Amplitude-modulated acoustic radiation force experienced by elastic and viscoelastic spherical shells in progressive waves

The dynamic acoustic radiation force resulting from a dual-frequency beam incident on spherical shells immersed in an inviscid fluid is examined theoretically in relation to their thickness and the contents of their interior hollow regions. The theory is modified to include a hysteresis type of absorption inside the shells' material. The results of numerical calculations are presented for stainless steel and absorbing lucite (PolyMethyMethacrylAte) shells with the hollow region filled with water or air. Significant differences occur when the interior fluid inside the hollow region is changed from water to air. It is shown that the dynamic radiation force function Yd deviates from the static radiation force function Yp when the modulation size parameter deltax = mid R:x2 - x1mid R: (x1 = k1a, x2 = k2a, k1 and k2 are the wave vectors of the incident ultrasound waves, and a is the outer radius of the shell) starts to exceed the width of the resonance peaks in the Yp curves.     

椭球粒子声辐射力计算及分析

针对水下椭球粒子,以声散射理论为基础,采用分波序列的方法,建立了椭球粒子声辐射力的理论计算模型。进而根据声辐射力计算公式,以刚性椭球粒子和液体椭球粒子为例,计算并分析不同Bessel波束作用下椭球粒子的轴向声辐射力函数特征。数值仿真计算结果表明,对于刚性椭球粒子,扁平椭球粒子相对于细长椭球粒子更有助于激发负声辐射力;对于液体椭球粒子,细长椭球粒子相对于扁平椭球粒子更加容易产生负声辐射力;对于不同介质的椭球粒子,不同的入射波束激发的负声辐射力的效果也存在明显的差异。该结果为复杂的尺寸和介质粒子声操控技术提供了理论的可行性。     

Multifrequency radiation force of acoustic waves in fluids

In this article we introduce the concept of multifrequency radiation force produced by a polychromatic acoustic beam propagating in a fluid. This force is a generalization of dynamic radiation force due to a bichromatic wave. We analyse the force exerted on a rigid sphere by a plane wave with N frequency components. Our approach is based on solving the related scattering problem, taking into account the nonlinearity of the fluid. The radiation force is calculated by integrating the excess of pressure in the quasilinear approximation over the surface of the sphere. Results reveal that the spectrum of the multifrequency radiation force is composed of up to N(N−1)/2 distinct frequency components. In addition, the radiation force generated by plane progressive waves is predominantly caused by parametric amplification. This is a phenomenon due to the nonlinear nature of wave propagation in fluids.     

Mechanism of the quasi-zero axial acoustic radiation force experienced by elastic and viscoelastic spheres in the field of a quasi-Gaussian beam and particle tweezing

The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w₀ and a diffraction convergence length known as the Rayleigh range z_R. Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere’s resonance frequencies for kw₀ ? 1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force.     

Axial acoustic radiation force on an elastic spherical shell near an impedance boundary for zero-order quasi-Bessel–Gauss beam

Shell structures have increasingly widespread applications in biomedical ultrasound fields such as contrast agents and drug delivery,which requires the precise prediction of the acoustic radiation force under various circumstances to improve the system efficiency.The acoustic radiation force exerted by a zero-order quasi-Bessel-Gauss beam on an elastic spherical shell near an impedance boundary is theoretically and numerically studied in this study.By means of the finite series method and the image theory,a zero-order quasi-Bessel-Gauss beam is expanded in terms of spherical harmonic functions,and the exact solution of the acoustic radiation force is derived based on the acoustic scattering theory.The acoustic radiation force function,which represents the radiation force per unit energy density and per unit cross-sectional surface,is especially investigated.Some simulated results for a polymethyl methacrylate shell and an aluminum shell are provided to illustrate the behavior of acoustic radiation force in this case.The simulated results show the oscillatory property and the negative radiation force caused by the impedance boundary.An appropriate relative thickness of the shell can generate sharp peaks for a polymethyl methacrylate shell.Strong radiation force can be obtained at small half-cone angles and the beam waist only affects the results at high frequencies.Considering that the quasi-Bessel-Gauss beam possesses both the energy focusing property and the non-diffracting advantage,this study is expected to be useful in the development of acoustic tweezers,contrast agent micro-shells,and drug delivery applications.     

Modeling the acoustic radiation force in microfluidic chambers

A procedure is demonstrated to quantitatively evaluate the acoustic radiation forces in microfluidic particle manipulation chambers. Typical estimates of the acoustic pressure and the acoustic radiation force are based on an analytical solution for a simple one-dimensional standing wave pattern. The complexities of a typical microfluidic channel limit the usefulness of this approach. By leveraging finite elements, and a generalized equation for the acoustic radiation force, channel designs can be investigated in two and three dimensions. Calculations and experimental observations in this report and the literature, confirm these claims.     

