Precise tracking of impulsive acoustic radiation force induced small displacements for shear wave speed estimation

Acoustic radiation force impulse (ARFI) imaging generates localized small displacements (typically less than 20 microns) in soft tissues and would induce shear waves. The shear wave speed (SWS), which is determined by the tissue elastic properties and can offer quantitative tissue stiffness, can be monitored from the displacement field. Therefore, precise tracking of small displacements is of great importance. At present, small displacements are commonly tracked by phase-shift estimation, such as Kasai´s 1-D autocorrelation phase-shift method and Loupas´ 2-D autocorrelation phase-shift algorithm. The goal of this study is to introduce a novel phase-shift based algorithm being able to track the small displacements (even smaller than sample distance) in a more precise and quick way. This new phase-shift algorithm was developed based on Hilbert Transform (HT) approach using adaptive gradient of the phase angle to track the information of phase-shifts. A comparison was performed among the introduced HT phase-shift method, Kasai´s algorithm and Loupas´ approach to check the performance, and the errors of estimated displacement were given for each different specified shift values between two successively ultrasound signals. The SWS was estimated by means of the lateral time to peak (LTTP) time-of-flight (TOF) method from the calculated ARFI displacement field.