Journal of Biomedical Physics and Engineering

Current Issue

By Issue

By Author

By Subject

Author Index

Keyword Index

About Journal

Aims and Scope

Staff Members

Editorial Board

Publication Ethics

Indexing and Abstracting

Related Links

FAQ

Peer Review Process

News

Simulation Study on the Dynamics of Cavitation Bubbles in Multi-Frequency Ultrasound

Document Type : Original Research

Authors

1 School of Information Science and Engineering, Changsha Normal University, Changsha 410100, China

2 School of Information Science and Engineering, Xinyu University, Xinyu, 338004, China

10.31661/jbpe.v0i0.2410-1841

Abstract

Background: High-intensity focused ultrasound (HIFU) therapy is an effective minimally invasive treatment technique.
Objective: This work aimed to present a theoretical foundation for transient cavitation control in HIFU treatment and investigate cavitation bubbles in multi-frequency ultrasound.
Material and Methods: In this theoretical study, the nonlinear vibrations of bubbles in different mediums (water, urine, kidney, and muscle) were simulated using Gilmore-Akulichev and modified Keller-Miksis equations. The dynamic changes of bubble radius during irradiation by multi-frequency combined ultrasound were analyzed, and the effects of multi-frequency ultrasound combinations and frequency differences on the maximum and minimum values of bubble expansion radius and bubble collapse time were investigated.
Results: At the same highest frequency, the triple-frequency produced the largest bubble expansion radius (Rmax) while the single-frequency resulted in the smallest bubble expansion radius (Rmin). At the same lowest frequency, the single-frequency had the biggest bubble expansion radius and the triple-frequency had the smallest bubble expansion radius. Compared to the combination with a large frequency difference at high frequency, the triple-frequency combination with a small frequency difference at low frequency exhibited a noticeably larger Rmax, but Rmin showed the opposite behavior. Rmax/Rmin decreased for the same ultrasonic combination when the medium viscosity increased. The bubble expansion radius ratio Rmax/Rmin was positively correlated with the bubble collapse time. 
Conclusion: There was a strong correlation between the frequency difference and the multi-frequency ultrasound combination and the maximum and minimum values of the cavitation bubble radius and the collapse time.

Highlights

Hu Dong (PubMed)

