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Normal ultrasound contrast agents (UCAs) loaded with magnetic nanoparticles are called magnetic microbubbles (MMBs), which can be used in multimodal imaging, thrombolytic therapy, and targeted drug delivery. The MMBs are often studied by in situ measurement techniques, however scattering model is the basis of inversion techniques. Therefore, we develop a scattering model of multilayer structured MMBs with magnetic fluid inner layer and phospholipid outer layer, in which outer layer’s viscoelasticity and the effect of nanoparticles on inner layer’s density are considered, while scattered sound fields in each region are obtained by solving normal series. The MMB model is compared with other bubbles, and its acoustic scattering characteristics are analyzed numarically, including the effects of radius, magnetic nanoparticle volume fraction, inner layer thickness and outer layer characteristics parameters. The results show that when the volume fraction α of magnetic nanoparticles in the inner layer does not exceed 0.1, magnetic nanoparticles have a two-sided effect on resonant scattering of MMBs, depending mainly on its radius, and the bubble has a critical radius value. If the radius of MMBs exceeds this critical value, the particles will enhance scattering, on the contrary, if the radius of MMBs is smaller than this critical value, the particles will reduce scattering; for a given microbubble radius, when α is not more than 0.1, the larger the α value, the stronger the resonant scattering of MMBs will be; the smaller the thickness of the inner film layer and outer film layer or the Larmé constant, the stronger the scattering will be. This study provides a theoretical guidance for the optimal structural design of MMBs and its in situ monitoring and therapeutic applications.
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Keywords:
- multilayer membrane structure /
- magnetic microbubbles /
- normal series solution /
- scattering cross section
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Google Scholar
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Google Scholar
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Google Scholar
Chen J S, Zhu Z M 2005 Acta Acust. 30 5
Google Scholar
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[21] Dong X J, Su M X, Cai X S 2012 Particuology 1 1
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Zhao L X, Wang C H, Mo R Y 2021 Acta Phys. Sin. 70 014301
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Google Scholar
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图 1 MMBs物理模型
Figure 1. Physical model of MMBs.
图 2 球形单泡散射模型对比
Figure 2. Comparison of scattering models for spherical single bubbles.
图 3 MMBs的(a)共振曲线及(b)共振散射(σ vs. f )
Figure 3. (a) Resonance curves and (b) resonance scattering (σ vs. f ) of MMBs.
图 4 α = 0.1与α = 0两种微泡的共振散射截面 (a) σmax随R3变化的曲线; (b) Δ与R3的关系
Figure 4. Scattering cross sections of bubbles when α = 0.1 and α = 0: (a) The curves of σmax vs. R3; (b) the relationship of Δ and R3.
图 5 求解频率曲线的两种方法对比
Figure 5. Comparison of two methods for solving frequency curves.
图 6 R3 = 5 μm时, f0, σmax与α的关系 (a) f0 vs. α; (b) σmax vs. α
Figure 6. Relationships between f0, σmax and α with R3 = 5 μm, respectively: (a) f0 vs. α; (b) σmax vs. α.
图 7 R3 = 5 μm时, f0, σmax与d1的关系 (a) f0 vs. d1; (b) σmax vs. d1
Figure 7. Relationships between f0, σmax and d1 with R3 = 5 μm, respectively: (a) f0 vs. d1; (b) σmax vs. d1.
图 8 R3 = 5 μm时, f0, σmax与μv的关系 (a) f0 vs. μv; (b) σmax vs. μv
Figure 8. Relationship between f0, σmax and μv with R3 = 5 μm, respectively: (a) f0 vs. μv; (b) σmax vs. μv.
表 1 载磁微泡结构及各区域介质参数
Table 1. Structure of MMBs and the media parameters.
