基于有限元分析和集中参数模型微血管与超声微泡声学响应的模拟
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摘要
背景:研究特定超声激励下微血管与内部单个微泡间的非线性声学响应,对于最大化超声能量的沉积,促进定量成像算法的发展,揭示损害机制或评价靶向治疗的效果,克服传统方法主要适用于大尺寸血管的局限性、测量微血管弹性意义重大。目的:构建微血管中超声微泡模型,揭示超声、微泡与血管、血流间的内在机制。方法:基于有限元分析和集中参数模型,在Comsol Multiphysics 3.5a平台上进行微血管中超声微泡三维模型构建和模拟仿真。结果与结论:(1)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)相同声压下,激励频率增加会减弱微血管的缩放且更快趋于稳定;在相同频率下,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;(3)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;振动频率则随血管壁杨氏模量的增加而增加;(4)结果表明,微血管尺寸越小,对微泡振动频率和幅值的限制越强烈,超声激励频率的增大会使微泡振动频率增大、幅值减小;声压对微泡和血管振动的影响则相反。此外,研究首次发现,血管壁弹性与微泡振动幅度呈近似线性正相关,说明利用微泡测定血管壁弹性是可能的。
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.
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.
引文
[1]Miller DL,Williams AR,Morris JE,et al.Sonoporation of erythrocytes by lithotripter shockwaves in vitro.Ultrasonics.1998;36(9):947-952.
[2]Hynynen K,McD annold N,Vykhodtseva N,et al.Noninvasive MR imaging-guided focal opening of the blood-brain barrier in rabbits.Radiology.2001;220(3):640-646.
[3]Meairs S,Alonso A.Ultrasound,microbubbles and the blood-brain barrier.Prog.Biophys Mol Biol.2007;93:354-362.
[4]Martynov S,Stride E,Saffari N.The natural frequencies of microbubble oscillation in elastic vessels.The Journal of the Acoustical Society of America,2009;126(6):2963.
[5]Stride E,Pancholi K,Edirisinghe MJ,et al.Increasing the nonlinear character of microbubble oscillations at low acoustic pressures.J R Soc Interface.2008;24:807-811.
[6]郭维,刘光达,焦阳,等.基于脉搏波信号和血管弹性腔模型的动脉血压连续测量方法[J].生物医用力学,2012,27(1):85.
[7]Morgan KE,Allen JS,Dayton PA,et al.Experimental and theoretical evaluation of microbubble behavior:Effect of transmitted phase and bubble size.IEEE Trans Ultrason Ferroelectr Freq Control.2000;47(6):1494-1509.
[8]Allen JS,May DJ,Ferrara KW.Dynamics of therapeutic ultrasound contrast agents.Ultrasound Med Biol.2002;28(6):805-816.
[9]Sassaroli E,Hynynen K.Resonance frequency of microbubbles in small blood vessels:a numerical study.Phys Med Biol.2005;50(22):5293-5305.
[10]Plesset MS,Prosperetti A.Bubble dynamics and cavitation.Ann Rev Fluid Mech.1977;9:145-185.
[11]Caskey CF,Kruse DE,Dayton PA,et al.Microbubble oscillation in tubes with diameters of 12,25,and 195microns.Appl Phys Lett.2006;88(3):033902.
[12]Caskey CF,Kruse DE,Dayton P,et al.On the oscillations of microbubbles in tubes with diameters as small as 12microns[C]//Ultrasonics Symposium,2005 IEEE.IEEE,2005;2:854-857.
[13]Qin S,Ferrara KW.The natural frequency of nonlinear oscillation of ultrasound contrast agents in microvessels.Ultrasound Med Biol.2007;33:1140-1148.
[14]Martynov S,Stride E,Saffari N.The natural frequencies of microbubble oscillation in elastic vessels.J Acoust Soc Am.2009;126:2963-2972.
[15]Doinikov AA,Aired L,Bouakaz A.Modeling and experiments on the far-field scattering.J Fr Ophtalmol.2010;36(15):1133-1136.
