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超声溶栓的核心机制源于空化气泡溃灭产生的瞬态冲击波与微射流对血栓结构的破坏作用. 尽管该效应已在实验与临床中被证实具备溶栓潜力, 但其疗效受限于空化作用能量传递效率低和损伤可控性差等问题, 其本质在于单气泡空蚀效应不足与多气泡协同作用规律不明确. 本研究通过构建气-液-固多物理场耦合模型来量化分析血栓附近空化气泡溃灭动力学特性, 流-固耦合部分引入结构阻尼项来表征血栓运动过程中的能量耗散; 在此基础上, 结合参数分析详细讨论了多气泡射流序列冲击作用下的协同效应, 其对应力累积的影响完全考虑了血栓的力学特性, 即结合实验确定的超-黏弹性血栓本构模型. 数值模拟表明射流冲击强度与血栓质量、超声振幅正相关, 与无量纲距离、超声频率、气泡初始半径负相关; 多气泡协同效应存在相对优化的半径分布范围, 通过射流序列匹配可使血栓内部正应力或剪应力获得显著增幅. 建议给出的协同空蚀效应预测方程为超声溶栓控制策略提供了理论依据.
Ultrasound thrombolysis primarily relies on transient shockwaves and microjets from collapsing cavitation bubbles to mechanically disrupt thrombus structures. Although it shows clinical potential, its efficacy is still limited by low cavitation energy transfer efficiency and unpredictable tissue damage, due to incomplete understanding of single bubble dynamics and the synergistic mechanisms of multi-bubble interactions. This study introduces a hyper-viscoelastic constitutive model incorporating blood clot mechanics to analyze stress accumulation under sequential microbubble impacts. A gas-liquid-solid coupling multi-physics model quantifies bubble collapse dynamics near thrombi, and integrates structural damping terms to represent energy dissipation during fluid-solid interactions. Parameter analysis shows that the intensity of jet impact is positively correlated with thrombus mass and ultrasound amplitude, but inversely related to dimensionless distance, ultrasound frequency, and initial bubble radius. The proposed rate-dependent Ogden-Prony model effectively captures thrombus behaviors under transient impacts, including strain hardening, rate-dependent strengthening, and stress relaxation. Sequential jet impacts induce cumulative stress through strain hardening, with multi-bubble synergy achieving significantly higher stresses than single-bubble impact. Optimal bubble radius distribution can amplify the normal/shear stress inside thrombi—maximum normal stress generated by the double bubble impact sequences is 6.02 MPa, exceeding the tensile strength of the thrombus, while the maximum stress generated by single bubble impact is 1.45 MPa. The key quantitative relationships between bubble cluster parameters, dimensionless distance, thrombus mass, and stress accumulation provide optimization guidelines for ultrasound thrombolysis. Notably, controlled multi-bubble jet impact sequences with attenuated pressure peaks demonstrate enhanced therapeutic potential through cumulative mechanical effects rather than a single high-intensity impact. -
Keywords:
- ultrasonic thrombolysis /
- cavitation effect /
- jet sequence /
- stress accumulation
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Google Scholar
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图 1 血栓附近超声空化模型示意图
Fig. 1. Schematic diagram of ultrasound cavitation model near thrombus.
图 2 气泡半径的数值解与实验数据的对比
Fig. 2. Comparison between numerical solution of bubble radius and experimental data.
图 3 超声作用下血栓附近空化气泡演化压力云图(黑色实线为气泡轮廓) (a) t = 17.9 μs; (b) t = 38.2 μs; (c) t = 39.3 μs; (d) t = 40.7 μs
Fig. 3. Evolution pressure cloud map of cavitation bubbles near thrombus under ultrasound (black solid line represents bubble contour): (a) t = 17.9 μs; (b) t = 38.2 μs; (c) t = 39.3 μs; (d) t = 40.7 μs.
图 4 (a)超声振幅对壁面冲击的影响; (b)超声频率对壁面冲击的影响
Fig. 4. (a) Influence of ultrasonic amplitude on wall impact; (b) influence of ultrasonic frequency on wall impact.
