A Simulation Study of Sample Volume Sensitivity for Oblique Pulsed Finite Beam Insonation of Doppler Ultrasound Flow

Our previous analysis of the lumen pressure in Doppler ultrasound flow phantoms subject to continuous wave, infinite beam excitation is extended here to consider the pressure and Doppler sample volume complex sensitiv- ity within a range of solid absorbent tubes typical of those used in Doppler ultrasound flow phantoms insonated with a focussed pulsed ultrasound heam. The beam may he in- cident on the cylindrical shell from any angle and with any offset from the shell axis. The examples considered are of a 5 MHz beam with a 6 dB lateral fullwidth of 1 mm at the focus and a transducer surface acceleration pulse with stan- dard deviation of 1 ps propagating through 10 mm outer di- ameter, 8 mm inner diameter, Cflex, low-density polyethy- lene (LDPE), high-density polyethylene (HDPE), and poly- inethylmethacrylate (PMMA) shells surrounded by water at various heam-vessel angles. Our results confirm earlier analyses suggesting that PMMA, being less well matched 1.0 the surrounding media, causes much greater distortion of the sample volume sensitivity than Cflex. for infinite plane-wave harmonic insonation and compared the results with an approximate calculation based on the infinite plate pressure transmission coefficient. This analy- sis demonstrated good agreement for Cflex, but for harder materials the agreement was much less close. The reasons for this disagreement, such as backwall reflection and re- fra'ction, were analyzed in our earlier paper and allowed a good understanding of the pressure fields within the lu- men by using ray-tracing arguments combined with the plate transmission and reflection coefficients. However, in practice, insonation is more often a focussed, pulsed beam and the large effect of the backwall reflection seen with harmonic insonation will be less relevant when pulsed in- sonation is used (except near to the walls). In this paper we extend this previous analysis by constructing the in- cident beam of a focussed apodized transducer using the angular spectrum technique, then combining the resulting harmonic beams in an inverse Fourier transform in time to achieve pulsed insonation. We also present the extension to calculating the Doppler sample volume sensitivity as well as the lumen pressure. The typical pulse we consider is of order 1 mm in size, although wall effects can lead to pulse fragmentation and make definition of sample volume size less straightforward. The method allows the contribution of both the shear wave and the longitudinal wave in wall transmission to be clearly seen.