Keywords

References
  1. Song M, Sapozhnikov OA, Khokhlova VA, Khokhlova TD. Dynamic Mode Decomposition for Transient Cavitation Bubbles Imaging in Pulsed High-Intensity Focused Ultrasound Therapy. IEEE Trans Ultrason Ferroelectr Freq Control. 2024;71(5):596-606. doi: 10.1109/TUFFC.2024.3387351. PubMed PMID: 38598407. PubMed PMCID: PMC11141145.
  2. Fu B, Shan D, Pu C, Guo L, Xu H, Peng C. A systematic investigation of thermal effects of high-intensity focused ultrasound therapy for ultrasound neuromodulation. IEEE Transactions on Instrumentation and Measurement. 2024;73:1-12. doi: 10.1109/TIM.2024.3366278.
  3. McDannold N, Wen PY, Reardon DA, Fletcher SM, Golby AJ. Cavitation monitoring, treatment strategy, and acoustic simulations of focused ultrasound blood-brain barrier disruption in patients with glioblastoma. J Control Release. 2024;372:194-208. doi: 10.1016/j.jconrel.2024.06.036. PubMed PMID: 38897294. PubMed PMCID: PMC11299340.
  4. Wang M, Zhang W, Chen Z, Paulus YM, Wang X, Yang X. Real-Time Cavitation Monitoring During Optical Coherence Tomography Guided Photo-Mediated Ultrasound Therapy of the Retina. IEEE Trans Biomed Eng. 2024;71(8):2473-2482. doi: 10.1109/TBME.2024.3377115. PubMed PMID: 38478443. PubMed PMCID: PMC11257808.
  5. Iqbal MF, Shafique MA, Abdur Raqib M, Fadlalla Ahmad TK, Haseeb A, MA Mhjoob A, Raja A. Histotripsy: an innovative approach for minimally invasive tumour and disease treatment. Ann Med Surg (Lond). 2024;86(4):2081-7. doi: 10.1097/MS9.0000000000001897. PubMed PMID: 38576932. PubMed PMCID: PMC10990312.
  6. Mustapha AT, Wahia H, Ji Q, Fakayode OA, Zhang L, Zhou C. Multiple‐frequency ultrasound for the inactivation of microorganisms on food: A review. Journal of Food Process Engineering. 2024;47(4):e14587. doi: 10.1111/jfpe.14587.
  7. Chen Z, Shen R, Xie J, Zeng Y, Wang K, Zhao L, et al. Multi-frequency ultrasonic-assisted enzymatic extraction of coconut paring oil from coconut by-products: Impact on the yield, physicochemical properties, and emulsion stability. Ultrason Sonochem. 2024;109:106996. doi: 10.1016/j.ultsonch.2024.106996. PubMed PMID: 39032371. PubMed PMCID: PMC11325078.
  8. Diao X, Wang Y, Jia R, Chen X, Liu G, Liu D, Guan H. Influences of ultrasonic treatment on the physicochemical properties and microstructure of diacylglycerol-loaded emulsion stabilized with soybean protein isolate and sodium alginate. Ultrason Sonochem. 2024;108:106981. doi: 10.1016/j.ultsonch.2024.106981. PubMed PMID: 38981339. PubMed PMCID: PMC11280087.
  9. Kumar S, Prajapat A, Panja SK, Shukla M. Ultrasound irradiation: fundamental theory, electromagnetic spectrum, important properties, and physical principles. In: Green Chemical Synthesis with Microwaves and Ultrasound. Weinheim: Wiley‐VCH GmbH; 2024. p. 1-19.
  10. Condezo-Hoyos L, Cortés-Avendaño P, Lama-Quispe S, Calizaya-Milla YE, Méndez-Albiñana P, Villamiel M. Structural, chemical and technofunctional properties pectin modification by green and novel intermediate frequency ultrasound procedure. Ultrason Sonochem. 2024;102:106743. doi: 10.1016/j.ultsonch.2023.106743. PubMed PMID: 38150956. PubMed PMCID: PMC10765486.
  11. Moholkar VS, Rekveld S, Warmoeskerken MM. Modeling of the acoustic pressure fields and the distribution of the cavitation phenomena in a dual frequency sonic processor. Ultrasonics. 2000;38(1-8):666-70. doi: 10.1016/s0041-624x(99)00204-8. PubMed PMID: 10829749.
  12. Tatake PA, Pandit AB. Modelling and experimental investigation into cavity dynamics and cavitational yield: influence of dual frequency ultrasound sources. Chemical Engineering Science. 2002;57(22-23):4987-95. doi: 10.1016/ s0009-2509(02)00271-3.
  13. Servant G, Laborde JL, Hita A, Caltagirone JP, Gérard A. On the interaction between ultrasound waves and bubble clouds in mono- and dual-frequency sonoreactors. Ultrason Sonochem. 2003;10(6):347-55. doi: 10.1016/S1350-4177(03)00105-6. PubMed PMID: 12927611.
  14. Ye L, Zhu X, He Y, Song T. Effect of frequency ratio and phase difference on the dynamic behavior of a cavitation bubble induced by dual-frequency ultrasound. Chemical Engineering and Processing-Process 2021;165:108448. doi: 10.1016/j.cep. 2021. 108448.
  15. Brotchie A, Grieser F, Ashokkumar M. Sonochemistry and sonoluminescence under dual-frequency ultrasound irradiation in the presence of water-soluble solutes. The Journal of Physical Chemistry C. 2008;112(27):10247-50. doi: 10.1021/jp801763v.
