非线性声参量计算机模拟成像

非线性声参量Ｂ／Ａ是生物组织超声辨认的一个重要的新参量．本文从Ｂｕｒｇｅｒｓ’方程出发分析了有限振幅平面声波在层状介质中的非线性传播理论，并将它用于二次谐波的声成像，利用通常的ＣＴ算法而得的二次谐波数据进行了非线性声参量的计算机模拟成像，用滤波逆投影算法进行图像重建，对简单的样品模型得到了较好的非线性声参量断层图像．     

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.     

聚焦超声波在层状生物媒质中的二次谐波声场的理论与实验研究

基于Khokhlov-Zabolotkaya-Kuznetsov(KZK)方程，在频域提出了聚焦超声波在层状生物媒质中传播的理论模型，该模型计及生物媒质的吸收、非线性和边界，同时考虑声源的衍射对声传播的影响.数值研究了聚焦超声波的基波和二次谐波在层状生物媒质中的声传播，并与实验结果相比较.研究结果表明，此方法可以有效地描述聚焦超声波在层状生物媒质中的二次谐波声场. 关键词： 聚焦超声波 层状生物媒质 二次谐波     

基于空域分解的非线性有限声束快速计算

研究非线性有限声束的一种快速数值计算算法.理论研究表明非线性有限声束存在多种耦合:谐波之间的全耦合,各场点沿轴向的递推耦合以及沿径向的局部耦合,因此可以通过声场的径向空间区域分割提高计算效率,采用多线程实现并行计算.对非线性高斯聚焦波的计算结果表明,当声场计算规模与分割线程数合理匹配时,算法能够显著提高计算速度同时保证计算精度,计算结果与理论分析相符.     

光声信号的声透镜层析成像研究

提出了一种用声透镜实现光声层析成像的新模式。从理论上计算出了声透镜的响应，测出了已知声场中标准物像面处的声场分布。考虑到圆形活塞振源的指向性，对代表物成像进行了理论修正，并与实验结果做了对比分析。研究表明，利用声透镜可以实现光声层析成像，并经图像重构得到了生物组织中异物的光声图像，横向、纵向分辨力较高。     

高频聚焦超声声场和温度场的仿真研究

为探究临床常用的7 MHz高频聚焦超声在多层生物组织中的声传播以及毫秒级时间内的生物传热规律问题,基于Westervelt方程和Pennes传热方程,使用有限元方法建立高频聚焦超声辐照多层组织的非线性热黏性声传播及传热模型。首先分析了线性模型和非线性模型之间的差异,然后在非线性模型下探究换能器的参数对声场和温度场的影响。仿真结果显示：在7 MHz频率下,当换能器输出声功率超过5 W时,声波传播的非线性效应不可忽视(p <0.05);当声功率从5 W增大到15 W时,非线性模型与线性模型预测的温度偏差从20%增加到34.703%;高频聚焦超声波的非线性行为比低频更加显著,基频能量向高次谐波转移的程度增大,声功率为10 W和15 W时4次谐波与基波之比分别达到7.33%和12.12%;高频换能器参数的改变对组织中声场和温度场分布的影响较大,换能器焦距从12 mm减小到11.2 mm,焦点处最高温度增加了77%。结果表明,7 MHz聚焦超声的非线性声传播需要考虑到4次谐波的影响。该文提出的多层组织非线性仿真模型可为高频聚焦超声换能器参数优化及制定安全、有效的术前治疗方案提供理论参考。     

有限声束的二阶积累声场研究

将有限声束分解为一系列平面波,结合声非线性相互作用理论,对有限声束的二阶积累声场进行了分析和计算。结果表明,任意两个平面波相互作用不产生二阶积累波,伴随有限声束传播所发生的二阶积累波仅是各个平面波非线性自作用的结果。此外,本文还得到了具有直观物理意义的有限声束二阶积累声场的表达式。     

圆形平面换能器产生的二次谐波声场及对非线性声参量成像的影响

在利用二次谐波进行非线性声参量B／A层析成像中,发射换能器的声场特性,尤其是在近场区域的特性对成像结果的定性及定量分析极其重要。本文从理论及实验上分析了圆形平面活塞换能器在传播介质中产生的二次谐波声场,就其对非线性声参量成像的影响进行了分析和讨论．研究结果有助于在非线性声参量成像中降低重建误差,提高分辨灵敏度．     

