Liquid lens using acoustic radiation force

A liquid lens is proposed that uses acoustic radiation force with no mechanical moving parts. It consists of a cylindrical acrylic cell filled with two immiscible liquids (degassed water and silicone oil) and a concave ultrasound transducer. The focal point of the transducer is located on the oil-water interface, which functions as a lens. The acoustic radiation force is generated when there is a difference in the acoustic energy densities of different media. An acoustic standing wave was generated in the axial direction of the lens and the variation of the shape of the oil-water interface was observed by optical coherence tomography (OCT). The lens profile can be rapidly changed by varying the acoustic radiation force from the transducer. The kinematic viscosity of silicone oil was optimized to minimize the response times of the lens. Response times of 40 and 80 ms when switching ultrasonic radiation on and off were obtained with a kinematic viscosity of 200 cSt. The path of a laser beam transmitted through the lens was calculated by ray-tracing simulations based on the experimental results obtained by OCT. The transmitted laser beam could be focused by applying an input voltage. The liquid lens could be operated as a variable-focus lens by varying the input voltage.     

Rapid method for assessing relative tissue stiffness using MR acoustic radiation force imaging

Acoustic radiation force imaging (ARFI) has been suggested as a tool for remote palpation. In this study an MR‐ARFI sequence, based on echo‐planar‐imaging, is introduced, for remote semi‐quantitative assessment of local tissue stiffness. The focal zone of a high intensity focused ultrasound (HIFU) is positioned at the region of interest and a single HIFU burst is transmitted. The method then measures the entire time integral of the resulting displacement at the focal zone. Combining this measurement with the Kelvin–Voigt viscoelastic tissue model, a local stiffness index is obtained. The method was implemented on gel phantoms, ex‐vivo bovine brain and chicken liver specimens. The results have demonstrated the ability to evaluate the relative local stiffness within 600 ms and to distinguish between different tissues on the basis of their stiffness index. The method may potentially be used for remote palpation of suspicious regions for diagnostic purposes, or for providing a mechanical feedback during therapeutic procedures, such as thermal ablation.     

Regularization of tissue shear modulus reconstruction using strain variance

An effective setting method (that is, a method using the variances of strain tensor component measurements) is described for the properly spatially varied regularization parameters for our shear modulus reconstruction. At each position, the respective strain variances can be experimentally evaluated using plural field measurements or single field measurement, for example, when using all crosscorrelation- based methods, by using the Ziv-Zakai Lower Bound (ZZLB). The demonstrated regularization by the single field measurement using the cross-spectrum phase gradient method (MCSPGM) in experiments confirms that the use of the axial strain variance estimated by the echo signal-to-noise ratio and correlations (the combined SNRc) effectively stabilizes the 1-D reconstruction on an agar phantom and a human in vivo liver carcinoma during interstitial microwave thermal treatment. The regularization yields a spatially uniform stability in reconstruction.     

Dynamic mechanical response of elastic spherical inclusions to impulsive acoustic radiation force excitation

Acoustic radiation force impulse imaging has been used clinically to study the dynamic response of lesions relative to their background material to focused, impulsive acoustic radiation force excitations through the generation of dynamic displacement field images. Dynamic displacement data are typically displayed as a set of parametric images, including displacement immediately after excitation, maximum displacement, time to peak displacement, and recovery time from peak displacement. To date, however, no definitive trends have been established between these parametric images and the tissues' mechanical properties. This work demonstrates that displacement magnitude, time to peak displacement, and recovery time are all inversely related to the Young's modulus in homogeneous elastic media. Experimentally, pulse repetition frequency during displacement tracking limits stiffness resolution using the time to peak displacement parameter. The excitation pulse duration also impacts the time to peak parameter, with longer pulses reducing the inertial effects present during impulsive excitations. Material density affects tissue dynamics, but is not expected to play a significant role in biological tissues. The presence of an elastic spherical inclusion in the imaged medium significantly alters the tissue dynamics in response to impulsive, focused acoustic radiation force excitations. Times to peak displacement for excitations within and outside an elastic inclusion are still indicative of local material stiffness; however, recovery times are altered due to the reflection and transmission of shear waves at the inclusion boundaries. These shear wave interactions cause stiffer inclusions to appear to be displaced longer than the more compliant background material. The magnitude of shear waves reflected at elastic lesion boundaries is dependent on the stiffness contrast between the inclusion and the background material, and the stiffness and size of the inclusion dictate when shear wave reflections within the lesion will interfere with one another. Jitter and bias associated with the ultrasonic displacement tracking also impact the estimation of a tissue's dynamic response to acoustic radiation force excitation.     