  16. Saletes I, Gilles B, Bera JC. Promoting inertial cavitation by nonlinear frequency mixing in a bifrequency focused ultrasound beam. Ultrasonics. 2011;51(1):94-101. doi: 10.1016/j.ultras.2010.06.003. PubMed PMID: 20637485.
  17. Koufaki M, Fotopoulou T, Heropoulos GA. Synergistic effect of dual-frequency ultrasound irradiation in the one-pot synthesis of 3,5-disubstituted isoxazoles. Ultrason Sonochem. 2014;21(1):35-9. doi: 10.1016/j.ultsonch.2013.05.012. PubMed PMID: 23769747.
  18. Suo D, Govind B, Zhang S, Jing Y. Numerical investigation of the inertial cavitation threshold under multi-frequency ultrasound. Ultrason Sonochem. 2018;41:419-26. doi: 10.1016/j.ultsonch.2017.10.004. PubMed PMID: 29137770.
  19. Zhao X, Wang Z, Bai X, Cheng H, Ji B. Unsteady cavitation dynamics and pressure statistical analysis of a hydrofoil using the compressible cavitation model. Physics of Fluids. 2023;35(10):103307. doi: 10.1063/5.0164191.
  20. Khanna S, Chakma S, Moholkar VS. Phase diagrams for dual frequency sonic processors using organic liquid medium. Chemical Engineering Science. 2013;100:137-44. doi: 10.1016/j.ces.2013.02.016.
  21. Zhang Y, Billson D, Li S. Influences of pressure amplitudes and frequencies of dual-frequency acoustic excitation on the mass transfer across interfaces of gas bubbles. International Communications in Heat and Mass Transfer. 2015;66:167-71. doi: 10.1016/j.icheatmasstransfer.2015.05.026.
  22. Guédra M, Inserra C, Gilles B. Accompanying the frequency shift of the nonlinear resonance of a gas bubble using a dual-frequency excitation. Ultrason Sonochem. 2017;38:298-305. doi: 10.1016/j.ultsonch.2017.03.028. PubMed PMID: 28633830.
  23. Ye L, Zhu X, Liu Y. Numerical study on dual-frequency ultrasonic enhancing cavitation effect based on bubble dynamic evolution. Ultrason Sonochem. 2019;59:104744. doi: 10.1016/j.ultsonch.2019.104744. PubMed PMID: 31473426.
  24. Azam SR, Ma H, Xu B, Devi S, Stanley SL, Siddique MA, et al. Multi-frequency multi-mode ultrasound treatment for removing pesticides from lettuce (Lactuca sativa L.) and effects on product quality. 2021;143:111147. doi: 10.1016/j.lwt. 2021.111147.
  25. Liao J, Tan J, Peng L, Xue H. Numerical investigation on the influence of dual-frequency coupling parameters on acoustic cavitation and its analysis of the enhancement and attenuation effect. Ultrason Sonochem. 2023;100:106614. doi: 10.1016/j.ultsonch.2023.106614. PubMed PMID: 37801994. PubMed PMCID: PMC10568426.
  26. Wang X, Yan X, Min Q. Mass transfer of microbubble in liquid under multifrequency acoustic excitation - A theoretical study. Ultrason Sonochem. 2024;102:106760. doi: 10.1016/j.ultsonch.2024.106760. PubMed PMID: 38199078. PubMed PMCID: PMC10788794.
  27. Wang M, Zhou Y. Numerical investigation of the inertial cavitation threshold by dual-frequency excitation in the fluid and tissue. Ultrason Sonochem. 2018;42:327-38. doi: 10.1016/j.ultsonch.2017.11.045. PubMed PMID: 29429677.
  28. Carvell KJ, Bigelow TA. Dependence of cavitation bubble size on pressure amplitude at therapeutic levels. AIP Conf Proc. 2009;1113(1):63-67. doi: 10.1063/1.3131472.
  29. Sojahrood AJ, Haghi H, Li Q, Porter TM, Karshafian R, Kolios MC. Nonlinear power loss in the oscillations of coated and uncoated bubbles: Role of thermal, radiation and encapsulating shell damping at various excitation pressures. Ultrason Sonochem. 2020;66:105070. doi: 10.1016/j.ultsonch.2020.105070. PubMed PMID: 32279052.
  30. Filonets T, Solovchuk M, Sheu Tw. The Inertial Cavitation Threshold in Soft Tissue Using a Dual-Frequency Driving Signal. In: 14th WCCM-ECCOMAS Congress; 2021. p. 1-10
  31. Abu-Nab AK, Mohamed KG, Abu-Bakr AF. An analytical approach for microbubble dynamics in histotripsy based on a neo-Hookean model. Arch Appl Mech. 2023;93(4):1565-77. doi: 10.1007/s00419-022-02346-4.
  32. Gaudron R, Warnez MT, Johnsen E. Bubble dynamics in a viscoelastic medium with nonlinear elasticity. Journal of Fluid Mechanics. 2015;766:54-75. doi: 10.1017/jfm.2015.7.
  33. Chu YM, Rehman MI, Khan MI, Nadeem S, Kadry S, Abdelmalek Z, Abbas N. Transportation of heat and mass transport in hydromagnetic stagnation point flow of Carreau nanomaterial: Dual simulations through Runge-Kutta Fehlberg technique. International Communications in Heat and Mass Transfer. 2020;118:104858. doi: 10.1016/j.icheatmasstransfer.2020.104858.
  34. Noar NA, Apandi NI, Rosli N. A comparative study of Taylor method, fourth order Runge-Kutta method and Runge-Kutta Fehlberg method to solve ordinary differential equations. AIP Conf Proc. 2024;2895(1):020003. doi:10.1063/5.0192085.
