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.     

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.     

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.     

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.     

Theoretical Analysis of Shear Wave Interference Patterns by Means of Dynamic Acoustic Radiation Forces

Acoustic radiation forces associated with high intensity focused ultrasound stimulate shear wave propagation allowing shear wave speed and shear viscosity estimation of tissue structures. As wave speeds are meters per second, real time displacement tracking over an extend field-of-view using ultrasound is problematic due to very high frame rate requirements. However, two spatially separated dynamic external sources can stimulate shear wave motion leading to shear wave interference patterns. Advantages are shear waves can be imaged at lower frame rates and local interference pattern spatial properties reflect tissue's viscoelastic properties. Here a theoretical analysis of shear wave interference patterns by means of dynamic acoustic radiation forces is detailed. Using a viscoelastic Green's function analysis, tissue motion due to a pair of focused ultrasound beams and associated radiation forces are presented. Overall, this paper theoretically demonstrates shear wave interference patterns can be stimulated using dynamic acoustic radiation forces and tracked using conventional ultrasound imaging.     

Fast topological imaging

Mathematical optimization methods based on the topological sensitivity analysis have been used to develop innovative ultrasonic imaging methods. With a single illumination of the medium, they have proved experimentally to yield a lateral resolution comparable to classical multiple-illumination techniques. As these methods are based on the numerical simulations of two wave fields, they require extensive computation. A time-domain finite-difference scheme is usually used for that purpose. This paper presents the development of an experimental imaging method based on the topological sensitivity. The numerical cost is reduced by replacing the numerical simulations by simple mathematical operations between the radiation patterns of the array’s transducers and the frequency-domain signals to be emitted. These radiation patterns are preliminary computed once and for all. They were obtained with a finite element model for the anisotropic elastodynamic case and with semi-analytical integrations for the acoustic case. Experimental results are presented for a composite material sample and for a prefractal network immersed in water. A lateral resolution below 2.5 times the wavelength is obtained with a single plane wave illumination. The method is also applied with multiple illuminations, so that objects hidden in complex media can be investigated.     

Shear strain estimation and lesion mobility assessment in elastography

Elastography typically measures and images the normal strain component along the insonification/compression axis, i.e., in the axial direction. We have recently shown that, by using interpolation and cross-correlation methods of transversely displaced RF echo segments, it is possible to measure and image displacement and strain transversely to the beam with good precision. This enables the estimation and imaging of all three principal normal strain components. Generally, motion in a direction other than that in which strain is estimated may result in decorrelation noise, severely corrupting the estimates. Therefore, a correction method is applied to correct the displacement and strain estimates for decorrelating motion. In this paper, we show how corrected displacement estimates can also be used to estimate and image the shear strain components. This may allow us to identify regions of decorrelation noise in the normal strain measurement that are due to shear strain. Shear strain estimates provide supplementary information, which can characterize different tissue elements based on their mobility. In the case of breast lesions, low mobility is related to malignancy. Following an in vivo case, we show with 2D simulations how assessment of tumor mobility can be achieved with shear strain estimation.     

Investigation of transmit and receive performance at the fundamental and third harmonic resonance frequency of a medical ultrasound transducer

In this study, the phenomenon of higher harmonic thickness resonance of a piezoelectric transducer was used to investigate potentially additional sensitivity at the third harmonic frequency for conventional medical transducers. The motivation for this research is that some applications in medical ultrasound (e.g. third harmonic transmit phasing and contrast imaging) need probes which are sensitive around both the fundamental and third harmonic frequencies, and that these higher harmonic thickness modes, although often considered as undesired, might be used beneficially. The novelty aspect in this study is the presented transmit and receive potential at both the fundamental and third harmonic of a conventional cardiac probe with modified electrical tuning. Elements of an experimental PZT-based phased-array probe (f_c = 3 MHz, 64 elements, element width = 0.3 mm, elevation aperture = 13 mm) were electrically retuned with series inductors around the third harmonic resonance frequency at 10 MHz. Hydrophone measurements with 10-MHz-tuned elements showed that, as compared to a conventionally tuned element, the transmit transfer function at the third harmonic increased more than 23 dB, while the sensitivity at the fundamental frequency was only 6 dB lower. Pulse-echo measurements showed that the two-way transfer function of a 10-MHz-tuned element resulted in 20 dB increased sensitivity around the third harmonic as compared to an untuned element. Simulated transfer functions, from both a 1D KLM and 2D finite element model of an element of the experimental array transducer, confirmed the measured sensitivity peaks at the fundamental and third harmonic. In conclusion, this study demonstrated the effect of changing the electrical tuning on a conventional array transducer which increased the sensitivity around the third harmonic resonance frequency, while maintaining good sensitivity at the fundamental frequency.     

