Interaction between encapsulated microbubbles: A finite element modelling study

doi:10.1088/1674-1056/27/8/084302

中国物理B ›› 2018, Vol. 27 ›› Issue (8): 84302-084302.doi: 10.1088/1674-1056/27/8/084302

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Interaction between encapsulated microbubbles: A finite element modelling study

Chen-Liang Cai(蔡晨亮), Jie Yu(于洁), Juan Tu(屠娟), Xia-Sheng Guo(郭霞生), Pin-Tong Huang(黄品同), Dong Zhang(章东)

1 Key Laboratory of Modern Acoustics(MOE), Department of Physics, Collaborative Inovation Center of Advanced Microstructure, Nanjing University, Nanjing 210093, China;
2 Department of Ultrasound, the Second Affiliated Hospital of Zhejiang University School of Medicine, Hangzhou 310009, China;
3 The State Key Laboratory of Acoustics, Chinese Academy of Sciences, Beijing 100190, China

收稿日期:2018-01-31 修回日期:2018-05-24 出版日期:2018-08-05 发布日期:2018-08-05
通讯作者: Juan Tu, Dong Zhang E-mail:juantu@nju.edu.cn;dzhang@nju.edu.cn
基金资助:
Projects supported by the National Natural Science Foundation of China (Grant Nos. 11474161, 11474001, 116741731, 1774166, 11774168, 81527803, 81627802, and 81420108018), the Fundamental Research Funds for the Central Universities, China (Grant No. 020414380109, and the Qing Lan Project, China.

Interaction between encapsulated microbubbles: A finite element modelling study

Chen-Liang Cai(蔡晨亮)¹, Jie Yu(于洁)¹, Juan Tu(屠娟)¹, Xia-Sheng Guo(郭霞生)¹, Pin-Tong Huang(黄品同)², Dong Zhang(章东)^1,3

1 Key Laboratory of Modern Acoustics(MOE), Department of Physics, Collaborative Inovation Center of Advanced Microstructure, Nanjing University, Nanjing 210093, China;
2 Department of Ultrasound, the Second Affiliated Hospital of Zhejiang University School of Medicine, Hangzhou 310009, China;
3 The State Key Laboratory of Acoustics, Chinese Academy of Sciences, Beijing 100190, China

Received:2018-01-31 Revised:2018-05-24 Online:2018-08-05 Published:2018-08-05
Contact: Juan Tu, Dong Zhang E-mail:juantu@nju.edu.cn;dzhang@nju.edu.cn
Supported by:
Projects supported by the National Natural Science Foundation of China (Grant Nos. 11474161, 11474001, 116741731, 1774166, 11774168, 81527803, 81627802, and 81420108018), the Fundamental Research Funds for the Central Universities, China (Grant No. 020414380109, and the Qing Lan Project, China.

摘要/Abstract

摘要： Theoretical studies on the multi-bubble interaction are crucial for the in-depth understanding of the mechanism behind the applications of ultrasound contrast agents (UCAs) in clinics. A two-dimensional (2D) axisymmetric finite element model (FEM) is developed here to investigate the bubble-bubble interactions for UCAs in a fluidic environment. The effect of the driving frequency and the bubble size on the bubble interaction tendency (viz., bubbles' attraction and repulsion), as well as the influences of bubble shell mechanical parameters (viz., surface tension coefficient and viscosity coefficient) are discussed. Based on FEM simulations, the temporal evolution of the bubbles' radii, the bubble-bubble distance, and the distribution of the velocity field in the surrounding fluid are investigated in detail. The results suggest that for the interacting bubble-bubble couple, the overall translational tendency should be determined by the relationship between the driving frequency and their resonance frequencies. When the driving frequency falls between the resonance frequencies of two bubbles with different sizes, they will repel each other, otherwise they will attract each other. For constant acoustic driving parameters used in this paper, the changing rate of the bubble radius decreases as the viscosity coefficient increases, and increases first then decreases as the bubble shell surface tension coefficient increases, which means that the strength of bubble-bubble interaction could be adjusted by changing the bubble shell visco-elasticity coefficients. The current work should provide a powerful explanation for the accumulation observations in an experiment, and provide a fundamental theoretical support for the applications of UCAs in clinics.