  35. Hong S, Son G. Numerical modelling of acoustic cavitation threshold in water with non-condensable bubble nuclei. Ultrason Sonochem. 2022;83:105932. doi: 10.1016/j.ultsonch.2022.105932. PubMed PMID: 35121570. PubMed PMCID: PMC8818585.
  36. Church CC, Labuda C, Nightingale K. A theoretical study of inertial cavitation from acoustic radiation force impulse imaging and implications for the mechanical index. Ultrasound Med Biol. 2015;41(2):472-85. doi: 10.1016/j.ultrasmedbio.2014.09.012. PubMed PMID: 25592457. PubMed PMCID: PMC4297318.
  37. Kolebaje OT, Vincent UE, Benyeogor BE, McClintock PVE. Effect of a modulated acoustic field on the dynamics of a vibrating charged bubble. Ultrasonics. 2023;135:107110. doi: 10.1016/j.ultras.2023.107110. PubMed PMID: 37499283.
  38. Arienti M, Hwang J, Pickett L, Shekhawat Y. A thermally-limited bubble growth model for the relaxation time of superheated fuels. International Journal of Heat and Mass Transfer. 2020;159:120089. doi: 10.1016/j.ijheatmasstransfer.2020.120089.
  39. Webb IR, Payne SJ, Coussios CC. The effect of temperature and viscoelasticity on cavitation dynamics during ultrasonic ablation. J Acoust Soc Am. 2011;130(5):3458-66. doi: 10.1121/1.3626136. PubMed PMID: 22088020.
  40. Zhang D, Wang X, Lin J, Xiong Y, Lu H, Huang J, Lou X. Multi-frequency therapeutic ultrasound: A review. Ultrason Sonochem. 2023;100:106608. doi: 10.1016/j.ultsonch.2023.106608. PubMed PMID: 37774469. PubMed PMCID: PMC10543167.
  41. Guo J, Zhang X, Fang Y, Qu R. An extremely-thin acoustic metasurface for low-frequency sound attenuation with a tunable absorption bandwidth. International Journal of Mechanical Sciences. 2022;213:106872. doi: 10.1016/j.ijmecsci.2021.106872.
  42. Kanthale PM, Gogate PR, Pandit AB. Modeling aspects of dual frequency sonochemical reactors. Chemical Engineering Journal. 2007;127(1-3):71-9. doi: 10.1016/j.cej.2006.09.023.
  43. Qin D, Lei S, Chen B, Li Z, Wang W, Ji X. Numerical investigation on acoustic cavitation characteristics of an air-vapor bubble: Effect of equation of state for interior gases. Ultrason Sonochem. 2023;97:106456. doi: 10.1016/j.ultsonch.2023.106456. PubMed PMID: 37271030. PubMed PMCID: PMC10251073.
  44. Wang Z, Zhou W, Shu T, Xue Q, Zhang R, Wiercigroch M. Modelling of low-frequency acoustic wave propagation in dilute gas-bubbly liquids. International Journal of Mechanical Sciences. 2022;216:106979. doi: 10.1016/j.ijmecsci.2021.106979.
  45. Ye Y, Song M, Liang Y, Li S, Dong C, Bu Z, Hu G. Numerical modelling and theoretical analysis of the acoustic attenuation in bubbly liquids. Engineering Applications of Computational Fluid Mechanics. 2023;17(1):2210193. doi: 10.1080/19942060.2023.2210193.
  46. Gubaidullin DA, Fedorov YV. Acoustics of a viscoelastic medium with encapsulated bubbles. J Hydrodyn. 2021;33:55-62. doi: 10.1007/s42241-021-0003-2.
  47. Wang X, Ning Z, Lv M, Yao J, Sun C. The secondary bjerknes force between two bubbles in ultrasonic field. Journal of the Physical Society of Japan. 2022;91(1):014401. doi: 10.7566/JPSJ.91.014401.
  48. Zhang X, Li F, Wang C, Mo R, Hu J, Guo J, Lin S. Effects of translational motion on the Bjerknes forces of bubbles activated by strong acoustic waves. Ultrasonics. 2022;126:106809. doi: 10.1016/j.ultras.2022.106809. PubMed PMID: 35905527.
  49. Beckwith C, Djambazov G, Pericleous K, Tonry C. Comparison of frequency domain and time domain methods for the numerical simulation of contactless ultrasonic cavitation. Ultrason Sonochem. 2022;89:106138. doi: 10.1016/j.ultsonch.2022.106138. PubMed PMID: 36049449. PubMed PMCID: PMC9441332.
  50. Kashyap SR, Jaiman RK. Unsteady cavitation dynamics and frequency lock-in of a freely vibrating hydrofoil at high Reynolds number. International Journal of Multiphase Flow. 2023;158:104276. doi: 10.1016/j.ijmultiphaseflow.2022.10427.
  51. Khavari M, Priyadarshi A, Morton J, Porfyrakis K, Pericleous K, Eskin D, Tzanakis I. Cavitation-induced shock wave behaviour in different liquids. Ultrason Sonochem. 2023;94:106328. doi: 10.1016/j.ultsonch.2023.106328. PubMed PMID: 36801674. PubMed PMCID: PMC9975297.
  52. Kalmár P, Hegedűs F, Klapcsik K. A comparative study of measurements and numerical simulations of acoustically excited non-spherical bubbles oscillation. International Journal of Multiphase Flow. 2024;179:104947. doi: 10.1016/j.ijmultiphaseflow.2024.104947.
Journal of Biomedical Physics and Engineering
Volume 15, Issue 2 - Serial Number 1
70
April 2025
Pages 185-198
Files
Share
How to cite
Statistics