Vibration Dynamics for Cell Nuclei Under Ultrasonic Excitations
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(Contributed by LIU Shaobao, M.AMM Editorial Board)-
摘要: 超声波因其非侵入性、可精确定位、副作用小等优势在临床治疗中得到了广泛应用.近年来，利用超声波选择性激励癌细胞核振动治疗肿瘤的研究引起了学者们的关注.然而，细胞核动力学特性尤其受迫振动行为及共振机理仍不清楚.本研究建立了超声波激励下细胞核受迫振动力学模型，探究低强度超声波激励下典型具有不同细胞整体基质刚度的淋巴细胞(悬浮细胞)、胶质细胞、软骨细胞的振动响应特性.研究结果表明：超声波激励频率和强度越大，作用在细胞核上的声力也越大.超声波激励频率和强度一定时，作用在细胞核上的声力随细胞整体基质刚度减小而减小.超声波激励细胞可以引起细胞核共振，细胞整体基质刚度越大，细胞核共振频率越大.细胞核的相对振幅随细胞整体基质刚度增大而减小，淋巴细胞具有最大的共振幅度，胶质细胞次之，软骨细胞最小.该研究为超声波激励细胞核振动提供了理论分析框架，有利于推动发展基于超声波的肿瘤力学疗法.Abstract: The ultrasonic wave, owing to its non-invasiveness, precise targeting, and minimal side effects, has found extensive applications in clinical therapy. In recent years, tumor treatment utilizing ultrasonic exciting to induce vibration behaviors in cancer cell nuclei has drawn much attention. However, the dynamical characteristics and resonance mechanisms of cell nuclei, particularly under forced vibration, remain unclear. A model for cell nuclei was established to investigate the vibration responses under low-intensity ultrasonic excitations. Typical lymphocytes (suspended cells), glial cells, and chondrocytes with different substrate stiffnesses were taken as examples. The results indicate that, the higher the frequency and intensity of ultrasonic excitation are, the larger the acoustic force acting on the cell nucleus will be. Under certain frequency and intensity of ultrasonic excitation, the acoustic force acting on the cell nucleus will increase with the cell matrix stiffness. Ultrasonic excitation on cells can cause cell nuclear resonance, and the greater the cell matrix stiffness is, the higher the cell nuclear resonance frequency will be. The relative vibration amplitude of the cell nucleus decreases with the matrix stiffness, with lymphocytes having the largest resonance amplitudes, glial cells the next largest, and chondrocytes the smallest. This study provides a theoretical and analytical framework for ultrasound-excited cell nucleus vibration, and is conducive to promoting the development of ultrasound-based tumor mechanotherapy.
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Key words:
- cell nucleus /
- cytoskeleton /
- ultrasonic /
- excitation /
- resonance
edited-byedited-by1) (我刊编委刘少宝来稿) -
图 1 超声波激励细胞核振动力学模型
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 1. Mechanical modeling of vibrations of a cell nucleus excited by ultrasound
图 2 不同频率超声波激励下，细胞核所受声力的时程曲线
Figure 2. Time-history curves of acoustic forces on cell nucleus under ultrasonic excitations with different frequencies
图 3 超声波激励下，细胞核振动位移时程曲线
Figure 3. Time-history curves of vibrational displacements of cell nuclei under ultrasonic excitations
图 4 超声波激励下，细胞核振动速度时程曲线
Figure 4. Time-history curves of vibrational velocities of cell nuclei under ultrasonic excitations
图 5 超声波激励下，细胞核振动的幅频响应曲线
Figure 5. Amplitude-frequency vibration responses of cell nuclei under ultrasonic excitations
图 6 超声波声强对细胞核振动振幅的影响
Figure 6. Effects of ultrasonic sound intensities on the vibrational amplitudes of cell nuclei
表 1 细胞核振动力学模型参数
Table 1. Parameters of the vibrational mechanics model of the nucleus
