High-intensity focused ultrasound (HIFU) is becoming popular in the treatment of solid tumors because of its non-invasiveness with few complications. The acoustic field is of importance in evaluating the safe focus shifting distance and determining the treatment plan.
The propagation of finite-amplitude acoustic wave from a 331-element HIFU phased-array with focus steering along and transverse to the transducer axis and 4-foci shifting on the focal plane was simulated using the angular spectrum approach (ASA) with a marching second-order operator-splitting scheme. In addition, the acoustic field produced by a truncated asymmetric transesophageal HIFU annular array was also simulated, and the effects of driving frequency and the number of concentric rings were investigated.
Because of the nonlinear effects, the peak negative pressure is lower than that of peak positive pressure at the main lobe but has a larger beam size. However, the peak positive and negative pressures at the grating lobe are quite similar. The effects of the focus shifting distances on the main and grating lobe (both acoustic pressure and − 6 dB beam size) were evaluated. With the focus shifting axially away from the transducer surface, the main lobe has decreased acoustic pressure by ~ 1.9 fold and increased beam size by ~ 4.5 fold while the grating lobe has the increased acoustic pressure by ~ 1.8 fold. The focus shifting laterally leads to the reduced pressure at the main lobe by ~ 1.4 fold but the slight decrease at the grating lobe by ~ 1.1 fold. In comparison, the shifting of multi-foci has similar influences on the main lobe but increases the pressure at the grating lobe. Driving frequency of annular array is found to have greater influences on the peak pressure and beam size.
Our algorithm can simulate the acoustic field of phased-array in arbitrary shape and optimize the transducer design, and the focus shifting distance and strategy should be selected appropriately for the safe HIFU exposure.
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Zhou, Y. (2015). Principles and applications of therapeutic ultrasound in healthcare. CRC Press. ISBN 1466510285.
Colen, R. R., & Jolesz, F. A. (2010). Future potential of MRI-guided focused ultrasound brain surgery. Neuroimaging Clinics, 20(3), 355–366. https://doi.org/10.1016/j.nic.2010.05.003.
Ebbini, E. S., & Cain, C. A. (1989). Multiple-focus ultrasound phased-array pattern synthesis: Optimal driving-signal distributions for hyperthermia. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 36(5), 540–548. https://doi.org/10.1109/58.31798.
Auboiroux, V., Dumont, E., Petrusca, L., Viallon, M., & Salomir, R. (2011). An MR-compliant phased-array HIFU transducer with augmented steering range, dedicated to abdominal thermotherapy. Physics in Medicine and Biology, 56(12), 3563. https://doi.org/10.1088/0031-9155/56/12/008.
Köhler, M. O., Mougenot, C., Quesson, B., Enholm, J., Le Bail, B., Laurent, C., et al. (2009). Volumetric HIFU ablation under 3D guidance of rapid MRI thermometry. Medical Physics, 36(8), 3521–3535. https://doi.org/10.1118/1.3152112.
Wan, H., VanBaren, P., Ebbini, E. S., & Cain, C. A. (1996). Ultrasound surgery: Comparison of strategies using phased array systems. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 43(6), 1085–1098. https://doi.org/10.1109/58.542052.
Ebbini, E. S., & Cain, C. A. (1991). A spherical-section ultrasound phased array applicator for deep localized hyperthermia. IEEE Transactions on Biomedical Engineering, 38(7), 634–643. https://doi.org/10.1109/10.83562.
Bailey, M., Khokhlova, V., Sapozhnikov, O., Kargl, S., & Crum, L. (2003). Physical mechanisms of the therapeutic effect of ultrasound (a review). Acoustical Physics, 49(4), 369–388. https://doi.org/10.1134/1.1591291.
Zhou, Y., Zhai, L., Simmons, R., & Zhong, P. (2006). Measurement of high intensity focused ultrasound fields by a fiber optic probe hydrophone. The Journal of the Acoustical Society of America, 120(2), 676–685. https://doi.org/10.1121/1.2214131.
