Analysis of nonlinear acoustic wave propagation in HIFU treatment using Westervelt equation

Document Type : Article


1 School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran

2 Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, P.O. BOX: 11155-9567, Tehran, Iran


Currently, the HIFU (High Intensity Focused Ultrasound) therapy method is known as one of the most advanced surgical techniques in tumor ablation therapy. Simulation of the non-linear acoustic wave and tissue interaction is essential in HIFU planning to improve the usefulness and efficiency of treatment.
In this paper, linear, thermoviscous and nonlinear equations are applied using two different media, namely liver and water. Transducer power of 8.3-134 Watts with the frequency of 1.1 MHz is considered as the range of study to analyze the wave and tissue interaction. Results indicate that the maximum focal pressure of about 0.5-4.3 MPa can be achieved for transducer power of 8.3 to 134 W. Simultaneous solving of the acoustic pressure equation and Pennes’s bio-heat equation are used to determine the temperature rise at focal point and the ablated area. Finally, the linear and nonlinear simulations are compared, and the turning point of transition from linearity to nonlinearity is determined.
The simulated results provide information about the behavior of the focalized ultrasound in interaction with liver tissue. The performance of phased array HIFU transducer can be improved for treatment considering the lesion size, temperature rise in tissue and choosing best range of operational power.


