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.     

球形集声器在生物组织中形成的组织损伤

球形集声器可在亚波长焦域内形成高强度声压,在高强度聚焦超声治疗中具有潜在应用前景.本文结合非线性声传播理论及生物传热学理论,研究球形集声器在生物组织中形成的组织损伤.实验中采用430 kHz,内径为240 mm的球形集声器对肝组织作用,结果表明:集声器表面声压为53 kPa时作用2 s,可以形成小于波长尺度的组织损伤.理论计算结果与实验结果符合得较好,并且理论模型可优化球形集声器的开口孔径.研究结果表明,球形集声器可应用于肿瘤的精细超声治疗.     

非均匀组织医学超声发射声场仿真

为了分析医学超声在非均匀组织中的分布特性,建立了超声发射声场的计算模型。采用交错网格有限差分法对耦合超声非线性方程进行数值求解,获得了声速、密度及非线性参数非均匀分布情况下人体腹壁组织内的超声声场分布数据。同均匀介质相比:当声速均匀而密度非均匀时,声束仍聚焦良好,焦点处声能下降了1.8 dB;当密度均匀而声速非均匀时,声束发散严重,焦点处声能下降了3.8 dB,下降程度与非均匀组织接近。组织声速在空间分布的非均匀性是导致聚焦声束能量分布畸变的主要原因。      

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.     

高强度聚焦超声螺旋扫描形成的组织损伤研究

为满足高强度聚焦超声(HIFU)治疗对组织损伤均匀性和高效性的需求,理论及实验研究了连续扫描模式下HIFU沿螺旋扫描路径形成的组织损伤。基于Khokhlov-Zabolotskaya-Kuznetsov方程和生物传热方程建立了声热耦合模型,数值模拟了螺旋路径栅格距离为3 mm和4 mm时不同扫描速度下HIFU辐照体模的温度场和组织损伤分布,并采用凝胶体模进行了实验验证。结果表明,采用连续螺旋模式可以使热扩散均匀化,产生分布均匀的热损伤;选择适当的栅格距离和扫描速度,发挥螺旋路径内外圈热扩散的相互影响,可以产生大范围的整体性的热损伤,同时提高治疗效率。本文工作对优化HIFU治疗效果具有指导意义。      

微泡对高强度聚焦超声焦域影响的研究

微泡对高强度聚焦超声(HIFU)治疗具有增效作用,而HIFU治疗中不同声学条件下微泡对HIFU治疗焦域的影响尚不清楚。本文基于声传播方程、Yang-Church气泡运动方程、生物热传导方程、时域有限差分法(FDTD)、龙格-库塔(RK)法数值仿真研究输入功率、激励频率和气泡初始半径对HIFU在含气泡体模中形成焦域的影响,并利用含Sono Vue造影剂的仿组织体模研究进行实验验证。结果表明,增大输入功率、气泡初始半径和升高激励频率均可增大焦域,随着输入功率的增大,焦域形状可能发生变化,而随着激励频率升高和气泡初始半径的增大,焦域会向远离换能器的方向移动。     

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。      

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。     

HIFU温度场可视化测量初探

本实验用蓖麻油模拟人体环境、热敏打印纸作为记录载体,测量高强度聚焦超声(HIFU)治疗系统焦点附近的温度分布情况。实验中热敏打印纸显影所指示的温度已经达到HIFU治疗所需要的温度,实验的结果对进一步研究HIFU温度场分布有借鉴作用。     

利用换能器电信号相位特征实时监测高强度聚焦超声治疗中的声空化

高强度聚焦超声(HIFU)激发的声空化可加速靶组织的热消融,但声空化的实时监测是一个亟需解决的问题。利用HIFU换能器驱动电信号的相位差与电阻抗之间的数学模型,建立了HIFU辐照及换能器驱动电信号、声空化信号实时检测实验系统,探究了HIFU辐照离体牛心组织过程中,换能器驱动电信号的相位差与B超影像灰度变化及宽频水听器检测到的次谐波和宽带噪声信号的变化规律。结果表明:当声空化发生时,换能器驱动电信号相位差的变化与水听器检测到的次谐波和宽带噪声信号变化具有一致性,通过相位差的变化可实现HIFU辐照靶组织中声空化的实时、精准监测,这为HIFU所致声空化的实时监测提供了一种有应用前景的解决方案。     

Nonlinear acoustic wave equations with fractional loss operators

Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations.     