Determination of the force acting on a spherical obstacle in an underexpanded jet

A method is proposed for determining the force acting on a spherical obstacle in an underexpanded jet. The method is based on the application of the momentum law.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 4, pp. 668–671, October, 1978.     

Determination of the elastic modulus of adherent cells using spherical atomic force microscope probe

When the conventional Hertz formula is used to extract the elastic modulus, E, of cells based on the compression test using atomic force microscope spherical probe, the inconsistency between the actual situation and the assumption of the formula will lead to a large error. Using the ABAQUS for finite element modeling and analysis, here, a modified Hertz formula was developed to reduce the effects of cell radius, cell thickness, probe radius and compression depth on the extracted E of cells. Experimentally, the insensitivity of the extracted E to the compression region of cell and probe radius reflects the validity of the modified formula. Owing to the poor resolution of spherical probes, it's unlikely to know the actual thickness of cell at the measured point, which can lead to a huge error. Based on the modified formula, we further proposed an approach to control the effect of the uncertainty of cell thickness and ensured that a 10% difference in cell thickness does not incur over 10% variation in the obtained elastic modulus.

     

Detection of tissue harmonic motion induced by ultrasonic radiation force using pulse-echo ultrasound and Kalman filter

A method using pulse echo ultrasound and the Kalman filter is developed for detecting submicron harmonic motion induced by ultrasonic radiation force. The method estimates the amplitude and phase of the motion at desired locations within a tissue region with high sensitivity. The harmonic motion generated by the ultrasound radiation force is expressed as extremely small oscillatory Doppler frequency shifts in the fast time (A-line) of ultrasound echoes, which are difficult to estimate. In slow time (repetitive ultrasound echoes) of the echoes, the motion also is presented as oscillatory phase shifts, from which the amplitude and phase of the harmonic motion can be estimated with the least mean squared error by Kalman filter. This technique can be used to estimate the traveling speed of a harmonic shear wave by tracking its phase changes during propagation. The shear wave propagation speed can be used to solve for the elasticity and viscosity of tissue as reported in our earlier study. Validation and in vitro experiments indicate that the method provides excellent estimations for very small (submicron) harmonic vibrations and has potential for noninvasive and quantitative stiffness measurements of tissues such as artery.     

Phase aberration correction using ultrasound radiation force and vibrometry optimization

We describe a phase aberration correction method that uses dynamic ultrasound radiation force to harmonically vibrate an object using amplitude modulated continuous wave ultrasound. The phase of each element of an annular array transducer is adjusted to maximize the radiation force and obtain optimal focus of the ultrasound beam. The maximization of the radiation force is performed by monitoring the velocity of scatterers in the focus region. We present theory that shows focal optimization with radiation force has a well-behaved cost function. Experimental validation is shown by correction of manual defocusing of an annular array as well as correcting for a lens-shaped aberrator placed near the transducer. A Doppler laser vibrometer and a pulse-echo Doppler ultrasound method were used to monitor the velocity of a sphere used as a target for the transducer. By maximizing the radiation force-induced vibration of scatterers in the focal region, the resolution of the ultrasound beam can be recovered after aberration defocusing.     

A finite-element method model of soft tissue response to impulsive acoustic radiation force

Several groups are studying acoustic radiation force and its ability to image the mechanical properties of tissue. Acoustic radiation force impulse (ARFI) imaging is one modality using standard diagnostic ultrasound scanners to generate localized, impulsive, acoustic radiation forces in tissue. The dynamic response of tissue is measured via conventional ultrasonic speckle-tracking methods and provides information about the mechanical properties of tissue. A finite-element method (FEM) model has been developed that simulates the dynamic response of tissues, with and without spherical inclusions, to an impulsive acoustic radiation force excitation from a linear array transducer. These FEM models were validated with calibrated phantoms. Shear wave speed, and therefore elasticity, dictates tissue relaxation following ARFI excitation, but Poisson's ratio and density do not significantly alter tissue relaxation rates. Increased acoustic attenuation in tissue increases the relative amount of tissue displacement in the near field compared with the focal depth, but relaxation rates are not altered. Applications of this model include improving image quality, and distilling material and structural information from tissue's dynamic response to ARFI excitation. Future work on these models includes incorporation of viscous material properties and modeling the ultrasonic tracking of displaced scatterers.     