超声相控阵在多层媒质中的声场模式优化

针对超声在多层媒质中的传播特性,引入相位补偿因子并结合遗传算法, 提出了一种可对多层媒质进行声聚焦控制的方法.利用该方法对16×16二维超声相控阵在多层生物媒质中的多焦点声场模式进行了仿真,计算了生物媒质不同厚度层和不同吸收系数时的声场. 结果表明:该方法能优化多焦点声场模式,抑制旁瓣,提高声场增益,将声强最大限度地聚焦在目标区域内; 改变生物组织不同层的厚度和不同层的吸收系数,焦点位置不发生变化,但焦域内的声强会有所变化.     

反射式非线性声参量层析成像的研究

非线性声参量Ｂ／Ａ描述了有限振幅波在媒质中传播的非线性特性，有可能成为生物组织定征的新参量。本文提出了利用复合式换能器进行反射式的非线性参量Ｂ／Ａ层析成像的新方法。利用反射二次谐波的传播理论及有限振幅波插入取代法给出了计算机重建Ｂ／Ａ层析像的理论方法。对部分流体及生物组织进行了计算机模拟成像及实验研究，取得了较为满意的结果。     

A Simple Model for Nonlinear Confocal Ultrasonic Beams

A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov （KZK） equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.     

Physical mechanisms of the therapeutic effect of ultrasound (a review)

Therapeutic ultrasound is an emerging field with many medical applications. High intensity focused ultrasound (HIFU) provides the ability to localize the deposition of acoustic energy within the body, which can cause tissue necrosis and hemostasis. Similarly, shock waves from a lithotripter penetrate the body to comminute kidney stones, and transcutaneous ultrasound enhances the transport of chemotherapy agents. New medical applications have required advances in transducer design and advances in numerical and experimental studies of the interaction of sound with biological tissues and fluids. The primary physical mechanism in HIFU is the conversion of acoustic energy into heat, which is often enhanced by nonlinear acoustic propagation and nonlinear scattering from bubbles. Other mechanical effects from ultrasound appear to stimulate an immune response, and bubble dynamics play an important role in lithotripsy and ultrasound-enhanced drug delivery. A dramatic shift to understand and exploit these nonlinear and mechanical mechanisms has occurred over the last few years. Specific challenges remain, such as treatment protocol planning and real-time treatment monitoring. An improved understanding of the physical mechanisms is essential to meet these challenges and to further advance therapeutic ultrasound.     

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.     

Extension of the angular spectrum method to calculate pressure from a spherically curved acoustic source

The angular spectrum method is an accurate and computationally efficient method for modeling acoustic wave propagation. The use of the typical 2D fast Fourier transform algorithm makes this a fast technique but it requires that the source pressure (or velocity) be specified on a plane. Here the angular spectrum method is extended to calculate pressure from a spherical transducer-as used extensively in applications such as magnetic resonance-guided focused ultrasound surgery-to a plane. The approach, called the Ring-Bessel technique, decomposes the curved source into circular rings of increasing radii, each ring a different distance from the intermediate plane, and calculates the angular spectrum of each ring using a Fourier series. Each angular spectrum is then propagated to the intermediate plane where all the propagated angular spectra are summed to obtain the pressure on the plane; subsequent plane-to-plane propagation can be achieved using the traditional angular spectrum method. Since the Ring-Bessel calculations are carried out in the frequency domain, it reduces calculation times by a factor of approximately 24 compared to the Rayleigh-Sommerfeld method and about 82 compared to the Field II technique, while maintaining accuracies of better than 96% as judged by those methods for cases of both solid and phased-array transducers.     

FDTD simulation of finite-amplitude pressure and temperature fields for biomedical ultrasound.

