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Theoretical Calculations and Numerical Modeling of High Intensity Ultrasonic Fields for Optimization of High Intensity Focused Ultrasound Transducers


  • Scientific Research Institute of Physics of the Southern Federal University, Rostov-on-Don, Russia
  • Moscow State University, Moscow, Russia


Objectives: This work focuses on development of the mathematical models and theoretical research of the ultrasound ablation system in respect of the calculation of High Intensity Focused Ultrasonic Fields and modeling of biological tissue heating. Methods: Theoretical calculations of acoustic fields in linear approximation were made using Rayleigh integral. For description of nonlinear High Intensity Ultrasonic Fields, finite-difference modeling of Westervelt and Khokhlov–Zabolotskaya–Kuznetsov (KZK) equations were used. Findings: Theoretical and numerical models of High Intensity Focused Ultrasound (HIFU) Transducers were developed. The results of theoretical modeling of HIFU Transducers were presented. The characteristics of High Intensity Ultrasonic Fields, including the acoustic pressure, intensity and heat sources at different excitation modes of Ultrasound Transducers were calculated. Numerical solutions of the Khokhlov–Zabolotskaya–Kuznetsov (KZK) parabolic equation were obtained for nonlinear Focused Ultrasonic Fields. The obtained results were discussed. Applications/Improvements: The obtained results can be used in the development of HIFU Transducers for Medical Ultrasound Ablation Complexes, for the treatment of socially significant diseases.


Acoustic Pressure, HIFU, Numerical Modeling, Nonlinear Fields, Transducers, Ultrasound.

