基于瑞利积分叠加法的聚焦换能器声场特性研究

基于经典的瑞利积分,提出考虑非线性传播、各次谐波衰减的声场瑞利积分线性叠加算法.分析其原理,并以凹球面聚焦换能器为例,采用该算法研究媒质衰减和非线性传播特性影响声焦域的规律.并与Khokhov-Zabolotskaya-Kuznesov(KZK)数值算法,以及实验结果进行比较,验证瑞利积分线性叠加算法描述高强度聚焦超声(HIFU)声场的有效性.     

热疗用聚焦超声换能器的研究

本文通过数值计算及实际测量,研究了凹球面声透镜聚焦换能器及凹球面自聚焦换能器产生的声场,证实此两种聚焦方式均可获得理想的聚焦效果,但自聚焦方式更适合高强度聚焦超声(HIFU)加热治疗。     

时间反转方法用于高强度聚焦超声的焦点偏移补偿

传统的高强度聚焦超声(HIFU)治疗中实际焦点和预设焦点容易出现偏移,为考察时间反转方法对HIFU治疗中焦点偏移的补偿效果,采用时域有限差分方法求解Westervelt方程,建立高强度聚焦声场数值模型。数值计算得到在人体软组织中进行HIFU治疗时,采用时间反转方法后焦点偏移距离最大仅为1.6 mm。脂肪层厚度及声源强度改变对时间反转聚焦精度影响不大,F数(焦点距离同换能器孔径的比值)降低时,焦点偏移减小。研究表明在人体软组织吸收系数和非线性系数范围内,时间反转方法可有效补偿焦点偏移,达到更好的聚焦效果。      

圆锥面PVDF聚焦换能器的非线性声场理论及实验研究

圆锥面聚焦换能器可在超声成像中获得较好径向分辨率的同时提高探测深度.利用高斯声源函数叠加法来近似表示圆锥面聚焦声源的分布函数，结合近轴近似的KZK方程，得到了圆锥面聚焦换能器在损耗媒质中产生的基波、二次谐波声场的解析解.在实验上制作了PVDF圆锥面聚焦换能器，测量了圆锥面聚焦换能器的基波及二次谐波声场，实验结果和理论计算相符.     

基于分数导数研究高强度聚焦超声的非线性声场

在高强度聚焦超声(high intensity focused ultrasound, HIFU) 的研究中, 生物组织的衰减和色散性质会对声能量的空间分布产生影响. 本文提出应用分数导数修正非线性Khokhlov-Zabolotskaya-Kuznetsov (KZK)方程, 研究生物组织中非线性HIFU声场. 对三种生物仿体的衰减和声速色散的理论实验研究表明分数导数应用的可行性, 在此基础上通过数值仿真分析研究了衰减及声速随频率的变化对HIFU焦域分布的影响. 研究结果表明, 在计算强非线性聚焦超声时, 由于高次谐波的强色散作用, 引入分数导数来解决生物组织特殊的衰减以及色散问题可进一步提高HIFU治疗的安全性. 关键词： 分数导数 声衰减 色散 高强度聚焦超声     

基于电阻抗层析成像的高强度聚焦超声温度监测技术

作为一种对正常组织无损伤且不易引起癌细胞转移的非入侵肿瘤治疗手段,高强度聚焦超声(HIFU)治疗过程中焦域的温度监测是实现剂量精准控制的关键.本文基于生物组织的温度-电阻抗的关系,将电阻抗层析成像(EIT)和HIFU治疗相结合,提出了一种利用组织焦平面的表面电压实现电阻抗重构的检测技术.建立了HIFU治疗和EIT综合系统模型,在考虑组织的声吸收条件下,对三维Helmholtz方程在柱坐标下的声场计算进行了二维简化,并引入Pennes生物热传导方程来计算HIFU焦域的声压和温升分布特性;引入生物组织的温度-电阻抗关系,基于麦克斯韦电磁场理论,建立了具有温度分布HIFU焦域的电流和电压计算模型,利用恒流注入的边界条件实现电场计算,获得焦平面的表面电压分布.在数值计算中,利用实验聚焦换能器参数,模拟了在固定声功率下组织焦域的声场和温度场分布,以及中心和偏心聚焦条件下不同治疗时刻的电导率分布;然后通过对称电极的循环电流注入,计算了组织模型焦平面内的电流密度和电势分布,获得了焦平面圆周分布的表面电极电压;进一步采用修正的牛顿-拉夫逊算法,利用32×32的表面电极电压实现了焦平面内电导率分布的重建.结果表明,基于温度-电阻抗关系的EIT电导率重建技术不但能准确定位HIFU焦域中心,还能恢复HIFU治疗中焦域的温度分布,证明了EIT用于HIFU治疗中温度监测的可行性,为其疗效评估和剂量控制提供了一种无创电阻抗测量和成像新方法.     

