Rapid tracking of small displacements with ultrasound

Time-delay estimators, such as normalized cross correlation and phase-shift estimation, form the computational basis for elastography, blood flow measurements, and acoustic radiation force impulse (ARFI) imaging. This paper examines the performance of these algorithms for small displacements (less than half the ultrasound pulse wavelength). The effects of noise, bandwidth, stationary echoes, kernel size, downsampling, interpolation, and quadrature demodulation on the accuracy of the time delay estimates are measured in terms of bias and jitter. Particular attention is given to the accuracy and resolution of the displacement measurements and to the computational efficiency of the algorithms. In most cases, Loupas´ two-dimensional (2-D) autocorrelator performs as well as the gold standard, normalized cross correlation. However, Loupas´ algorithm´s calculation time is significantly faster, and it is particularly suited to operate on the signal data format most commonly used in ultrasound scanners. These results are used to implement a real-time ARFI imaging system using a commercial ultrasound scanner and a computer cluster. Images processed with the algorithms are examined in an ex vivo liver ablation study.