Simulation of acoustic response of microvessel containing microbubble in ultrasound field based on finite element analysis and lumped parameter model

doi:10.3969/j.issn.2095-4344.2016.42.015

Abstract

Abstract:

BACKGROUND: Exploration on nonlinear acoustic response of the contrast agent microbubble contained in microvessel under ultrasound excitation is of great significance to maximizing ultrasonic energy deposition, promoting the development of quantitative imaging algorithm, revealing the damage mechanism or evaluating the targeted therapy, and overcoming the limitations of the traditional methods that are mainly used in large-size vessels, and measuring microvessel elasticity.
OBJECTIVE: To build a microvessel containing an ultrasound microbubble, revealing the internal mechanism among ultrasound, microbubble, blood flow and microvessel.
METHODS: Based on the finite element analysis and the lumped parameter model, three-dimensional microvessel containing microbubble model was built and simulated on Comsol Multiphysics 4.4 platform.
RESULTS AND CONCLUSION: Microbubble exhibited slower radial motion compared with axial motion due to vascular wall limitation, but maximum displacement and stress were found near the microbubble center because of the oscillation coupling of the microbubble with the vascular wall. Under the same ultrasound pressure, the excitation frequency increased, accompanied by decreased and stabilized microvessl constriction and dilation; under the same frequency, with the enhancement of ultrasound pressure, the local microbubble oscillation lasted longer. With the increase of Young’s modulus of the microvessel wall, the frequency of microbubble oscillation was reduced, while the amplitude increased. All these findings indicate that the frequency of microbubble oscillation increased with the reduction of microvessel size, while its amplitude decreased. The frequency of microbubble oscillation increased with the enhancement of ultrasound excitation, while the amplitude decreased. On the contrary, ultrasound pressure affected the dynamic characteristics of microbubble and microvessel. In particular, it was the first to demonstrate that the elasticity of microvessel has approximate linear positive correlation with the amplitude of microbubble oscillation, which reveals the relationship between microvessel elasticity and microbubble response so as to provide theoretical basis for indirect measurement of microvessel elasticity.

中国组织工程研究杂志出版内容重点：组织构建；骨细胞；软骨细胞；细胞培养；成纤维细胞；血管内皮细胞；骨质疏松；组织工程

Key words: Microvessels, Contrast Media, Tissue Engineering

CLC Number:

R318

Niu Chuan-xiao, Guo Sheng-wen, Qiu Lin, Lao Yong-hua, Jiang Xing-jun. Simulation of acoustic response of microvessel containing microbubble in ultrasound field based on finite element analysis and lumped parameter model[J]. Chinese Journal of Tissue Engineering Research, 2016, 20(42): 6330-6336.

Figures/Tables 1

2.1 血管和微泡响应的形变、血压变化及血管应力分布模型仿真得图2血管和微泡响应过程中的形变，血压变化及血管应力分布结果。微泡在超声激励下振动，影响周围血液流动，从而引起血管壁发生规律的弹性形变，交替收缩和扩张，图中血管壁形变的最小、最大外径分别为5.62 μm、6.19 μm。可见，微泡径向运动因受近处血管壁面限制，移动速度较轴向小；而血管壁因与微泡振动耦合，近微泡的中心处位移和应力最大。 2.2 激励超声对血管振动的影响图3模拟不同声压(Pu=0.01，0.02，0.05 MPa)和频率(f=1，2，5 MHz)超声对微血管振动的影响。图3A显示相同声压，激励频率增加会减弱微血管的缩放，且更快趋于稳定；图3B显示相同频率，激励声压越大，血管运动越强烈，振动传播产生的局部效应更持久。 2.3 血管尺寸对微泡振动的影响图4显示当f=1 MHz，Pu=0.05 MPa时，不同长度(Lv=80，100，150 μm)、内径(R0=4，5，6μm)、厚度(dv = 0.5，1，1.5 μm)的微血管，对半径为3 μm的微泡振动的影响。可见，管长的增长加大了对微泡的限制作用，且足够的长度能缓解沿血管传播的振动对微泡产生的二次激励[29]，因此微泡振动频率增加且振幅减小，与文献[14]中的仿真结果和文献[9，11-12]中的实验结果相符。当血管半径增大到6 μm以上时，血管限制作用低于该组模型参数的合理范围，微泡振动剧烈，半径急剧减小至破裂[30]。此外，血管内径和厚度的增加，均会使微泡振动频率、振幅减小。当血管壁趋于无限厚时，二者的耦合机制减弱，相当于刚性壁面的限制作用。 2.4 血管属性对微泡振动的影响由图5可知，微泡振动幅度随微血管壁杨氏模量的增加而降低，近似线性反比关系；振动频率随血管壁杨氏模量的增加而增加，结果与Martynov等[14]的发现一致。当血管杨氏模量减小到3 MPa以下时，微血管弹性超出该组模型参数的合理范围，微泡急剧缩小至破裂[30]。"

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