[16]Doinikov AA,Novell A,Bouakaz A.Dynamics of a Contrast Microbubble Between Two Elastic Walls.2012IEEE International Ultrasonics Symposium.2012;31:654-662.
[17]Wiedemair W,Tukovi??,Jasak H,et al.On ultrasound-induced microbubble oscillation in a capillary blood vessel and its implications for the blood-brain barrier.Phys Med Biol.2012;57(4):1020-1024.
[18]Hosseinkhah N,Hynynen K.A three-dimensional model of an ultrasound contrast agent gas bubble and its mechanical.Phys Med Biol.2012;57(3):785-808.
[19]de Jong N,Cornet R,Lancee CT.Higher harmonics of vibrating gas-filled microspheres:part 1.Simulation.Ultrasonics.1994;32(6):447-453.
[20]de Jong N,Cornet R,Lancee CT.Higher harmonics of vibrating gas-filled microspheres:part 2:Measurements.Ultrasonics.1994;32(6):455-459.
[21]Paul S,Katiyar A,Sarkar K,et al.Material characterization of the encapsulation of an ultrasound contrast microbubble and its subharmonic response:strain-softening interfacial model.J Acoust Soc Am.2010;127(6):3846-3850.
[22]Li Q,Matula TJ,Tu J,et al.Modeling complicated rheological behaviors in encapsulating shells of lipid-coated microbubbles accounting for nonlinear changes of both shell viscosity and elasticity.Phys Med Biol.2013;58(4):985-998.
[23]程茜,钱梦騄.超声微泡造影剂的低频动力学行为[J].声学技术,2006,25(4):292-298.
[24]邱晓晖,沈圆圆,钱建庭,等.刚性微管内微泡动力学行为的有限元数值分析[J].生物医学工程学杂志,2011,28(5):911-915.
[25]Shen YY,Wang TF,Diao X,et al.Numerical analysis of interaction between microbubble and elastic microvessel in low frequency ultrasound field using fluid solid interaction method[C].Biomedical and Health Informatics(BHI),2012 IEEE-EMBS International Conference on IEEE,2012:733-736.
[26]VanB avel E.Effects of shear stress on endothelial cells:possible relevance for ultrasound applications.Prog Biophys Mol Biol.2007;93:374-383.
[27]Mukundakrishnan K,Ayyaswamy PS,Eckmann DM.Bubble motion in a blood vessel:shear stress induced endothelial cell injury.Biomech Eng.2009;131:074516.
[28]Qin S,Ferrara KW.Acoustic response of compliable microvessels containing ultrasound contrast agents.Phys Med Biol.2006;51(20):5065.
[29]Sergey M,Erik K,Nader S,et al.Forced vibration of a bubble in a liquid-filled elastic vessel.J Acoust Soc Am.2012;130(5):2700-2708.
[30]Shen YY,Wang TF,Chin CT,et al.Interaction between microbubble and elastic microvessel in low frequency ultrasound field using finite element method.Chin Sci Bull.2013;58(3):291-298.
[31]Oishi Y,Kakimoto T,Yuan W,et al.Fetal Gene Therapy for Ornithine Transcarbamylase Deficiency by Intrahepatic Plasmid DNA-Micro-Bubble Injection Combined with Hepatic Ultrasound Insonation.Ultrasound Med Biol.2016;42(6):1357-1361.
[32]Wang G,Zhang Q,Zhuo Z,et al.Enhanced Homing of CXCR-4 Modified Bone Marrow-Derived Mesenchymal Stem Cells to Acute Kidney Injury Tissues by MicroBubble-Mediated Ultrasound Exposure.Ultrasound Med Biol.2016;42(2):539-548.
[33]Sajjadi B,Raman AA,Ibrahim S.Influence of ultrasound power on acoustic streaming and micro-bubbles formations in a low frequency sono-reactor:mathematical and 3D computational simulation.Ultrason Sonochem.2015;24:193-203.
