Experimental proof of Doppler bandwidth invariance

3D angle-independent Doppler and speckle tracking for the myocardium and blood flow

A technology based on velocity ratio indices is described for application in the myocardium. Angle-independent Doppler indices, such as the pulsatility index, which employ velocity ratios, can be measured even if the ultrasound beam vector at the moving target and the motion vector are not in a known plane. The unknown plane situation is often encountered when an ultrasound beam interrogates sites in the myocardium. The velocities employed in an index calculation must be close to the same or opposite directions. The Doppler velocity ratio indices are independent of angle in 3D space as are ratio indices based on 1D strain and 1D speckle tracking. Angle-independent results with spectral Doppler methods are discussed. Possible future imaging techniques based on velocity ratios are presented. By using indices that involve ratios, several other sources of error cancel in addition to that of angular dependence for example errors due to less than optimum gain settings and beam distortion. This makes the indices reliable as research or clinical tools. Ratio techniques can be readily implemented with current commercial blood flow pulsed wave duplex Doppler equipment or with pulsed wave tissue Doppler equipment. In 70 patients where the quality of the real-time B-mode looked suitable for the Doppler velocity ratio technique, there was only one case where clear spectra could not be obtained for both the LV wall and the septum. A reproducibility study of spectra from the septum of the heart shows a 12% difference in velocity ratios in the repeat measurements.

A simulation study of sample volume sensitivity for oblique pulsed finite beam insonation of Doppler ultrasound flow phantom cylindrical vessels

Our previous analysis of the lumen pressure in Doppler ultrasound flow phantoms subject to continuous wave, infinite beam excitation is extended here to consider the pressure and Doppler sample volume complex sensitivity within a range of solid absorbent tubes typical of those used in Doppler ultrasound flow phantoms insonated with a focussed pulsed ultrasound beam. The beam may be incident on the cylindrical shell from any angle and with any offset from the shell axis. The examples considered are of a 5 MHz beam with a 6 dB lateral fullwidth of 1 mm at the focus and a transducer surface acceleration pulse with standard deviation of 1 micros propagating through 10 mm outer diameter, 8 mm inner diameter, Cflex, low-density polyethylene (LDPE), high-density polyethylene (HDPE), and polymethylmethacrylate (PMMA) shells surrounded by water at various beam-vessel angles. Our results confirm earlier analyses suggesting that PMMA, being less well matched to the surrounding media, causes much greater distortion of the sample volume sensitivity than Cflex.

Doppler angle estimation of pulsatile flows using AR modeling

In quantitative ultrasonic flow measurements, the beam-to-flow angle (i.e., Doppler angle) is an important parameter. An autoregressive (AR) spectral analysis technique in combination with the Doppler spectrum broadening effect was previously proposed to estimate the Doppler angle. Since only a limited number of flow samples are used, real-time two-dimensional Doppler angle estimation is possible. The method was validated for laminar flows with constant velocities. In clinical applications, the flow pulsation needs to be considered. For pulsatile flows, the flow velocity is time-varying and the accuracy of Doppler angle estimation may be affected. In this paper, the AR method using only a limited number of flow samples was applied to Doppler angle estimation of pulsatile flows. The flow samples were properly selected to derive the AR coefficients and then more samples were extrapolated based on the AR model. The proposed method was verified by both simulations and in vitro experiments. A wide range of Doppler angles (from 3o degrees to 78 degrees) and different flow rates were considered. The experimental data for the Doppler angle showed that the AR method using eight flow samples had an average estimation error of 3.50 degrees compared to an average error of 7.08 degrees for the Fast Fourier Transform (FFT) method using 64 flow samples. Results indicated that the AR method not only provided accurate Doppler angle estimates, but also outperformed the conventional FFT method in pulsatile flows. This is because the short data acquisition time is less affected by the temporal velocity changes. It is concluded that real-time two-dimensional estimation of the Doppler angle is possible using the AR method in the presence of pulsatile flows. In addition, Doppler angle estimation with turbulent flows is also discussed. Results show that both the AR and FFT methods are not adequate due to the spectral broadening effects from the turbulence.

Pulsed Doppler flow-line spectrum for focused transducers with apodized apertures

The properties of the single flow-line Doppler spectrum using pulsed wave (PW) ultrasound is studied on the basis of previously developed spectral theory for transducers with apodized apertures. It has been shown previously that the spectral width of Doppler signals from a sample volume in low velocity-shear flow is independent of the sample volume depth but that is not true for the spectra from the individual streamlines. The work presented here on the Doppler flow-line spectrum shows that its width should be invariant with flow-line location, if the sample volume depth is fixed. At the same time, for a transducer operating in PW mode not only the Doppler spectral width depends on the sample volume depth, but also the modal Doppler frequency shift changes with flow-line displacement in the illuminating field except if the sample volume centre and the beam focus coincide. The variation of modal Doppler frequency shift is the more explicit manifestation of the effect of wavefront curvature increasing for lines and sounding depths distant from the focal point. The values of the Doppler shift and spectral bandwidth are reported taking account of beam diffraction and variations in its geometry due to focusing.

