Time Domain Formulation of Pulse-Doppler Ultrasound and Blood Velocity Estimation by Cross Correlation

Abstract

The Doppler effect is usually described as a frequency shift of the backscattered signals from moving targets with respect to the frequency transmitted. Recently, real-time blood flow imaging has become possible thanks to the development of a new velocity estimator based on phase-shift measurements of successive echoes. However, this method suffers from the well-known limitations of pulse-Doppler instruments. A new formulation is presented which describes the pulse-Doppler effect on the successive echoes from a cloud of moving targets as a progressive translation in time due to the displacement of the scatterers between two excitations. This approach allows us to generate efficiently computer-simulated data in order to evaluate accurately the various processing techniques. Furthermore, it leads to a novel class of velocity estimators in the time domain which measure the time shifts which are proportional to the local blood velocity. Among them, the cross correlation of the received rf signals turns out to be well suited. A local cross-correlation function is first calculated from a consecutive pair of range-gated echoes and the time shift is then determined by searching for the time position with the maximum correlation. The time-correlation technique is shown to provide accurate velocity profiles with broadband transducers. Moreover, the classical velocity limitation of pulse-Doppler is overcome because there is no ambiguity in measuring a time shift instead of a phase shift. These major advantages should make quantitative flow mapping possible and more reliable.

Functional Tissue Pulsatility Imaging of the Brain During Visual Stimulation

“…pulse-to-pulse, and scales the result by the wavelength of US at a reference frequency, typically the transmitted US center frequency, to derive velocity or displacement (Kasai et al 1985). The limitation of this method is that the result is biased by stochastic variation of the US center frequency (Bonnefous and Pesque 1986) and frequencydependent attenuation (Ferrara et al 1992). The 2D autocorrelator additionally estimates the mean change in phase of the signal in fast-time, i.e.…”

P6B-4 Multi-Dimensional Spectrum Analysis for 2-D Vector Velocity Estimation

“…Kasai and coworkers [1] proposed the autocorrelation estimator, where the axial velocity is found through the average phase shift along pulse repetitions. Bonnefous and Pesque proposed a cross-correlation estimator [2], where the consecutive columns of s(z, t) are cross-correlated to find the spatial shift and thus the velocity. Ferrara and Algazi [3] proposed a maximum likelihood estimator, essentially using both the envelope information and the phase information in the estimator.…”

Color velocity imaging and power Doppler sonography of the gallbladder wall: a new look at sonographic diagnosis of acute cholecystitis.

“…Colorvelocityimagingisanotherpromising technique.This technique (a proprietary prod uct of Philips,Best,the Netherlands) is based on the timing data contained in the gray-scale B-mode image scan lines rather than Doppler frequency shifts [15]. The flow velocity infor mation thus allows construction of a color flow display [15].…”

“…The flow velocity infor mation thus allows construction of a color flow display [15]. Colorvelocityimagingrequiresa smaller ensemble length, allowing all scan lines in a frame to be generated independently, thus improvinglateral resolution.…”

“…Also, with color velocity imaging, axial resolution is im proved. Becausecolor velocity imaging does not dependon the operatingfrequencyof the transducer,no aliasing is found with this tech nique [15]. Color velocity imaging has proven useful for the study ofperipheral artery athero sclerosis [16].…”