[34]Chiu AH,Haluszkiewicz E,Mc Auliffe W.Micro-bubble transcranial Doppler ultrasound for exclusion of right-to-left circulatory shunts:why should we provide the service?J Med Imaging Radiat Oncol.2014;58(4):464-468.
[35]Tong J,Ding J,Shen X,et al.Mesenchymal stem cell transplantation enhancement in myocardial infarction rat model under ultrasound combined with nitric oxide microbubbles.PLo S One.2013;8(11):e80186.
[36]Ren ST,Shen S,He XY,et al.The Effect of Docetaxel-Loaded Micro-Bubbles Combined with Low-Frequency Ultrasound in H22 Hepatocellular Carcinoma-Bearing Mice.Ultrasound Med Biol.2016;42(2):549-560.
[2]Hynynen K,McD annold N,Vykhodtseva N,et al.Noninvasive MR imaging-guided focal opening of the blood-brain barrier in rabbits.Radiology.2001;220(3):640-646.
[3]Meairs S,Alonso A.Ultrasound,microbubbles and the blood-brain barrier.Prog.Biophys Mol Biol.2007;93:354-362.
[4]Martynov S,Stride E,Saffari N.The natural frequencies of microbubble oscillation in elastic vessels.The Journal of the Acoustical Society of America,2009;126(6):2963.
[5]Stride E,Pancholi K,Edirisinghe MJ,et al.Increasing the nonlinear character of microbubble oscillations at low acoustic pressures.J R Soc Interface.2008;24:807-811.
[6]郭维,刘光达,焦阳,等.基于脉搏波信号和血管弹性腔模型的动脉血压连续测量方法[J].生物医用力学,2012,27(1):85.
[7]Morgan KE,Allen JS,Dayton PA,et al.Experimental and theoretical evaluation of microbubble behavior:Effect of transmitted phase and bubble size.IEEE Trans Ultrason Ferroelectr Freq Control.2000;47(6):1494-1509.
[8]Allen JS,May DJ,Ferrara KW.Dynamics of therapeutic ultrasound contrast agents.Ultrasound Med Biol.2002;28(6):805-816.
[9]Sassaroli E,Hynynen K.Resonance frequency of microbubbles in small blood vessels:a numerical study.Phys Med Biol.2005;50(22):5293-5305.
[10]Plesset MS,Prosperetti A.Bubble dynamics and cavitation.Ann Rev Fluid Mech.1977;9:145-185.
[11]Caskey CF,Kruse DE,Dayton PA,et al.Microbubble oscillation in tubes with diameters of 12,25,and 195microns.Appl Phys Lett.2006;88(3):033902.
[12]Caskey CF,Kruse DE,Dayton P,et al.On the oscillations of microbubbles in tubes with diameters as small as 12microns[C]//Ultrasonics Symposium,2005 IEEE.IEEE,2005;2:854-857.
[13]Qin S,Ferrara KW.The natural frequency of nonlinear oscillation of ultrasound contrast agents in microvessels.Ultrasound Med Biol.2007;33:1140-1148.
[14]Martynov S,Stride E,Saffari N.The natural frequencies of microbubble oscillation in elastic vessels.J Acoust Soc Am.2009;126:2963-2972.
[15]Doinikov AA,Aired L,Bouakaz A.Modeling and experiments on the far-field scattering.J Fr Ophtalmol.2010;36(15):1133-1136.
[16]Doinikov AA,Novell A,Bouakaz A.Dynamics of a Contrast Microbubble Between Two Elastic Walls.2012IEEE International Ultrasonics Symposium.2012;31:654-662.
[17]Wiedemair W,Tukovi??,Jasak H,et al.On ultrasound-induced microbubble oscillation in a capillary blood vessel and its implications for the blood-brain barrier.Phys Med Biol.2012;57(4):1020-1024.
[18]Hosseinkhah N,Hynynen K.A three-dimensional model of an ultrasound contrast agent gas bubble and its mechanical.Phys Med Biol.2012;57(3):785-808.