球形腔聚焦换能器的非线性声场建模

球形腔聚焦换能器是一种特殊形式的聚焦换能器。为理论证实球形腔聚焦换能器能突破传统超声聚焦在聚焦精度和聚焦增益上的限制,采用Westervelt非线性方程并结合时域有限差分法,建立了球形腔聚焦换能器的非线性声场的数值模型。数值计算了直径为120 mm的0.6 MHz球形腔聚焦换能器的非线性声场,并与传统球壳形聚焦换能器进行了对比。当激励声压为100 kPa时,球形腔聚焦换能器与同尺寸壳形聚焦换能器相比,焦点正声压增益提高约8.5倍,且焦域精度更高,-6 dB聚焦区域在z方向减小约20倍,达到次波长尺度。研究表明球形腔聚焦换能器在高强度聚焦超声精细治疗上具有潜在的应用前景。      

1-3型二维柱形凹面线聚焦换能器声场特性

设计并研制了柱面结构的1-3型复合材料凹面线聚焦换能器,在提高换能器带宽的同时,可以实现声场的线聚焦。将换能器内部PZT柱作为独立声源,应用瑞利积分和叠加原理,推导出了柱形凹面换能器总声场的理论表达式。通过仿真计算分析了换能器在聚焦线上的声场特点以及相关参数对聚焦性能的影响。对换能器参数做出合理设计,使换能器在实现线聚焦的同时,声场在聚焦线上的起伏较小,从而设计并制作出聚焦性能良好的线聚焦凹面换能器探头。实验测试结果表明采用本文方法计算得到的换能器声场与实测的声场分布基本符合,柱形凹面换能器在其几何焦点附近范围内均可实现聚焦,并在侧向上形成清晰的聚焦线,其聚焦线长度为换能器的侧向结构长度,在聚焦线上声场分布起伏较小。      

大学物理中流体力学问题的计算机模拟研究

格子玻尔兹曼模拟方法(Lattice Boltzmann Method,LBM)被广泛应用于流体力学问题的研究中,本文采用LBM方法对牛顿流体和非牛顿流体的泊肃叶流动进行了模拟,还通过模拟圆柱绕流问题演示了层流和湍流现象并阐明了雷诺数的概念.将LBM模拟结果与大学物理的相关流体力学知识相联系,不仅可以直观地解释抽象的流体力学概念,而且能够培养学生采用计算物理学手段解决实际问题的思维方式.     

相控阵高强度聚焦超声的研究进展

相控阵高强度聚焦超声(high Intensity focused ultrasound,HIFU)技术可以通过电子调相自由控制聚焦区域中焦点的形状、位置、个数等,实现高精度、高效率的治疗。文章主要介绍了相控聚焦超声的原理、阵型设计、声场优化、控制算法、电路设计以及换能器材料等几个方面。     

Modeling of Focused Acoustic Field of a Concave Multi-annular Phased Array Using Spheroidal Beam Equation

A theoretical model of focused acoustic field for a multi-annular phased array on concave spherical surface is proposed.In this model,the source boundary conditions of the spheroidal beam equation(SBE) for multi-annular phased elements are studied.Acoustic field calculated by the dynamic focusing model of SBE is compared with numerical results of the O'Neil and Khokhlov-Zabolotskaya-Kuznetsov(KZK) model,respectively.Axial dynamic focusing and the harmonic effects are presented.The results demonstrate that the dynamic focusing model of SBE is good valid for a concave multi-annular phased array with a large aperture angle in the linear or nonlinear field.     

