Motion of a solid sphere in a viscoelastic medium in response to applied acoustic radiation force: Theoretical analysis and experimental verification

The motion of a rigid sphere in a viscoelastic medium in response to an acoustic radiation force of short duration was investigated. Theoretical and numerical studies were carried out first. To verify the developed model, experiments were performed using rigid spheres of various diameters and densities embedded into tissue-like, gel-based phantoms of varying mechanical properties. A 1.5 MHz, single-element, focused transducer was used to apply the desired radiation force. Another single-element, focused transducer operating at 25 MHz was used to track the displacements of the sphere. The results of this study demonstrate good agreement between theoretical predictions and experimental measurements. The developed theoretical model accurately describes the displacement of the solid spheres in a viscoelastic medium in response to the acoustic radiation force.     

Generalized response of a sphere embedded in a viscoelastic medium excited by an ultrasonic radiation force

The response of an embedded sphere in a viscoelastic medium excited by acoustic radiation force has been studied in both the time- and frequency-domains. This model is important because it can be used to characterize the viscoelastic properties of the medium by fitting the response to the theoretical model. The Kelvin-Voigt model has been used exclusively in these models. An extension to the previously reported models is described so that any viscoelastic rheological model can be used. This theoretical development describes the generalized embedded sphere response both in the time and frequency domains. Comparing the results from derivations in both domains showed very good agreement with a median absolute error (MAE) ranging from 0.0044 to 0.0072. Good agreement is demonstrated with finite element model simulations and the theory with a MAE of 0.006. Lastly, results for characterization of gelatin and rubber materials with the new theory are shown where the MAE values were used to determine which rheological model best describes the measured responses.     

Harmonic pulsed excitation and motion detection of a vibrating reflective target

Elasticity imaging is an emerging medical imaging modality. Methods involving acoustic radiation force excitation and pulse-echo ultrasound motion detection have been investigated to assess the mechanical response of tissue. In this work new methods for dynamic radiation force excitation and motion detection are presented. The theory and model for harmonic motion detection of a vibrating reflective target are presented. The model incorporates processing of radio frequency data acquired using pulse-echo ultrasound to measure harmonic motion with amplitudes ranging from 100 to 10,000 nm. A numerical study was performed to assess the effects of different parameters on the accuracy and precision of displacement amplitude and phase estimation and showed how estimation errors could be minimized. Harmonic pulsed excitation is introduced as a multifrequency radiation force excitation method that utilizes ultrasound tonebursts repeated at a rate f(r). The radiation force, consisting of frequency components at multiples of f(r), is generated using 3.0 MHz ultrasound, and motion detection is performed simultaneously with 9.0 MHz pulse-echo ultrasound. A parameterized experimental analysis showed that displacement can be measured with small errors for motion with amplitudes as low as 100 nm. The parameterized numerical and experimental analyses provide insight into how to optimize acquisition parameters to minimize measurement errors.     

Heating of the phantom of a biological tissue by a phase conjugate ultrasonic beam

The local heating of an absorbing medium by an ultrasonic beam with a conjugate wave front has been experimentally demonstrated. Plastisol, which is a polymeric material close in acoustic properties to biological tissue, is used as the medium. An ultrasonic heating of 7.2°C has been obtained in a time of about 100 s when the sample equipped with a thermocouple is placed between a focused piezoelectric transducer emitting a “probe wave” with a frequency of 5.0 MHz and a system that reverses the ultrasonic wave front with amplification. The characteristic features of heating by ultrasonic beams with the conjugate front, as well as the prospects of applications of this effect in medicine and other fields, have been discussed.     

Quantitative observations of cavitation activity in a viscoelastic medium

Quantitative experimental observations of single-bubble cavitation in viscoelastic media that would enable validation of existing models are presently lacking. In the present work, single bubble cavitation is induced in an agar gel using a 1.15 MHz high intensity focused ultrasound transducer, and observed using a focused single-element passive cavitation detection (PCD) transducer. To enable quantitative observations, a full receive calibration is carried out of a spherically focused PCD system by a bistatic scattering substitution technique that uses an embedded spherical scatterer and a hydrophone. Adjusting the simulated pressure received by the PCD by the transfer function on receive and the frequency-dependent attenuation of agar gel enables direct comparison of the measured acoustic emissions with those predicted by numerical modeling of single-bubble cavitation using a modified Keller-Miksis approach that accounts for viscoelasticity of the surrounding medium. At an incident peak rarefactional pressure near the cavitation threshold, period multiplying is observed in both experiment and numerical model. By comparing the two sets of results, an estimate of the equilibrium bubble radius in the experimental observations can be made, with potential for extension to material parameter estimation. Use of these estimates yields good agreement between model and experiment.     

