Curvature affects Doppler investigation of vessels: implications for clinical practice

In clinical practice, blood velocity estimations from Doppler examination of curved vascular segments are normally different from those of nearby straight segments. The observed "accelerations," sometimes considered as a sort of stochastic disturbances, can actually be related to very specific physical effects due to vessel curvature (i.e., the development of nonaxial velocity [NAV] components) and the spreading of the axial velocity direction in the Doppler sample volume with respect to the insonation axis. The relevant phenomena and their dependence on the radius of curvature of the vessels and on the insonation angle are investigated with a beam-vessel geometry as close as possible to clinical setting, with the simplifying assumptions of steady flow, mild vessel curvature, uniform ultrasonic beam and complete vessel insonation. The insonation angles that minimize the errors are provided on the basis of the study results.

Doppler power spectrum from a Gaussian sample volume

A closed-form expression for the Doppler power spectrum due solely to the range of blood velocities passing through a Gaussian sample volume placed anywhere in a vessel under conditions of axisymmetric flow, uniform backscatter and negligible intrinsic spectral broadening has been derived. The formulation presented here allows the independent specification of the sample volume position and width, in the three dimensions, and enables simple estimations of spectral shape for pulsed wave Doppler systems. Simpler expressions were derived for the cases of symmetric sample volume projections onto the vessel cross-section and/or sample volumes centred in the vessel. Closed form expressions were derived for mean frequency and spectral width in the case of a symmetric sample volume projection centred in the vessel. The effects of sample volume size and position on the Doppler spectral width and mean frequency are shown for a range of velocity profiles.

Time-averaged mean velocity for volumetric blood flow measurements: an in vitro model validation study using physiological femoral artery flow waveforms

This study assesses the accuracy of the volume flow measurement of the ATL HDI 3000 duplex ultrasound scanner using a model of the femoral arterial circulation. The beam profile of the transducer was measured, and used to identify regions of the beam where there may be poor insonation characteristics. The flow measurement accuracy was not found to be influenced by the vessel depth between 1.0 cm and 8.0 cm in a 0.7 cm diameter vessel. Overall accuracy was 3%+/-9%. Vessels in excess of 0.9 cm produced larger errors. In the model system, pulse rates between 60 bpm and 120 bpm had no significant effect on the measurement accuracy (p > 0.01). The results of this study suggest that accurate measurements of femoral arterial blood flow are possible. Further work will be required to assess the accuracy of the technique in vivo.

Mean blood velocity measurement with a narrow ultrasound beam and an asymmetric velocity profile

Previous discussions of the measurement of spatial mean blood velocity using Doppler ultrasound with a narrow beam have required the velocity profile in the cross section to be symmetric about the vessel axis. A type of asymmetry is put forward which incurs no error in mean velocity measurement when the beam is directed through the point of maximum velocity. Assuming correct alignment of the beam, errors due to profile asymmetry are, therefore, related to the degree of departure of the asymmetry from this acceptable form.

Lower extremity volumetric arterial blood flow in normal subjects

The objective of this clinical study was to establish normal values for volumetric blood flow in the leg at rest using Doppler ultrasound, and to determine what biophysical factors influence resting volumetric flow. Arterial blood flow was measured at four sites in the legs of 40 healthy subjects using an ATL Ultramark 9 HDI system. All subjects were nonhypertensive nonsmokers with ankle brachial index values greater than 1 and no history of vascular disease. The subjects, 20 of each gender, in age ranging from 20 to 64 y were examined. Blood flow was calculated from the time-averaged, intensity-weighted mean velocity Doppler waveforms and vessel cross-sectional area at the same site. Thigh and calf circumference measurements were used to estimate muscle masses. The mean flow and standard error measured in four arteries in the leg were: 284+/-21 mL/min in the common femoral (CFA); 152+/-10 mL/min in the superficial femoral (SFA); 72+/-5 mL/min in the popliteal; and 3+/-1 mL/min in the dorsalis pedis. Although women tended to have higher time-averaged mean velocities in the CFA and SFA than men (t-test, p < 0.008), their arterial cross-sectional areas tended to be smaller (t-test, p < 0.004) and no statistically significant difference was found between men and women in volumetric flow at any site. No correlation was found between age, weight, height, muscle mass and volumetric flow at all four sites. These estimates of lower extremity volumetric flow in healthy subjects provide a baseline for future studies of flow rates in patients with vascular disease.

