Flow velocity profile via time-domain correlation: error analysis and computer simulation

Abstract

An ultrasonic human-blood-flow velocity profile measurement method using time-domain correlation of consecutive echo pairs has been developed. The time shift between a pair of range gated echoes is estimated by searching for the shift that results in the maximum correlation. The time shift indicates the distance a group of scatterers has moved, from which flow velocity is estimated. The basis for the computer simulations and error analyses of the scheme includes a band-passed white Gaussian noise signal model for an echo from a scattering medium, the estimate of flow velocity from both a single scatterer and multiple scatterers, and a derived precision estimation. The error analysis via computer simulation includes an evaluation of errors associated with the correlation method. For a uniform flow velocity profile, beamwidth modulation represents the greatest error source. However, for a nonuniform flow velocity profile, the jitter caused by a small flow velocity gradient can exceed the other error sources. A detailed computer simulation evaluated the interdependencies of window length, beam width, vessel diameter, and viewing angle on the estimation of flow velocity.

Subsample interpolation strategies for sensorless freehand 3D ultrasound

“…One of the few papers to address lateral interpolation is [9], in which the grid slopes algorithm is shown to be relatively unbiased in comparison with other techniques. More prone to bias are cosine [3,5,6], cubic spline [9] and parabolic interpolation [2,3,7]. Fourier reconstruction [3] has been shown to work well in the axial direction, provided the signal is bandlimited and the sampling frequency above the Nyquist limit.…”

Range/velocity limitations for time-domain blood velocity estimation

“…It is possible to find the shift in position of the scatterers, when they move between pulses by more than half a wavelength in the beam direction. A technique for doing that using cross-correlation has been suggested by a number of authors (Dotti et al 1976;Bonnefous et al 1986;Foster et al 1990). In this method the high frequency transducer signal is sampled following consecutive transmitted pulses.…”

Velocity estimation using synthetic aperture imaging [blood flow]

“…If the the velocity does not change significantly for several sequential acquisitions N c , then the estimate can be improved by averaging the estimated crosscorrelation functions: The estimate can be improved by fitting a second order curve to the estimate, and interpolating the time shift [4]: The stationary echo canceling is done only on the images that were obtained at every Nth emission, i.e. between images n and n − kN, where k ∈ Z.…”

“…The high-resolution images (HRI) have the highest overlap of spatial frequencies, and therefore they should give the best estimates. The correlation of the signals received from the blood cells decreases rapidly due to migration of scatterers, beam-width modulation, and flow gradients (change in the relative positions between the scatterers) [4]. The HRIs must be generated after every emission, which is possible using recursive ultrasound imaging.…”