Effect of vessel curvature on Doppler derived velocity profiles and fluid flow

Side-branches and curvatures in the arterial tree yield deviations from the axial oriented velocity. Velocity or volume flow estimates based on the assumption that flow is axially oriented are of limited value at these sites. This article evaluates information obtainable by using a multigate Doppler ultrasound (US) instrument used with curved phantoms, which resemble the human coronary arteries. The comparison of experimental velocity data with data provided by an accurate computational fluid dynamics (CFD) method shows differences in the range of 4 to 11% for four curvatures with different radii. Multigate data are also used to estimate the volume flow in the curved segments at different experimental conditions. An error lower than 15% is obtained, to be compared with a 24% error obtained by assuming a parabolic velocity profile. In particular, it is shown that the residual error is not related to the small deviation of the velocity vectors from the axial direction due to the presence of secondary velocity components, which are found to be of magnitude less than 10% with respect to the axial velocity component.

A novel ultrasound instrument for investigation of arterial mechanics

The study of arterial mechanics concerns functional characteristics depending on wall elasticity and flow profile. Wall elasticity can be investigated through the estimation of parameters like the arterial distensibility, which is of high clinical interest because of its known correlation not only with the advanced atherosclerotic disease, but also with aging and major risk factors for cardiovascular disease. The flow velocity profile is also clinically relevant, because it modulates endothelial function and can be responsible for the development and distribution of atherosclerotic plaques. A clinically relevant variable extracted from the blood velocity profile is the wall shear rate (WSR), which represents the spatial velocity gradient near the vessel wall. This paper describes an integrated ultrasound system, capable of detecting both the velocity profile and the wall movements in human arteries. It basically consists of a PC add-on board including a single high-speed digital signal processor. This is dedicated to the analysis of echo-signals backscattered from 128 range cells located along the axis of the interrogating ultrasound (US) beam. Echoes generated from the walls (characterized by high amplitudes and low Doppler frequencies) and from red blood cells (characterized by low amplitudes and relatively high Doppler frequencies) are independently processed in real-time. Wall velocity is detected through the autocorrelation algorithm, while blood velocity is investigated through a complete spectral analysis of all signals backscattered by erythrocytes and WSR is extracted from the estimated velocity profile. Preliminary applications of the new system, including the simultaneous analysis of blood flow and arterial wall movement in healthy volunteers and in a diseased patient, are discussed, and first results are presented.

Real-time identification and archiving of micro-embolic Doppler signals using a knowledge-based DSP system

Identification of micro-emboli in the cerebral circulation using transcranial Doppler ultrasound provides valuable clinical information, but, currently, embolic signal detection and analysis are significantly limited because they mainly rely on costly off-line analysis by human experts. In this study, a reliable, high-resolution, real-time automated system for the detection and archiving of embolic signals was designed and implemented using expert system theory and modern DSP technology. Preliminary tests were conducted to evaluate the functions and the performance of the system using data from ten carotid endarterectomy patients and two normal volunteers. Using the widely accepted 7 dB threshold for human reliability and a human expert, majority-decision gold standard, the real-time system reached sensitivity and specificity of 93.6% and 99.3%, respectively, which were close to the results obtained by three human experts under ideal laboratory conditions (90.1% and 99.8%, 98.4% and 99.9%, 98.9 and 99.9%). The new system has the potential to be used either as a bedside monitoring and signal acquisition device, or as a laboratory investigation tool.

On the interaction between ultrasound and contrast agents during Doppler investigations

Knowledge of interaction mechanisms between ultrasound (US) and contrast agents (CA) suspended in blood is important for a correct interpretation of clinical investigation results. Experiments performed in different laboratories have shown that, as a consequence of primary radiation force, CA tend to move away from the US transducer. Accordingly, Doppler spectra produced by particles suspended in moving water turn out to be significantly altered from what is theoretically expected. The purpose of this paper is twofold. First, an original model describing the bubble dynamics as the outcome of the balance between US radiation force and fluid drag force is validated for the case in which bubbles are suspended in blood. The high fluid viscosity is shown to prevent significant bubble deviations from the unperturbed fluid streamlines so that, in large vessels, a residual spectral distortion may exist only at the highest intensity levels permitted by current regulations. Finally, the relative importance and differences between the effect of primary radiation force and streaming mechanisms that, in principle, could lead to similar effects, are discussed.