Evaluation of cerebral arterial flow with transcranial Doppler ultrasound: theoretical development and phantom studies

Blood flow information available from transcranial Doppler ultrasound is usually derived from velocity alone because no knowledge of vessel caliber is available. In cases such as vasospasm, where vessel size changes, the inference of flow from velocity becomes questionable. A computational technique was used to calculate a flow index and 2 vessel area indices based on the first and zero moments of the Doppler power spectrum. These indices were tested in a steady and pulsatile flow phantom using 6 different diameter elastic tubes. Changes in the flow index showed good agreement with changes in timed volume flow for different flow rates. The vessel caliber indices correctly predicted changes in area when different diameter tubes were examined. These indices may prove useful in clinical settings where the constancy of flow or vessel diameter between studies are in question.

Origin of the Doppler ultrasound spectrum from blood

Backscattering of an incident ultrasound beam by blood gives rise to a Doppler spectrum whose characteristics are affected not only by the velocity distribution, but also by certain basic aspects of the RBC's behavior. Starting from fundamental assumptions, an explicit expression is derived for the Doppler spectrum in terms of the variance in the scatterer number density and the backscattering cross section. This shows that the Doppler power at a given frequency is weighted by the backscattering cross section and the manner in which the red blood cells (RBC's) are packed (packing factor). Since spatial variations in the flow field can result in changes in the variance and backscattering cross section, the mean Doppler frequency will not necessarily be proportional to the mean flow through the sample volume. Experimental results for two different flow fields are used to illustrate these effects. The implications of these findings are discussed in relation to volumetric flow estimation and the power mode display used in some color Doppler flow imaging systems.

The effect of geometrical spectral broadening on the estimation of mean blood velocity using wide and narrow ultrasound beams

If an ultrasound beam uniformly insonates the cross section of a blood vessel then the Doppler signal can be analyzed to give a frequency proportional to the spatial mean blood velocity. This is also possible if the beam can be thought of as negligibly thin compared to the blood vessel radius, centrally placed, and the blood velocity profile is axisymmetric and monotonic, although the analysis takes a different form. The immunity of these mean velocity estimators to broadening of the ideal frequency spectrum is studied. If the broadening of a frequency component is such that its mean frequency, weighted by intensity, is unchanged then the analysis with a uniformly insonating beam still leads to the correct mean velocity. In contrast, for any such broadening, the analysis if the beam is negligibly thin produces an underestimate of the mean velocity. Error expressions are derived for idealized cases and some practical results given.

The effect of noise and high-pass filtering on the estimation of mean blood velocity using wide and narrow ultrasound beams

Recently, a new method of analysis has been proposed for the calculation of a Doppler frequency proportional to mean blood velocity for the case where the Doppler beam is assumed to be of negligible thickness compared to the vessel diameter, and the velocity profile is axisymmetric and monotonic increasing from the vessel wall to the vessel center. Such analysis of the Doppler signal is an alternative to that commonly performed under the assumption that the beam insonates the vessel uniformly. Errors in each method are found and compared for the case where the Doppler signal is contaminated by noise, and for the case where the signal is subjected to an ideal high-pass filter. The frequency resulting from the new method of analysis is affected by low-frequency perturbations approximately twice as much as that resulting from the standard method. However, the new method is much more immune to high frequency perturbations. If each method is used with the beam shape for which it is appropriate then, for a given velocity profile, each method is equally affected by the use of the same ideal high-pass filter.

Volumetric flow estimation in vivo and in vitro using pulsed-Doppler ultrasound

The measurement of volumetric blood flow in small vessels in vitro and in vivo poses a significant technological challenge. In this study, two pulsatile flow models were developed, one with a 3.2-mm lumen diameter and one with a 12.7-mm lumen diameter, to assess the accuracy of volumetric flow estimation of two pulsed-Doppler devices, a Crystal Biotech VF1 20-MHz system with either a cuff-mounted or a needle-mounted probe and an Advanced Technology Laboratories Ultramark 9 High Definition Imaging system with a 5-MHz linear array transducer. The VF1 volumetric flow error was measured in the 3.2-mm phantom over a variety of pulsatile and continuous waveforms. The accuracy of the VF1 was also tested in porcine femoral and renal arteries. VF1 volumetric flow error ranged from 4.8% to 54.3% in the in vivo studies. The ATL demonstrated similar volumetric flow errors in the porcine femoral artery (approximately 3.2 mm diameter), but these errors were reduced to < or = 17.4% in the 12.7-mm-diameter in vitro flow model.