Intrinsic spectral broadening (ISB) in ultrasound Doppler as a combination of transit time and local geometrical broadening

Doppler signals collected with a focused transducer are known to be affected by the so-called intrinsic spectral broadening (ISB). This article aims to point out how ISB is, in general, related to both the limited lateral extent of a focused beam (leading to a finite transit time), and the presence of several local insonation angles around the beam axis, due to focusing and diffraction effects (local geometrical broadening). The influence of these two elementary spectral contributions on the whole ISB is shown by considering the Doppler signal as simultaneously modulated in amplitude and frequency, and applying well-known relationships employed in the communication field. Such an analysis reveals that transit time and local geometrical broadening are two different phenomena, whose simultaneous knowledge is necessary for correctly evaluating the overall ISB. Finally, thanks to a novel technique for separately measuring transit time and local geometrical broadening effects on transducers with markedly different focusing properties, more than 1000 experimental acquisitions show how a proper combination of such measured contributions gives an accurate ISB estimation, confirming the theoretical expectations.

Finite beam-width ray model for geometric spectral broadening

The purpose of the study was to compare measured spectral width and maximum frequency with that predicted from ray models of geometric spectral broadening. Zero and finite beam-width models were used. Spectral data were acquired from a string phantom using two commonly-used linear array systems. Beam width and Doppler aperture sizes were measured using a needle hydrophone. The results showed that the experimentally measured data agreed best with the finite beam-width model. The zero beam-width model was in error by up to 50% for calculated spectral width, and up to 10% for maximum frequency. It is concluded that spectral width and maximum frequency are best calculated using the finite beam-width model, and that ultrasound manufacturers could improve the variation in spectral broadening measured at different locations on a single machine by adjusting the aperture size to give a constant subtended angle and beam width.

Angle-insensitive flow measurement using Doppler bandwidth

The ability to measure the velocity of blood flow independent of the orientation of the blood vessel could aid in evaluation of many disease processes, such as coronary lesions. Conventional ultrasonic Doppler techniques require knowledge of the beam-to-flow angle, and the Doppler effect vanishes when this angle is 90 degrees . By employing a spherically symmetrical range cell and the Doppler bandwidth instead of the Doppler shift, preliminary results show that flow measurement of ideal uniform flow that has a blunt velocity profile can be made without knowledge of tile orientation of the vessel, even when the angle of orientation is around 90 degrees . But when the technique is applied to a real how that has a parabolic velocity profile, the Doppler bandwidth decreases as the beam-to-flow angle increases. Although the Doppler bandwidth is sensitive to the transducer angle in this situation, the error in determining flow velocity might be acceptable if the transducer angle can be estimated to be within a small range. For this method to be regarded as practical for clinical use, however, a consistent relationship between bandwidth and flow velocity must be demonstrated over some set of clinically relevant conditions. The experimental techniques and results for how measurements of both the ideal uniform flow and the real flow are presented in this paper.

Improved blood velocity estimation using the maximum Doppler frequency

In vessels whose diameter is smaller than the length of the range cell or measurement volume, the maximum blood velocity is often calculated from the maximum frequency of the Doppler spectrum, using the classical Doppler equation. It is shown that the accuracy of this procedure is significantly improved at large beam-to-flow angles, if a correction for transit time broadening is made. This finding is based on the demonstration that the maximum frequency of the Doppler spectrum depends only on the maximum velocity passing through the measurement volume, but in a manner which is a function both of the Doppler shift frequency as well as the transit time broadening associated with the passage of scatterers through the beam width.

Invariance of the Doppler bandwidth with range cell size above a critical beam-to-flow angle

For a sound beam impinging on a blood vessel, with a range cell much smaller than the vessel diameter, it is known that the breadth of the echo Doppler spectrum is proportional to the velocity of the flow through the range cell. As the range cell is lengthened to include a greater range of velocities, the spectrum is expected to widen proportionately. It is shown theoretically, and confirmed experimentally, that if the beam-to-flow angle is greater than a critical value, the Doppler spectrum bandwidth is independent of the length of the range cell, and depends only on the maximum velocity encompassed by it. This happens because for angles greater than the critical, the narrow spectra produced by lower velocity flows near the vessel walls are contained within the broader spectrum produced by the higher speed flow near the vessel axis. The critical angle is the angle at which the flow axis is normal to one of the beam edges.

Transverse Doppler spectral analysis for a correct interpretation of flow sonograms

The classic Doppler equation predicts that scatterers moving transversely to the ultrasound beam yield a zero frequency shift in the received echoes. An original theoretical approach, which has been developed in the last few years, has demonstrated that any focused beam leads to the generation of a Doppler spectrum with a nonzero bandwidth even for a transverse flow orientation. Based on this new theory, it is shown here that "transverse" Doppler spectral analysis can also be usefully applied in vivo. Experimental results obtained by observing normal and diseased carotid arteries at 90 degrees show that the information obtained with this approach is complementary to that provided by the mean frequency alone, which is given by the classic Doppler equation.

Experimental evaluation of intrinsic and nonstationary ultrasonic Doppler spectral broadening in steady and pulsatile flow loop models

Intrinsic and nonstationary Doppler spectral broadening, and the skewness of the spectral representation, were evaluated experimentally using porcine red cell suspensions as ultrasonic scatterers. Theoretically, the relative Doppler bandwidth, defined as the intrinsic bandwidth divided by the mean Doppler frequency shift, should be velocity independent. The relative Doppler bandwidth invariance theorem was experimentally verified with an in vitro steady laminar blood flow model. It is shown that the relative bandwidth is both independent of the flow velocity and blood hematocrit. Using a pulsatile laminar flow model, the authors demonstrated that the relative Doppler bandwidth invariance theorem did not hold during flow acceleration and deceleration. In addition, a positive skewness of the Doppler spectra was observed during acceleration while a negative skewness was measured during the deceleration of blood. The effect of the window duration used in the Fourier spectral computation, on nonstationary broadening, is characterized.