A simplified approach for real-time detection of arterial wall velocity and distension

Arterial stiffness is known to increase with age and with many vascular diseases, but its noninvasive assessment in patients still represents a difficult task. The measurement of diameter change during the cardiac cycle (distension) has been proposed as a means to estimate arterial compliance and stiffness. Therefore, we have developed a simple PC-based device and algorithm for noninvasive quantification of vessel wall motion and diameter change in humans. This goal is achieved in real-time by processing the base-band signals from a commercial ultrasound Doppler system. Real-time operation is of crucial importance, because it allows a rapid achievement of optimal measurement conditions. The system was evaluated in a laboratory using a string phantom and was tested on the carotid arteries of 10 volunteers. Wall velocities from 0.05 to 600 mm/s and displacements lower than 2 microns were detected with phantoms. The measured carotid diameter change in the volunteers ranged from 7.5 to 11.8% (mean = 9.8%) and agrees closely with values reported in the literature. The difference between values taken one hour apart ranged from 0.2 to 0.5%. We conclude that the new system provides rapid, accurate, and repeatable measurements of vessel distension in humans.

Velocity magnitude estimation with linear arrays using Doppler bandwidth

The dependence of pulsed wave Doppler bandwidth on parameters typical of linear transducer arrays used in commercial Duplex and color flow mapping systems is investigated experimentally. For a single flow line it is observed that this bandwidth generally depends not only on the scatterer velocity and the beam-to-flow angle, but also on the flow line range and orientation. This is due to the fact that in Duplex and color flow systems the transducer is differently focused in the scan and elevation planes and its aperture and focal lengths are often made to vary, depending on the distance of the flow line from the transducer. It is however experimentally demonstrated that, at points where the ultrasound beamwidths in the scan and elevation planes are both comparable to the sample volume length, the Doppler bandwidth is independent of the beam-to-flow angle. It is also shown that this invariance can be extended to other ranges by appropriately modifying the array aperture. Finally, as an application of this independence, the flow-line velocity magnitude in these beam regions is estimated with better than 5% uncertainty through a simple bandwidth measurement.

Selective transmission of a focused Doppler ultrasound beam through a plastic layer

Laboratory test objects are widely used in Doppler ultrasound (US). Although the acoustic properties of in vitro materials are usually known, they are unlikely to match each other, or their in vivo counterparts, exactly. We conducted theoretical and experimental studies of a focused ultrasound beam as it passes from one fluid, through an intervening plastic layer at an oblique angle, and then into a different fluid. Dual mode propagation may occur (i.e., both longitudinal and shear waves can propagate in the plastic layer). Our calculations show that the power transmitted by either mode drops very rapidly to zero at certain critical angles. A range of angles of incidence exists within a focused beam and this, combined with the highly angle-dependent power transmission behaviour, can produce major distortions of Doppler data. These may persist even when the beam axis is not oriented exactly at the critical angle. The total power transmitted depends on all the wave speeds, may involve mode conversion, and is a very complicated function of the angle of incidence. This study reports a practical method for the calculation of power transmission though a plastic layer, and shows how the resulting power vs. angle graph can be used to avoid artefacts in in vitro Doppler studies.

Application of autoregressive methods to multigate spectral analysis

Multigate analysis is known to be capable of detecting accurate blood velocity profiles from human vessels. Experimental systems so far presented in the literature use time-domain frequency estimations and, more recently, the fast Fourier transform (FFT) for real-time analysis of Doppler signals from multiple range cells. This experimental study is aimed at evaluating the application of an autoregressive (AR) method (Burg algorithm) to multigate Doppler analysis. Both in vitro and in vivo results were collected with a commercial Duplex scanner coupled with a prototype multigate unit developed in our laboratory. The same multigate signals are, thus, processed according to both the FFT and the Burg algorithms. The related spectral and maximum frequency profiles are reported and statistically compared. AR, implemented with the Burg algorithm, is demonstrated to be a way to perform multigate spectral analysis with reduced spectral variance, suitable for maximum velocity profile extraction through a simple threshold.

