Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid.

Based on the partial-wave series expansion (PWSE) method in spherical coordinates, a formal analytical solution for the acoustic scattering of a zeroth-order Bessel acoustic beam centered on a rigid fixed (oblate or prolate) spheroid is provided. The unknown scattering coefficients of the spheroid are determined by solving a system of linear equations derived for the Neumann boundary condition. Numerical results for the modulus of the backscattered pressure (θ = π) in the near field and the backscattering form function in the far field for both prolate and oblate spheroids are presented and discussed, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle of the Bessel beam, and the dimensionless frequency. The plots display periodic oscillations (versus the dimensionless frequency) because of the interference of specularly reflected waves in the backscattering direction with circumferential Franz' waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3-D directivity patterns illustrate the near- and far-field axisymmetric scattering. Investigations in underwater acoustics, particle levitation, scattering, and the detection of submerged elongated objects and other related applications utilizing Bessel waves would benefit from the results of the present study.

Acoustical pulling force of a limited-diffracting annular beam centered on a sphere.

A rigorous method is developed to investigate the generation of a negative (attracting) force acting in the opposite direction of wave propagation using a limited-diffracting single annular piezo-ring transducer. Based on the Rayleigh- Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions, the expression for the incident velocity potential field (which is an exact solution of the Helmholtz equation) is derived analytically, and exact closed-form partial-wave series expansions for the incident and scattered fields are obtained without any approximations. The total (incident + scattered) field expression is used to evaluate the time-averaged acoustic radiation force (ARF) on a sphere centered on the beam's axis in a nonviscous fluid. Numerical predictions for the scattering and ARF performed with particular emphasis on the annular-ring's radial thickness, the distance separating the sphere from the acoustic source, the size of the transducer, as well as the sphere's elastic properties, reveal some conditions where a pulling axial ARF directed toward the annular ring-source surface arises. The simplicity and reliability of the annular-ring geometry demonstrated here provides a substantial solution with widespread applications in the experimental design of acoustical limited-diffracting beams operating over an extended axial depth-of-field for contactless and dexterous particle manipulation.

Acoustical tweezers using single spherically focused piston, X-cut, and Gaussian beams.

Partial-wave series expansions (PWSEs) satisfying the Helmholtz equation in spherical coordinates are derived for circular spherically focused piston (i.e., apodized by a uniform velocity amplitude normal to its surface), X-cut (i.e., apodized by a velocity amplitude parallel to the axis of wave propagation), and Gaussian (i.e., apodized by a Gaussian distribution of the velocity amplitude) beams. The Rayleigh-Sommerfeld diffraction integral and the addition theorems for the Legendre and spherical wave functions are used to obtain the PWSEs assuming weakly focused beams (with focusing angle α ⩽ 20°) in the Fresnel-Kirchhoff (parabolic) approximation. In contrast with previous analytical models, the derived expressions allow computing the scattering and acoustic radiation force from a sphere of radius a without restriction to either the Rayleigh (a ≪ λ, where λ is the wavelength of the incident radiation) or the ray acoustics (a ≫λ) regimes. The analytical formulations are valid for wavelengths largely exceeding the radius of the focused acoustic radiator, when the viscosity of the surrounding fluid can be neglected, and when the sphere is translated along the axis of wave propagation. Computational results illustrate the analysis with particular emphasis on the sphere's elastic properties and the axial distance to the center of the concave surface, with close connection of the emergence of negative trapping forces. Potential applications are in single-beam acoustical tweezers, acoustic levitation, and particle manipulation.

Computing the acoustic radiation force exerted on a sphere using the translational addition theorem.

In this paper, the translational addition theorem for spherical functions is employed to calculate the acoustic radiation force produced by an arbitrary shaped beam on a sphere arbitrarily suspended in an inviscid fluid. The procedure is also based on the partial-wave expansion method, which depends on the beam-shape and scattering coefficients. Given a set of beam-shape coefficients (BSCs) for an acoustic beam relative to a reference frame, the translational addition theorem can be used to obtain the BSCs relative to the sphere positioned anywhere in the medium. The scattering coefficients are obtained from the acoustic boundary conditions across the sphere's surface. The method based on the addition theorem is particularly useful to avoid quadrature schemes to obtain the BSCs. We use it to compute the acoustic radiation force exerted by a spherically focused beam (in the paraxial approximation) on a silicone-oil droplet (compressible fluid sphere). The analysis is carried out in the Rayleigh (i.e., the particle diameter is much smaller than the wavelength) and Mie (i.e., the particle diameter is of the order of the wavelength or larger) scattering regimes. The obtained results show that the paraxial focused beam can only trap particles in the Rayleigh scattering regime.