The effect of refraction and assumed speeds of sound in tissue and blood on Doppler ultrasound blood velocity measurements

The combined effect of three assumptions relating to refraction, the speed of sound in tissue and the speed of sound in blood on the accuracy of Doppler ultrasound blood velocity measurements has been investigated. A theoretical relationship giving the net velocity measurement error introduced by these three assumptions has derived using a model in which tissue and blood layers are separated by straight, parallel boundaries. This net error is dependent on the assumed and actual speed of sound in tissue, the assumed speed of sound in blood and the Doppler angle, but is effectively independent of the actual speed of sound in blood. For clinical blood velocity measurements, the net error is estimated to be as much as an 8% overestimation of the actual velocity, higher than previously predicted for any of the factors individually. The relationship also predicts a net velocity measurement error in experimental flow systems and string phantoms which is dependent on the speed of sound in the liquid bath. A water bath at room temperature will give an overestimation of approximately 2%. Experimental investigations using conventional and modified string phantoms and a 5-MHz linear phased array system support these conclusions. The effect of perturbing the layers from their parallel orientation has also been considered theoretically and has provided additional support for the above conclusions. These results may help more accurate Doppler velocity measurements in both experimental and clinical settings.

A wall-less vessel phantom for Doppler ultrasound studies

Doppler ultrasound flow measurement techniques are often validated using phantoms that simulate the vasculature, surrounding tissue and blood. Many researchers use rubber tubing to mimic blood vessels because of the realistic acoustic impedance, robust physical properties and wide range of available sizes. However, rubber tubing has a very high acoustic attenuation, which may introduce artefacts into the Doppler measurements. We describe the construction of a wall-less vessel phantom that eliminates the highly attenuating wall and reduces impedance mismatches between the vessel lumen and tissue mimic. An agar-based tissue mimic and a blood mimic are described and their acoustic attenuation coefficients and velocities are characterised. The high attenuation of the latex rubber tubing resulted in pronounced shadowing in B-mode images; however, an image of a wall-less vessel phantom did not show any shadowing. We show that the effects of the highly attenuating latex rubber vessels on Doppler amplitude spectra depend on the vessel diameter and ultrasound beam width. In this study, only small differences were observed in spectra obtained from 0.6 cm inside diameter thin-wall latex, thick-wall latex and wall-less vessel phantoms. However, a computer model predicted that the spectrum obtained from a 0.3-cm inside diameter latex-wall vessel would be significantly different than the spectrum obtained from a wall-less vessel phantom, thus resulting in an overestimation of the average fluid velocity. These results suggest that care must be taken to ensure that the Doppler measurements are not distorted by the highly attenuating wall material. In addition, the results show that a wall-less vessel phantom is preferable when measuring flow in small vessels.

Analysis of pulsed wave Doppler ultrasound spectra obtained from a model intracoronary catheter

Abnormal arterial blood flow patterns have been implicated in the evolution of various vascular disease processes. Intravascular ultrasound techniques using the pulsed wave Doppler catheter offer the opportunity to characterize these abnormal flow patterns. We have developed a mathematical model that predicts the first two moments of the Doppler spectrum obtained using a Doppler catheter based on the distribution of ultrasonic beam power and velocity profile of fluid flow with an arbitrary distribution of flow disturbances. A scaled-up, in vitro experimental arterial system was used to confirm the validity of the model. Comparison of the predicted first two moments of the Doppler spectrum to the experimental values in this system demonstrated that the distribution of beam power significantly affects the magnitude of the first two moments. Additionally, both velocity gradient and velocity fluctuation broadening effects play prominent roles in determining the magnitude of the second moment. These phenomena must therefore be considered when evaluating in vivo Doppler spectra used for the characterization of abnormal flow patterns.

A mean blood velocity statistic for the Doppler signal from a narrow ultrasound beam

An easily calculable statistic proportional to the instantaneous spatial mean blood velocity through a vessel cross section is derived from Doppler power spectral estimates for the case where the Doppler beam is assumed to be of negligible thickness compared to the vessel diameter. This is an alternative statistic to that derived where uniform insonation is assumed, an assumption thought to be poorer in many real cases. The main requirement is that the velocity profile is monotonic increasing from the vessel wall to the vessel center. Errors in each statistic are compared for a variety of true beam dimensions, using a variety of velocity profiles, and the new statistic is shown to incur less error for Gaussian beam response profiles with a standard deviation less than 0.4 of the vessel radius, or for rectangular response profiles with a width less than 0.65 of the vessel diameter. If an estimate can be made of the true beam dimensions and vessel diameter, a weighted sum of the two statistics can give a more accurate estimate of mean velocity. The case of a beam displaced from the center of the vessel is also considered, and errors are found to be less than 4% for a displacement of 20% of the vessel radius.