Doppler spectra from contrast agents crossing an ultrasound field

When contrast agents are injected in a fluid, it is implicitly assumed that they move at the same velocity as the fluid itself. However, a series of in vitro tests performed by using air-filled microbubbles suspended in distilled water, have shown that the Doppler spectrum generated in this case may be notably different from that obtained from non-resonating scatterers. In this paper, we show, through a simple simulation model, that the actual movement of microbubbles may be predicted as the result of the complex balance between two forces: the ultrasound radiation force, which tends to move the particles along the sound beam direction, and the fluid drag force, which tends to move the particles along the fluid stream. The contrast agents turn out to be displaced only during the passage of the ultrasound burst; during the remaining time, they are maintained at the fluid velocity by the drag force. Based on the total particle displacement estimated between consecutive pulses, a series of Doppler spectra corresponding to different intensity levels was computed. This series was shown to be in excellent agreement with the experimental spectra obtained in vitro using Levovist (Schering AG, Berlin, Germany) particles suspended in distilled water flowing at a steady rate.

Detection of vascular haemodynamics through a high-speed velocity profiler

OBJECTIVE

This paper aims at demonstrating that ultrasound Doppler multigate spectral analysis performed with advanced equipment may provide detailed and significant haemodynamic information.

METHODS

A novel multigate system was recently introduced and shown capable of performing real-time spectral analysis of Doppler data from 64 resolution cells located at different depths from the transducer. The system extends the typical capabilities of conventional Pulsed Wave (PW) equipment by displaying the full spectral content of Doppler signals over an ultrasound scan line rather than in a single resolution cell. In cases where it is appropriate to display the available information in a simpler form, parameters such as the maximum frequency can be extracted from each spectrum, by using conventional or advanced image processing methods.

RESULTS

In-vitro experiments show that the multigate system can perform velocity measurements with good accuracy and precision. Examples of in vivo profiles detected from carotid, femoral and radial arteries are presented. In particular, the first results obtained from the aorta are shown.

CONCLUSIONS

Blood flow behavior can be accurately investigated using a real-time multigate system which extends Doppler spectral analysis to a whole scan line.

PSpice modelling of ultrasound transducers: comparison of software models to experiment

This paper presents a complete PSpice model of an ultrasound single-element transducer, including electrical and mechanical matching as well as the focusing lens. By using this model, it is possible to obtain a relation between the electrical driving source and the acoustic velocity on the transducer surface. This boundary condition then allows the acoustic field to be calculated by numerical methods. Experimental data obtained with two different transducers are in good agreement with results predicted by the related models.

Quantitative analysis of Doppler spectrum modifications yielded by contrast agents insonified at high pressure

In this report, the authors consider the modifications yielded in the Doppler spectrum when acoustic fields of increasing intensities are applied to encapsulated gas bubbles. Their in vitro experimental results show that the spectrum bandwidth is nearly proportional to the incident acoustic pressure, when its amplitude is maintained below about 200 kPa. At higher pressure levels, it even may happen that, in a steady, unidirectional flow (which should generate only positive Doppler frequencies), the Doppler spectrum is enlarged up to the point that negative Doppler shifts also are produced. Possible explanations in terms of either radiation force or streaming are discussed for this asymmetrical bandwidth enlargement.

Flow imaging with pulsed Doppler ultrasound and flow phantoms

The use of a multigate profiling system with steady laminar flow in plastic tubes revealed spectral artifacts not previously described. In particular, a double or split profile was often observed. In this paper, these artifacts are related to the dual mode ultrasound propagation in the plastic tube. The propagation speeds and, therefore, refraction angles and propagation paths are different for the longitudinal and the shear wave. The power transmission can be extraordinarily sensitive to small variations in the angle of incidence, and this may combine with the existence of a range of angles of incidence within any focused ultrasound beam to produce spectral distortions. The plastic tube is thus shown equivalent to a selective filter, which diminishes some frequency components in the Doppler spectrum relative to others. The spectral artifacts are explained in terms of the relative power transmitted by each mode, and the degree of beam defocusing experienced by each. Spectral distortions persist even when the beam-to-flow orientation is well away from the critical angle. The results of this study show that it is feasible to understand the acoustic transmission behavior of a flow phantom, based on a knowledge of the material properties, and to demonstrate the usefulness of doing so.

