An Analysis of Pulsed Wave Ultrasound Systems for Blood Velocity Estimation

Pulsed wave ultrasound systems can be used for determining blood's velocity non-invasively in the body. A region of interest is selected, and the received signal is range gated to measure data from the region. One complex sample value is acquired for each pulse emission after complex demodulation of the received signal. The time evolution and distribution of velocity can then be found by using samples from a number of pulse-echo lines. Making a short-time Fourier transform of the data reveals the velocity distribution in the range gate over time. Such systems are called Doppler ultrasound systems implying that they use the classical Doppler eect. The velocity is typically on the order of 0.5 to 1 m/s giving a relative shift of 2 to 4 kHz of the center frequency of the received spectrum for a 3 MHz transducer. Finding such a shift is impossible since the unknown frequency shift from attenuation in tissue can be tens of kilohertz. Some recent reviews and articles state that the Doppler eect is used, and contradictory and wrong results and erroneous system diagrams arise from this assumption. Research done in the last fteen years has revealed that it is the movement of the scatterers between pulse emissions, that is used for nding the velocity. This fnding gives new insight into the role of the complex demodulation stage, and shows that this can be replaced by a matched lter and quadrature RF sampling. A derivation of this result is presented in this paper, and it reveals how the bandwidth of the pulse and the number of pulse emissions aect the result. The nal equation for the received signal is quite complicated, and a simplied interpretation is therefore also given. This readily reveals the infuence from
transducer bandwidth, attenuation, non-linear eects, classical Doppler eect, and scattering.