Cavitation mapping by sonochemiluminescence with less bubble displacement induced by acoustic radiation force in a 1.2 MHz HIFU

An acoustic radiation force counterbalanced appliance was employed to map the cavitation distribution in water. The appliance was made up of a focused ultrasound transducer and an aluminum alloy reflector with the exactly same shape. They were centrosymmetry around the focus of the source transducer. Spatial–temporal dynamics of cavitation bubble clouds in the 1.2 MHz ultrasonic field within this appliance were observed in water. And they were mapped by sonochemiluminescence (SCL) recordings and high-speed photography. There were significant differences in spatial distribution and temporal evolution between normal group and counterbalanced group. The reflector could avoid bubble directional displacement induced by acoustic radiation force under certain electric power (⩽50 W). As a result, the SCL intensity in the pre-focal region was larger than that of normal group. In event of high electric power (⩾70 W), most of the bubbles were moving in acoustic streaming. When electric power decreased, bubbles kept stable and showed stripe structure in SCL images. Both stationary bubbles and moving bubbles have been captured, and exhibited analytical potential with respect to bubbles in therapeutic ultrasound.     

Long-time temperature rise due to absorption of focused gaussian beams in tissue

An analytical technique previously developed to study tissue displacement due to acoustic radiation force is extended to analyze temperature rise in tissue for exposure times that are comparable to, or longer than, the tissue perfusion time. A focused transducer with Gaussian amplitude shading is assumed to radiate into a perfused tissue medium with constant thermal and acoustic properties. A simple closed-form expression is derived for the steady-state temperature rise, and a transient correction term is constructed that allows for computation of the equilibrium time of the medium. Comparisons with temperature calculations for non-Gaussian transducers show that the model may be applied to more general intensity profiles.     

Optimal design and experimental investigation of surfactant encapsulated microbubbles

The diagnostic capabilities of ultrasound imaging can be improved with contrast-specific nonlinear imaging modalities such as harmonic and subharmonic imaging. The nonlinear response of an encapsulated microbubble in an acoustic field is strongly influenced by the shell viscoelastic properties that are determined by the shell composition and thickness. In this paper, the subharmonic performance of a surfactant encapsulated microbubble was optimized by choosing the appropriate composition of shell material with the aid of theoretical model. To study the effects of viscoelastic properties of microbubble shell materials on the nonlinear scattered response of microbubbles, a theoretical model-modified Herring equation for the oscillation of encapsulated microbubbles in the ultrasound field was employed. Based on this model, a computer aided design system was developed to optimize and analyze the acoustic properties, particularly subharmonic responses, of microbubbles under different shell parameters. Furthermore, surfactant encapsulated microbubbles with different viscoelastic properties were prepared by changing the shell composition. Their shell viscoelastic behavior was measured indirectly as dilational modulus of monolayer film formed with surfactant molecular. Moreover, in vitro quantitative acoustic properties measurements of these microbubbles were carried out to evaluate their subharmonic performance. Both of the theoretical simulation and acoustic measurement showed that the surfactant encapsulated microbubbles with good subharmonic properties could be designed and prepared by adjusting the shell material composition with the guide of the computer aided design system.     

On the feasibility of remote palpation using acoustic radiation force

A method of acoustic remote palpation, capable of imaging local variations in the mechanical properties of tissue, is under investigation. In this method, focused ultrasound is used to apply localized (on the order of 2 mm3) radiation force within tissue. and the resulting tissue displacements are mapped using ultrasonic correlation based methods. The tissue displacements are inversely proportional to the stiffness of the tissue, and thus a stiffer region of tissue exhibits smaller displacements than a more compliant region. In this paper, the feasibility of remote palpation is demonstrated experimentally using breast tissue phantoms with spherical lesion inclusions, and in vitro liver samples. A single diagnostic transducer and modified ultrasonic imaging system are used to perform remote palpation. The displacement images are directly correlated to local variations in tissue stiffness with higher contrast than the corresponding B-mode images. Relationships between acoustic beam parameters, lesion characteristics and radiation force induced tissue displacement patterns are investigated and discussed. The results show promise for the clinical implementation of remote palpation.     