Critical issues in breast imaging by vibro-acoustography

Clinically, there are two important issues in breast imaging: detection of microcalcifications and identification of mass lesions. X-ray mammography is the main imaging method used for detection of microcalcification, and ultrasound imaging is normally used for detection of mass lesions in breast. Both these methods have limitations that reduce their clinical usefulness. For this reasons, alternative breast imaging modalities are being sought. vibro-acoustography is an imaging modality that has emerged in recent years. This method is based on low-frequency harmonic vibrations induced in the object by the radiation force of ultrasound. This paper describes potential applications of vibro-acoustography for breast imaging and addresses the critical imaging issues such as detection of microcalcifications and mass lesions in breast. Recently, we have developed a vibro-acoustography system for in vivo breast imaging and have tested it on a number of volunteers. Resulting images show soft tissue structures and calcifications within breast with high contrast, high resolution, and no speckles. The results have been verified using X-ray mammography. The encouraging results from in vitro and in vivo experiments suggest that further development of vibro-acoustography technology may lead to a new clinical tool that can be used to detect microcalcifications as well as mass lesions in breast.     

超声虚源成像中自适应双向空间逐点聚焦方法

针对传统超声成像中图像分辨率和对比度随深度下降的问题,提出了一种基于虚源的自适应双向空间逐点聚焦超声成像方法。首先,使用超声换能器线列阵分子孔径分别定焦点发射和接收超声波,采集扫描线数据;然后将焦点视为虚拟点声源,计算虚源到空间成像点的延时,利用合成孔径原理再次进行空间逐点聚焦;在合成过程中采用相干系数进行自适应加权。采用空间脉冲响应法对不同深度的点目标和囊目标仿真成像,从而量化分辨率和对比度。在F数为1.5、焦距为10 mm时(对应子孔径阵元数为17)可以获得与64通道定焦点发射、动态聚焦接收相当的图像质量且在所有深度上保持一致。实际硬件平台的体模成像实验进一步验证了方法的有效性。该方法可在整个成像深度范围内保持和常规成像一致的分辨率和对比度,从而获得更优的整体成像效果。      

Analytical estimation of the noise due to a rotating shaft

This article focuses on noise prediction of a rotating shaft. The governing equations of motion for a Rayleigh beam, rotating about its longitudinal axis and subjected to a harmonic force, are first established using the Hamilton’s principle and Galerkin’s method. Then, the vibrating displacement of the shaft is solved for. The aeroacoustic theory, introduced by Lighthill and improved by Ffowcs Williams and Hawkings, is used for calculating the developed noise of the shaft in motion. The dominant effect to the noise is the surface pressure on the moving shaft. Parametric studies also presented. From the numerical data, the noise value, from a rotating shaft, corresponding to the higher significant resonance is greater than that related to the first resonant mode. This phenomenon has not been found in the frequency response of the shaft’s displacement.     

Comparison of two methods of treatment for intraluminal thermal ablation using an ultrasound cylindrical phased array

Intraluminal (within the alimentary tract) thermal surgery has been shown to be a useful therapeutic option when extracorporeal focused ultrasound applicators cannot be used since their beam may not reach the target site. If plane transducers are used for the treatment of alimentary tract tumours, the applicator must be rotated in order to generate a cylindrical volume of necrosis. However, rotating these applicators and controlling their shooting direction presents technical difficulties. If tubular transducers are used it is difficult to treat arbitrary angles with a large therapeutic length. To solve these difficulties, the feasibility of an ultrasound phased array applicator has been evaluated using a cylindrical prototype (outer diameter 10.6 mm), which is composed of 16 elementary transducers working at 4.55 MHz and arranged on a quarter of the cylinder. Using this applicator it is possible to generate plane or cylindrical waves. Plane waves were generated by exciting eight successive elements of the array with appropriate delay times. The exposure direction was changed by exciting a different set of eight elements. In this way, the ultrasound beam was electronically rotated through the tissues. Cylindrical waves were generated by exciting several transducers without delay times. Imaging was provided using a miniature echographic probe. Ex vivo experiments were carried out in pig liver to compare two approaches of treatment. The first consisted of generating successive plane waves separated from each other by a 6 degrees angle. The second one consisted of exciting all the 16 elements without delay times. In the two cases, the lesions were well-defined and occupied a quarter of cylinder. In both sets of experiments, the sonication time and the intensity were 20 s and 17 W/cm(2), respectively. In the first case, the depth was up to 17 mm compared to 6 mm in the second case.     