Circumferential resonance modes of solid elastic cylinders excited by obliquely incident acoustic waves

When an immersed solid elastic cylinder is insonified by an obliquely incident plane acoustic wave, some of the resonance modes of the cylinder are excited. These modes are directly related to the incidence angle of the insonifying wave. In this paper, the circumferential resonance modes of such immersed elastic cylinders are studied over a large range of incidence angles and frequencies and physical explanations are presented for singular features of the frequency-incidence angle plots. These features include the pairing of one axially guided mode with each transverse whispering gallery mode, the appearance of an anomalous pseudo-Rayleigh in the cylinder at incidence angles greater than the Rayleigh angle, and distortional effects of the longitudinal whispering gallery modes on the entire resonance spectrum of the cylinder. The physical explanations are derived from Resonance Scattering Theory (RST), which is employed to determine the interior displacement field of the cylinder and its dependence on insonification angle.     

The radiation power of elastic waves excited in a solid half-space by a subsurface time-harmonic source

The method of Fourier transforms is used to solve the problem of excitation of longitudinal, transverse, and Rayleigh surface waves by a time-harmonic point source placed in a homogeneous isotropic, perfectly elastic half-space and acting along the normal surface. Expressions for the time-average radiation powers of the aforementioned waves are obtained by the method of radiation reaction without using any approximations. The distribution of radiation power over different types of waves depending on their velocities and the source’s depth is investigated in detail.     

Scheme of negative acoustic radiation force based on a multiple-layered spherical structure

Acoustic radiation force(ARF), as an important particle manipulation method, has been extensively studied in recent years. With the introduction of the concept of “acoustic tweezers”, negative acoustic radiation has become a research hotspot. In this paper, a scheme of realizing negative ARF based on the multiple-layered spherical structure design is proposed. The specific structure and design idea are presented. Detailed theoretical calculation analysis is carried out.Numerical simulations have...     

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.     

Axial time-averaged acoustic radiation force on a cylinder in a nonviscous fluid revisited

Objective

The present research examines the acoustic radiation force of axisymmetric waves incident upon a cylinder of circular surface immersed in a nonviscous fluid. The attempt here is to unify the various treatments of radiation force on a cylinder with arbitrary radius and provide a formulation suitable for any axisymmetric incident wave.

Method and results

Analytical equations are derived for the acoustic scattering field and the axial acoustic radiation force. A general formulation for the radiation force function, which is the radiation force per unit energy density per unit cross-sectional surface, is derived. Specialized forms of the radiation force function are provided for several types of incident waves including plane progressive, plane standing, plane quasi-standing, cylindrical progressive diverging, cylindrical progressive converging and cylindrical standing and quasi-standing diverging waves (with an extension to the case of spherical standing and quasi-standing diverging waves incident upon a sphere).

Significance and some potential applications

This study may be helpful essentially due to its inherent value as a canonical problem in physical acoustics. Potential applications include particle manipulation of cylindrical shaped structures in biomedicine, micro-gravity environments, fluid dynamics properties of cylindrical capillary bridges, and the micro-fabrication of new cylindrical crystals to better control light beams.     

Theoretical calculation of the acoustic radiation force acting on elastic and viscoelastic cylinders placed in a plane standing or quasistanding wave field

In this work, a new expression of the acoustic radiation force function Yst for solid cylindrical targets, suspended in inviscid fluids in a plane standing wave field, is presented. The case of a plane quasistanding wave field is also considered. Numerical calculations of the radiation force function Yst are performed in a wide range of frequencies for elastic and viscoelastic cylinders and compared to those of rigid cylinders. The fluid-loading effect on the radiation force function curves is also analysed. The results show several features quite different from the rigid cylinder solution.     

自由空间中球形粒子的负向声辐射力

针对一定声场作用下自由空间中的球形粒子,首先分析了声散射过程中的吸收声功率、散射声功率和损失声功率以及三者之间的关系,并通过计算发现了由于参数选取不当导致的负吸收现象。接着从动量守恒定律出发推导了声辐射力的一般表达式,阐释了声辐射力与声能流之间的关系,并从理论和计算两方面验证了负向声辐射力的存在。当负向声辐射力产生时,声波的背向散射被抑制。在此基础上,进一步研究了粒子的偏心特性和流体的黏度这两种常见因素对负向声辐射力的影响。利用球函数的加法公式推导了偏心球的散射系数和声辐射力公式,结果显示偏心距离、粒子的材料等都会显著改变负向声辐射力的产生条件。在低频近似下,由于流体黏度附加的正向声辐射力是否能完全抵消原来的负向声辐射力将决定最终的声辐射力方向。该结果对利用负向声辐射力制成单行波声学镊子来实现对特定粒子的操控有着理论指导意义。     

