Abstract
Shear wave elasticity imaging (SWEI) has been used to measure the local tissue elasticity. The local tissue shear modulus can be reconstructed from the displacement field of shear waves using an algebraic Helmholtz inversion (AHI) equation or a time-of-flight (TOF)-based algorithm. The shear waves, which are generated by successive focusing of ultrasonic beams at different depths, propagate at oblique angles rather than along the lateral position. The wave propagation at oblique angles can result in bias in shear modulus reconstruction using the AHI equation or the TOF-based algorithm. In this study, the effect of wave propagation at oblique angles on the tissue shear modulus reconstruction was investigated using in silico finite element (FE) simulation. An FE elastic tissue with a hard inclusion model was designed. The shear waves with propagation angles of 0°, 5°, and 10° were applied to the model. The shear modulus and the percentage error in the model were computed using the AHI equation and the TOF-based algorithm at each propagation angle from 0° to 10°. For the AHI equation, the percentage error was 0% at propagation angles of 0° and 5°, and 1% at a propagation angle of 10° in the inclusion. In the surrounding tissue, the percentage error was 0% at propagation angles of 0°, 5°, and 10°. For the TOF-based algorithm, the percentage error was 0% at propagation angles of 0° and 5°, and 40% at a propagation angle of 10° in the inclusion. In the surrounding tissue, the percentage error was 0% at propagation angles of 0° and 5°, and 35% at a propagation angle of 10° in the inclusion. Therefore, whereas the TOF-based algorithm produced critical bias in shear modulus reconstruction by the shear wave propagation at oblique angles, the AHI equation was not affected by the propagation.
Similar content being viewed by others
References
Sarvazyan AP, Rudenko OV, Swanson SD, Fowlkes JB, Emelianov SY (1998) Shear wave elasticity imaging: a new ultrasonic technology of medical diagnostics. Ultrasound Med Biol 24(9):1419–1435
Bercoff J, Tanter M, Fink M (2004) Supersonic shear imaging: a new technique for soft tissue elasticity mapping. IEEE Trans Ultrason Ferroelectr Freq Control 51(4):396–409
Sandrin L, Fourquet B, Hasquenoph J, Yon S, Fournier C, Mal F, Christidis C, Ziol M, Poulet B, Kazemi F, Beaugrand M, Palau R (2003) Transient elastography: a new noninvasive method for assessment of hepatic fibrosis. Ultrasound Med Biol 29(12):1705–1713
Nightingale K, McAleavey S, Trahey G (2003) Shear-wave generation using acoustic radiation force: in vivo and ex vivo results. Ultrasound Med Biol 29(12):1715–1723
Wang MH, Palmeri ML, Rotemberg VM, Rouze NC, Nightingale KR (2010) Improving the robustness of time-of-flight based shear wave speed reconstruction methods using RANSAC in human liver in vivo. Ultrasound Med Biol 36:802–813
Rouze NC, Wang MH, Palmeri ML, Nightingale KR (2010) Robust estimation of time-of-flight shear wave speed using a radon sum transformation. IEEE Trans Ultrason Ferroelectr Freq Control 57(12):2662–2670
Deng Y, Rouze NC, Palmeri ML, Nightingale KR (2017) Ultrasonic shear wave elasticity imaging sequencing and data processing using a verasonics research scanner. IEEE Trans Ultrason Ferroelectr Freq Control 64(1):164–176
Song P, Manduca A, Zhao H, Urban MW, Greenleaf JF, Chen S (2014) Fast shear compounding using robust two-dimensional shear wave speed calculation and multi-directional filtering. Ultrasound Med Biol 40(6):1343–1355
Palmeri ML, Wang MH, Dahl JJ, Frinkley KD, Nightingale KR (2008) Quantifying hepatic shear modulus in vivo using acoustic radiation force. Ultrasound Med Biol 34:546–558
Tanter M, Bercoff J, Athanasiou A, Deffieux T, Gennisson JL, Montaldo G, Muller M, Tardivon A, Fink M (2008) Quantitative assessment of breast lesion viscoelasticity: initial clinical results using supersonic shear imaging. Ultrasound Med Biol 34:1373–1386
Manduca A, Lake DS, Kruse SA, Ehman RL (2003) Spatiotemporal directional filtering for improved inversion of MR elastography images. Med Image Anal 7(4):465–473
Park DW (2016) Ultrasound shear wave simulation of breast tumor using nonlinear tissue elasticity. Comput Math Methods Med 2016:1–6
Poynard T, Munteanu M, Luckina E, Perazzo H, Ngo Y, Royer L, Fedchuk L, Sattonnet F, Pais R, Lebray P, Rudler M, Thabut D, Ratziu V (2013) Liver fibrosis evaluation using real-time shear wave elastography: applicability and diagnostic performance using methods without a gold standard. J Hepatol 58(5):928–935
Erkamp RQ, Skovoroda AR, Emelianov SY, O’Donnell M (2004) Measuring the nonlinear elastic properties of tissue-like phantoms. IEEE Trans Ultrason Ferroelectr Freq Control 51(4):410–419
Gennisson JL, Deffieux T, Macé E, Montaldo G, Fink M, Tanter M (2010) Viscoelastic and anisotropic mechanical properties of in vivo muscle tissue assessed by supersonic shear imaging. Ultrasound Med Biol 36(5):789–801
Gupta S, Chauhan RC, Sexana SC (2004) Wavelet-based statistical approach for speckle reduction in medical ultrasound images. Med Biol Eng Comput 42(2):189–192
Funding
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2017R1E1A1A03070297) and the Ministry of Education, Science and Technology (MEST) (No. 2018R1D1A1B07046796).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
There are no conflicts of interest to declare.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Informed consent
All study participants provided informed consent, and the study design was approved by the appropriate ethics review board. We have read and understood your journal’s policies, and we believe that neither the manuscript nor the study violates any of these.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Park, D.W., Cho, Hc. Ultrasound shear wave simulation of wave propagation at oblique angles. Australas Phys Eng Sci Med 42, 665–670 (2019). https://doi.org/10.1007/s13246-019-00748-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13246-019-00748-3