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Simulation of three-dimensional nonlinear fields of ultrasound therapeutic arrays

  • Nonlinear Acoustics
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Abstract

A novel numerical model was developed to simulate three-dimensional nonlinear fields generated by high intensity focused ultrasound (HIFU) arrays. The model is based on the solution to the Westervelt equation; the developed algorithm makes it possible to model nonlinear pressure fields of periodic waves in the presence of shock fronts localized near the focus. The role of nonlinear effects in a focused beam of a two-dimensional array was investigated in a numerical experiment in water. The array consisting of 256 elements and intensity range on the array elements of up to 10 W/cm2 was considered. The results of simulations have shown that for characteristic intensity outputs of modern HIFU arrays, nonlinear effects play an important role and shock fronts develop in the pressure waveforms at the focus.

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References

  1. M. Pernot, J.-F. Aubry, M. Tanter, J.-L. Thomas, and M. Fink, Phys. Med. Biol. 48, 2577 (2003).

    Article  Google Scholar 

  2. K. Hynynen, N. McDannold, G. Clement, F. A. Jolesz, E. Zadicario, R. Killiany, T. Moore, and D. Rosen, Eur. J. Radiol. 59, 149 (2006).

    Article  Google Scholar 

  3. B. Quesson, M. Merle, M. O. Köhler, C. Mougenot, S. Roujol, B. D. de Senneville, and C. T. Moonen, Med. Phys. 37, 2533 (2010).

    Article  Google Scholar 

  4. J. W. Hand, A. Shaw, N. Sadhoo, S. Rajagopal, R. J. Dickinson, and L. R. Gavrilov, Phys. Med. Biol. 54, 5675 (2009).

    Article  Google Scholar 

  5. L. R. Gavrilov and J. W. Hand, IEEE Trans. Ultrason. Ferroelec. Freq. Control 41, 125 (2000).

    Article  Google Scholar 

  6. L. R. Gavrilov, Akust. Zh. 49, 604 (2003) [Acoust. Phys. 49, 508 (2003)].

    Google Scholar 

  7. S. Bobkova, L. Gavrilov, V. Khokhlova, A. Shaw, and J. Hand, Ultrasound. Med. Biol. 36, 888 (2010).

    Article  Google Scholar 

  8. M. Pernot, M. Tanter, and M. Fink, Ultrasound. Med. Biol. 30, 1239 (2004).

    Article  MATH  Google Scholar 

  9. M. S. Canney, M. R. Bailey, L. A. Crum, V. A. Khokhlova, and O. A. Sapozhnikov, J. Acoust. Soc. Am. 124, 2406 (2008).

    Article  ADS  Google Scholar 

  10. O. V. Bessonova, V. A. Khokhlova, M. R. Bailey, M. S. Canney, and L. A. Crum, Akust. Zh. 55, 445 (2009) [Acoust. Phys. 55, 463 (2009)].

    Google Scholar 

  11. V. A. Burov, N. P. Dmitrieva, and O. V. Rudenko, Dokl. Akad. Nauk, Biokhim. Biofiz. Mol. Biol. 383, 401 (2002).

    Google Scholar 

  12. M. Canney, V. Khokhlova, O. Bessonova, M. Bailey, and L. Crum, Ultrasound. Med. Biol. 36, 250 (2010).

    Article  Google Scholar 

  13. J. Tavakkoli, D. Cathignol, R. Souchon, and O. A. Sapozhnikov, J. Acoust. Soc. Am. 104, 2061 (1998).

    Article  ADS  Google Scholar 

  14. V. A. Khokhlova, A. E. Ponomarev, M. A. Averk’yu, and L. A. Crum, Akust. Zh. 52, 560 (2006) [Acoust. Phys. 52, 481 (2006)].

    Google Scholar 

  15. Y. Jing and R. Cleveland, J. Acoust. Soc. Am. 122, 1352 (2007).

    Article  ADS  Google Scholar 

  16. W. Kreider, O. Sapozhnikov, V. Khokhlova, N. Farr, M. Bailey, P. Kaczkowski, A. Partanen, and D. Brazzle, in Proceedings of the 2nd International Symposium on Current and Future Applications of MR-guided Focused Ultrasound 2010, 17–20 Oct. 2010, Washington DC, USA, p. 79.

  17. P. J. Westervelt, J. Acoust. Soc. Am. 35, 535 (1963).

    Article  ADS  Google Scholar 

  18. R. J. Zemp, J. Tavakkoli, and R. S. Cobbold, J. Acoust. Soc. Am. 113, 139 (2003).

    Article  ADS  Google Scholar 

  19. T. Varslot and G. Taraldsen, IEEE T. Ultrason. Ferr. 52, 1473 (2005).

    Article  Google Scholar 

  20. P. V. Yuldashev, L. M. Krutyanskii, V. A. Khokhlova, A. P. Brysev, and F. V. Bunkin, Akust. Zh. 56, 463 (2010) [Acoust. Phys. 56, 467 (2010)].

    Google Scholar 

  21. P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 507 (1991).

    Article  ADS  Google Scholar 

  22. A. R. Kurganov and E. Tadmor, J. Comp. Phys. 160, 241 (2000).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. M. V. Aver’yanov, Candidate’s Dissertation in Mathematical Physics (Moscow, 2008).

  24. V. A. Khokhlova, R. Souchon, J. Tavakkoli, O. A. Sapozhnikov, and D. Cathignol, J. Acoust. Soc. Am. 110, 95 (2002).

    Article  ADS  Google Scholar 

  25. E. A. Filonenko and V. A. Khokhlova, Akust. Zh. 47, 541 (2001) [Acoust. Phys. 47, 468 (2001)].

    Google Scholar 

  26. O. V. Bessonova, V. A. Khokhlova, M. S. Canney, M. R. Bailey, and L. A. Crum, Akust. Zh. 56, 380 (2010) [Acoust. Phys. 56, 354 (2010)].

    Google Scholar 

  27. O. V. Rudenko and S. I. Soluyan, Theoretical Foundations of Nonlinear Acoustics (Nauka, Moscow, 1975; Consultants Bureau, New York, 1977).

    Google Scholar 

  28. T. Christopher, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53, 2188 (2006).

    Article  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, 119991, Russia

    P. V. Yuldashev & V. A. Khokhlova

  2. Center for Industrial and Medical Ultrasound, Applied Physics Laboratory, University of Washington, Seattle, WA, 98105, USA

    V. A. Khokhlova

Authors
  1. P. V. Yuldashev
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  2. V. A. Khokhlova
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Correspondence to P. V. Yuldashev.

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Original Russian Text © P.V. Yuldashev, V.A. Khokhlova, 2011, published in Akusticheskii Zhurnal, 2011, Vol. 57, No. 3, pp. 337–347.

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Yuldashev, P.V., Khokhlova, V.A. Simulation of three-dimensional nonlinear fields of ultrasound therapeutic arrays. Acoust. Phys. 57, 334–343 (2011). https://doi.org/10.1134/S1063771011030213

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  • DOI: https://doi.org/10.1134/S1063771011030213

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