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The combination of superparamagnetic iron oxide nanoparticles (SPIOs) with ultrasonic contrast agent (UCA) microbubble is called magnetic microbubble (MMB) and has been used to produce multimodal contrast agents to enhance medical ultrasound and magnetic resonance imaging. The nanoparticles are either covalently linked to the shell or physically entrapped into the shell. Considering the effect of the volume fraction of SPIOs on the shell density and viscosity, a nonlinear dynamic equation of magnetic microbubbles (MMBs) with multilayer membrane structure is constructed based on the basic theory of bubble dynamics. The influences of the driving sound pressure and frequency, particle volume fraction, shell thickness and surface tension on the acoustic-dynamics behavior of microbubbles are numerically analyzed. The results show that when the volume fraction of magnetic particles is small and α ≤ 0.1, the acoustic properties of magnetic microbubbles are similar to those of ordinary UCA microbubbles. The acoustic response of the microbubble depends on its initial size and driving pressure. The critical sound pressure of microbubble vibration instability is lowest when the driving sound field frequency is twice the magnetic microbubble resonance frequency f0 (f = 2f0). The presence of magnetic particles inhibits the bubbles from expanding and contracting, but the inhibition effect is very limited. The surface tension parameter K of the outer film material and thickness of the shell also affect the vibration of the microbubble. When K and film thickness are 0.2–0.4 N/m and 50–150 nm respectively, it is observed that the bubble has an unstable vibration response region.
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Keywords:
- magnetic microbubbles /
- nonlinear vibration /
- power spectrum /
- bifurcation diagram
[1] He W, Yang F, Wu Y H, Wen S, Chen P, Zhang Y, Gu N 2012 Mater. Lett. 68 64
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图 1 磁性微泡几何模型. 1-空气, 2-磁流体层, 3-磷脂薄层
Figure 1. The geometric model of MMBs. 1-air, 2-magnetic fluid, 3-thin layer of phospholipid regardless of thickness.
图 2 声压响应分岔图 (R20 = 5 μm) (a) f = f0/2; (b) f = f0; (c) f = 2f0
Figure 2. Bifurcation diagram of an MMB with pressure amplitude for R20 =5 μm: (a) f = f0/2; (b) f = f0; (c) f = 2f0.
图 3 基频激励时MMB频谱图 ((a)—(c))和庞加莱截面图((d)—(f)) (R20 = 5 μm) (a), (d) Pa = 100 kPa; (b), (e) Pa = 255 kPa; (c), (f) Pa = 350 kPa
Figure 3. Spectra diagram and Poincaré cross-section of an MMB at f = f0 (R20 = 5 μm): (a), (d) Pa = 100 kPa; (b), (e) Pa =255 kPa; (c), (f) Pa = 350 kPa
图 4 不同尺寸MMB频响曲线(Pa = 150 kPa) (a) R20 = 3 μm; (b) R20 = 4 μm; (c) R20 = 5 μm
Figure 4. Bifurcation diagrams of an MMB with driving frequency as the control parameter at Pa = 150 kPa: (a) R20 = 3 μm; (b) R20 = 4 μm; (c) R20 = 5 μm.
图 5 混沌态微泡振动相图 (Pa = 150 kPa, R20 = 5 μm) (a) f = 350 kHz; (b) f = 381 kHz; (c) f = 550 kHz
Figure 5. MMB phase diagram in chaotic motion (Pa = 150 kPa, R20 = 5 μm): (a) f = 350 kHz; (b) f = 381 kHz; (c) f = 550 kHz.
图 6 α对R2/R20的影响
Figure 6. R2/R20 responses to α.
图 7 K值响应
Figure 7. MMB responses to K.
图 8 膜厚响应
Figure 8. MMB responses to film thickness.