材料非线性衰减系数的二次谐波测量方法研究

采用有限幅值法测量材料在基波和非线性引起的二次谐波作用下的衰减系数:利用准线性下的KZK方程推导基波和二次谐波的声压分布,并提取波束修正系数;采用短纯音信号进行非线性实验,对检测得到的基波和二次谐波声压进行衍射修正处理,有效抑制衍射对衰减系数测量的不利影响,继而通过线性拟合的方法计算得到更精确的基波和二次谐波的衰减系数。以水为例进行实验,研究了实验测量所得衰减系数的频率依赖关系,结果表明在非线性条件下水的衰减系数与频率间存在较强的线性关系,而线性条件下衰减系数随频率呈现二次方增长的特性则不适用于非线性条件。该研究提出了准确测量非线性声波衰减系数的方法,为更有效地应用非线性超声检测提供理论依据。      

Time-domain modeling of finite-amplitude sound beams in three-dimensional Cartesian coordinate system

A three-dimensional time-domain algorithm,which is based on the augmented KZK (Khokhlov-Zabolotskaya-Kuznetsov) equation,is proposed to simulate the nonlinear field of the parametric array.First,KZK equation is transformed into TBE(Transformed beam equation). Then,the effects of diffraction(in parabolic approximation),thermoviscous absorption,relaxation, and nonlinearity are solved with finite difference methods.The numerical results of this code agree well with the theoretical and experimental results presented in previous studies, which demonstrates the validity of the three-dimensional algorithm.Using this code to calculate the nonlinear field of the parametric array in air,it is found that the small time interval is important to the accuracy of the simulation results of the difference frequency wave in the case of high sound pressure level,and the errors caused by taking relaxation absorption for thermoviscous absorption are influenced by the characteristic frequency.     

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.     

条状障碍物对超声非线性声场的影响研究

基于Khokhlov-Zabolotkaya-Kuznetsov(KZK)方程，在频域建立了求解三维非轴对称声场的方法，理论及实验研究了声波通过肋骨条状障碍物后的非线性声场分布，数值计算与实验结果相符.本文还讨论了条状障碍物对空间平均-时间平均声强(I_SATA)的影响. 关键词： 非轴对称 频域法 肋骨 衍射场     

Modeling of an electrohydraulic lithotripter with the KZK equation.

The acoustic pressure field of an electrohydraulic extracorporeal shock wave lithotripter is modeled with a nonlinear parabolic wave equation (the KZK equation). The model accounts for diffraction, nonlinearity, and thermoviscous absorption. A numerical algorithm for solving the KZK equation in the time domain is used to model sound propagation from the mouth of the ellipsoidal reflector of the lithotripter. Propagation within the reflector is modeled with geometrical acoustics. It is shown that nonlinear distortion within the ellipsoidal reflector can play an important role for certain parameters. Calculated waveforms are compared with waveforms measured in a clinical lithotripter and good agreement is found. It is shown that the spatial location of the maximum negative pressure occurs pre-focally which suggests that the strongest cavitation activity will also be in front of the focus. Propagation of shock waves from a lithotripter with a pressure release reflector is considered and because of nonlinear propagation the focal waveform is not the inverse of the rigid reflector. Results from propagation through tissue are presented; waveforms are similar to those predicted in water except that the higher absorption in the tissue decreases the peak amplitude and lengthens the rise time of the shock.     

格子玻尔兹曼方法对不同张角聚焦声束的建模

高强度聚焦超声(HIFU)是一种新型的无创治疗肿瘤新技术,其中换能器声场数值计算能够为HIFU治疗提供重要的依据。传统非线性KZK和SBE模型广泛应用于换能器声场数值计算,但依然存在某些不足。我们采用一种介观尺度的新型流体力学方法,即格子Boltzmann方法(LBM),基于2维9离散速度(D2Q9)格子构建了轴对称多弛豫参数LBM模型,并通过调节弛豫参数分析其对模型的影响;利用该模型对两个具有不同张角的球面聚焦换能器的声场进行数值模拟,并与KZK和SBE模型的计算结果进行比较。结果表明LBM模型能够很好地描述超声波的激发和传播机制,从流体力学的角度描述聚焦声场的分布,具有清晰的物理意义,且计算过程不受换能器张角的限制,在换能器声场的理论分析和模拟计算及其在HIFU治疗中的应用有着积极的意义。      

The transmission of finite amplitude sound beam in multi-layered biological media

Based on the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, a model in the frequency domain is given to describe the transmission of finite amplitude sound beam in multi-layered biological media. Favorable agreement between the theoretical analyses and the measured results shows this approach could effectively describe the transmission of finite amplitude sound wave in multi-layered biological media.     

Space-time structure of the low-frequency acoustic field in an underwater sound channel

Experimental data are presented on the fine structure of the sound field in an underwater sound channel for low and infralow sound frequencies. The experiments are performed in the Black Sea, on a 600-km-long path, with explosive sound sources. The intensity, space-time, and frequency characteristics of the sound field are analyzed. The geometric dispersion of the first normal wave is experimentally studied. The role of the channel inhomogeneities in the violation of the sound field coherence is determined for different frequency bands. On the basis of the experimental data, the vertical distribution of the critical frequencies of the waveguide is obtained, and the validity limits are established for the wave and ray calculation methods. The applicability of the phase methods for calculating the sound fields in waveguides with dispersion is discussed. The frequency-angular dependence of the effective sound attenuation coefficient in an underwater waveguide is revealed and explained.