Estimating 2-D vector velocities using multidimensional spectrum analysis

• Published in: IEEE transactions on ultrasonics, ferroelectrics, and frequency control Vol. 55; no. 8; pp. 1744 - 1754
• Main Authors: Oddershede, N., Lovstakken, L., Torp, H., Jensen, J.A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adult; Apodization; Biological and medical sciences; Biomedical materials; Blood flow; Blood Flow Velocity - physiology; Cardiovascular system; Carotid Arteries - diagnostic imaging; Carotid Arteries - physiology; Computer Simulation; Estimators; Exact sciences and technology; Flow velocity; Fluid dynamics; Fourier analysis; Fourier transforms; Fundamental areas of phenomenology (including applications); Goniometers; Humans; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Imaging phantoms; In vivo; Instrumentation for fluid dynamics; Investigative techniques, diagnostic techniques (general aspects); Male; Mathematical analysis; Medical sciences; Models, Cardiovascular; Multidimensional systems; Performance evaluation; Physics; Pilot Projects; Planes; Rheology - methods; Sampling methods; Standard deviation; Studies; Surgical implants; Testing; Ultra wideband technology; Ultrasonic investigative techniques; Ultrasonography - methods; Human; Fourier transformation; Flow measurement; Modeling; Spectral analysis; Artery; Beam forming; Blood flow; Tilt angle; Minimal variance; Wide band; Carotid; Flow velocity; Circulatory system; Hemodynamics; Flowmetry; Sampling; Axial flow; Apodization; Power spectrum; A scan
• ISSN: 0885-3010; 1525-8955
• DOI: 10.1109/TUFFC.2008.859

Wilson (1991) presented an ultrasonic wideband estimator for axial blood flow velocity estimation through the use of the 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. Later, it was shown that this approach could also be used for finding the lateral velocity component by also including a lateral sampling. A single velocity component would then be concentrated along a plane in the 3-D Fourier space, tilted according to the 2 velocity components. This paper presents 2 new velocity estimators for finding both the axial and lateral velocity components. The estimators essentially search for 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. Several phantom measurements, for flow-to-depth angles of 60, 75, and 90 degrees, were performed. Multiple parallel lines were beamformed simultaneously, and 2 different receive apodization schemes were tried. The 2 estimators were then applied to the data. The axial velocity component was estimated with an average standard deviation below 2.8% of the peak velocity, while the average standard deviation of the lateral velocity estimates was between 2.0% and 16.4%. The 2 estimators were also tested on in vivo data from a transverse scan of the common carotid artery, showing the potential of the vector velocity estimation method under in vivo conditions.