Volume scattering of distributed microbubbles and its influence on blood flow estimation

In recent years, microbubble contrast agents have become a potential adjunct in Doppler ultrasound diagnosis. In this paper, we show that volume scattering makes the effective band in Doppler spectrum shift downward after injection of microbubbles. Because the insonified volume comprises a collection of distributed microbubbles, the statistical properties such as the autocorrelation function and ensemble average power spectrum of the echoes from a collection of distributed microbubbles were derived first. It can be observed that, beyond a critical frequency, the theoretical volume backscattering cross section derived from the ensemble average power spectrum of microbubbles decreases with frequency. On the contrary, the volume backscattering cross section of red cells increases with frequency. Using two-dimensional (2-D) Fourier transform, the variation in Doppler spectrum caused by different volume backscattering cross section can be demonstrated, and the consequential downward shifts of the estimated Doppler parameters (e.g., the mean and maximum Doppler shifts, and the variance of Doppler power spectrum) after microbubble injection are shown. In addition, it can be observed that the variation gets larger as the transmitted bandwidth increases. And, the variations in Doppler parameters estimated with experimental data are presented to verify the theoretical deviations.