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搭载有磁性纳米颗粒的包膜微泡, 作为一种新型试剂在多模造影、溶栓治疗及靶向药物输运等多领域得以应用及研究. 常通过原位测量技术进行微泡研究, 而散射解析模型是声反演技术的基础. 由空气内核、均匀悬浮磁纳米颗粒的磁流体层及磷脂外层组成多膜层结构载磁微泡, 考虑磁流体密度变化及磷脂层黏弹性, 通过简正级数法求解多层结构微泡各区域的散射声场. 将载磁微泡散射模型与其他气泡进行对比, 并数值分析载磁微泡共振散射特性, 包括初始半径、磁纳米颗粒体积分数、磁流体层厚度及磷脂层特性参数等对微泡散射影响. 结果表明: 当膜层中磁纳米颗粒的体积分数α不超过0.1时, 颗粒对微泡共振散射的影响具有两面性, 既可增强也可减弱散射, 主要取决于微泡半径; 存在一个临界微泡半径值, 微泡半径超过此临界则颗粒将增强微泡散射, 反之减弱; 微泡半径一定, α不超过0.1时, α取值越高微泡散射越强; 膜层材料的拉梅常数和厚度越小的同尺度微泡散射更强. 该研究对载磁微泡结构优化设计、原位监测及诊疗应用有理论意义.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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图 3 MMBs的(a)共振曲线及(b)共振散射(σ vs. f )
Fig. 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
Fig. 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 6 R3 = 5 μm时, f0, σmax与α的关系 (a) f0 vs. α; (b) σmax vs. α
Fig. 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
Fig. 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
Fig. 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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