Main Subjects

1. Zhou, M., Chen, J.Y., Tang, L.D., Chen, W.Z., and
Wang, Z.B. \Ultrasound-guided high-intensity focused
ultrasound ablation for adenomyosis: the clinical experience
of a single center", Fertil. Steril., 95(3), pp.
900-905 (2011).
2. Leslie, T.A. and Kennedy, J.E. \High intensity focused
ultrasound in the treatment of abdominal and gynecological
diseases", Int. J. Hyperthermia., 23, pp. 173-
182 (2007).
3. Bailey, M.R., Khokhlova, V.A., Sapozhnikov, O.A.,
Kargl, S.G., and Crum, L.A. \Physical mechanisms
of the therapeutic e ect of ultrasound", Acoust. Phys.,
49(4), pp. 369-388 (2003).
4. Hynynen, K., Chung, A.H., Colucci, V., and Jolesz,
F.A. \Potential adverse e ects of high-intensity focused
ultrasound exposure on blood vessels in vivo",
Ultrasound in Medicine & Biology, 22.2, pp. 193-201
5. Bjorno, L. \Forty years of nonlinear ultrasound",
Ultrasonics, 40, pp. 11-17 (2002).
6. Hallaj, I.M., and Cleveland, R.O. \FDTD simulation
of nite-amplitude pressure and temperature elds for
biomedical ultrasound", J. Acoust. Soc. Am., 105(5),
pp. L7-12 (1999).
7. Curra, F.P., Mourad, P.D., Khokhlova, V.A., Cleveland,
R.O., and Crum, L. A. "Numerical simulations of
heating patterns and tissue temperature response due
to high-intensity focused ultrasound", IEEE Trans.
Ultrason. Ferroelectr. Freq. Control., 47(4), pp. 1077-
1089 (2000).
8. Hariharan, P., Myers, M.R., and Banerjee, R.K.
\HIFU procedures at moderate intensities e ect of
large blood vessels", Phys. Med. Biol., 52(12), pp.
3493-513 (2007).
9. Okita, K., Ono, K., Takagi, S., and Matsumoto, Y.
\Development of high intensity focused ultrasound
simulator for large-scale computing", Int. J. Numer.
Methods. Fluids., 65(1-3), pp. 43-66 (2011).
10. Wong, S.H., Kupnik, M., Butts-Pauly, K., and Khuri-
Yakub, B.T. \P1B-10 advantages of capacitive micromachined
ultrasonics transducers (CMUTs) for high
intensity focused ultrasound (HIFU)", IEEE Int. Ultrason.
Symp. (2007).
11. Hamilton, M.F., Morfey, C.L., and Blackstock, D.T.
\Model equations", Nonlinear Acoustics, 427, San
Diego: Academic press. (1998).
12. Soneson, J.E. \A parametric study of error in the
parabolic approximation of focused axisymmetric ultrasound
beams", J. E. Soneson, J. Acoust. Soc. Am.,
131(6), pp. EL481-486 (2012).
13. Tjo, J.N. and Vefring, E.H. \E ects of focusing on
the nonlinear interaction between two collinear nite
amplitude sound beams", J. Acoust. Soc. Am., 89(3),
pp. 1017-1027 (1991).
14. Tavakkoli, J., Cathignol, D., Souchon, R., and Sapozhnikov,
O.A. \Modeling of pulsed nite-amplitude focused
sound beams in time domain", J. Acoust. Soc.
Am., 104(4), pp. 2061-2072 (1998).
15. Yuldashev, P.V. and Khokhlova, V.A. \Simulation
of three-dimensional nonlinear elds of ultrasound
therapeutic arrays", Acoust. Phys., 57(3), pp. 334-343
16. Wojcik, G., Mould, J., Abboud, N., Ostromogilsky, M.,
and Vaughan, D. \Nonlinear modeling of therapeutic
ultrasound", In Ultrasonics Symposium, Proceedings.,
IEEE, 2, pp. 1617-1622 (1995).
17. Khokhlova, V.A., Bessonova, O.V., Soneson, J.E.,
Canney, M.S., Bailey, M.R., and Crum, L.A. \Bandwidth
limitations in characterization of high intensity
S. Haddadi and M.T. Ahmadian/Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 2087{2097 2097
focused ultrasound elds in the presence of shocks",
In K. Hynynen and J. Souquet Eds., AIP Conference
Proceedings, 1215(1), pp. 363-366, AIP (2010).
18. Joshua E. Soneson \A user-friendly software package
for HIFU simulation", AIP Conference Proceedings,
Emad S. Ebbini, Ed., 1113(1), AIP (2009).
19. Solovchuk, M., Sheu, T.W., and Thiriet, M. \Simulation
of nonlinear Westervelt equation for the investigation
of acoustic streaming and nonlinear propagation
e ects", J. Acoust. Soc. Am., 134(5), pp. 3931-3942
20. Sapareto, S.A. and Dewey, W.C. \Thermal dose determination
in cancer therapy", Int. J. Radiat. Oncol.
Biol. Phys., 10(6), pp. 787-800 (1984).
21. Karaboce, B. and Durmus, H.O. \Visual investigation
of heating e ect in liver and lung induced by a
HIFU transducer", Phys. Procedia., 70, pp. 1225-1228
22. Hynynen, K. \The threshold for thermally signi cant
cavitation in dog's thigh muscle in vivo", Ultrasound
in Medicine & Biology, 17(2), pp. 157-169 (1991).
23. Clarke, R.L. and Ter Haar, G.R. \Temperature rise
recorded during lesion formation by high-intensity focused
ultrasound", Ultrasound in Medicine & Biology,
23(2), pp. 299-306 (1997).
24. Chapelon, J.Y., Prat, F., Delon, C., Margonari, J.,
Gelet, A., and Blanc, E. \E ects of cavitation in the
high intensity therapeutic ultrasound", In Ultrasonics
Symposium, Proceedings, IEEE 1991, pp. 1357-1360
25. Chapelon, J.Y., Dupenloup, F., Cohen, H., and Lenz,
P. \Reduction of cavitation using pseudorandom signals
[therapeutic US]", IEEE Transactions on Ultrasonics,
Ferroelectrics, and Frequency Control, 43(4),
pp. 623-625 (1996).
26. Chapelon, J.Y., Cathignol, D., Cain, C., Ebbini,
E., Kluiwstra, J.U., Sapozhnikov, O.A., Fleury, G.,
Berriet, R., Chupin, L., and Guey, J.L. \New piezoelectric
transducers for therapeutic ultrasound", Ultrasound
in Medicine & Biology, 26(1), pp. 153-159
27. Sibille, A., Prat, F., Chapelon, J.Y., et al. \Characterization
of extracorporeal ablation of normal and
tumor-bearing liver tissue by high intensity focused
ultrasound", Ultrasound in Medicine & Biology, 19(9),
pp. 803-813 (1993).