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[1] He W, Yang F, Wu Y H, Wen S, Chen P, Zhang Y, Gu N 2012 Mater. Lett. 68 64
Google Scholar
[2] Porter T R, Feinstein S B, Ten Cate F J, Van den Bosch A E 2020 Ultrasound Med. Biol. 46 1071
Google Scholar
[3] Stride E, Porter C, Prieto A G, Pankhurs Q 2009 Ultrasound Med. Biol. 35 861
Google Scholar
[4] Dimcevski G, Kotopoulis S, Bjnes T, Hoem D 2016 J. Controlled Release 243 172
Google Scholar
[5] Duan L, Yang F, Song L N, Fang K,Tian J L, Liang Y J, Li M X, Xu N, Chen Z D, Zhang Y, Gu N 2015 Soft Matter 11 5492
Google Scholar
[6] Cho E, Chung S K, Rhee K 2015 Ultrasonics 62 66
Google Scholar
[7] Hyun S M, Sejin S, Dong G Y, Tae W L, Jangwook L, Sangmin L, Ji Y Y, Jaeyoung L, Moon H H, Jae H P, Sun H K, Kuiwon C, Kinam P, Kwangmeyung K, Ick C K 2016 Biomaterials 108 57
Google Scholar
[8] Gao Y, Chan C U, Gu Q S, Lin X D, Zhang W C, David Yeo C L, Astrid M A, Manish A, Mark Chong S K, Shi P, Claus D O and Xu C J 2016 NPG. Asia Mater. 8 e260
Google Scholar
[9] Zhou T, Cai W B, Yang H L, Zhang H Z, Hao M H, Yuan L J, Liu J, Zhang L, Yang Y L, Liu X, Deng J L, Zhao P, Yang G D, Duan Y Y 2018 J. Controlled Release 276 113
Google Scholar
[10] Sciallero C, Grishenkov D, Kothapalli S V, Oddo L, Trucco A 2013 J. Acoust. Soc. Am. 134 3918
Google Scholar
[11] Gu Y Y, Chen C Y, Tu J, Guo X S, Wu H Y, Zhang D 2016 Ultrason. Sonochem. 29 309
Google Scholar
[12] Marlies O, Valeria G, Jeroen S, Benjamin D, Nico D J, Detlef L, Michel V 2010 Ultrasound Med. Biol. 36 2080
Google Scholar
[13] Mulvana H, Eckersley R J, Tang M X, Pankhurst Q, Stride E 2012 Ultrasound Med. Biol. 38 864
Google Scholar
[14] Behnia S, Mobadersani F, Yahyavi M, Rezavand A 2013 Nonlinear Dyn. 74 559
Google Scholar
[15] Hongray T, Ashok B, Balakrishnan J 2015 Pramana 84 517
Google Scholar
[16] Shi J, Yang D S, Shi S G, Hu B, Zhang H Y, Hu S Y 2016 Chin. Phys. B 25 024304
Google Scholar
[17] Church C C 1995 J. Acoust. Soc. Am. 97 1510
Google Scholar
[18] Beguin E, Bau L, Shrivastava S, Stride E 2019 ACS Appl. Mater. Interfaces 11 1829
Google Scholar
[19] Malvar S, Gontijo R G, Cunha F R 2018 J. Eng. Math. 108 143
Google Scholar
[20] 莫润阳, 吴临燕, 詹思楠, 张引红 2015 物理学报 64 124301
Google Scholar
Mo R Y, Wu L Y, Zhan S N, Zhang Y H 2015 Acta Phys. Sin. 64 124301
Google Scholar
[21] Zhang D, Guo G P, Lu L, Yin L L, Tu J, Guo X S, Xu D, Wu J R 2014 Phys. Med. Biol. 59 6729
Google Scholar
[22] Hosseini S M, Ghasemi E, Fazlali A, Henneke E 2012 J. Nanopart. Res. 14 858
Google Scholar
[23] 陈伟中 2014 声空化物理 (北京 科学出版社) 第415−417页
Chen W Z 2014 Acoustic Cavitation Physics (Beijing: Science Press) pp415−417 (in Chinese)
[24] Doinikov A, Dayton P A 2007 J. Acoust. Soc. Am. 121 3331
Google Scholar
[25] Sijl J, Dollet B, Overvelde M, Garbinet V, Rozendal T, De Jong N, Lohse De, Versluis M 2010 J. Acoust. Soc. Am. 128 3239
Google Scholar
[26] 杨芳, 李熠鑫, 陈忠平, 顾宁 2009 科学通报 54 1181
Yang F, Li Y X, Chen Z P, Gu N 2009 Chin. Sci. Bull. 54 1181
[27] 沈壮志, 林书玉 2011 物理学报 60 104302
Google Scholar
Shen Z Z, Lin S Y 2011 Acta Phys. Sin. 60 104302
Google Scholar
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