关键词: ultrasound contrast agent microbubbles, bubble-bubble interaction, finite element model, shell parameter

Abstract: Theoretical studies on the multi-bubble interaction are crucial for the in-depth understanding of the mechanism behind the applications of ultrasound contrast agents (UCAs) in clinics. A two-dimensional (2D) axisymmetric finite element model (FEM) is developed here to investigate the bubble-bubble interactions for UCAs in a fluidic environment. The effect of the driving frequency and the bubble size on the bubble interaction tendency (viz., bubbles' attraction and repulsion), as well as the influences of bubble shell mechanical parameters (viz., surface tension coefficient and viscosity coefficient) are discussed. Based on FEM simulations, the temporal evolution of the bubbles' radii, the bubble-bubble distance, and the distribution of the velocity field in the surrounding fluid are investigated in detail. The results suggest that for the interacting bubble-bubble couple, the overall translational tendency should be determined by the relationship between the driving frequency and their resonance frequencies. When the driving frequency falls between the resonance frequencies of two bubbles with different sizes, they will repel each other, otherwise they will attract each other. For constant acoustic driving parameters used in this paper, the changing rate of the bubble radius decreases as the viscosity coefficient increases, and increases first then decreases as the bubble shell surface tension coefficient increases, which means that the strength of bubble-bubble interaction could be adjusted by changing the bubble shell visco-elasticity coefficients. The current work should provide a powerful explanation for the accumulation observations in an experiment, and provide a fundamental theoretical support for the applications of UCAs in clinics.

Key words: ultrasound contrast agent microbubbles, bubble-bubble interaction, finite element model, shell parameter

中图分类号: (Nonlinear acoustics of bubbly liquids)

43.25.Yw

43.35.Wa (Biological effects of ultrasound, ultrasonic tomography) 43.80.+p (Bioacoustics)

蔡晨亮, 于洁, 屠娟, 郭霞生, 黄品同, 章东. Interaction between encapsulated microbubbles: A finite element modelling study[J]. 中国物理B, 2018, 27(8): 84302-084302.

Chen-Liang Cai(蔡晨亮), Jie Yu(于洁), Juan Tu(屠娟), Xia-Sheng Guo(郭霞生), Pin-Tong Huang(黄品同), Dong Zhang(章东). Interaction between encapsulated microbubbles: A finite element modelling study[J]. Chin. Phys. B, 2018, 27(8): 84302-084302.