Determination of object resonances by vibro-acoustography and their associated modes

Vibro-acoustography technique known by its noncontact excitation was used to detect resonance frequencies of objects in water. Two intersecting ultrasound beams generated by a 40 mm-diameter annular array transducer, focused at 35 mm and driven at f1=2.2 MHz and f2=2.22 MHz respectively, were targeted inside the object under test to produce a radiation force beating at the difference frequency f2-f1. This low frequency radiation force was used to excite the resonance vibration modes of the object by sweeping the frequency f2 between 2.22 and 2.275 MHz. The amplitude of the acoustic emission produced by the vibrations of the object was detected by a low frequency hydrophone (BW=60 kHz). By this approach, it was possible to detect resonance frequencies through amplitude variations of the measured acoustic emission. Experiments were conducted in a water tank for objects of different shapes and sizes. With a chalk sphere (15 mm-diameter) two resonance frequencies were detected at 45.75 and 68.75 kHz, and with a cylinder (10.38 mm-diameter and 32.20 mm-length) four principal resonance frequencies were identified in the 60 kHz-bandwidth of the hydrophone. It was shown with finite element calculations performed with Ansys, in which both solid and fluid parts were modelled, that the measured resonance frequencies corresponded to compressional or dilatation vibration modes of the object. It was verified that shear waves generated by torsional vibration modes were not propagated in water, as it is well known. The use of this technique to characterize heterogeneities in different media seems to be relatively more advantageous to other ultrasonic methods.     

Design of a self-calibrating simulated acoustic emission source

The use of conical piezoelectric transducers as point acoustic sources has been investigated. It has been shown that transducers based on a design originally developed at the National Institute for Standards and Technology in the USA can be used as point transmitters over the frequency range of interest in acoustic emission measurements (100 kHz to around 1 MHz). They should, therefore, be suitable for use in experiments to calibrate structures so that acoustic emission source strengths can be determined. It has also been shown that measurements of the response of the transmitting transducer backing can be used to assess the coupling efficiency, and hence to remove concerns about inconsistent coupling affecting the calibration measurements. The results indicate that the variation of the backing response with coupling is due to a shift in the resonance frequencies of the transducer with the mechanical load impedance. If other transducers can be shown to behave in a similar fashion this effect could be used to measure coupling in standard acoustic emission and ultrasonic transducers.     

调频超声脉冲驱动微气泡运动偏移的研究

提出调频超声辐射力技术驱动微泡群,以加强微泡的吸附效率.基于改进的RP方程及粒子轨迹方程研究了微泡群整体的运动位移与调频信号的中心频率、调频范围、信号声压,以及微泡半径分布关系.研究结果表明调频信号在驱动半径具有宽泛分布的气泡群,以及半径分布远离谐振半径的气泡群时,作用效果好于传统正弦波信号.例如中心频率1 MHz、调频范围0.75 MHz的调频脉冲作用高斯分布（平均半径3.5 μm、均方差为1）的微泡群200 μs,可比同等声压的正弦波多约12%的微气泡产生位移30 μm. 关键词： 超声辐射力 调频波 高斯分布     

超声造影剂微气泡的包膜黏弹特性的定量表征研究

包膜黏弹特性显著影响微气泡超声造影剂的诊断及治疗应用效果. 本文结合原子力显微镜技术及声衰减特性测量提出了一种对微气泡造影剂包膜黏弹特性定量表征的新方法. 首先采用原子力显微镜技术进行机械特性分析得到包膜微气泡的有效硬度及体弹性模量; 然后测量声衰减特性, 基于微气泡动力学理论, 计算包膜微气泡的体黏度系数. 为验证方法的有效性, 实验制备了直径为1-5 μm的白蛋白包膜微气泡造影剂, 原子力显微镜测量的有效硬度和体弹性模量分别为0.149±0.012 N/m和8.31±0.667 MPa, 并与粒径无关. 声衰减特性测量和动力学理论拟合的包膜微气泡的体黏度系数为0.374±0.003 Pa·s. 该方法可推广至其他种类包膜微气泡的黏弹特性表征, 对超声造影剂的制备及其诊断和治疗应用有积极意义.     

Internal deformation of a uniform elastic solid by acoustic radiation force

Tissue elasticity estimation is a growing area of ultrasound research. One proposed approach would apply acoustic radiation force to displace tissue and use ultrasonic motion tracking techniques to measure the resultant displacement. Such a technique might allow noninvasive imaging of tissue elastic properties. The potential of this method will be limited by the magnitude of displacements which can be generated at reasonable acoustic intensity levels. This paper presents methods for estimating the internal displacements induced in an elastic solid by acoustic radiation force. These methods predict displacements on the order of 400 microns in the human vitreous body, 0.008 micron in human breast, and 0.020 micron in human liver at an acoustic intensity of 1.0 W/cm2 (in water) and an operating frequency of 10 MHz. While the displacement generated in the vitreous should be readily detectable using ultrasonic methods, the displacements generated in the breast and liver will be much more difficult to detect. Methods are also developed for predicting the time dependent temperature increases associated with attenuated acoustic fields in the absence of perfusion. These results indicate promise for radiation force imaging in the vitreous, but potential difficulties in applying these techniques in other parts of the body.     