Measurement of mean velocity during pulsatile flow using time-averaged maximum frequency of Doppler ultrasound waveforms

It has been suggested that mean velocity of flow could be estimated by the time-averaged maximum frequency over an integral number of cardiac cycles (Gill 1985). The present study verified this theory experimentally with a computer-controlled flow phantom. The effects of some parameters on the relationship between mean velocity and time-averaged maximum frequency were also studied. Parameters investigated included beam-vessel angle, diameter of tubing, pulsatility, flow rate and stenosis. The velocities measured by the Doppler system were compared with the actual velocities. A simple theoretical model was also developed to compare with the experimental results. The results showed that, in a long straight tube, the mean velocity can be estimated to within about 5% from the time-averaged maximum Doppler shift at various flow rates and pulsatilities. The error due to geometrical spectral broadening, especially for large beam-vessel angles, can be estimated to within 3% and therefore corrected.

The present status of ultrasonic imaging in medicine

The ultrasonic techniques that are used routinely in medical imaging have resulted from basic scientific discoveries, new methods of signal analysis and image processing, the development of transducer materials and fabrication techniques, and the application of digital electronics. The system designer is constrained by the ultrasonic properties of tissues, especially speed and attenuation: these properties determine the optimum choices of ultrasonic frequency, and spatial contrast and temporal resolutions. Ultrasonic Doppler techniques provide information about moving targets, including blood flow. Two-dimensional images of anatomical structure and blood flow can be combined in real-time displays. Other advances include sonoelasticity imaging, computed tomography, three-dimensional imaging, contrast agents and quality assurance. Contemporary ultrasonic diagnostic techniques seem to be safe, but the search for possible hazards is continuing with emphasis on thermal effects and cavitation.

Calculation of Doppler spectral power density functions

A volume integral method for the calculation of Doppler ultrasound spectral power density (spd) functions is described. Axisymmetric flow in a circular tube with a power law velocity profile is assumed. The spd function is regarded as a probability density function for scatterer velocity, and the assumptions under which this is justified are considered. It is shown that the spd function is independent of Doppler angle except in the presence of wall reflection effects. A coordinate system centered on the beam is used and this enables the integrals to be easily formulated for arbitrary beams. Irregularly shaped and nonuniform beams can be treated. For the common flow and beam patterns, which exhibit symmetry, the volume integrals can often be reduced to a single integral and evaluated directly. The method is applied and the spectra are calculated for various different cases. Results are obtained for uniform rectangular and circular insonating beams, and for nonuniform beams with Gaussian, jinc, and sinc profiles. The effects of narrow beams and wall reflection are shown. The method may be readily applied to other beam and flow patterns, and extension to more complicated situations is also discussed.

A computer controlled flow phantom for generation of physiological Doppler waveforms

A flow phantom for the generation of physiological Doppler waveforms is described. The suspension of scattering particles is driven by a gear pump powered by a stepping motor. The speed of the stepping motor is controlled by a BBC microcomputer. The waveform shape is selected from a library of waveforms from disc. Use of the microcomputer allows the waveform shape and mean flow to be easily changed. Sephadex particles suspended in a solution of glycerol were used as artificial blood. Thin walled heat shrink tubing which had been moulded around metal rods was used. Distortions in the waveforms caused by reflections from the end of the tubing were largely removed by reducing the pipe diameter to half of its value for 30 cm from the end of the pipe. There was good agreement between the control waveforms and the Doppler waveforms over a wide range of waveform pulsatility.

Influence of spectral broadening on continuous wave Doppler ultrasound spectra: a geometric approach

A model is presented that enables the detailed effects of spectral broadening to be calculated for a continuous wave (CW) Doppler system by using geometric boundary arguments. The model assumes a uniform distribution of isotropic scatterers and treats the transmitter and receiver crystals as incremental sources and receivers. Detailed results for rectangular and circular geometries are presented in order to provide a physical understanding of the manner in which spectral broadening arises. Results are given for the circular geometry, to illustrate the manner in which the received spectrum is affected by the transducer size and distance from the vessel.

Spectral analysis of Doppler flow velocity signals: assessment of objectives, methods, and interpretation

The objective of this paper is to review the theoretical basis and clinical application of electrical impedance plethysmography in the noninvasive evaluation of peripheral arterial and venous disease. Theoretical, experimental and clinical studies have not demonstrated a direct relationship between electrical impedance changes and limb volume changes. Potential sources of error have also been identified. This has led to the development of clinical tests based on impedance plethysmography for the detection of peripheral arterial disease, venous insufficiency and venous outflow obstruction. Impedance plethysmography, using the method of venous occlusion, is presently the most commonly employed noninvasive method for the detection of deep venous thrombosis.