Previously, a synthetic aperture vector velocity estimation method was proposed. Data are beamformed at different directions through a point, where the velocity is estimated. The flow direction is estimated by a search for the direction where the normalized cross-correlation peaks and the velocity magnitude along this direction are found.In this paper, different effects that influence the focusing in this method are investigated. These include the effect of phase errors in the emitted spherical waves, motion effects, and the effect of various interpolation methods in beamforming.A model based on amplitude drop and phase error for spherical waves created using the virtual source concept is derived. This model can be used to determine the opening angle of a virtual source. Simulations for different virtual source placements are made, and it is recommended that the virtual sources be placed behind the aperture when shallow structures are imaged, and when deeper-lying structures are imaged the virtual sources be placed in front of the aperture.Synthetic aperture methods involve summation of data from numerous emissions. Motion between these emissions results in incoherence and affects resolution, contrast, and the signal-to-noise ratio. The effects of motion on the synthetic aperture vector velocity estimation method are investigated, and it is shown that for both axial and lateral motion, the contrast and signal-to-noise ratio can be seriously affected. A compensation method using the previous vector velocity estimate, when new data are beamformed, is implemented and tested. It is shown from a number of flow phantom experiments that a significant improvement with respect to bias and standard deviation of the velocity estimates can be obtained by using this compensation. Increased performance is gained at the expense of computation time.Different interpolation methods can be used for beamforming the data. In this paper, the velocity estimation performance using various more complex interpolation schemes are compared to that using linear interpolation. No significant difference in the performance of the method is seen when other interpolation methods are used.

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Abstract-A method for determining both velocity magnitude and angle in a synthetic aperture ultrasound system is described. The approach uses directional beamforming along the flow direction and cross correlation to determine velocity magnitude. The angle of the flow is determined from the maximum normalized correlation calculated as a function of angle. This assumes the flow direction is within the imaging plane. Simulations of the angle estimation method show both biases and standard deviations of the flow angle estimates below 3 for flow angles from 20 to 90 (transverse flow). The method is also investigated using data measured by an experimental ultrasound scanner from a flow rig. A commercial 128 element 7-MHz linear array transducer is used, and data are measured for flow angles of 60 and 90 . Data are acquired using the RASMUS experimental ultrasound scanner, which samples 64 channels simultaneously. A 20-s chirp was used during emission and eight virtual transmit sources were created behind the transducer using 11 transmitting elements. Data from the eight transmissions are beamformed and coherently summed to create high-resolution lines at different angles for a set of points within the region of flow. The velocity magnitude is determined with a precision of 0.36% (60 ) and 1.2% (90 ), respectively. The 60 angle is estimated with a bias of 0.54 and a standard deviation of 2.1 . For 90 the bias is 0.0003 and standard deviation 1.32 . A parameter study with regard to correlation length and number of emissions is performed to reveal the accuracy of the method. Real time data covering 2.2 s of the carotid artery of a healthy 30-year-old male volunteer is acquired and then processed offline using a computer cluster. The direction of flow is estimated using the above mentioned method. It is compared to the flow angle of 106 with respect to the axial direction, determined visually from the -mode image. For a point in the center of the common carotid artery, 76% of the flow angle estimates over the 2.2 s were within 10 of the visually determined flow angle. The standard deviation of these estimates was below 2.7 . Full color flow maps from different parts of the cardiac cycle are presented, including vector arrows indicating both estimated flow direction and velocity magnitude.

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