Determination of acoustic impedances of multi matching layers for narrowband ultrasonic airborne transducers at frequencies <2.5 MHz - Application of a genetic algorithm

The effective ultrasonic energy radiation into the air of piezoelectric transducers requires using multilayer matching systems with accurately selected acoustic impedances and the thickness of particular layers. One major problem of ultrasonic transducers, radiating acoustic energy into air, is to find the proper acoustic impedances of one or more matching layers. This work aims at developing an original solution to the acoustic impedance mismatch between transducer and air. If the acoustic impedance defences between transducer and air be more, then finding best matching layer(s) is harder. Therefore we consider PZT (lead zirconate titanate piezo electric) transducer and air that has huge acoustic impedance deference. The vibration source energy (PZT), which is used to generate the incident wave, consumes a part of the mechanical energy and converts it to an electrical one in theoretical calculation. After calculating matching layers, we consider the energy source as layer to design a transducer. However, this part of the mechanical energy will be neglected during the mathematical work. This approximation is correct only if the transducer is open-circuit. Since the possibilities of choosing material with required acoustic impedance are limited (the counted values cannot always be realized and applied in practice) it is necessary to correct the differences between theoretical values and the possibilities of practical application of given acoustic impedances. Such a correction can be done by manipulating other parameters of matching layers (e.g. by changing their thickness). The efficiency of the energy transmission from the piezoceramic transducer through different layers with different thickness and different attenuation enabling a compensation of non-ideal real values by changing their thickness was computer analyzed (base on genetic algorithm). Firstly, three theoretical solutions were investigated. Namely, Chebyshev, Desilets and Souquet theories. However, the obtained acoustic impedances do not necessarily correspond to a nowadays available material. Consequently, the values of the acoustic impedances are switched to the nearest values in a large material database. The switched values of the acoustic impedances do not generally give efficient transmission coefficients. Therefore, we proposed, in a second step, the use of a genetic algorithm (GA) to select the best acoustic impedances for matching layers from the material database for a narrow band ultrasonic transducer that work at frequency below the 2.5 MHz by considering attenuation. However this bank is rich, the results get better. So the accuracy of the propose method increase by using a lot of materials with exact data for acoustic impedance and their attenuation, especially in high frequency. This yields highly more efficient transmission coefficient. In fact by using increasing number of layer we can increase our chance to find the best sets of materials with valuable both in acoustic impedance and low attenuation. Precisely, the transmission coefficient is almost equal to unity for the all studied cases. Finally the effect of thickness on transmission coefficient is investigated for different layers. The results showed that the transmission coefficient for air media is a function of thickness and sensitive to it even for small variation in thickness. In fact, the sensitivity increases when the differences of acoustic impedances to be high (difference between PZT and air).     

Reflector-based phase calibration of ultrasound transducers

Recently, the measurement of phase transfer functions (PTFs) of piezoelectric transducers has received more attention. These PTFs are useful for e.g. coding and interference based imaging methods, and ultrasound contrast microbubble research. Several optical and acoustic methods to measure a transducer’s PTF have been reported in literature. The optical methods require a setup to which not all ultrasound laboratories have access to. The acoustic methods require accurate distance and acoustic wave speed measurements. A small error in these leads to a large error in phase, e.g. an accuracy of 0.1% on an axial distance of 10 cm leads to an uncertainty in the PTF measurement of ±97° at 4 MHz. In this paper we present an acoustic pulse-echo method to measure the PTF of a transducer, which is based on linear wave propagation and only requires an estimate of the wave travel distance and the acoustic wave speed. In our method the transducer is excited by a monofrequency sine burst with a rectangular envelope. The transducer initially vibrates at resonance (transient regime) prior to the forcing frequency response (steady state regime). The PTF value of the system is the difference between the phases deduced from the transient and the steady state regimes. Good agreement, to within 7°, was obtained between KLM simulations and measurements on two transducers in a 1-8 MHz frequency range. The reproducibility of the method was ±10°, with a systematic error of 2° at 1 MHz increasing to 16° at 8 MHz. This work demonstrates that the PTF of a transducer can be measured in a simple laboratory setting.     

