Stokes equations solved by a finite-difference procedure employing pressure and velocity as dependent variables. The influence of Reynolds number and mass flow ratio on the velocity field, streamlines, local shear stress and pressure drop are quantified and shown to be substantial. The circulation patterns and shear stresses are examined in view of available data regarding the formation of atherotic plaques in the human circulatory system. The calculated velocity profiles are compared with measurements obtained with laser Doppler anemometry and the agreement is shown to be satisfactory. Calculations outside the range of measurements which are of value to biomechanics are also presented.