parameter symbol value baseline nucleus density of glial cells ρn 1.4 g/cm3[7] 2.0 g/cm3 cytoplasmic density of glial cells ρ 1.0 g/cm3[20] 1.0 g/cm3 cytoplasmic shear modulus of glial cells G 100 Pa[21] 100 Pa spatial peak temporal average sound intensity I 10 000 W/cm2 acoustic velocity cU 1 500 m/s[18] 1 500 m/s glial cell nucleus radius R 4.0 μm[22] (microglial cell in a glial scar) 4.0 μm lymphocyte nucleus radius R 3~6 μm 4.0 μm shear modulus of cytoplasm of chondrocytes G 1~5 kPa[7] 1 000 Pa cytoplasmic density of lymphocytes ρ 1.0 g/cm3(assumed) cytoplasmic shear modulus of lymphocytes G 100 Pa(assumed) nucleus density of chondrocytes ρn 2.0 g/cm3(assumed) cytoplasmic density of chondrocytes ρ 1.05~1.10 g/cm3[7] 1.0 g/cm3 Poisson’s ratio of extracellular matrix υECM 0.3(assumed) Young’s modulus of extracellular matrix of glial cells EECM 0.2~1.2×102 Pa[7] 1.2×102 Pa(assumed) Young’s modulus of extracellular matrix of cartilage EECM 0.4~1.18×106 Pa[7] 4×105 Pa Young’s modulus of extracellular matrix of lymphocytes EECM 0 Pa(assumed) number of cytoskeletal filaments N 16 000[7] 16 000 Young’s modulus of cytoskeletal filament Ef 2 GPa (microtubules)[23]
2.6 GPa[23]
1.2 GPa (microtubules)[24]1 GPa length of cytoskeleton filaments l=Rcell-R Young’s modulus of nucleus En rigidity 1 kPa critical displacement of each glial cytoskeletal filament $u_{\mathrm{cr}}=\frac{\mathtt{π}^2 d^2}{4 l}$ 2.47×10-4 μm(calculated) glial cell unit radius Rcell 5.0 μm (microglial cell in a glial scar)[22] 5.0 μm chondrocyte cell unit radius Rcell ~4.0 μm[25] 5.0 μm lymphocyte cell unit radius Rcell 4.65~5.85 μm[26] 5 μm critical displacement of each lymphocyte skeletal filament $u_{\mathrm{cr}}=\frac{\mathtt{π}^2 d^2}{4 l}$ 2.47×10-4 μm(calculated) cross-section diameter of cytoskeletal filament d 25 nm[27] 10 nm Poisson’s ratio of nucleus υn 0.3~0.5[7] 0.3 nucleus radius of chondrocytes R ~2.5 μm[25] 4.0 μm critical displacement of each cytoskeletal filament of chondrocytes $u_{\mathrm{cr}}=\frac{\mathtt{π}^2 d^2}{4 l}$ 2.47×10-4 μm(calculated) shear modulus of extracellular matrix $G_{\mathrm{ECM}}=\frac{E_{\mathrm{ECM}}}{2\left(1+v_{\mathrm{ECM}}\right)}$ nucleus density of lymphocytes ρn 2.0 g/cm3[28] 2.0 g/cm3 
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[1] ANAND U, DEY A, CHANDEL A K S, et al. Cancer chemotherapy and beyond: current status, drug candidates, associated risks and progress in targeted therapeutics[J]. Genes Dis, 2023, 10(4): 1367-1401. [2] TIJORE A, MARGADANT F, YAO M X, et al. Ultrasound-mediated mechanical forces selectively kill tumor cells[J/OL]. 2020(2020-10-09)[2024-05-14]. DOI: https://doi.org/10.1101/2020.10.09.332726 .[3] MITTELSTEIN D, YE J, SCHIBBER E F, et al. Selective ablation of cancer cells with low intensity pulsed ultrasound[J]. Applied Physice Letters, 2020(2020-10-09)[2024-05-14], 116(1): 013701. [4] LIU S, LI Y, HONG Y, et al. Mechanotherapy in oncology: targeting nuclear mechanics and mechanotransduction[J]. Advanced Drug Delivery Reviews, 2023, 194: 114722. [5] HEYDEN S, ORTIZ M. Oncotripsy: targeting cancer cells selectively via resonant harmonic excitation[J]. Journal of the Mechanics and Physics of Solids, 2016, 92: 164-175. [6] SCHIBBER E F, MITTELSTEIN D R, GHARIB M, et al. A dynamical model of oncotripsy by mechanical cell fatigue: selective cancer cell ablation by low-intensity pulsed ultrasound[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2020, 476(2236): 20190692. [7] LIU S, YANG H, WANG M, et al. Torsional and translational vibrations of a eukaryotic nucleus, and the prospect of vibrational mechanotransduction and therapy[J]. Journal of the Mechanics and Physics of Solids, 2021, 155: 104572. [8] OESTREICHER H L. Field and impedance of an oscillating sphere in a viscoelastic medium with an application to biophysics[J]. Acoustical