大张角共焦换能器对振动声成像的影响*

振动声成像是超声成像的一种重要形式,它可以得到包含共焦区组织的弹性信息和声衰减信息的信号,将接收到的信号用于成像即可获得反映组织特性的图像。该文对大张角共焦换能器作用下振动声成像中声辐射力和切变位移进行了理论计算和数值模拟,并通过改变张角变化及频率大小研究其对声辐射力和切变位移的影响。这项工作为大张角共焦换能器在振动声成像中的应用提供了理论支持。     

Acoustic power measurement of high intensity focused ultrasound in medicine based on radiation force

How to measure the acoustic power of HIFU is one of the most important tasks in its medical application. In the paper a whole series of formula for calculating the radiation force related to the acoustic power radiated by a single element focusing transducer and by the focusing transducer array were given. Various system of radiation force balance (RFB) to measure the acoustic power of HIFU in medicine were designed and applied in China. In high power experiments, the dependence of radiation force acting the absorbing target on the target position at the beam axis of focusing transducer was fined. There is a peak value of "radiation force" acting the absorbing target in the focal region when the acoustic power through the focal plane exceeds some threshold. In order to avoid this big measurement error caused by the 'peak effect' in focal region, the distance between the absorbing target of RFB and the focusing transducer or transducer array was defined to be equal to or less than 0.7 times of the focal length in the National Standard of China for the measurements of acoustic power and field characteristics of HIFU. More than six different therapeutic equipments of HIFU have been examined by RFB for measuring the acoustic power since 1998. These results show that RFB with the absorbing target is valid in the acoustic power range up to 500W with good linearity for the drive voltage squared of focusing transducer or array. The uncertainty of measurement is within +/-15%.     

Comparison of laser interferometry and radiation force method of measuring ultrasonic power

The aim of this paper is to compare two different methods for the calculation of the ultrasonic output power of underwater transducers: the radiation force balance, which is the standard method, and the laser heterodyne interferometry, which is rather used to depict displacement or velocity distributions of the acoustic field. Here it is shown that the latter can also be used to calculate the acoustic time-average power with an uncertainty of about 22%, the radiation force balance giving an uncertainty of 12% (with 95% confidence). The interferometry experiments performed with two transducers working at 2.25 MHz and 8.25 MHz showed that they produce different acoustic fields (respectively Gaussian and Lorentz-sigmoidal distributions). Taking into account the acoustic field profiles, the acoustic time-average power from interferometry was calculated. It was found very similar to the time-average power measured with the radiation force balance in the plane-wave assumption.     

Estimating localized oscillatory tissue motion for assessment of the underlying mechanical modulus

The technique of harmonic motion imaging (HMI) uses the localized stimulus of the oscillatory ultrasonic radiation force as produced by two overlapping beams of distinct frequencies, and estimates the resulting harmonic displacement in the tissue in order to assess its underlying mechanical properties. In this paper, we studied the relationship between measured displacement and stiffness in gels and tissues in vitro. Two focused ultrasound transducers with a 100 mm focal length were used at frequencies of 3.7500 MHz and either 3.7502 (or 3.7508 MHz), respectively, in order to produce an oscillatory motion at 200 Hz in the gel or tissue. A 1.1 MHz diagnostic transducer (Imasonics, Inc.) was also focused at 100 mm and acquired 5 ms RF signals (pulse repetition frequency (PRF)=3.5 kHz) at 100 MHz sampling frequency during radiation force application. First, three 50x50 mm(2) acrylamide gels were prepared at concentrations of 4%, 8% and 16%. The resulting displacement was estimated using crosscorrelation techniques between successively acquired RF signals with a 2 mm window and 80% window overlap at 1260 W/cm(2). A normal 1-D indentation instrument (TeMPeST) applied oscillatory loads at 0.1-200 Hz with a 5 mm-diameter flat indenter. Then, 12 displacement measurements in 6 porcine muscle specimens (two measurements/case, as above) were made in vitro, before and after ablation which was performed for 10 s at 1260 W/cm(2). In all gel cases, the harmonic displacement was found to linearly increase with intensity and exponentially decrease with gel concentration. The TeMPeST measurements showed that the elastic moduli for the 4%, 8% and 16% gels equaled 3.93+/-0.06, 17.1+/-0.2 and 75+/-2 kPa, respectively, demonstrating that the HMI displacement estimate depends directly on the gel stiffness. Finally, in the tissues samples, the mean displacement amplitude showed a twofold decrease between non-ablated and ablated tissue, demonstrating a correspondence between the HMI response and an increase in stiffness measured with the TeMPeST instrument.