Dynamic analysis of a multi-span uniform beam carrying a number of various concentrated elements

This paper employs the numerical assembly method (NAM) to determine the “exact” frequency–response amplitudes of a multiple-span beam carrying a number of various concentrated elements and subjected to a harmonic force, and the exact natural frequencies and mode shapes of the beam for the case of zero harmonic force. First, the coefficient matrices for the intermediate concentrated elements, pinned support, applied force, left-end support and right-end support of a beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact dynamic response amplitude of the forced vibrating system corresponding to each specified exciting frequency of the harmonic force is determined by solving the simultaneous equations associated with the last overall coefficient matrix. The graph of dynamic response amplitudes versus various exciting frequencies gives the frequency–response curve for any point of a multiple-span beam carrying a number of various concentrated elements. For the case of zero harmonic force, the above-mentioned simultaneous equations reduce to an eigenvalue problem so that natural frequencies and mode shapes of the beam can also be obtained.     

Multiferroic domain dynamics in strained strontium titanate

Multiferroicity can be induced in strontium titanate by applying biaxial strain. Using optical second harmonic generation, we report a transition from 4/mmm to the ferroelectric mm2 phase, followed by a transition to a ferroelastic-ferroelectric mm2 phase in a strontium titanate thin film. Piezoelectric force microscopy is used to study ferroelectric domain switching. Second harmonic generation, combined with phase-field modeling, is used to reveal the mechanism of coupled ferroelectric-ferroelastic domain wall motion. These studies have relevance to multiferroics with coupled polar and axial phenomena.     

Model for bubble pulsation in liquid between parallel viscoelastic layers

A model is presented for a pulsating spherical bubble positioned at a fixed location in a viscous, compressible liquid between parallel viscoelastic layers of finite thickness. The Green's function for particle displacement is found and utilized to derive an expression for the radiation load imposed on the bubble by the layers. Although the radiation load is derived for linear harmonic motion it may be incorporated into an equation for the nonlinear radial dynamics of the bubble. This expression is valid if the strain magnitudes in the viscoelastic layer remain small. Dependence of bubble pulsation on the viscoelastic and geometric parameters of the layers is demonstrated through numerical simulations.     

Radiation force and shear motions in inhomogeneous media

An action of radiation force induced by ultrasonic beam in waterlike media such as biological tissues (where the shear modulus is small as compared to the bulk compressibility) is considered. A new, nondissipative mechanism of generation of shear displacement due to a smooth (nonreflecting) medium inhomogeneity is suggested, and the corresponding medium displacement is evaluated. It is shown that a linear primary acoustic field in nondissipative, isotropic elastic medium cannot excite a nonpotential radiation force and, hence, a shear motion, whereas even smooth inhomogeneity makes this effect possible. An example is considered showing that the generated displacement pulse can be significantly longer than the primary ultrasound pulse. It is noted that, unlike the dissipative effect, the nondissipative action on a localized inhomogeneity (such as a lesion in a tissue) changes its sign along the beam axis, thus stretching or compressing the focus area.     

Measuring viscous dissipative interactions in dynamic force microscopy

The periodic motion of a harmonic pendulum in an arbitrary force field including viscous damping is studied as it pertains to dynamic force microscopy. It is shown that the damping constant as a function of tip-sample distance and thus the dissipative force can be obtained unambiguously by measuring the driving-force amplitude versus displacement of the force sensor. This methodology provides the basis for quantitative force spectroscopy of dissipative interactions.     

A two-way optical interconnection network using a single mode fiber array

We present a dynamic free space interconnection network for single mode fibers. The architecture consists of a two-way imaging geometry involving only one single mode fiber array. Input and output fibers belong to the same fiber array. Programmable and fixed diffractive optical elements are used for beam steering and wavefront correction. We show that the network ensures favorable conditions for launching and allows for a high interconnection volume with minimal insertion losses at 2.5 Gb/s. The architecture is also adapted to the use of binary electrically addressed spatial light modulators.     

非线性声参量成像及其在医学诊断中应用

本文介绍了我们对于反射模式非线性参量B／A的成像技术的研究结果，包括：(1)基于二次谐波的非线性参量层析成像(2)基于参量阵差频波的非线性参量层析成像(3)非线性参量的等深度C-扫成像。利用这三种成像方法对多种生物组织，特别对正常和病变的生物组织进行非线性参量成像。结果表明，非线性声参量成像可以比线性声参量更容易地判别生物组织的病理状态，从而展示了它在医学超声诊断中的应用前景。     

Study of acoustic nonlinearity parameter imaging methods in reflection mode for biological tissues

Three novel methods for acoustic nonlinearity parameter B/A imaging in reflection mode are developed in this paper. They are: (1) the acoustic nonlinearity parameter B/A tomography by detecting reflective second harmonic wave, (2) the B/A tomography in reflection mode via the measurement of the difference frequency wave generated by a parametric array, and (3) the C-scan imaging of B/A via the measurement of the echo second-harmonic signal. A theoretical analysis and the experimental imaging of normal and pathological biological tissues by using these methods are also present and discussed. Results show that using the acoustic nonlinearity parameter imaging we can more easily distinguish the diseased tissue from the normal one than using the linear acoustic parameters.