Assessing and improving acoustic radiation force image quality using a 1.5-D transducer design

A 1.5-D transducer array was proposed to improve acoustic radiation force impulse (ARFI) imaging signal-to-noise ratio (SNRARFI) and image contrast relative to a conventional 1-D array. To predict performance gains from the proposed 1.5-D transducer array, an analytical model for SNRARFI upper bound was derived. The analytical model and 1.5-D ARFI array were validated using a finite element modelbased numerical simulation framework. The analytical model demonstrated good agreement with numerical results (correlation coefficient = 0.995), and simulated lesion images yielded a significant (2.92 dB; p < 0.001) improvement in contrast-tonoise ratio when rendered using the 1.5-D ARFI array.     

Langevin acoustic radiation force of a high-order bessel beam on a rigid sphere

The acoustic radiation force of Langevin type resulting from the interaction of a high-order Bessel beam with a rigid immovable sphere in an ideal fluid is theoretically investigated. The analysis is based on applying the generalized Rayleigh series used in the near-field acoustic scattering problem to calculate the force. With appropriate selection of specific Bessel beam parameters, results for the rigid sphere unexpectedly reveal a negative radiation force caused by the Lagrangean energy density. Specifically, the negative force on the rigid sphere arises when the kinematic energy density is larger than the potential energy density. This condition provides an impetus for further designing acoustic tweezers operating with high-order Bessel beams of progressive waves for potential applications in particle entrapment and manipulation.     

Hashin–Shtrikman bounds on the shear modulus of a nanocomposite with spherical inclusions and interface effects

The recently developed variational framework for polarization methods in nanocomposites is applied to the determination of a lower-bound on the shear modulus of a nanocomposite with monosized, spherical inclusions. This bound explicitly accounts for linear elastic effects in the matrix–inclusion interface. Even if the polarization fields involved in its derivation are much more intricate, this bound is closely related to the classical Hashin–Shtrikman bound, with which it coincides when surface stresses are disregarded. More strikingly, when surface stresses are not disregarded, it also coincides with previously established Mori–Tanaka estimates. This result provides firm ground for the practical use of these estimates, for example for design purposes.     

Eccentricity effects on acoustic radiation from a spherical source suspended within a thermoviscous fluid sphere

Acoustic radiation from a spherical source undergoing angularly periodic axisymmetric harmonic surface vibrations while eccentrically suspended within a thermoviscous fluid sphere, which is immersed in a viscous thermally conducting unbounded fluid medium, is analyzed in an exact fashion. The formulation uses the appropriate wave-harmonic field expansions along with the translational addition theorem for spherical wave functions and the relevant boundary conditions to develop a closed-form solution in form of infinite series. The analytical results are illustrated with a numerical example in which the vibrating source is eccentrically positioned within a chemical fluid sphere submerged in water. The modal acoustic radiation impedance load on the source and the radiated far-field pressure are evaluated and discussed for representative values of the parameters characterizing the system. The proposed model can lead to a better understanding of dynamic response of an underwater acoustic lens. It is equally applicable in miniature transducer analysis and design with applications in medical ultrasonics.     

Image quality, tissue heating, and frame rate trade-offs in acoustic radiation force impulse imaging

The real-time application of acoustic radiation force impulse (ARFI) imaging requires both short acquisition times for a single ARFI image and repeated acquisition of these frames. Due to the high energy of pulses required to generate appreciable radiation force, however, repeated acquisitions could result in substantial transducer face and tissue heating. We describe and evaluate several novel beam sequencing schemes which, along with parallel-receive acquisition, are designed to reduce acquisition time and heating. These techniques reduce the total number of radiation force impulses needed to generate an image and minimize the time between successive impulses. We present qualitative and quantitative analyses of the trade-offs in image quality resulting from the acquisition schemes. Results indicate that these techniques yield a significant improvement in frame rate with only moderate decreases in image quality. Tissue and transducer face heating resulting from these schemes is assessed through finite element method modeling and thermocouple measurements. Results indicate that heating issues can be mitigated by employing ARFI acquisition sequences that utilize the highest track-to-excitation ratio possible.     