区域 名称 几何尺寸 材料参数 1 空气 0 < r < R1 ρ1, c1 2 磁流体层 R1 < r < R2,
层厚d1 ($\ll $R1)ρ2, c2 3 磷脂薄层 R2 < r < R3,
层厚d2 ($\ll $R1)ρ3, c3d, c3s,
λe, λv, µe, µv4 水 r > R3 ρ4, c4 
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[1] Dhiman C, Pankaj J, Kausik S 2005 Phys. Fluids 17 100603
Google Scholar
[2] Averkiou M A, Bruce M F, Powers J E, Sheeran P S, Burns P N 2019 Ultrasound Med. Biol. 46 3
Google Scholar
[3] Gramiak R, Shah P M 1968 Invest. Radiol. 3 5
Google Scholar
[4] Sirsi S, Borden M 2009 Bubble Sci. Eng. Technol. 1 1
Google Scholar
[5] Liu Y, Yang F, Yuan C X, Li M X, Wang T T, Chen B, Jin J, Zhao P, Tong J Y, Luo S H, Gu N 2017 ACS Nano 11 2
Google Scholar
[6] Yang F, Wang Q, Gu Z X, Fang K, Marriott G, Gu N 2013 ACS Appl. Mater. Interfaces 5 18
Google Scholar
[7] Wen H, Fang Y, Wu Y H, Wen S, Chen P, Zhang Y, Gu N 2012 Mater. Lett. 68 22
Google Scholar
[8] Mulvana H, Eckersley R J, Tang M X, Pankhurst Q, Stride E 2012 Ultrasound Med. Biol. 5 38
Google Scholar
[9] Yang F, Li Y X, Chen Z P, Zhang Y, Wu J R, Gu N 2009 Biomaterials 30 23
Google Scholar
[10] Park J I, Jagadeesan D, Williams R, Oakden W, Chung S, Stanisz G J, Kumacheva E 2010 Acs Nano 4 11
Google Scholar
[11] Owen J, Pankhurst Q A, Stride E 2012 Int. J. Hyperthermia 28 4
Google Scholar
[12] Beguin E, Gray M D, Logan K A, Nesbitt H, Sheng Y J, Kamila S, Barnsley L C, Bau L, McHale A P, Callan J F, Stride E 2020 J. Controlled. Release. 317 23
Google Scholar
[13] Victor M S, Carugo D, Barnsley L C, Owe J, Coussios C C, Stride E 2017 Phys. Med. Biol. 62 18
Google Scholar
[14] Sun Y, Zheng Y Y, Ran H T, et al. 2012 Biomaterials 33 24
Google Scholar
[15] Beguin E, Bau L, Shrivastava S, Stride E 2019 ACS Appl. Mater. Interfaces 11 2
Google Scholar
[16] Yang F, Gu Z X, Jin X, Wang H Y, Gu N 2013 Chin. Phys. B 22 104301
Google Scholar
[17] Xu G, Lu H M, Yang H Y, Li D, Liu R, Su M, Jin B, Li C C, Lü T, Du S D, Yang J Y, Qiu W B, Mao Y, Li F 2021 IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 68 12
Google Scholar
[18] Gu Y Y, Chen C Y, Tu J, Guo X S, Wu H Y, Zhang D 2016 Ultrason. Sonochem. 29 309
Google Scholar
[19] 陈九生, 朱哲民 2005 声学学报 30 5
Google Scholar
Chen J S, Zhu Z M 2005 Acta Acust. 30 5
Google Scholar
[20] Alexandra M P, Thomas C W 2021 J. Acoust. Soc. Am. 149 4
Google Scholar
[21] Dong X J, Su M X, Cai X S 2012 Particuology 1 1
Google Scholar
[22] Song X, Loskutova K, Chen H J, Shen G F, Grishenkov D 2021 J Acoust. Soc. Am. 150 3
Google Scholar
[23] 赵丽霞, 王成会, 莫润阳 2021 物理学报 70 014301
Google Scholar
Zhao L X, Wang C H, Mo R Y 2021 Acta Phys. Sin. 70 014301
Google Scholar
[24] Zhao L X, Shi H M, Bello I, Hu J, Wang C H, Mo R Y 2022 Chin. Phys. B 31 034302
Google Scholar
[25] 史慧敏, 莫润阳, 王成会 2022 物理学报 71 084302
Google Scholar
Shi H M, Mo R Y, Wang C H, 2022 Acta Phys. Sin. 71 084302
Google Scholar
[26] 史慧敏, 胡静, 王成会, 凤飞龙, 莫润阳 2021 物理学报 70 214303
Google Scholar
Shi H M, Hu J, Wang C H, Feng F L, Mo R Y 2021 Acta Phys. Sin. 70 214303
Google Scholar
[27] Chen J, Zhao L X, Wang C H, Mo R Y 2021 J. Magn. Magn. Mater. 538 168293
Google Scholar
[28] Hosseini S M, Ghasemi E, Fazlali A, Henneke D E 2012 J. Nanopart. Res. 14 858
Google Scholar
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