Numerical analysis of synergistic cavitation effect of multiple bubbles in ultrasound thrombolysis

JIA Yuhao; ZHANG Xiaomin; ZHAO Zhipeng; WU Qiong; ZHANG Linlin

doi:10.7498/aps.74.20250430

Abstract

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:

Authors and contacts

School of Aeronautics and Astronautics, Chongqing University, Chongqing 400044, China

Corresponding author: ZHANG Xiaomin, xiaomin@cqu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12272065) and the Graduate Research Innovation Project in Chongqing, China (Grant No. CYB22026).

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References

[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
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[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
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[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
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[30]	Hong S, Son G 2023 Ultrason. Sonochem. 92 106252 Google Scholar
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[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
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[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
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[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
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[43]	Liu Y, Zheng Y, Reddy A S, et al. 2021 J. Neurosurg. 134 893 Google Scholar
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Cited By

图 1 血栓附近超声空化模型示意图

Figure 1. Schematic diagram of ultrasound cavitation model near thrombus.

DownLoad: Full-Size Img PowerPoint

图 2 气泡半径的数值解与实验数据的对比

Figure 2. Comparison between numerical solution of bubble radius and experimental data.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

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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

Figure 4. (a) Influence of ultrasonic amplitude on wall impact; (b) influence of ultrasonic frequency on wall impact.

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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

Figure 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.

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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

Figure 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.

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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

Figure 7. The influence of initial bubble radius on the arrival time and pressure peak of jet impact.

DownLoad: Full-Size Img PowerPoint

图 8 双气泡冲击载荷序列构建　(a) ΔR/R_c > 8.3%; (b) ΔR/R_c ≤ 8.3%

Figure 8. Construction of double bubble impact load sequence: (a) ΔR/R_c > 8.3%; (b) ΔR/R_c ≤ 8.3%.

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图 9 射流冲击血栓模型示意图

Figure 9. Schematic diagram of jet impingement thrombus model.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

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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

Figure 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.

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图 12 泡群初始半径分布范围对应力累积效应的影响

Figure 12. Influence of initial radius distribution range of bubble group on stress accumulation effect.

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图 13 最大冲击压力P_Dmax/P_Smax与间距S/R之间的关系(P_Dmax为双气泡最大冲击压力, P_Smax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)

Figure 13. The relationship between the maximum impact pressure P_Dmax/P_Smax and the interval S/R (P_Dmax is the maximum impact pressure of a double bubble, P_Smax 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).

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图 14 泡间耦合效应对血栓内应力累积效果的影响

Figure 14. Influence of bubble coupling effect on stress accumulation effect in thrombus.

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图 15 剪应力增幅η的三维云图

Figure 15. Three dimensional cloud map of shear stress amplification η.

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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)	$1.34 \times 1{0^{ - 5}}$

DownLoad: CSV

表 2 泡群初始半径分布设计(以中心半径R_c = 60 μm 为基准)

Table 2. Design of initial radius distribution for bubble groups (based on the center radius R_c = 60 μm).

分布范围 (ΔR/R_c)/%	半径区间/μm	R_max与R_min 射流时序差/μs
1.7	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

DownLoad: CSV

[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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