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基于声波在细胞操控中的应用, 建立了一个三层内置偏心液滴的弹性球壳模型模拟具有细胞核、细胞质和细胞膜的有核细胞, 并分析细胞在声场中受到的声辐射力. 从薄球壳理论出发, 结合球函数加法定理推导了平面波声场中内置偏心液滴的充液球壳所受声辐射力的函数表达式. 数值分析了偏心液滴偏心距、半径以及液体腔内外介质特性阻抗对于充液球壳所受声辐射力的影响. 结果表明, 充液球壳受到的声辐射力对偏心液滴的位置及大小非常敏感, 偏心液滴偏心程度越大, 充液球壳所受的声辐射力越大. 声辐射力随着偏心液滴半径的变化在无量纲粒子半径ka < 3范围内出现共振峰值点增多的现象, 在ka > 3范围内曲线腹点位置发生偏移. 当液体腔内液滴位置及半径同时变化时, 位置变化对充液球壳所受声辐射力的影响更加显著, 且二者产生的影响会相互叠加. 对照细胞核相对特性阻抗分别为0.8, 0.9, 1, 1.1和1.2 时的辐射力函数随ka变化曲线发现特性阻抗的变化主要影响辐射力的大小且随着细胞核阻抗的增大, 在ka = 5附近的起伏幅度逐步增加, 且腹点位置有右移的趋势. 因此, 细胞核阻抗的增大在一定的频率或者细胞尺寸范围内可增强其辐射力响应. 本文的研究结果对有核细胞的操作、分选及靶向治疗具有潜在的价值.Based on the application of acoustic waves in cell manipulation, a model consisting of an elastic spherical shell and eccentric droplet is established to simulate a eukaryotic cell and analyze the acoustic radiation force (ARF) on the cell. In this work, we derive an exact expression for the ARF on the liquid-filled spherical shell. The influence of eccentric distance, radius of the eccentric droplet and impedance of the medium inside the liquid-filled spherical shell on the ARF are analyzed numerically. The results show that the ARF is very sensitive to the position and size of the eccentric droplet. As the eccentricity of the eccentric droplet increases, the ARF becomes greater. In a low frequency region (ka<3) the resonance peak point increases, and the position of the curve ventral point shifts to the high frequency region (ka>3) with the increase of the radius of the eccentric droplet. The effect of the position variation on the ARF is more significant than that of the radius change, and both of their effects will be superimposed on each other. The ARF, as a function of ka, is mainly affected by the variation of the nucleus characteristic impedance. The ARF amplitude around ka = 5 increases and the position of the ventral point tends to shift rightwards with the enlargement of the nucleus impedance. Therefore, the radiation response at a certain frequency or in a cell size range can be enhanced when the nucleus impedance increases. The results of this study provide theoretical basis for the cell sorting and targeted therapy.
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Zang Y C, Lin W J, Su C, Wu P F, Chang Q 2022 Acta Acustica 47 379
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Xiao N, Gao Y T, Xiao S B, Chen C W 2021 J. Clin. Exp. Psychopathol. 37 1496
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图 2 弹性壳厚度对球体所受声辐射力的影响
Fig. 2. Influence of elastic shell thickness on ARF of the sphere.
图 3 不同流体介质中球体所受声辐射力 (a) 甘油; (b) 水银
Fig. 3. ARF on the sphere in different fluid medium: (a) Glycerol; (b) mercury.
图 4 细胞核不同偏心距细胞所受声辐射力(d/a = 0, 0.05, 0.10, 0.20)
Fig. 4. ARF on the cell with different nucleus eccentric distances (d/a = 0, 0.05, 0.10, 0.20).
图 5 不同大小细胞核细胞所受声辐射力(b/a = 0.5, 0.6, 0.7)
Fig. 5. ARF on the cell with different nucleus size (b/a = 0.5, 0.6, 0.7).
图 6 细胞核不同大小和偏心距下细胞所受声辐射力函数曲线 (d/a = 0实线, d/a = 0.1虚线)
Fig. 6. ARF on the cell with different nuclear size and eccentricity distances (d/a = 0 is shown by the solid line, d/a = 0.1 is shown by the dotted line).
图 7 不同阻抗下细胞所受声辐射力 (a) 细胞核; (b) 细胞质
Fig. 7. ARF on the cell with different impedance: (a) Nucleus; (b) cytoplasm.
表 B1 液体介质参数值
Table B1. Some parameter of liquid medium.
细胞质 细胞核 水 水银 甘油 声速/(m·s–1) 1508.0 1508. 5 1500.0 1407.0 1923.0 密度/(kg·m–3) 1000 1430 1000 13600 1260 阻抗/MRayl 1.51 2.16 1.50 19.1 2.42 
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表 B2 弹性球壳参数值
Table B2. Some parameters of elastic shell.