图 5 (a)血栓质量对壁面冲击的影响; (b)近壁距离对壁面冲击的影响; (c)气泡初始半径对壁面冲击的影响
Fig. 5. (a) Influence of thrombus quality on wall impact; (b) influence of close wall distance on wall impact; (c) influence of initial bubble radius on wall impact.
图 6 (a)准静态下应力-应变曲线对比, Ogden模型参数${\mu _1} = 5946.78{\text{ }}{\mathrm{Pa}}$, ${\alpha _1} = 11.05$; (b)不同加载速率下血栓应力-应变响应, Prony级数参数${g_i} = \left[ {0.2, 0.2, 0.1, 0.1, 0.1} \right]$, ${\tau _i} = \left[ {1 \times {{10}^{ - 6}}, 5 \times {{10}^{ - 5}}, 1 \times {{10}^{ - 3}}, 0.1, 10} \right]{\text{ }}{\mathrm{s}}$; (c)不同应变-加载速率下的应力时程曲线
Fig. 6. (a) Comparison of stress-strain curves under quasi-static conditions, Ogden model parameters:${\mu _1} = 5946.78{\text{ }}{\mathrm{Pa}}$, ${\alpha _1} = 11.05$; (b) stress strain response of thrombus under different loading rates, Prony series parameters: ${g_i} = $$ \left[ {0.2, 0.2, 0.1, 0.1, 0.1} \right]$, ${\tau _i} = [ 1 \times {{10}^{ - 6}}, 5 \times {{10}^{ - 5}}, 1 \times {{10}^{ - 3}}, $$ 0.1, 10 ]{\text{ }}{\mathrm{s}}$; (c) stress time history curves under different strain loading rates.
图 7 气泡初始半径对射流冲击到达时间及压力峰值的影响
Fig. 7. The influence of initial bubble radius on the arrival time and pressure peak of jet impact.
图 8 双气泡冲击载荷序列构建 (a) ΔR/Rc > 8.3%; (b) ΔR/Rc ≤ 8.3%
Fig. 8. Construction of double bubble impact load sequence: (a) ΔR/Rc > 8.3%; (b) ΔR/Rc ≤ 8.3%.
图 10 血栓内剪应力分布(AB为凹陷侧截线) (a) t = 4.6 μs; (b) t = 5.0 μs; (c) t = 20.0 μs;血栓内正应力分布(CD为轴线) (d) t = 4.6 μs; (e) t = 5.5 μs; (f) t = 20.0 μs
Fig. 10. The distribution of shear stress within the thrombus, where AB is the concave side intercept line: (a) t = 4.6 μs; (b) t = 5.0 μs; (c) t = 20.0 μs; normal stress distribution within the thrombus, with CD as the axis: (d) t = 4.6 μs; (e) t = 5.5 μs; (f) t = 20.0 μs.
图 11 (a)双气泡冲击下截线AB上剪应力时空演变; (b)双气泡冲击下轴线上距壁面0.2 mm位置处正应力应变响应
Fig. 11. (a) Temporal and spatial evolution of shear stress on section AB under double bubble impact; (b) normal stress-strain response at a distance of 0.2 mm from the wall on the axis under double bubble impact.
图 12 泡群初始半径分布范围对应力累积效应的影响
Fig. 12. Influence of initial radius distribution range of bubble group on stress accumulation effect.
图 13 最大冲击压力PDmax/PSmax与间距S/R之间的关系(PDmax为双气泡最大冲击压力, PSmax为单气泡最大冲击压力, S为两个气泡中心的间距, R为气泡半径)
Fig. 13. The relationship between the maximum impact pressure PDmax/PSmax and the interval S/R (PDmax is the maximum impact pressure of a double bubble, PSmax is the maximum impact pressure of a single bubble, S is the distance between the centers of two bubbles, and R is the bubble radius).
图 14 泡间耦合效应对血栓内应力累积效果的影响
Fig. 14. Influence of bubble coupling effect on stress accumulation effect in thrombus.