[19]de Jong N,Cornet R,Lancee CT.Higher harmonics of vibrating gas-filled microspheres:part 1.Simulation.Ultrasonics.1994;32(6):447-453.
[20]de Jong N,Cornet R,Lancee CT.Higher harmonics of vibrating gas-filled microspheres:part 2:Measurements.Ultrasonics.1994;32(6):455-459.
[21]Paul S,Katiyar A,Sarkar K,et al.Material characterization of the encapsulation of an ultrasound contrast microbubble and its subharmonic response:strain-softening interfacial model.J Acoust Soc Am.2010;127(6):3846-3850.
[22]Li Q,Matula TJ,Tu J,et al.Modeling complicated rheological behaviors in encapsulating shells of lipid-coated microbubbles accounting for nonlinear changes of both shell viscosity and elasticity.Phys Med Biol.2013;58(4):985-998.
[23]程茜,钱梦騄.超声微泡造影剂的低频动力学行为[J].声学技术,2006,25(4):292-298.
[24]邱晓晖,沈圆圆,钱建庭,等.刚性微管内微泡动力学行为的有限元数值分析[J].生物医学工程学杂志,2011,28(5):911-915.
[25]Shen YY,Wang TF,Diao X,et al.Numerical analysis of interaction between microbubble and elastic microvessel in low frequency ultrasound field using fluid solid interaction method[C].Biomedical and Health Informatics(BHI),2012 IEEE-EMBS International Conference on IEEE,2012:733-736.
[26]VanB avel E.Effects of shear stress on endothelial cells:possible relevance for ultrasound applications.Prog Biophys Mol Biol.2007;93:374-383.
[27]Mukundakrishnan K,Ayyaswamy PS,Eckmann DM.Bubble motion in a blood vessel:shear stress induced endothelial cell injury.Biomech Eng.2009;131:074516.
[28]Qin S,Ferrara KW.Acoustic response of compliable microvessels containing ultrasound contrast agents.Phys Med Biol.2006;51(20):5065.
[29]Sergey M,Erik K,Nader S,et al.Forced vibration of a bubble in a liquid-filled elastic vessel.J Acoust Soc Am.2012;130(5):2700-2708.
[30]Shen YY,Wang TF,Chin CT,et al.Interaction between microbubble and elastic microvessel in low frequency ultrasound field using finite element method.Chin Sci Bull.2013;58(3):291-298.
[31]Oishi Y,Kakimoto T,Yuan W,et al.Fetal Gene Therapy for Ornithine Transcarbamylase Deficiency by Intrahepatic Plasmid DNA-Micro-Bubble Injection Combined with Hepatic Ultrasound Insonation.Ultrasound Med Biol.2016;42(6):1357-1361.
[32]Wang G,Zhang Q,Zhuo Z,et al.Enhanced Homing of CXCR-4 Modified Bone Marrow-Derived Mesenchymal Stem Cells to Acute Kidney Injury Tissues by MicroBubble-Mediated Ultrasound Exposure.Ultrasound Med Biol.2016;42(2):539-548.
[33]Sajjadi B,Raman AA,Ibrahim S.Influence of ultrasound power on acoustic streaming and micro-bubbles formations in a low frequency sono-reactor:mathematical and 3D computational simulation.Ultrason Sonochem.2015;24:193-203.
[34]Chiu AH,Haluszkiewicz E,Mc Auliffe W.Micro-bubble transcranial Doppler ultrasound for exclusion of right-to-left circulatory shunts:why should we provide the service?J Med Imaging Radiat Oncol.2014;58(4):464-468.
[35]Tong J,Ding J,Shen X,et al.Mesenchymal stem cell transplantation enhancement in myocardial infarction rat model under ultrasound combined with nitric oxide microbubbles.PLo S One.2013;8(11):e80186.
[36]Ren ST,Shen S,He XY,et al.The Effect of Docetaxel-Loaded Micro-Bubbles Combined with Low-Frequency Ultrasound in H22 Hepatocellular Carcinoma-Bearing Mice.Ultrasound Med Biol.2016;42(2):549-560.
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