MO Fan; ZHANG Xiaomin; ZHAO Zhipeng; WU Qiong; ZHENG Chaochao; ZHANG Linlin; ZHAO Libo; CHENG Ke; LIU Shudong; TANG Ge

doi:10.7498/aps.74.20250555

Abstract

Ultrasound thrombolysis stands out among various treatment methods due to its safety and high efficiency. Although the cavitation and mechanical mechanisms behind this technique have been well-established, the effect of the concentration-dependent strain hardening properties of thrombotic biomaterials on ultrasound-induced shockwave effects remains a subject of concern. Furthermore, the extremely short time window for effective clinical intervention requires precise spatial localization of rapidly formed shockwaves and determination of their energy thresholds for optimizing treatment protocols.Considering that the main mechanical properties of blood clots are dominated by the fibrin network, their stress-strain relationship is significantly dependent on fibrin concentration. Based on the results obtained from quasi-static compression tests performed on clots with different fibrin concentrations, a power-law constitutive equation capable of characterizing the progressive hardening characteristics of clots is proposed in this work. By incorporating the changes in wave speed caused by strain-hardening characteristics into a third-order nonlinear ultrasound propagation wave equation, the dynamic characteristics of shock wave formation during ultrasound propagation in clot media are studied via numerical simulations. The results show that the significant stress discontinuity prior to this process is due to a sudden displacement change caused by the progressive hardening of the clot. In order to accurately locate the starting position, the average steepening factor (ASF) based on threshold limitation is used for localization. However, this method is severely limited by the problem of mesh convergence, and the improvement in finite accuracy leads to an exponential increase in computation time. In contrast, the total harmonic distortion (THD) using the extremum of frequency-domain energy for localization is less sensitive to truncation errors and provides computational efficiency advantages. Parametric analysis indicates that a maximum localization error between the two methods is 2.55%, and the peak stress determined by the THD criterion is much higher than that determined by the ASF method.Based on experimental fitting of constitutive equations at different concentrations, numerical simulations of wave propagation show that according to the THD criterion, the increase in fibrin concentration from 10 mg/mL to 35 mg/mL delays the formation of shockwave by 91.7% and increases the peak stress by 60%. Corresponding fitting formulas are derived. Through real-time THD feedback and acoustic field parameter adjustment, a theoretical basis is provided for rapidly localizing and flexibly controlling shockwave effects in clinical ultrasound thrombolysis.

Keywords:

Authors and contacts

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

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12272065).

FullText HTML

References

[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]

Cited By

DownLoad: Full-Size Img PowerPoint

纤维蛋白浓度C_f/(mg·mL^–1)	最大相对标准差/%
10 15 25	16.6 26.2 2.66
35	5.76

DownLoad: CSV

参数	描述	数值
$ {\rho _0} $/(kg·m^–3)	凝块密度	1050
$ {U_0} $/m	振幅	1 × 10^–4
$ \alpha $	无量纲系数	6.1
$ \kappa $/(kPa·mg^–1·mL)	比例系数	1.2
$ \eta $	幂指数	1.8

DownLoad: CSV

频率f / kHz	硬化指数n	比值β/γ (γ = -1)	x_ASF / m (ASF = 100)	x_THD / m	误差/%
15	2	5	1.12×10^–3	1.10×10^–3	≤1.79
25	2	5	7.58×10^–4	7.62×10^–4	≤0.53
20	4.84	5	3.61×10^–4	3.57×10^–4	≤1.11
20	6.20	5	2.43×10^–4	2.38×10^–4	≤2.06
20	2	20	8.06×10^–4	7.97×10^–4	≤1.12
20	2	40	7.93×10^–4	7.78×10^–4	≤1.89
15	6.20	40	5.48×10^–4	5.34×10^–4	≤2.55

