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

Thin-beam ultrasound overestimation of blood flow: how wide is your beam?

It has been predicted that the development of thin-beam ultrasound could lead to an overestimation of mean blood velocity by up to 33% as beam width approaches 0% of vessel diameter. If both beam and vessel widths are known, in theory, this overestimation may be correctable. Therefore, we updated a method for determining the beam width of a Doppler ultrasound system, tested the utility of this technique and the information it provides to reliably correct for the error in velocity measurements, and explored how error-corrected velocity estimates impact the interpretation of in vivo data. Using a string phantom, we found the average beam width of four different probes varied across probes from 2.93 ± 0.05 to 4.41 ± 0.06 mm (mean ± SD) and with depth of insonation. Using this information, we tested the validity of a calculated correction factor to minimize the thin-beam error in mean velocity observed in a flow phantom with known diameter. Use of a correction factor reduced the overestimation from 39 ± 11 to 7 ± 9% (P < 0.05). Lastly, in vivo we explored how knowledge of beam width improves understanding of physiological flow conditions. In vivo, use of a correction factor reduced the overestimation of mean velocity from 23 ± 11 to -4 ± 9% (P < 0.05). Thus this large source of error is real, has been largely ignored by the early adaptors of Doppler ultrasound for vascular physiology studies in humans, and is correctable by the described techniques.

Umbilical venous blood flow measurement: accuracy and reproducibility

Umbilical venous blood flow could be considered a direct and physiological measurement of vascular placental function, representing the quantity of oxygen and nutrients reaching the fetus. The advent of high-technology ultrasound and pulsed Doppler has overcome some of the limitations of early studies. Indeed, Doppler measurement of umbilical venous blood flow has been found to be accurate when compared with several gold standards for in-vivo flow calculation. Nevertheless, small errors in volume flow components, the vessel area and the mean velocity, result in large errors in the calculation of volume flow. Therefore, technique standardization is of paramount importance. Validation studies in animal models have demonstrated accurate venous blood flow measurements by estimating the vessel's cross-sectional area from perpendicular views of longitudinal sections of free-floating portions of the cord. On the other hand, estimation of the mean velocity from the maximum velocity, rather than using the intensity-weighted mean velocity, is less software-dependent and more clearly defined, yielding estimates with more predictable and systematic errors. By adhering to stringent methodological recommendations, umbilical venous blood flow calculation has moderate to good intra- and interobserver reproducibility. Having been found to be accurate and reproducible, further studies are required to establish the clinical value of umbilical vein flow measurement.

Discontinuous doppler signals simulating respiratory misregistration: Effect on autoregressive frequency spectra

In this study, we have produced discontinuous Doppler signals of carotid artery and internal jugular vein, simulating respiratory misregistration. The aim of the study is to observe the effect of signal discontinuity and its duration on power spectral density vs. frequency graphs obtained by Autoregressive Modeling. The signals were recorded from ten male volunteers. Signal interruption was performed by moving the sampling volume in and out of the vessel bidirectionally. To estimate the effect of on-line recording time and signal discontinuity on frequency spectra, we have worked on a control data of 30s with continuous signal, and three sets of data with artificially interrupted signals of 30, 60 and 90s duration. Maximum power spectral density, area under the power spectral density, and frequency level corresponding to maximum power spectral density were calculated on frequency spectra. The frequency level corresponding to maximum power spectral density provides the most statistically stable finding in our preliminary data. The signal duration of the signal had no significant effect on the statistical stability of the frequency level.

Spectral power density calculations for pulsed Doppler

Range-gated pulsed Doppler can be used to make localized velocity measurements within a blood vessel. A spectral flow profile can be created by stepping a sufficiently small sample volume across the lumen, but no set of spectra will correspond directly to the true velocity profile. Spectral flow profiles are affected by a complex interplay between different sources of spectral broadening. In this study we developed a systematic theoretical method which allows spectral power density functions to be calculated under a very wide range of conditions, and used it to obtain simulated flow spectra. The model was formulated analytically. It is based on the weighted-volume approach and incorporates, through the concept of a spread function, the intrinsic spectral broadening associated with a focused transducer. It can be applied for arbitrary values of the spread parameter; for non-uniform beam profiles; with maximal (continuous wave-type) or minimal (pulse wave-type) range-gated sample volumes; and for beams that intersect the flow tube axis, or are off centre. Results are presented for a Gaussian beam and parabolic flow. Simulated spectral flow profiles are given which illustrate how a profile's appearance can be altered by the different sources of spectral broadening.