Three-dimensional acoustic radiation force of a eukaryotic cell arbitrarily positioned in a Gaussian beam

Expressions are derived for calculating the three-dimensional acoustic radiation force(ARF) on a multilayer microsphere positioned arbitrarily in a Gaussian beam. A theoretical model of a three-layer microsphere with a cell membrane, cytoplasm, and nucleus is established to study how particle geometry and position affect the three-dimensional ARF, and its results agree well with finite-elemen numerical results.The microsphere can be moved relative to the beam axis by changing its structure and p...     

二维阵列换能器声辐射力分布的计算分析

利用角谱理论得到了圆形活塞换能器阵元组阵后作用在平面悬浮物体上的声辐射力分布公式。通过数值仿真,分析了换能器频率、阵元间距以及阵元数目对声辐射力分布的影响。计算结果表明,换能器组阵使得声辐射力分布的指向性变窄,强度增强;随着换能器频率的提高、阵元间距的增大以及阵元数目的增多,声辐射力分布的主瓣更尖锐,但阵元间距的增大会使声辐射力分布的旁瓣增高。为了改善声辐射力的空间分布,采用伪逆矩阵算法,以能量增益为目标函数,通过调节换能器阵元表面振动速度的幅值和相位来形成多焦点的声辐射力分布,为阵列换能器声辐射力分布的调控和声悬浮稳定性的研究提供帮助。     

A penny-shaped crack above the pole of a spherical inhomogeneity

Stress investigation for the problem of a penny-shaped crack located above the pole of a spherical particle (inhomogeneity) in 3D elastic solid under tension has been carried out. Both the inhomogeneity and the solid are isotropic but have different elastic moduli. The analysis is based on Eshelby's equivalent inclusion method and superposition theory of elasticity. An approximation according to the Saint-Venant principle is made in order to decouple the interaction between the crack and the inhomogeneity. An analytical solution for the stress intensity factors on the boundary of the crack is thus evaluated. It is found that both Mode I and Mode II intensity factors exist, even the loading applied at infinity is uniform tension. Results obtained show that shielding and anti-shielding (amplifying) effects of the inhomogeneity to the crack are solely determined by the modulus ratios of the inhomogeneity to the matrix. Numerical examples also indicate the interaction between the crack and the inhomogeneity is strongly influenced by the distance between the centers.     

Young's modulus and shear modulus of a composite shaft from resonance measurements

A simple method which uses axial and torsional vibration resonance for the measurement of Young's modulus, E, and shear modulus, G, of shafting is described. The moduli are used to calculate the resonance frequency of transverse vibration for comparison with a measured value. The agreement is extremely good so the measurements of E and G, and the theory used to calculate the transverse resonant frequency, must be precise.This method can be used in materials research but its simplicity also commends it for the quality control of composite material components in production.     

Narrowband shear wave generation by a Finite-Amplitude radiation force: The fundamental component

A highly localized source of low-frequency shear waves can be created by the modulated radiation force resulting from two intersecting quasi-continuous-wave ultrasound beams of slightly different frequencies. In contrast to most other radiation force-based methods, these shear waves can be narrowband. Consequently, different frequency-dependent effects will not significantly affect their spectrum as they propagate within a viscoelastic medium, thereby enabling the viscoelastic shear properties of the medium to be determined at any given modulation frequency. This can be achieved by tracking the shear wave phase delay and change in amplitude over a specific distance. In this paper we explore the properties of short duration (dynamic) low-frequency shear wave propagation and study how the shear displacement field depends on the excitation conditions. Our investigations make use of the approximate Green's functions for viscoelastic media, and the evolution of such waves is studied in the spatiotemporal domain from a theoretical perspective. Although nonlinearities are included in our confocal source model, just the properties of the fundamental shear component are examined in this paper. We examine how the shear wave propagation is affected by the shear viscosity, the coupling wave, the spatial distribution of the force, the shear speed, and the duration of the modulated wave. A method is proposed for estimating the shear viscosity of a viscoelastic medium. In addition, it is shown how the Voigt model paremeters can be extracted from the frequency-dependent speed and attenuation.