DownLoad: CSV

i	网格数	计算时长 (20核 AMD Epyc 7763 64-core processor × 256)	$ x_i^{{\mathrm{ASF}}} $/m (ASF = 100)	相对误差变化 $ \left( \left( {x_{i - 1}^{\mathrm{ASF}} - x_i^{\mathrm{ASF}}} \right) \left/ x_{i - 1}^{{\mathrm{ASF}}}\right. \right) \big/{\text{%}}$
1	6000	24 min	5.48×10^–4	—
2	17000	1 h 49 min	5.42×10^–4	1.09
3	24000	3 h 39 min	5.40×10^–4	0.37
4	37500	6 h 45 min	5.39×10^–4	0.19
5	52100	11 h 44 min	5.38×10^–4	0.19

DownLoad: CSV

i	基频倍数	$ x_i^{{\mathrm{THD}}} $	相对误差变化 $ \left( \left\| \left( x_{i - 1}^{{\mathrm{THD}}} - x_i^{{\mathrm{THD}}} \right)\left/ x_{i - 1}^{{\mathrm{THD}}}\right. \right\| \right) \big/{\text{%}}$
1	6	5.26×10^–4	—
2	12	5.30×10^–4	0.76
3	18	5.33×10^–4	0.57
4	24	5.35×10^–4	0.38
5	30	5.36×10^–4	0.19

DownLoad: CSV

map

[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]

