Ultrasound shear wave simulation of wave propagation at oblique angles

  • Dae Woo Park
  • Hyun-chong ChoEmail author
Scientific Paper


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.


Shear modulus Shear wave elasticity imaging Time of flight Ultrasound Wave propagation 



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).

Compliance with ethical standards

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.


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Copyright information

© Australasian College of Physical Scientists and Engineers in Medicine 2019

Authors and Affiliations

  1. 1.Division of Convergence Technology, National Cancer CenterGoyang-siRepublic of Korea
  2. 2.Department of Electronic Engineering and Interdisciplinary Graduate Program for BIT Medical ConvergenceKangwon National UniversityChuncheon-siRepublic of Korea

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