Acoustical Physics

, Volume 52, Issue 4, pp 481–489 | Cite as

Nonlinear pulsed ultrasound beams radiated by rectangular focused diagnostic transducers

  • V. A. Khokhlova
  • A. E. Ponomarev
  • M. A. Averkiou
  • L. A. Crum


A numerical model for simulating nonlinear pulsed beams radiated by rectangular focused transducers, which are typical of diagnostic ultrasound systems, is presented. The model is based on a KZK-type nonlinear evolution equation generalized to an arbitrary frequency-dependent absorption. The method of fractional steps with an operator-splitting procedure is employed in the combined frequency-time domain algorithm. The diffraction is described using the implicit backward finite-difference scheme and the alternate direction implicit method. An analytic solution in the time domain is employed for the nonlinearity operator. The absorption and dispersion of the sound speed are also described using an analytic solution but in the frequency domain. Numerical solutions are obtained for the nonlinear acoustic field in a homogeneous tissue-like medium obeying a linear frequency law of absorption and in a thermoviscous fluid with a quadratic frequency law of absorption. The model is applied to study the spatial distributions of the fundamental and second harmonics for a typical diagnostic ultrasound source. The nonlinear distortion of pulses and their spectra due to the propagation in tissues are presented. A better understanding of nonlinear propagation in tissue may lead to improvements in nonlinear imaging and in specific tissue harmonic imaging.

PACS numbers

43.80.Vj 43.20.El 43.25.-x 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Y. S. Lee and M. F. Hamilton, J. Acoust. Soc. Am. 97, 906 (1995).ADSCrossRefGoogle Scholar
  2. 2.
    J. Tavakkoli, D. Cathignol, R. Souchon, and O. A. Sapozhnikov, J. Acoust. Soc. Am. 104, 2061 (1998).ADSCrossRefGoogle Scholar
  3. 3.
    M. A. Averkiou and M. F. Hamilton, J. Acoust. Soc. Am. 102, 2539 (1997).ADSCrossRefGoogle Scholar
  4. 4.
    A. C. Baker, A. M. Berg, and A. Sahin, J. Acoust. Soc. Am. 97, 3510 (1995).ADSCrossRefGoogle Scholar
  5. 5.
    T. Kamakura, M. Tani, Y. Kumamoto, and K. Ueda, J. Acoust. Soc. Am. 91, 3144 (1992).ADSCrossRefGoogle Scholar
  6. 6.
    M. D. Cahill and A. C. Baker, J. Acoust. Soc. Am. 104, 1274 (1998).ADSCrossRefGoogle Scholar
  7. 7.
    A. Bouakaz, C. T. Lancee, and N. de Jong, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 730 (2003).CrossRefGoogle Scholar
  8. 8.
    M. A. Averkiou, in Proceedings of the 2000 IEEE Ultrasonic Symposium, San Juan, Puerto Rico, 2000, Vol. 1, pp. 1563–1572.Google Scholar
  9. 9.
    V. A. Khokhlova, A. E. Ponomarev, M. A. Averkiou, and L. A. Crum, J. Acoust. Soc. Am. 112, 2370 (2002).ADSGoogle Scholar
  10. 10.
    A. E. Ponomaryov, V. A. Khokhlova, M. A. Averkiou, and L. A. Crum, in Proceedings of the 3rd International Symposium on Therapeutic Ultrasound, France, Lyon, 2003, Ed. by J.-Y. Chapelon and C. P. Lafon, pp. 309–315.Google Scholar
  11. 11.
    X. Yang and R. Cleveland, J. Acoust. Soc. Am. 117, 113 (2005).zbMATHADSCrossRefGoogle Scholar
  12. 12.
    L. V. Osipov, Ultrasonic Diagnostic Instruments: User Manual (Vidar, Moscow, 1999) [in Russian].Google Scholar
  13. 13.
    S. S. Kashcheeva, V. A. Khokhlova, O. A. Sapozhnikov, et al., Akust. Zh. 46, 211 (2000) [Acoust. Phys. 46, 170 (2000)].Google Scholar
  14. 14.
    E. A. Filonenko and V. A. Khokhlova, Akust. Zh. 47, 541 (2001) [Coust. Phys. 47, 468 (2001)].Google Scholar
  15. 15.
    Physical Principles of Medical Ultrasonics, Ed. by C. R. Hill, J. C. Bamber, and G. R. ter Haar (Ellis Horwood, Chichester, 1986; Mir, Moscow, 1989).Google Scholar
  16. 16.
    A. G. Kudryavtsev and O. A. Sapozhnikov, Akust. Zh. 44, 808 (1998) [Acoust. Phys. 44, 704 (1998)].Google Scholar
  17. 17.
    I. R. S. Makin, M. A. Averkiou, and M. F. Hamilton, J. Acoust. Soc. Am. 108, 1505 (2000).ADSCrossRefGoogle Scholar
  18. 18.
    S. K. Godunov and V. S. Ryaben’kiĭ, Difference Schemes (Nauka, Moscow, 1973) [in Russian].Google Scholar
  19. 19.
    W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN (Cambridge Univ. Press, New York, 1992).Google Scholar
  20. 20.
    D. Hope Simpson, C. T. Chin, and P. N. Burns, IEEE Trans. Ultrason. Ferroelect. Freq. Control 46, 372 (1999).CrossRefGoogle Scholar
  21. 21.
    G. A. Brock-Fisher, Mc. D. Poland, and P. G. Rafter, US Patent No. 5577505 (1996).Google Scholar
  22. 22.
    G. A. Brock-Fisher, Mc. D. Poland, P. G. Rafter, and M. G. Mooney, in Proceedings of the 5th Heart Centre European Symposium on Ultrasound Contrast Imaging, Rotterdam, the Netherlands, 2000.Google Scholar
  23. 23.
    R. E. Apfel and C. K. Holland, Ultrasound Med. Biol. 17(2), 179 (1991).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2006

Authors and Affiliations

  • V. A. Khokhlova
    • 1
  • A. E. Ponomarev
    • 1
  • M. A. Averkiou
    • 2
  • L. A. Crum
    • 3
  1. 1.Moscow State UniversityVorob’evy gory, MoscowRussia
  2. 2.Philips UltrasoundBothellUSA
  3. 3.Center for Industrial and Medical Ultrasound, Applied Physics LaboratoryUniversity of WashingtonSeattleUSA

Personalised recommendations