图 15 剪应力增幅η的三维云图
Fig. 15. Three dimensional cloud map of shear stress amplification η.
表 1 仿真中使用的参数值
Table 1. Parameter values used in simulation.
参数 参数值 参考压力 ${p_0}$/Pa 101325 血液密度 ${\rho _0}$/(kg·m–3) 1059 血液黏度 ${\mu _{\text{l}}}$/(Pa·s) 0.005 血液体积模量 ${K_0}$/GPa 2.5 血液密度指数 $n$ 7.15 血液表面张力系数 $\sigma $/(N·m–1) 0.072 损耗因子[38] $\tilde \eta $ 0.03 气体黏度${\mu _{\text{g}}}$/(Pa·s) $1.34 \times 1{0^{ - 5}}$ 
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表 2 泡群初始半径分布设计(以中心半径Rc = 60 μm 为基准)
Table 2. Design of initial radius distribution for bubble groups (based on the center radius Rc = 60 μm).
分布范围
(ΔR/Rc)/%半径区间/μm Rmax与Rmin
射流时序差/μs1.7 59—61 0.4 3.3 58—62 0.9 5.0 57—63 1.3 8.3 55—65 2.2 16.7 50—70 4.4 33.3 40—80 9.0
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[1] Millett E R C, Peters S A E, Woodward M 2018 Br. Med. J. 363 k4247
[2] GBD 2017 Causes of Death Collaborators (CORPORATE) 2018 Lancet 392 1736
Google Scholar
[3] Ren S T, Long L H, Wang M, Li Y P, Qin H, Zhang H, Jing B B, Li Y X, Zang W J, Wang B, Shen X L 2012 J. Thromb. Thrombolysis 33 74
Google Scholar
[4] Alexandrov A V, Köhrmann M, Soinne L, et al. 2019 Lancet Neurol. 18 338
Google Scholar
[5] 夏青青, 刘俐 2019 心血管病学进展 40 564
Xia Q Q, Liu L 2019 Adv. Cardiovasc. Dis. 40 564
[6] Papadopoulos N, Kyriacou P A, Damianou C 2017 J. Stroke Cerebrovasc. 26 2447
Google Scholar
[7] Bußmann A, Riahi F, Gökce B, Adami S, Barcikowski S, Adams N A 2023 Phys. Fluids 35 016115
Google Scholar
[8] Iga Y, Sasaki H 2023 Phys. Fluids 35 023312
Google Scholar
[9] Bokman G T, Biasiori P L, Lukić B, Bourquard C, Meyer D W, Rack A, Supponen O 2023 Phys. Fluids 35 013322
Google Scholar
[10] Li S, Zhang A M, Han R 2018 Phys. Fluids 30 121703
Google Scholar
[11] Reese H, Ohl S W, Ohl C D 2023 Phys. Fluids 35 076122
Google Scholar
[12] Ren Z B, Han H, Zeng H, Sun C, Tagawa Y, Zuo Z G, Liu S H 2023 J. Fluid Mech. 976 A11
Google Scholar
[13] Turangan C K, Ong G P, Klaseboer E, Khoo B C 2006 J. Appl. Phys. 100 054910
Google Scholar
[14] Brujan E A, Zhang A M, Liu Y L, Ogasawara T, Takahira H 2022 J. Fluid Mech. 948 A6
Google Scholar
[15] Andrews E D, Rivas D F, Peters I R 2023 J. Fluid Mech. 962 A11
Google Scholar
[16] Li S, Zhang A M, Han R, Liu Y Q 2017 Phys. Fluids 29 092102
Google Scholar
[17] 王德鑫, 那仁满都拉 2018 物理学报 67 037802
Google Scholar
Wang D X, Naranmandula 2018 Acta Phys. Sin. 67 037802
Google Scholar
[18] Zhang L L, Chen W Z, Wu Y R, Shen Y, Zhao G Y 2021 Chin. Phys. B 30 104301
Google Scholar
[19] Shen Y, Zhang L L, Wu Y R, Chen W Z 2021 Ultrason. Sonochem. 73 105535