Kuznetsov, V. P. (1971). Equations of nonlinear acoustics. Soviet Physics Acoustics, 16(4), 467–470.
Zabolotskaya, E. A., & Khokhlov, R. V. (1969). Quasi-plane waves in the nonlinear acoustics of confined beams. Soviet Physics Acoustics, 15(1), 35–40.
Hand, J., Shaw, A., Sadhoo, N., Rajagopal, S., Dickinson, R., & Gavrilov, L. (2009). A random phased array device for delivery of high intensity focused ultrasound. Physics in Medicine and Biology, 54(19), 5675. https://doi.org/10.1088/0031-9155/54/19/002.
Wang, M., & Zhou, Y. (2016). Simulation of non-linear acoustic field and thermal pattern of phased-array high-intensity focused ultrasound (HIFU). International Journal of Hyperthermia, 32(5), 569–582. https://doi.org/10.3109/02656736.2016.1160154.
Yuldashev, P., & Khokhlova, V. (2011). Simulation of three-dimensional nonlinear fields of ultrasound therapeutic arrays. Acoustical Physics, 57(3), 334–343. https://doi.org/10.1134/s1063771011030213.
Westervelt, P. J. (1963). Parametric acoustic array. The Journal of the Acoustical Society of America, 35(4), 535–537.
Doinikov, A. A., Novell, A., Calmon, P., & Bouakaz, A. (2014). Simulations and measurements of 3-D ultrasonic fields radiated by phased-array transducers using the Westervelt equation. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 61(9), 1470–1477. https://doi.org/10.1109/tuffc.2014.3061.
Kreider, W., Yuldashev, P. V., Sapozhnikov, O. A., Farr, N., Partanen, A., Bailey, M. R., et al. (2013). Characterization of a multi-element clinical HIFU system using acoustic holography and nonlinear modeling. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 60(8), 1683. https://doi.org/10.1109/tuffc.2013.2750.
Lee, Y. S., & Hamilton, M. F. (1995). Time-domain modeling of pulsed finite-amplitude sound beams. The Journal of the Acoustical Society of America, 97(2), 906–917. https://doi.org/10.1016/s0041-624x(99)00112-2.
Seip, R., Sanghvi, N. T., Uchida, T., & Umemura, S.-I. (2001). Comparison of split-beam transducer geometries and excitation configurations for transrectal prostate HIFU treatments. In IEEE ultrasonics symposium (pp. 1343–1346). https://doi.org/10.1109/ultsym.2001.991969.
Constanciel, E., N’Djin, W. A., Bessiere, F., Chavrier, F., Grinberg, D., Vignot, A., et al. (2013). Design and evaluation of a transesophageal HIFU probe for ultrasound-guided cardiac ablation: simulation of a HIFU mini-maze procedure and preliminary ex vivo trials. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 60(9), 1868–1883. https://doi.org/10.1109/tuffc.2013.2772.
Goss, S. A., Frizzell, L. A., Kouzmanoff, J. T., Barich, J. M., & Yang, J. M. (1996). Sparse random ultrasound phased array for focal surgery. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 43(6), 1111–1121. https://doi.org/10.1109/58.542054.
Chen, D., & McGough, R. J. (2008). A 2D fast near-field method for calculating near-field pressures generated by apodized rectangular pistons. The Journal of the Acoustical Society of America, 124(3), 1526–1537. https://doi.org/10.1121/1.2950081.
Vyas, U., & Christensen, D. (2012). Ultrasound beam simulations in inhomogeneous tissue geometries using the hybrid angular spectrum method. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 59(6), 1093–1100. https://doi.org/10.1109/tuffc.2012.2300.
Zemp, R. J., Tavakkoli, J., & Cobbold, R. S. (2003). Modeling of nonlinear ultrasound propagation in tissue from array transducers. The Journal of the Acoustical Society of America, 113(1), 139–152. https://doi.org/10.1109/ultsym.2002.1192634.