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  • Physical principles of medical ultrasonics. Hill CR, Bamber JC, terHaar GR, editors. 2nd ed. John Wiley and Sons Ltd; 2004. ISBN: 978-0-471-97002-6.
  • terHaar GR. Therapeutic application of ultrasound. Prog Biophys Mol Biol. 2007; 93:111. DOI: 10.1016/j.pbiomolbio.2006.07.005.
  • Rybyanets AN. Recent advances in medical ultrasound. Piezoelectrics and Related Materials: Investigations and Applications. Nova Science Publishers Inc. 2012; 5:143–87. ISBN: 978-1-60876-459-4.
  • Summer W, Patrick MK. Ultrasonic therapy. A textbook for physiotherapists. London: Elsevier; 1964.
  • Physical principles of medical ultrasonics. Hill CR, Bamber JC, terHaar GR, editors. Translated from English. Gavrilov LR, Khokhlova VA, Sapozhnikova OA, editors. Moscow: Fizmatlit; 2008. ISBN: 978-5-9221-0894-2.
  • Khokhlova V, Ponomarev A, Averkiou M, Crum L. Nonlinear pulsed ultrasound beams radiated by rectangular focused diagnostic transducers. Acoustical Physics. 2006; 52:481–9. DOI: 10.1134/S1063771006040178.
  • Rybyanets AN. New dynamical focusing method for HIFU therapeutic applications. AIP Conference Proceedings; 2010. 287–90. Available from:
  • Rybyanets AN, Lugovaya MA, Rybyanets AA. Multi-frequency harmonics technique for HIFU tissue treatment. AIP Conference Proceedings; 2010. 291–4. Available from:
  • Sarvazyan AP, Fillingera L, Gavrilov LR. A comparative study of systems used for dynamic focusing of ultrasound. Acoustical Physics. 2009; 55:630. DOI: 10.1134/S1063771009040198.
  • Rybyanets AN. Porous piezoelectric ceramics- A historical overview. Ferroelectrics. 2011; 419(1):90–6. DOI: 10.1080/00150193.2011.594751.
  • Rybyanets AN. Porous piezoсeramics: Theory, technology, and properties. IEEE Trans UFFC. 2011; 58(7):1492-1507. DOI: 10.1109/TUFFC.2011.1968.
  • Rybyanets AN, Rybyanets AA. Ceramic piezocomposites: Modeling, technology, and characterization. IEEE Trans UFFC. 2011; 58(9):1757–73. DOI: 10.1109/TUFFC.2011.2013.
  • Rybyanets AN. Advanced functional materials: Modeling, technology, characterization, and applications. Advanced materials: Manufacturing, physics, mechanics and applications. Springer Proceedings in Physics. ISBN: 978-3-319-26324-3. 2016; 175(15):211–28.
  • Rybyanets AN, Naumenko AA, Lugovaya MA, Shvetsova NA. Electric power generations from pzt composite and porous ceramics for energy harvesting devices. Ferroelectrics. 2015; 484(1):95–100. DOI: 10.1080/00150193.2015.1060065.
  • Shcherbinin SA, Naumenko AA, Shvetsova NA, Berkovich AE, Rybyanets AN. Theoretical modeling and experimental study of high intensity focused ultrasound transducers: An update. Proceedings of the 2015 International Conference on Physics, Mechanics of New Materials and their Applications. Nova Science Publishers Inc. 2016; 65:493–500. ISBN: 978-1-63484-577-9.
  • Rybyanets AN, Naumenko AA. New combinational method for noninvasive treatments of superficial tissues for body aesthetics applications. Physics Procedia. 2015; 70:1148–51. DOI: 10.1016/j.phpro.2015.08.246.
  • Rybyanets AN, Naumenko AA, Sapozhnikov OA, Khokhlova VA. New method and transducer designs for ultrasonic diagnostics and therapy. Physics Procedia. 2015; 70:1152–6. DOI: 10.1016/j.phpro.2015.08.247.
  • Rybyanets AN. New methods and transducer designs for ultrasonic diagnostic and therapy. Advanced materials: manufacturing, physics, mechanics and applications. Springer Proceedings in Physics. 2016; 175(43):603–20. ISBN: 978-3-319-26324-3.
  • Rybyanets AN, Naumenko AA, Shvetsova NA, Khokhlova VA, Sapozhnikov OA, Berkovich AE. Theoretical modeling and experimental study of HIFU transducers and acoustic fields. Advanced materials: Manufacturing, physics, mechanics and applications. Springer Proceedings in Physics. 2016; 175(44):621–38. ISBN: 978-3-319-26324-3.
  • Shenderov EL. Radiation and scattering of sound. Leningrad: Sudostroyeniye; 1989.
  • Strett JV. The Theory of Sound [Russian translation]. V. 2, Moscow: Izd. Gos. Tekh.-Teor. Lit., 1955.
  • O’Neil HT. Theory of focusing radiators. J Acoust Soc Am. 1949; 21(5):516–26. Available from:
  • Madsen EL, Goodsitt MM, Zagzebski JA. Continuous waves generated by focused radiators. J Acoust Soc Am. 1981; 70:1508–17. Available from:
  • Sapozhnikov OA, Sinilo TV. Acoustic field of concave radiating surface by taking into account diffraction on it. Acoust J. 2002; 48(6):813–21.
  • Hart TS, Hamilton MF. Nonlinear effects in focused sound beams. J Acoust Soc Am. 1988; 84(4):1488−96. Available from:
  • Cathignol D, Sapozhnikov OA, Theillere Y. Comparison of acoustic fields radiated from piezoceramic and piezocomposite focused radiator. J Acoust Soc Am. 1999; 105(5):2612−7. Available from:
  • Jing Y, Tao M, Clement GT. Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation. J Acoust Soc Am. 2011; 129:32–46. Available from:
  • Ginter S, Liebler M, Steiger E, Dreyer T, Riedlinger R. Full-wave modeling of therapeutic ultrasound: Nonlinear ultrasound propagation in ideal fluids. J Acoust Soc Am. 2002; 111:2049–59.
  • Kuznetsov VP. Equations of nonlinear acoustics. Sov Phys Acoust. 1971; 16:467–70.
  • Khokhlova V, Bailey M, Reed J, Cunitz B, Kaczkowski P, Crum L. Effects of nonlinear propagation, cavitation, and boiling in lesion formation by high intensity focused ultrasound in a gel phantom. J Acoust Soc Am. 2006; 119:1834–48. Available from:
  • Filonenko EA, Khokhlova VA. Effect of acoustic nonlinearity on heating of biological tissue induced by high intensity focused ultrasound. Acous Phys. 2001; 47(4):468–75.
  • Vinogradova MB, Rudenko OV, Sukhorukov AP. Theory of waves. Nauka; 1990.
  • Duck FA. Physical properties of tissue: A comprehensive reference book. CA: Academic Press; 1990.
  • O’Donnell M, Janes ET, Miller JG. Kramers-Kronig relationship between ultrasonic attenuation and phase velocity. J Acoust Soc Am. 1981; 69(3):696–701. Available from:
  • Pathak M, Sadawarti H, Singh S. A technique to suppress speckle in ultrasound images using nonlocal mean and cellular automata. Indian Journal of Science and Technology. 2016 Mar; 9(13).
  • Sathishkumar R, Vimalajuliet A, Prasath JS, Selvakumar K, Reddy VHSV. Micro size ultrasonic transducer for marine applications. Indian Journal of Science and Technology. 2011 Jan; 4(1).


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