Ultrasonic error compensation method to correct instrumental and systematic errors in volumetric flow measurements: a theoretical study

A computational model has been developed to observe the effects of several instrumental parameters and systematic error sources on ultrasonic volumetric flow measurements in vessels using an error compensation method proposed previously by the authors. The effects of two essential instrumental parameters, the gate length and pulse duration, on two intermediate flow results and an optimal correction factor as a function of the beam width-to-vessel diameter ratio (BWR) have been studied under steady flow conditions. The corrected flow results under typical combinations of those parameters show that by proper selection of a correction factor, the proposed method can compensate for those systematic errors. If the estimated BWR is within +/- 0.1 of the actual BWR value, the systematic error can be limited to within 6.5%. The study also shows that the compensation method can effectively reduce the errors caused by other systematic error sources such as the system sensitivity and high-pass filter function, as well as misalignment of the ultrasound beam from the center of the vessel.

A review of the measurement of blood velocity and related quantities using Doppler ultrasound

Ultrasound systems can be used to investigate blood flow by use of the Doppler effect. The flow information may be displayed as either a real-time sonogram or a two-dimensional colour image. Estimates of maximum velocity using commercial systems are in error by typically 10-100 per cent; this is associated with the inability of the single-beam Doppler method to measure the true direction of flow, and with geometric spectral broadening. Vector Doppler systems acquire Doppler information along two beam directions and are able to measure accurately the velocity and direction of motion within the scan plane. The small beam width of modern Doppler systems means that the condition of uniform insonation, required for estimation of mean velocity from mean frequency shift, is not valid except for the very smallest vessels. Other quantities related to the velocity may also be estimated, such as the volumetric flow and wall shear stress. Flow visualization using colour flow imaging suffers from dependence of the displayed colour on the direction of blood motion. The vector Doppler technique may be extended to colour flow to give improved visualization of flow, in which there is no angle dependence within the scan plane.

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.

Developments in cardiovascular ultrasound. Part 2: Arterial applications

Many of the changes resulting from arterial disease can be measured, using Doppler ultrasound for measurement of blood velocity and B-scan imaging for measurement of tissue structure and composition. Wall thickness, the degree of arterial narrowing and plaque volume can be measured using B-scan imaging, and 3D ultrasound can be used to improve the accuracy of measurements of plaque volume and for improved visualisation of complex arterial geometries. Measurement of the dynamic properties of the arterial wall permits estimation of wall elasticity and plaque motion. From the Doppler signal, measurements of blood velocity are used to estimate the degree of arterial narrowing and volumetric flow, although measurement errors can be large. Wall shear stress can be estimated by measuring the velocity gradient at the vessel wall. The problems of inadequate spatial resolution and interference from overlying tissue are largely removed when intravascular systems are used, and these have superior capability in the assessment of arterial structure and tissue composition. However, measurement of quantities relating to blood flow is more difficult using the intravascular approach, as the indwelling cather disturbs the blood flow pattern, and currently, assessment of flow and vessel cross-section are not performed at the same site.

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 blood flow calculation using a narrow ultrasound beam

Spectral analysis of the Doppler signal from a negligibly thin ultrasound beam directed through the centre of the blood vessel can, for certain forms of velocity profile, produce a statistic deemed to be proportional to spatial mean blood velocity. A statistic recently derived for the case of an axisymmetric, monotonic velocity profile is generalised to the situation where the profile is axisymmetric and made up of a central monotonic section inside a region of reverse flow which is itself symmetric. Using the theory of oscillating flow in a rigid tube, instantaneous velocity profiles were derived for samples of actual cardiac cycles recorded from various arterial sites. In every case the profiles satisfied the assumptions for the statistic to be valid throughout considerable regions of each cycle. The resulting error in the use of the statistic to measure the volumetric flow in a cycle had a magnitude less than 0.01% for the carotid, radial and brachial artery recordings, was typically small and positive (+2.5%) for the common femoral artery, and was typically negative (0 to -8%) for the superficial femoral artery, with outlying value of -16%.

Statistical bias and variance in blood flow estimation by spectral analysis of Doppler signals

The stochastic nature of the Doppler signal is discussed as a source of variability and bias in estimation of mean blood velocity and flow performed using the Discrete or Fast-Fourier Transform. The estimators studied are those appropriate when the ultrasound beam is assumed to be wide enough to insonate the cross-section of the vessel uniformly, and assumed to be narrow enough to insonate only a diameter. Approximate expressions are derived theoretically for the biases and variances of these statistics when the Doppler power spectrum is uniform. For more complex spectra numerical evaluation is carried out by computer. Results for the double-sided spectra obtained from mixed flow are inferred from the single-sided cases. Typically, an estimate of instantaneous mean velocity has very little bias added (< 1%) but might have a standard error of approximately 10% of its mean value, and an estimate of flow in one cardiac cycle a standard error of approximately 1% of its mean value.