Temperature rise induced by an annular focused transducer with a wide aperture angle in multi-layer tissue

In order to improve the operability and accuracy of high-intensity focused ultrasound(HIFU), an annular focused transducer, whereby a B-ultrasound probe is placed in its center, is used to realize the real time monitoring and control of the treatment. In this paper, the spheroidal beam equation(SBE) was used to calculate the sound field by an annular focused transducer with a wide aperture angle to first derive the heat deposition and the Pennes equation was used to calculate the temperature field in multi-layer tissue. We studied the effect of different parameters on the temperature of the tissues. The result shows that the focal length has a significant influence on both maximum liver temperature rise and skin temperature rise, and both increase with the increase in the focal length. When the frequency increases, the temperature rise first undergoes a rapid increase before gradually reaching a maximum, and then finally decreasing. The temperature rise increases while the inner radius decreases or the sound pressure increases. By choosing suitable parameters, the proper temperature rise both on the target tissue and skin via an annular focused transducer with a wide aperture angle can be obtained.     

Nonlinear absorption in biological tissue for high intensity focused ultrasound

In recent years the propagation of the high intensity focused ultrasound (HIFU) in biological tissue is an interesting area due to its potential applications in non-invasive treatment of disease. The base principle of these applications is the heat effect generated by ultrasound absorption. In order to control therapeutic efficiency, it is important to evaluate the heat generation in biological tissue irradiated by ultrasound. In his paper, based on the Khokhlov-Zabolotkaya-Kuznetsov (KZK) equation in frequency-domain, the numerical simulations of nonlinear absorption in biological tissues for high intensity focused ultrasound are performed. We find that ultrasound thermal transfer effect will be enhanced with the increasing of initial acoustic intensity due to the high harmonic generation. The concept of extra absorption factor is introduced to describe nonlinear absorption in biological tissue for HIFU. The theoretical results show that the heat deposition induced by the nonlinear theory can be nearly two times as large as that predicated by linear theory. Then, the influence of the diffraction effect on the position of the focus in HIFU is investigated. It is shown that the sound focus moves toward the transducer compared with the geometry focus because of the diffraction of the sound wave. The position of the maximum heat deposition is shifted to the geometry focus with the increase of initial acoustic intensity because the high harmonics are less diffraction. Finally, the temperature in the porcine fat tissue changing with the time is predicated by Pennes' equation and the experimental results verify the nonlinear theoretical prediction.     

Sound field prediction of ultrasonic lithotripsy in water with spheroidal beam equations

With converged shock wave,extracorporeal shock wave lithotripsy(ESWL)has become a preferable way to crush human calculi because of its advantages of efficiency and non-intrusion.Nonlinear spheroidal beam equations(SBE)are employed to illustrate the acoustic wave propagation for transducers with a wide aperture angle.To predict the acoustic field distribution precisely,boundary conditions are obtained for the SBE model of the monochromatic wave when the source is located on the focus of an ESWL transducer.Numerical results of the monochromatic wave propagation in water are analyzed and the influences of half-angle,fundamental frequency,and initial pressure are investigated.According to our results,with optimization of these factors,the pressure focal gain of ESWL can be enhanced and the effectiveness of treatment can be improved.     

Wide-Angle Parabolic Approximation for Modeling High-Intensity Fields from Strongly Focused Ultrasound Transducers

A novel numerical algorithm based on the wide-angle parabolic approximation is developed for modeling linear and nonlinear fields generated by axially symmetric ultrasound transducers. An example of a strongly focused single-element transducer is used to compare the results of ultrasound field simulations based on the Westervelt equation, Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation with differently modified boundary condition, and nonlinear wide-angle parabolic equation. It is demonstrated that having a computational speed comparable to modeling the KZK equation, the use of wide-angle parabolic approximation makes it possible to obtain solutions for highly focused ultrasound beams that are closer in accuracy to solutions based on the Westervelt equation.     

自聚焦换能器的声场研究

高强度聚焦超声（HIFU）治疗局部肿瘤是一项无创伤的新技术,有着很好的应用前景,因此对其声场的研究是有实际的价值的。对声场的研究不仅有利于换能器的设计,提高治疗的效果;而且有助声场测量方案的设计,提高对治疗超声剂量的安全保证。本文采用时域有限差分法研究了自聚焦换能器的声场,分别对简谐波,脉冲波进行了研究。比较清楚地看出在焦区的声场可以认为是平面波,这对光纤端面法声场测量提供了有力的支持。