Estimation of mechanical properties of a viscoelastic medium using a laser-induced microbubble interrogated by an acoustic radiation force

An approach to assess the mechanical properties of a viscoelastic medium using laser-induced microbubbles is presented. To measure mechanical properties of the medium, dynamics of a laser-induced cavitation microbubble in viscoelastic medium under acoustic radiation force was investigated. An objective lens with a 1.13 numerical aperture and an 8.0 mm working distance was designed to focus a 532 nm wavelength nanosecond pulsed laser beam and to create a microbubble at the desired location. A 3.5 MHz ultrasound transducer was used to generate acoustic radiation force to excite a laser-induced microbubble. Motion of the microbubble was tracked using a 25 MHz imaging transducer. Agreement between a theoretical model of bubble motion in a viscoelastic medium and experimental measurements was demonstrated. Young's modulii reconstructed using the laser-induced microbubble approach were compared with those measured using a direct uniaxial method over the range from 0.8 to 13 kPa. The results indicate good agreement between methods. Thus, the proposed approach can be used to assess the mechanical properties of a viscoelastic medium.     

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.     

Contactless and non-invasive delivery of micro-particles lying on a non-customized rigid surface by using acoustic radiation force

In the existing acoustic micro-particle delivery methods, the micro-particles always lie and slide on the surface of platform in the whole delivery process. To avoid the damage and contamination of micro-particles caused by the sliding motion, this paper deals with a novel approach to trap micro-particles from non-customized rigid surfaces and freely manipulate them. The delivery process contains three procedures: detaching, transporting, and landing. Hence, the micro-particles no longer lie on the surface, but are levitated in the fluid, during the long range transporting procedure. It is very meaningful especially for the fragile and easily contaminated targets. To quantitatively analyze the delivery process, a theoretical model to calculate the acoustic radiation force exerting upon a micro-particle near the boundary in half space is built. An experimental device is also developed to validate the delivery method. A 100 μm diameter micro-silica bead adopted as the delivery target is detached from the upper surface of an aluminum platform and levitated in the fluid. Then, it is transported along the designated path with high precision in horizontal plane. The maximum deviation is only about 3.3 μm. During the horizontal transportation, the levitation of the micro-silica bead is stable, the maximum fluctuation is less than 1 μm. The proposed method may extend the application of acoustic radiation force and provide a promising tool for microstructure or cell manipulation.     

A note on the acoustic radiation from point-forced elastic beams

An exact expression for the acoustic power radiated by a point-excited damped bar is derived through direct integration of the theoretical surface acoustic intensity distribution. The effects of structural damping and wavenumber ratio on the power are presented. Expressions are obtained for the contributions to the total acoustic power arising from the propagating portion of the vibratory response and the non-propagating or flexural near field portion of the vibratory response, separately. It is shown that as the ratio of the acoustic wavenumber to the flexural wavenumber increases above 0·1, the power radiated by the propagating response increases while that radiated by the non-propagating response decreases by the same amount, so that the net power remains unchanged. When the ratio exceeds approximately 0·5, however, the propagating response power dominates. At the critical frequency, the portion of the total power contributed by the flexural near field is a minimum but begins to increase above the critical frequency. In a qualitative sense, these relative effects increase with increasing structural damping.     

Estimation of complex arterial elastic modulus from ring resonance excited by ultrasound radiation force

Pulse wave velocity (PWV) is widely used for estimating the stiffness of an artery. PWV is an average measurement of artery stiffness between two measuring sites. From measured PWV, the diameter and thickness are needed to calculate the elastic modulus of the artery. In this paper a new method of using ring resonant mode for estimation of arterial elastic modulus is proposed. To generate the ring resonance, a localized radiation force of ultrasound is remotely and non-invasively applied at the artery. The vibration response of the artery is measured by optical techniques. Three ring resonant modes are identified for estimation of the elastic modulus. The viscoelasticity and the complex modulus of the artery can be obtained. Experiments were carried out on a porcine artery embedded in gelatin. The estimation only requires the diameter of the artery, but does not need the thickness of the artery which is difficult to measure with accuracy and precision.     

Measuring the radiation force of megahertz ultrasound acting on a solid spherical scatterer

The paper considers the problem of precise measurement of the acoustic radiation force of an ultrasonic beam on targets in the form of solid spherical scatterers. Using known analytic relations, a numerical model is developed to perform calculations for different sizes of spherical scatterers and arbitrary frequencies of the incident acoustic wave. A novel method is proposed for measuring the radiation force, which is based on the principle of acoustic echolocation. The radiation force is measured experimentally in a wide range of incident wave intensities using two chosen methods differing in the way the location of the target is controlled.