[1]	JIA Yuhao, ZHANG Xiaomin, ZHAO Zhipeng, WU Qiong, ZHANG Linlin. Numerical analysis of synergistic cavitation effect of multiple bubbles in ultrasound thrombolysis. Acta Physica Sinica, 2025, 74(14): 144303. doi: 10.7498/aps.74.20250430
[2]	Wang Jin-Ling, Zhang Kun, Lin Ji, Li Hui-Jun. Generation and modulation of shock waves in two-dimensional polariton condensates. Acta Physica Sinica, 2024, 73(11): 119601. doi: 10.7498/aps.73.20240229
[3]	Yang Wei-Ming, Duan Xiao-Xi, Zhang Chen, Li Yu-Long, Liu Hao, Guan Zan-Yang, Zhang Huan, Sun Liang, Dong Yun-Song, Yang Dong, Wang Zhe-Bin, Yang Jia-Min. Optimization and application of shock wave measurement technology for shock-timing experiments on small-scale capsules. Acta Physica Sinica, 2024, 73(12): 125203. doi: 10.7498/aps.73.20232000
[4]	Wang Zhi-Huan, Jia Lei-Ming, He Zeng, Tian Zhou. Method of theoretically calculating spherical stress wave field in linear-hardening materials under impact load. Acta Physica Sinica, 2022, 71(1): 018301. doi: 10.7498/aps.71.20210954
[5]	Wang Xiao-Feng, Tao Gang, Xu Ning, Wang Peng, Li Zhao, Wen Peng. Molecular dynamics analysis of shock wave-induced nanobubble collapse in water. Acta Physica Sinica, 2021, 70(13): 134702. doi: 10.7498/aps.70.20210058
[6]	Ding Zhao-Nan, Yang Yi-Tao, Song Yin, Zhang Li-Qing, Gou Jie, Zhang Chong-Hong, Luo Guang-Nan. Hardening of reduced activation ferritic/martensitic steels under the irradiation of high-energy heavy-ion. Acta Physica Sinica, 2017, 66(11): 112501. doi: 10.7498/aps.66.112501
[7]	He Min-Qing, Dong Quan-Li, Sheng Zheng-Ming, Zhang Jie. Shock wave amplification by shock wave self-generated magnetic field driven by laser and the external magnetic field. Acta Physica Sinica, 2015, 64(10): 105202. doi: 10.7498/aps.64.105202
[8]	Wang Feng, Peng Xiao-Shi, Mei Lu-Sheng, Liu Shen-Ye, Jiang Xiao-Hua, Ding Yong-Kun. Shock timing experiment based on imaging velocity interferometer system for any reflector. Acta Physica Sinica, 2012, 61(13): 135201. doi: 10.7498/aps.61.135201
[9]	Yu Yin, Wang Wen-Qiang, Yang Jia, Zhang You-Jun, Jiang Dong-Dong, He Hong-Liang. Mesoscopic picture of fracture in porous brittle material under shock wave compression. Acta Physica Sinica, 2012, 61(4): 048103. doi: 10.7498/aps.61.048103
[10]	Wang Feng, Peng Xiao-Shi, Liu Shen-Ye, Jiang Xiao-Hua, Xu Tao, Ding Yong-Kun, Zhang Bao-Han. Shock experiment with sandwiched target in laser indirect-drive experiment. Acta Physica Sinica, 2011, 60(11): 115203. doi: 10.7498/aps.60.115203
[11]	Wang Feng, Peng Xiao-Shi, Liu Shen-Ye, Jiang Xiao-Hua, Ding Yong-Kun. Shock timing experiment in polystyrene target based on imaging velocity interferometer system for any reflector. Acta Physica Sinica, 2011, 60(8): 085203. doi: 10.7498/aps.60.085203
[12]	Chen Kai-Guo, Zhu Wen-Jun, Ma Wen, Deng Xiao-Liang, He Hong-Liang, Jing Fu-Qian. Propagation of shockwave in nanocrystalline copper: Molecular dynamics simulation. Acta Physica Sinica, 2010, 59(2): 1225-1232. doi: 10.7498/aps.59.1225
[13]	He Min-Qing, Dong Quan-Li, Sheng Zheng-Ming, Weng Su-Ming, Chen Min, Wu Hui-Chun, Zhang Jie. Ion acceleration by shock wave induced by laser plasma interaction. Acta Physica Sinica, 2009, 58(1): 363-372. doi: 10.7498/aps.58.363
[14]	Yu Yu-Ying, Tan Hua, Hu Jian-Bo, Dai Cheng-Da, Chen Da-Nian, Wang Huan-Ran. Effective shear modulus in shock-compressed aluminum. Acta Physica Sinica, 2008, 57(4): 2352-2357. doi: 10.7498/aps.57.2352
[15]	Jiang Dong-Dong, Du Jin-Mei, Gu Yan, Feng Yu-Jun. Resistivity of PZT 95/5 ferroelectric ceramic under shock wave compression. Acta Physica Sinica, 2008, 57(1): 566-570. doi: 10.7498/aps.57.566
[16]	Zhang Yi, Zheng Zhi-Yuan, Li Yu-Tong, Liu Feng, Li Han-Ming, Lu Xin, Zhang Jie. Collision process of two shockwaves. Acta Physica Sinica, 2007, 56(10): 5931-5936. doi: 10.7498/aps.56.5931
[17]	Bian Bao-Min, Yang Ling, Zhang Ping, Ji Yun-Jing, Li Zhen-Hua, Ni Xiao-Wu. General self-simulating motion mode of spherical strong shock waves in ideal gas. Acta Physica Sinica, 2006, 55(8): 4181-4187. doi: 10.7498/aps.55.4181
[18]	Gu Yong-Yu, Zhang Yong-Kang, Zhang Xing-Quan, Shi Jian-Guo. Theoretical study on the influence of the overlay on the pressure of laser shock wave in photomechanics. Acta Physica Sinica, 2006, 55(11): 5885-5891. doi: 10.7498/aps.55.5885
[19]	Cui Xin-Lin, Zhu Wen-Jun, Deng Xiao-Liang, Li Ying-Jun, He Hong-Liang. Molecular dynamic simulation of shock-induced phase transformation in single crystal iron with nano-void inclusion. Acta Physica Sinica, 2006, 55(10): 5545-5550. doi: 10.7498/aps.55.5545
[20]	GU YUAN, NI YUAN-LONG, WANG YONG-GANG, MAO CHU-SHENG, WU FENG-CHUN, WU JIANG, ZHU JIAN, WAN BING-GEN. EXPERIMENTAL OBSERVATION OF LASER DRIVEN HIGH PRESSURE SHOCK WAVES. Acta Physica Sinica, 1988, 37(10): 1690-1693. doi: 10.7498/aps.37.1690

Catalog

Vol. 74, Issue 15 - 2025-08-05

Metrics

Abstract views: 1364
PDF Downloads: 29
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

Abstract

Authors and contacts

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

FullText HTML

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

Abstract

Authors and contacts

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

FullText HTML

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About