An FFT-based flow profiler for high-resolution in vivo investigations

Pulsed Doppler spectral analysis is a well-established diagnostic technique in the assessment of arterial diseases. Because of hardware limitations, its use has been so far restricted to the analysis of a single sample volume located along the ultrasound beam axis. In this paper, we discuss the operation of a newly developed multigate instrument capable of performing, in real time, 64-point fast Fourier transforms of Doppler signals sampled from 64 different range cells. The new instrument is capable of accurately detecting the actual blood flow behavior in major human vessels. Significant examples of velocity profiles obtained in real time from carotid arteries in healthy subjects are reproduced here for the first time. Multigate extension of spectral analysis is demonstrated to be a suitable means for detailed in vivo investigation of blood flow dynamics.

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.

Comparison of conventional and transverse Doppler sonograms

When measuring flow velocity using the conventional ultrasonic Doppler effect, beam axis-to-flow angles approaching 90 degrees are avoided as the Doppler spectrum frequency shift is known to go to zero at this angle. In this paper, the conventional Doppler technique is compared with the transverse Doppler method, in which the Doppler spectrum bandwidth is used to estimate flow, allowing flow to be probed at 90 degrees. The comparison is made using a moving thread flow phantom capable of executing various velocity profiles. This technique may allow the probing of vessels that are inaccessible to conventional oblique probing, thus complementing the conventional Doppler technique.

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 proof of Doppler bandwidth invariance

A line flow of scatterers crossing the sound field produced by a focused circular transducer at uniform velocity originates a quasi-triangular Doppler spectrum. It is known that the spectrum shape and width depend on the line flow to beam axis angle, as well as on the transducer geometry. It has recently been theoretically predicted that this spectrum width is independent of the flow line location in the sound field. Experimental verification of the new theorem, based on the use of a thread phantom operated at various orientations, ranges, and offsets, with respect to the ultrasound transducer, is presented. The tests were made with a computerized pulsed Doppler system designed to perform optimal real-time spectral analysis of data obtained in this application. The prototype system and the experimental procedure adopted for demonstrating in vitro the invariance of the Doppler spectral bandwidth are described.

A tracking FFT processor for pulsed Doppler analysis beyond the Nyquist limit

A tracking procedure for processing ultrasound pulsed Doppler signals with instantaneous frequencies beyond the Nyquist limit is discussed. It is based on the observation that the frequency translation required to properly reconstruct an aliased spectrum can be achieved by means of a simple reordering of data provided by a digital fast Fourier transform (FFT) unit. The amount of reordering is automatically derived by the computed value of a spectral parameter, e.g., the mean frequency. The procedure has been tested by introducing some modifications at the output of an FFT unit included in a conventional pulsed Doppler system. As a result, the dynamic evolution of the full Doppler spectrum and related mean frequency can be followed in real time over an extended range. In vitro and in vivo experiments, as well as quantitative measurements carried on with test signals are presented.

Synchronous dynamic focusing for ultrasound imaging

An approach to dynamic focusing of ultrasound linear array scanners is presented, leading to the unique capability of implementing a focus that continuously tracks the return signal along the penetration depth. An electronically variable lens is obtained by a heterodyning process, in which the phases of echo signals at the array elements are equalized by mixing with suitable reference oscillations. These are generated by control of a single voltage-controlled oscillator, whose frequency is properly varied in synchronism with the delay of signal from different depths. The technique has been experimentally demonstrated by modifying the focusing processor of a conventional echographic linear scanner. Superior performances have been obtained with respect to fixed-focus operation mode. The image quality results are comparable with those of multizone-focus operation mode, in which the focus is varied over more transmit/receive cycles at the expense of lower frame rate.