Google Scholar
[20] Fong S W, Adhikari D, Klaseboer E, Khoo B C 2009 Exp. Fluids 46 705
Google Scholar
[21] Bremond N, Arora M, Ohl C D, Lohse D 2005 Phys. Fluids 17 091111
Google Scholar
[22] Lauterborn W, Hentschel W 1985 Ultrasonics 23 260
Google Scholar
[23] Zhang A M, Yao X L 2008 Chin. Phys. B 17 927
Google Scholar
[24] 徐珂, 许龙, 周光平 2021 物理学报 70 194301
Google Scholar
Xu K, Xu L, Zhou G P 2021 Acta Phys. Sin. 70 194301
Google Scholar
[25] Qin D, Lei S, Zhang B Y, Liu Y P, Tian J, Ji X J, Yang H 2024 Ultrason. Sonochem. 104 106808
Google Scholar
[26] 许龙, 汪尧 2023 物理学报 72 024303
Google Scholar
Xu L, Wang Y 2023 Acta Phys. Sin. 72 024303
Google Scholar
[27] Wang X, Chen W Z, Zhou M, Zhang Z K, Zhang L L 2022 Ultrason. Sonochem. 84 105952
Google Scholar
[28] 张凌新, 闻仲卿, 邵雪明 2013 力学学报 45 861
Zhang L X, Wen Z Q, Shao X M 2013 Chin. J. Theor. Appl. Mech. 45 861
[29] Terasaki S, Kiyama A, Kang D, Tomita Y, Sato K 2024 Phys. Fluids 36 012115
Google Scholar
[30] Hong S, Son G 2023 Ultrason. Sonochem. 92 106252
Google Scholar
[31] Sankin G N, Yuan F, Zhong P 2010 Phys. Rev. Lett. 105 078101
Google Scholar
[32] Lauer E, Hu X Y, Hickel S, Adams N A 2012 Phys. Fluids 24 052104
Google Scholar
[33] Chahine G L, Hsiao C T 2015 Interface Focus 5 20150016
Google Scholar
[34] Ochiai N, Ishimoto J 2017 J. Fluid Mech. 818 562
Google Scholar
[35] Ochiai N, Ishimoto J 2020 Ultrason. Sonochem. 61 104818
Google Scholar
[36] Hosseinkhah N, Hynynen K 2012 Phys. Med. Biol. 57 785
Google Scholar
[37] Ri J, Pang N, Bai S, Xu J L, Xu L S, Ri S, Yao Y D, Greenwald S E 2023 Phys. Fluids 35 011904
Google Scholar
[38] Chetty A, Kovacs J, Sulyok Z, Meszaros A, Fekete J, Domjan A, Szilagyi A, Vargha V 2013 Express Polym. Lett. 7 95
Google Scholar
[39] Ma X J, Huang B, Zhao X, Wang Y, Chang Q, Qiu S C, Fu X Y, Wang G Y 2018 Ultrason. Sonochem. 43 80
Google Scholar
[40] Cahalane R M E, de Vries J J, de Maat M P M, van Gaalen K, van Beusekom H M, van der Lugt A, Fereidoonnezhad B, Akyildiz A C, Gijsen F J H 2023 Ann. Biomed. Eng. 51 1759
Google Scholar
[41] Kim T H, Kim H Y 2014 J. Fluid Mech. 750 355
Google Scholar
[42] Vyas N, Dehghani H, Sammons R L, Wang Q X, Leppinen D M, Walmsley A D 2017 Ultrasonics 81 66
Google Scholar
[43] Liu Y, Zheng Y, Reddy A S, et al. 2021 J. Neurosurg. 134 893
Google Scholar
[44] Maksudov F, Daraei A, Sesha A, Marx K A, Guthold M, Barsegov V 2021 Acta Biomater. 136 327
Google Scholar
[45] Tomita Y, Shima A, Ohno T 1984 J. Appl. Phys. 56 125
Google Scholar
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