Estimation of Velocity Vectors in Synthetic Aperture Ultrasound Imaging

Abstract

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.

Comparison of vector velocity imaging using directional beamforming and transverse oscillation for a convex array transducer

“…Both the beamformation and velocity estimator are more computationally intensive for the directional method, and it should be further noticed that the beam-to-flow angle has been known prior to beamforming. This can be estimated as described in, 16 but again with a substantial increase in the number of calculations. …”

Directional Transverse Oscillation Vector Flow Estimation

“…For other angles the approach breaks down and focusing signals along the flow direction was suggested in [5], [29]. This yields the velocity magnitude, if the proper direction is used as described in [30], [31]. The key idea in this paper is, however, to introduce a lateral oscillation and not to have to focus along the flow, as this necessitates knowing the beam-to-flow angle.…”

Preliminary investigation of an ultrasound method for estimating pressure changes in deep-positioned vessels

“…The high precision and temporal frame-rate offered by synthetic aperture flow 16,17 allows for tracking of particles, which intuitively can be visualized by a streamline representation. Rewriting (1) into a one-dimensional equation following a streamline, where the influences of gravity and viscosity are omitted, yields the Euler equation;…”