参考文献 38

[1]	Zhang D, Gong Y, Gong X, Liu Z, Tan K and Zheng H 2007 Phys. Med. Biol. 52 5531
[2]	Tu J, Guan J F, Matula T J, Crum L A and Wei R J 2008 Chin. Phys. Lett. 25 172
[3]	Ferrara K, Pollard R and Borden M 2007 Ann. Rev. Biomed. Eng. 9 415
[4]	Qin S, Caskey C F and Ferrara K W 2009 Phys. Med. Biol. 54 R27
[5]	Stride E P and Coussios C C 2010 Proc. Inst. Mech. Eng. Part. H J. Eng. Med. 224 171
[6]	Zhou Y F 2011 World J. Clin. Oncol. 2 8
[7]	Cai X W, Yang F and Gu 2012 Theranostics 2 103
[8]	Arvanitis C D, Gregory T C and Nathan M 2015 IEEE Trans. Med. Imaging 34 1270
[9]	Lee J, Min H S, You D G, Kim K, Kwon I C, Rhim T and Lee K Y 2016 J. Control. Release 223 197
[10]	Zhou Y F and Gao X W 2016 Phys. Med. Biol. 61 6651
[11]	Plesset M S and Prosperetti A 1977 Annu. Rev. Fluid Mech. 9 145
[12]	Doinikov A A 2001 Phys. Rev. E 64 026301
[13]	Martynov S, Stride E and Saffari N 2009 J. Acoust. Soc. Am. 126 2963
[14]	Qin S and Ferrara K W 2006 Phys. Med. Biol. 51 5065
[15]	Miao H Y and Gracewski S M 2008 Comput. Mech. 42 95
[16]	Chen C, Gu Y, Tu J, Guo X and Zhang D 2016 Ultrasonics 66 54
[17]	Chatterjee D and Sarkar K 2003 Ultrasound Med. Biol. 29 1749
[18]	Fuster D, Conoir J M and Colonius T 2014 Phys. Rev. E 90 063010
[19]	Cui B, Ni B and Wu Q 2016 Adv. Mech. Eng. 8 1687814016631708
[20]	Leighton T 1994 The Acoustic Bubble (London: Academic Press)
[21]	Tu J, Guan J, Qiu Y and Matula T J 2009 J. Acous. Soc. Am. 126 2954
[22]	Dayton P A, Morgan K E, Klibanov A L, Brandenburger G, Nightingale K R and Ferrara K W 1997 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44 1264
[23]	Rychak J J, Klibanov A L and Hossack J A 2005 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52 421
[24]	Xi X 2013 “Controlled Translation and Oscillation of Micro-bubbles Near a Surface in an Acoustic Standing Wave Field”, Ph. D. Diserlation (London: Imperial College)
[25]	Pelekasis N A and Tsamopoulos J 1993 J. Fluid Mech. 254 501
[26]	Masato I 2003 Phys. Rev. E 67 056617
[27]	de Jong N and Hoff L 1993 Ultrasonics 31 175
[28]	Shi W T, Forsberg F, Hall A L, Chiao R Y, Liu J B, Miller S, Thomenius K E, Wheatley M A and Goldberg B B 1999 Ultrasonic Imaging 21 79
[29]	Frinking P J and de Jong N 1998 Ultrasound Med. Biol. 24 523
[30]	Guo X, Li Q, Zhang Z, Zhang D and Tu J 2013 J. Acoust. Soc. Am. 134 1622
[31]	Guo G, Lu L, Yin L, Tu J, Guo X, Wu J, Xu D and Zhang D 2014 Phys. Med. Biol. 59 6729
[32]	Wang L, Tu J, Guo X, Xu D and Zhang D 2014 Chin. Phys. B 23 124302
[33]	Goldberg B B, Raichlen J S and Forsberg F 2001 Ultrasound contrast agents: basic principles and clinical applications (Boca Raton CRC Press)
[34]	Gorce J M, Arditi M and Schneider M 2000 Invest. Radiol. 35 661
[35]	Tu J, Swalwell J E, Giraud D, Cui W, Chen W and Matula T J 2011 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58 955
[36]	Doinikov A A and Bouakaz A 2011 IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58 981
[37]	Doinikov A A and Bouakaz A 2013 Phys. Med. Biol. 58 6797
[38]	Sadighi-Bonabi R, Rezaee N, Ebrahimi H and Mirheydari M 2010 Phys. Rev. E 82 016316

Interaction between encapsulated microbubbles: A finite element modelling study

Interaction between encapsulated microbubbles: A finite element modelling study

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 38

相关文章 4

Metrics

本文评价

推荐阅读 0

[1]	Ling-Ling Zhang(张玲玲), Wei-Zhong Chen(陈伟中), Yao-Rong Wu(武耀蓉), Yang Shen(沈阳), and Guo-Ying Zhao(赵帼英). Repulsive bubble-bubble interaction in ultrasonic field[J]. 中国物理B, 2021, 30(10): 104301-104301.
[2]	Habimana Jean Willy, 李辛未, Yong Hao Tan, 陈哲, Mehmet Cagirici, Ramadan Borayek, Tun Seng Herng, Chun Yee Aaron Ong, 李朝将, 丁军. Overview of finite elements simulation of temperature profile to estimate properties of materials 3D-printed by laser powder-bed fusion[J]. 中国物理B, 2020, 29(4): 48101-048101.
[3]	项延训, 朱武军, 邓明晰, 轩福贞. Experimental and numerical studies of nonlinear ultrasonic responses on plastic deformation in weld joints[J]. 中国物理B, 2016, 25(2): 24303-024303.
[4]	黄蓓, 张艳丽, 章东, 龚秀芬. Finite element modeling of acoustic scattering from an encapsulated microbubble near rigid boundary[J]. 中国物理B, 2010, 19(5): 54302-054302.