P6B-4 Multi-Dimensional Spectrum Analysis for 2-D Vector Velocity Estimation

Wilson (1991) presented a wide-band estimator for axial blood flow velocity estimation through the use of the two-dimensional (2-D) Fourier transform. It was shown how a single velocity component was concentrated along a line in the 2-D Fourier space, where the slope was given by the axial velocity. This paper presents an expansion of this study. If data are sampled within a region, instead of along a line, a three- dimensional (3-D) data matrix is created along lateral space, axial space, and pulse repetitions. It is shown, that a single velocity component will be concentrated along a plane in the 3-D Fourier space, which is found through the 3-D Fourier transform of the data matrix, and that the plane is tilted according to the axial and lateral velocity components. Two estimators are derived for finding the plane in the 3-D Fourier space, where the integrated power spectrum is largest. The first uses the 3-D Fourier transform to find the power spectrum, while the second uses a minimum variance approach. Based on this plane, the axial and lateral velocity components are estimated. A number of phantom flow measurements, for flow-to-beam angles of 60, 75, and 90 degrees, were performed to test the estimator. The data were collected using our RASMUS experimental ultrasound scanner and a 128 element commercial linear array transducer. The receive apodization function was manipulated, creating an oscillation in the lateral direction, and multiple parallel lines were beamformed simultaneously. The two estimators were then applied to the data. Finally, an in-vivo scan of the common carotid artery was performed. The average standard deviation was found across the phantom tube, for both the axial and the lateral velocity estimate. Twenty independent estimates were made for each positions. The average standard deviation of the lateral velocity estimates ranged from 16.4%c to 2.1%, relative to the peak velocity, while the average standard deviation of the axial velocity ranged from 2.05% to 0.2%. Both estimators performed best for flow-to-beam angles of 90 degrees. The in-vivo scan showed the potential of the method, yielding an estimate of the velocity magnitude independent of vessel orientation.