Time domain formulation of pulse-Doppler ultrasound and blood velocity estimation by cross correlation

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.