Fourier-Domain Shift Matching: A Robust Time-of-Flight Approach for Shear Wave Speed Estimation

Abstract

Our primary objective of this work was to design and test a new time-of-flight (TOF) method that allows measurements of shear wave speed (SWS) following impulsive excitation in soft tissues. Particularly, under the assumption of the local plane shear wave, this work named the Fourier-domain shift matching (FDSM) method, estimates SWS by aligning a series of shear waveforms either temporally or spatially using a solution space deduced by characteristic curves of the well-known 1-D wave equation. The proposed SWS estimation method was tested using computer-simulated data, and tissue-mimicking phantom and ex vivo tissue experiments. Its performance was then compared with three other known TOF methods: lateral time-to-peak (TTP) method with robust random sampling consensus (RANSAC) fitting method, Radon sum transformation method, and a modified cross correlation method. Hereafter, these three TOF methods are referred to as the TTP-RANSAC, Radon sum, and X-corr methods, respectively. In addition to an adapted form of the 2-D Fourier transform (2-D FT)-based method in which the (group) SWS was approximated by averaging phase SWS values was considered for comparison. Based on data evaluated, we found that the overall performance of the above-mentioned temporal implementation of the proposed FDSM method was most similar to the established Radon sum method (correlation = 0.99, scale factor = 1.03, and mean difference = 0.07 m/s), and the 2-D FT (correlation = 0.98, scale factor = 1.00, and mean difference = 0.10 m/s) at high signal quality. However, results obtained from the 2-D FT method diverged (correlation = 0.201) from these of the proposed temporal implementation in the presence of diminished signal quality, whereas the agreement between the Radon sum approach and the proposed temporal implementation largely remained the same (correlation = 0.98).

Quantitative Shear Wave Speed Assessment for Muscles With the Diagnosis of Taut Bands and/or Myofascial Trigger Points Using Probe Oscillation Shear Wave Elastography: A Pilot Study

“…Second, SWS estimation methods that assume a lateral propagation direction may produce biased estimates of SWS in this study. Different SWS calculation approaches 28,29 can be used to further improve the SWS estimation performance. Finally, the PPT measured by a digital pressure algometer is one of the indicators to assess the pain scale of TBs and/or MTrP syndrome; however, the averaged PPT values may be influenced by gender and age of a patient.…”

An innovative ultrasonic time of flight method based on extended Kalman filter for wind speed measurement

“…These techniques aim to overcome the fact that the noise and the transient response of receiving signal varies with time of flight changes what makes difficult the location of the beginning in received ultrasound signal. Furthermore, techniques that estimate the time of flight based on phase difference between transmitter and receiver restrict the measuring range to one signal cycle [2,7,8,13,16,17].…”

“…The time difference based on time of flight estimation can be implemented by conventional techniques such as threshold and phase difference detection or by the use of signal processing techniques such as cross-correlation, phase difference in the frequency domain (DFT, Discrete Fourier Transform), Wavelet transform and Kalman filter [1,[7][8][9][10][11][12][13][14][15].…”

A comparison of hyperelastic constitutive models applicable to shear wave elastography (SWE) data in tissue-mimicking materials

“…The Verasonics system was first used for the creation of one single push-pulse excitation followed by ultrafast imaging of the resulting waveforms. A published Fourier domain shift-matching (FDSM) method (Rosen and Jiang, 2018) was used to estimate SWS. Both the SWE data acquisition, the FDSM method and its validation can be found in our previous publication (Rosen and Jiang, 2018).…”

“…A published Fourier domain shift-matching (FDSM) method (Rosen and Jiang, 2018) was used to estimate SWS. Both the SWE data acquisition, the FDSM method and its validation can be found in our previous publication (Rosen and Jiang, 2018). A maximum of 40% compression was applied to each phantom with a load increment of 2.75% compression.…”