Full wave simulations provide a valuable tool for studying the spatial and temporal nature of an acoustic field. One method for producing such simulations is the finite-difference time-domain (FDTD) method. This method uses discrete differences to approximate derivatives in the governing partial differential equations. We used the FDTD method to model the propagation of finite-amplitude sound in a homogeneous thermoviscous fluid. The calculated acoustic pressure field was then used to compute the transient temperature rise in the fluid; the heating results from absorption of acoustic energy by the fluid. As an example, the transient temperature field was calculated in biological tissue in response to a pulse of focused ultrasound. Enhanced heating of the tissue from finite-amplitude effects was observed. The excess heating was attributed to the nonlinear generation of higher-frequency harmonics which are absorbed more readily than the fundamental. The effect of nonlinear distortion on temperature rise in tissue was observed to range from negligible at 1 MPa source pressure to an 80% increase in temperature elevation at 10 MPa source pressure.     

Use of focused ultrasonic receivers for remote measurements in biological tissues

The feasibility of using a focusing ultrasonic transducer as a sound pressure receiver is discussed. It is shown theoretically that, at certain angular apertures of the receiver, its output signal is proportional to the sound pressure in the field point coincident with the receiver center of curvature. The receivers of this type have been demonstrated suitable for remote measurements of field spatial distribution of plane and focused ultrasonic radiators. Data are presented on the experimental testing of focused receivers in measuring acoustic fields in water, air, and certain samples of biological tissues. The instruments are sufficiently universal and allow the measurement not only of acoustic fields, but also of temperature increments in locally heated media, as well as permit one to follow the initiation and development of ultrasonic cavitation and study nonlinear effects. The remote sensing ability and high sensitivity of focused ultrasonic receivers allow their practical use in biomedical acoustics for noninvasive measurements.     

Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects.     

Ultrasound elastomicroscopy using water jet and osmosis loading: potentials for assessment for articular cartilage

Research in elasticity imaging typically relies on 1-10 MHz ultrasound. Elasticity imaging at these frequencies can provide strain maps with a resolution in the order of millimeters, but this is not sufficient for applications to skin, articular cartilage, or other fine structures. In this paper, we introduced two methods of ultrasound elastomicroscopy using water jet and osmosis loading for imaging the elasticity of biological soft tissues with high resolutions. In the first system, the specimens were compressed using water jet compression. A water jet was used to couple a focused 20 MHz ultrasound beam into the specimen and meanwhile served as a "soft" indenter. Because there was no additional attenuation when propagating from the ultrasound transducer to the specimen, the ultrasound signal with high signal-to-noise ratio could be collected from the specimens simultaneously with compressing process. The compression was achieved by adjusting the water flow. The pressure measured inside the water pipe and that on the specimen surface was calibrated. This system was easily to apply C-scan over sample surfaces. Experiments on the phantoms showed that this water jet indentation method was reliable to map the tissue stiffness distribution. Results of 1D and 2D scanning on phantoms with different stiffness are reported. In the second system, we used osmotic pressure caused by the ion concentration change in the bathing solutions for the articular cartilage to deform them. When bovine articular cartilage specimens were immerged in solutions with different salt concentration, a 50 MHz focused ultrasound beam was used to monitor the dynamic swelling or shrinkage process. Results showed that the system could reliably map the strain distribution induced by the osmotic loading. We extract intrinsic layered material parameters of the articular cartilage using a triphasic model. In addition to biological tissues, these systems have potential applications for the assessment of bioengineered tissues, biomaterials with fine structures, or some engineering materials. Further studies are necessary to fully realize the potentials of these two new methods.     

离散坐标法在计算生物组织内光场空间角分布中的应用

从辐射传输理论出发,研究了准直光照下层状生物组织内漫射光场的角分布.在辐射传输方程的基础上,采用离散坐标法得到了描述层状生物组织内漫射光传输问题的微分方程组形式,并用特征值-特征矢量方法对其进行了求解,给出了通解形式.结合边界条件对两类典型生物组织内漫射光场角分布进行了数值计算-各向同性组织和前向散射组织,给出了组织内不同深度处漫射光场空间角分布曲线.通过对计算结果比较分析,得到了生物组织内漫射光场空间角分布随深度的变化规律,及边界效应和光学参量对组织内漫射光场空间角分布的影响.