Society of America Journal, 1951, 23(6): 707. [9] FRIZZELL L A, CARSTENSEN E L. Shear properties of mammalian tissues at low megahertz frequencies[J]. The Journal of the Acoustical Society of America, 1976, 60(6): 1409-1411. [10] ILINSKII Y A, DOUGLAS MEEGAN G, ZABOLOTSKAYA E A, et al. Gas bubble and solid sphere motion in elastic media in response to acoustic radiation force[J]. Journal of the Acoustical Society of America, 2005, 117(4 Pt 1): 2338-2346. [11] SURESH S. Biomechanics and biophysics of cancer cells[J]. Acta Biomaterialia, 2007, 3(4): 413-438. [12] QI Bing, LIN Shujuan, GUO Yaohua, et al. Local resonance of mechanosensitive channels[J]. Journal of the Mechanics and Physics of Solids, 2025, 203: 106249. [13] LOVE A E H. The stress produced in a semi-infinite solid by pressure on part of the boundary[J]. Philosophical Transactions of the Royal Society of London (Series A): Containing Papers of a Mathematical or Physical Character, 1929, 228: 377-420. [14] JOHNSON K L. Contact Mechanics[M]. Cambridge: Cambridge University Press, 1987. [15] MAXEY M R, RILEY J J. Equation of motion for a small rigid sphere in a nonuniform flow[J]. Physics of Fluids, 1983, 26(4): 883-889. [16] WANG Q, RIAUD A, ZHOU J, et al. Acoustic radiation force on small spheres due to transient acoustic fields[J]. Physical Review Applied, 2021, 15(4): 044034. [17] OR M, KIMMEL E. Modeling linear vibration of cell nucleus in low intensity ultrasound field[J]. Ultrasound in Medicine & Biology, 2009, 35(6): 1015-1025. [18] LANDAU L D, LIFSHITZ E M. Fluid Mechanics[M]. Oxford: Pergamon, 1987. [19] 范惠康, 尤一龙, 尤凤翔. 弹簧振子非线性振动动力响应分析[J]. 民营科技, 2012(10): 52-54.FAN Huikang, YOU Yilong, YOU Fengxiang. Dynamic response analysis of nonlinear vibration of spring oscillator[J]. Private Science and Technolog, 2012(10): 52-54. (in Chinese) [20] 郝卓芳, 罗欣鸣, 黄世章, 等. 星形细胞瘤瘤细胞核的密度参数和形状参数的分析[J]. 广州医学院学报, 1993, 21(1): 22-25.HAO Zhuofang, LUO Xinming, HUANG Shizhang, et al. Analysis of density and shape parameters of tumor cell nuclei in astrocytoma[J]. Academic Journal of Guangzhou Medical College, 1993, 21(1): 22-25. (in Chinese) [21] LIM C T, DAO M, SURESH S, et al. Large deformation of living cells using laser traps[J]. Acta Materialia, 2004, 52(7): 1837-1845. [22] MOSHAYEDI P, NG G, KWOK J C F, et al. The relationship between glial cell mechanosensitivity and foreign body reactions in the central nervous system[J]. Biomaterials, 2014, 35(13): 3919-3925. [23] CAILLE N, THOUMINE O, TARDY Y, et al. Contribution of the nucleus to the mechanical properties of endothelial cells[J]. Journal of Biomechanics, 2002, 35(2): 177-187. [24] KARDAS D, NACKENHORST U, BALZANI D. Computational model for the cell-mechanical response of the osteocyte cytoskeleton based on self-stabilizing tensegrity structures[J]. Biomechanics and Modeling in Mechanobiology, 2013, 12(1): 167-183. [25] LEIPZIG N D, ATHANASIOU K A. Static compression of single chondrocytes catabolically modifies single-cell gene expression[J]. Biophysical Journal, 2008, 94(6): 2412-2422. [26] ROZMAN C, MIONTSERRAT E, FELIU E, et al. Lymphocyte size and survival of patients with chronic lymphocytic leukaemia (B-type)[J]. Scandinavian Journal of Haematology, 1980, 24(4): 315-320. [27] WADE R H. On and around microtubules: an overview[J]. Molecular Biotechnology, 2009, 43(2): 177-191. [28] BIRNIE G D. Subnuclear Components: Preparation and Fractionation[M]. London: Butterworths, 1976. -
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