Nonlinear acoustic beam propagation modeling in dissipative media


  • Jahan Tavakkoli Department of Physics, Ryerson University, 350 Victoria Street, Toronto, ON M5B 2K3, Canada
  • Shahram Mashouf Department of Medical Biophysics, Sunnybrook Research Institute, University of Toronto, 2075 Bayview Ave., Toronto, ON M4N 3M5, Canada


Diffraction, Geometry, Numerical methods, Tissue, Ultrasonic testing, Ultrasonics, 3D numerical model, 3D solutions, Axisymmetric, Biomedical ultrasound, Computational tools, Continuous wave ultrasound, Definition method, Dissipative media, Experimental data, High intensity focused ultrasound, Non-invasive, Non-linear acoustics, Non-linear numerical model, Non-linear ultrasound, Non-Linearity, Nonlinear propagation, Nonlinear propagation effect, Second-order operators, Soft tissue, Source geometry, Treatment modality, Ultrasound beams


Accurate simulation of an intensive ultrasound beam requires taking nonlinear propagation effects into account. A notable example in the field of biomedical ultrasound where the effect of nonlinearity may play a significant role is the high intensity focused ultrasound (HIFU) as a non-invasive energy-based treatment modality. In this work, a 3D numerical model to simulate nonlinear propagation of continuous wave ultrasound beams in dissipative homogeneous tissue-like media is presented. The model implements a second-order operator splitting method in which the effects of diffraction, nonlinearity and attenuation are propagated over incremental steps. The model makes use of an arbitrary 3D source geometry definition method and a non axi-symmetric propagation scheme, which leads to a 3D solution to the resulting nonlinear ultrasound field. This work builds on methods developed by Tavakkoli et al. (1998) and Zemp et al. (2003) and offers an efficient way to calculate nonlinear field of continuous wave ultrasound sources. The proposed model is a particularly useful computational tool in carrying out simulations of high intensity focused ultrasound beams in soft tissue where the effects of nonlinearity, diffraction, and attenuation are important. The model was validated through comparisons with other established linear and nonlinear numerical models as well as published experimental data.

Additional Files



How to Cite

Tavakkoli J, Mashouf S. Nonlinear acoustic beam propagation modeling in dissipative media. Canadian Acoustics [Internet]. 2011 Dec. 1 [cited 2024 Mar. 2];39(4):19-25. Available from:



Technical Articles

Most read articles by the same author(s)