Ji, X., Bai, J.-F., Shen, G.-F., & Chen, Y.-Z. (2009). High-intensity focused ultrasound with large scale spherical phased array for the ablation of deep tumors. Journal of Zhejiang University SCIENCE B: Biomedicine and Biotechnology, 10(9), 639–647. https://doi.org/10.1631/jzus.b0920130.
Daum, D. R., & Hynynen, K. (1999). A 256-element ultrasonic phased array system for the treatment of large volumes of deep seated tissue. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 46(5), 1254–1268. https://doi.org/10.1109/58.796130.
Gavrilov, L. R., & Hand, J. W. (2000). A theoretical assessment of the relative performance of spherical phased arrays for ultrasound surgery. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 47(1), 125–139. https://doi.org/10.1109/58.818755.
Yang, X., & Cleveland, R. O. (2005). Time domain simulation of nonlinear acoustic beams generated by rectangular pistons with application to harmonic imaging. The Journal of the Acoustical Society of America, 117(1), 113–123. https://doi.org/10.1121/1.1828671.
Ginter, S., Liebler, M., Steiger, E., Dreyer, T., & Riedlinger, R. E. (2002). Full-wave modeling of therapeutic ultrasound: Nonlinear ultrasound propagation in ideal fluids. The Journal of the Acoustical Society of America, 111(5), 2049–2059. https://doi.org/10.1121/1.1468876.
Jing, Y., Wang, T., & Clement, G. T. (2012). A k-space method for moderately nonlinear wave propagation. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 59(8), 1664–1673. https://doi.org/10.1109/tuffc.2012.2372.
Clement, G. T., & Hynynen, K. (2003). Forward planar projection through layered media. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 50(12), 1689–1698. https://doi.org/10.1109/tuffc.2003.1256310.
Christopher, P. T., & Parker, K. J. (1991). New approaches to nonlinear diffractive field propagation. The Journal of the Acoustical Society of America, 90(1), 488–499. https://doi.org/10.1121/1.401274.
Wu, P., Kazys, R., & Stepinski, T. (1997). Optimal selection of parameters for the angular spectrum approach to numerically evaluate acoustic fields. The Journal of the Acoustical Society of America, 101(1), 125–134. https://doi.org/10.1121/1.418013.
Turnbull, D. H., & Foster, F. S. (1991). Beam steering with pulsed two-dimensional transducer arrays. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 38(4), 320–333. https://doi.org/10.1109/58.84270.
Dolph, C. L. (1946). A current distribution for broadside arrays which optimizes the relationship between beam width and side-lobe level. Proceedings of the IRE, 34(6), 335–348. https://doi.org/10.1109/jrproc.1946.225956.
Payne, A., Vyas, U., Todd, N., De Bever, J., Christensen, D. A., & Parker, D. L. (2011). The effect of electronically steering a phased array ultrasound transducer on near-field tissue heating. Medical Physics, 23(5), 767–776. https://doi.org/10.1118/1.3618729.
Hutchinson, E., Buchanan, M., & Hynynen, K. (1996). Design and optimization of an aperiodic ultrasound phased array for intracavitary prostate thermal therapies. Medical Physics, 23(5), 767–776. https://doi.org/10.1118/1.597741.
Dupenloup, F., Chapelon, J. Y., Cathignol, D. J., & Sapozhnikov, O. (1996). Reduction of the grating lobes of annular arrays used in focused ultrasound surgery. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 43(6), 991–998. https://doi.org/10.1109/58.542044.
Wang, M., & Zhou, Y. (2018). High-intensity focused ultrasound (HIFU) ablation by the frequency chirp excitation: Reduction of the grating lobe in axial focus shifting. Journal of Physics D: Applied Physics, 51(28), 285402. https://doi.org/10.1088/1361-6463/aacaed.
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Lean, H.Q., Zhou, Y. Acoustic Field of Phased-Array Ultrasound Transducer with the Focus/Foci Shifting. J. Med. Biol. Eng. 39, 919–931 (2019). https://doi.org/10.1007/s40846-019-00464-z
- High-intensity focused ultrasound (HIFU)
- Nonlinear wave propagation
- Angular spectrum algorithm (ASA)
- Focus shifting