球壳材料 密度ρ/(kg·m–3) 杨氏模量E/GPa 泊松比ν 聚糖 600 0.2 0. 4 不锈钢 7900 200.0 0. 264
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[1] Alan B, Utangaç M, Göya C, Dağgülli M 2016 Med. Sci. Monit 22 4523
Google Scholar
[2] Carugo D, Ankrett D N, Glynne-Jones P, Capretto L, Boltryk R J, Zhang X L, Townsend P A, Hill M 2011 Biomicrofluidics 5 044108
Google Scholar
[3] Rapoport N, Kennedy A M, Shea J E, Scaife C L, Nam K H 2009 Mol. Pharmaceutics 7 22
[4] Meng L, Cai F Y, Li F, Zhou W, Niu L L, Zheng H R 2019 J. Phys. D Appl. Phys. 52 1
[5] Wu J R, Pepe J, Rincón M 2006 Ultrasonics 44 e21
Google Scholar
[6] Wang W B, Chen Y S, Farooq U, Xuan W P, Jin H, Dong S R, Luo J K 2017 Appl. Phys. Lett. 110 143504
Google Scholar
[7] Mishra P, Hill M, Glynne-Jones P 2014 Biomicrofluidics 8 034109
Google Scholar
[8] Silva G T, Tian L F, Franklin A, Wang X J, Han X J, Mann S, Drinkwater B W 2019 Phy. Rev. E 99 063002
Google Scholar
[9] Zhang R Q, Guo H L, Deng W Y, Huang X Q, Li F, Lu J Y, Liu Z Y 2020 Appl. Phys. Lett. 116 123503
Google Scholar
[10] Settnes M, Bruus H 2012 Phys. Rev. E 85 016327
Google Scholar
[11] Barmatz M, Collas P 1985 J. Acoust. Soc. Am. 77 928
Google Scholar
[12] Silva G T 2014 J. Acoust. Soc. Am. 136 2405
Google Scholar
[13] Léon F, Lecroq F, Décultot D, Mazé G 1992 J. Acoust. Soc. Am. 91 1388
Google Scholar
[14] Sharma G S, Marsick A, Maxit L, Skvortsov A, MacGillivray I, Kessissoglou N 2021 J. Acoust. Soc. Am. 150 4308
Google Scholar
[15] King L V 1934 Proc. Roy. Soc. A 137 212
[16] Rajabi M, Mojahed A 2016 J. Sound Vib. 383 265
Google Scholar
[17] Flax L, Dragonette L R, Überall H 1978 J. Acoust. Soc. Am. 63 723
Google Scholar
[18] Sapozhnikov O A, Bailey M R 2013 J. Acoust. Soc. Am. 133 661
Google Scholar
[19] Baasch T, Dual J 2020 Phys. Rev. Appl. 14 024052
Google Scholar
[20] Hasegawa T, Hino Y, Annou A, Noda H, Kato M, Naoki Inoue 1992 J. Acoust. Soc. Am. 93 154
[21] Junger M C 1952 J. Acoust. Soc. Am. 24 366
Google Scholar
[22] Mitri F G 2005 Ultrasonics 43 681
Google Scholar
[23] Wang H B, Liu X Z, Gao S, Cui J, Liu J H, He A J, Zhang G T 2018 Chin. Phys. B 27 034302
Google Scholar
[24] Wang Y Y, Yao J, Wu X W, Wu D J, Liu X J 2017 J. Appl. Phys. 122 094902
Google Scholar
[25] Thompson W 1973 J. Acoust. Soc. Am. 54 1694
Google Scholar
[26] Roumeliotis J A, Kanellopoulos J D, Fikioris J G 1991 J. Acoust. Soc. Am. 90 1144
Google Scholar
[27] Hasheminejad S M, Azarpeyvand M 2004 Mech. Res. Commun. 31 493
Google Scholar
[28] 臧雨宸, 林伟军, 苏畅, 吴鹏飞, 常钦 2022 声学学报 47 379
Zang Y C, Lin W J, Su C, Wu P F, Chang Q 2022 Acta Acustica 47 379
[29] Ivanov Y A 1970 NASA Tech. Transl. F-597
[30] Mo R Y, Hu J, Chen S, Wang C H 2020 Chin. Phys. B 29 094301
Google Scholar
[31] Hunt J W, Worthington A E, Xuan A, Kolios M C, Czarnota G J, Sherar M D 2002 Ultrasound in Medicine and Biology 28 217
Google Scholar
[32] 肖娜, 高雨彤, 肖述兵, 陈从文 2021 临床与实验病理学杂志 37 1496
Xiao N, Gao Y T, Xiao S B, Chen C W 2021 J. Clin. Exp. Psychopathol. 37 1496
[33] Jo M C, Guldiken R 2012 Sens. Actuators, A 187 22
Google Scholar
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