Application of vibro-acoustography in prostate tissue imaging.

PURPOSE: To evaluate the potential of the imaging modality vibro-acoustography (VA) for imaging of the prostate. METHODS: Excised cadaver prostate specimens were embedded in tissue mimicking gel to simulate the properties of surrounding soft tissues. The samples were imaged at various depths using a laboratory prototyped VA imaging system. The recorded signals were used for offline processing and image reconstruction. In a selected subgroup of tissue samples, conventional ultrasound (B-mode) and x-ray imaging were performed for further analysis, evaluation, and validation of the VA images. RESULTS: The imaging results of prostate tissue samples indicate the capability of VA imaging to detect prostatic nodules and lesions. In the prostate sample with an adenocarcinoma, the lesion appears with a clear contrast with respect to its surrounding tissue. The VA images could also identify the presence of calcifications deep inside the prostate tissue. Further, quantifications of the imaging results demonstrate that VA imaging has higher sensitivity to detect the calcifications compared to conventional ultrasound imaging. VA is also capable of visualizing prostatic tissue structures and in some cases can identify the anatomical zones. More specifically, the observed higher texture level in peripheral zones demonstrates the ability of VA to differentiate between prostatic anatomical zones. CONCLUSIONS: Imaging results of ex vivo prostate tissues, reveals the potency of VA as a promising tool to detect abnormalities, delineate tissue structures and anatomical zones, and locate calcifications. The results of this pilot study suggest that in vivo VA imaging of the prostate may be of clinical utility.

Off-axial acoustic radiation force of repulsor and tractor bessel beams on a sphere.

Acoustic Bessel beams are known to produce an axial radiation force on a sphere centered on the beam axis (on-axial configuration) that exhibits both repulsor and tractor behaviors. The repulsor and the tractor forces are oriented along the beam's direction of propagation and opposite to it, respectively. The behavior of the acoustic radiation force generated by Bessel beams when the sphere lies outside the beam's axis (off-axial configuration) is unknown. Using the 3-D radiation force formulas given in terms of the partial wave expansion coefficients for the incident and scattered waves, both axial and transverse components of the force exerted on a silicone- oil sphere are obtained for a zero- and a first-order Bessel vortex beam. As the sphere departs from the beam's axis, the tractor force becomes weaker. Moreover, the behavior of the transverse radiation force field may vary with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on ka values. These results are particularly important for the design of acoustical tractor beam devices operating with Bessel beams.

Interaction of an acoustical quasi-Gaussian beam with a rigid sphere: linear axial scattering, instantaneous force, and time-averaged radiation force.

This work focuses on the interaction of an acoustical quasi-Gaussian beam centered on a rigid immovable sphere, during which at least three physical phenomena arise--the (axial) acoustic scattering, the instantaneous force, and the time-averaged radiation force--which are investigated here. The quasi-Gaussian beam is an exact solution of the source-free Helmholtz wave equation and is characterized by an arbitrary waist, w(0), and a diffraction convergence length known as the Rayleigh range, z(R). Specialized formulations for the scattering and the instantaneous force function, as well as the (time-averaged) radiation force function, are provided. Numerical computations illustrate the variations of the backscattering form function, the instantaneous force function, and the (time-averaged) radiation force function versus the dimensionless frequency ka (where k is the wave number and a is the radius of the sphere); the results show significant differences from the plane wave limit when the dimensionless beam waist parameter kw(0) <25. The radiation force function may be used to calibrate high-frequency transducers operating with this type of beam. Furthermore, the theoretical analysis can be readily extended to the case of other types of spheres (i.e., elastic, viscoelastic, shells, and coated spheres and shells), providing that their appropriate scattering coefficients are used.

Generalized theory of resonance excitation by sound scattering from an elastic spherical shell in a nonviscous fluid.

This work presents the general theory of resonance scattering (GTRS) by an elastic spherical shell immersed in a nonviscous fluid and placed arbitrarily in an acoustic beam. The GTRS formulation is valid for a spherical shell of any size and material regardless of its location relative to the incident beam. It is shown here that the scattering coefficients derived for a spherical shell immersed in water and placed in an arbitrary beam equal those obtained for plane wave incidence. Numerical examples for an elastic shell placed in the field of acoustical Bessel beams of different types, namely, a zero-order Bessel beam and first-order Bessel vortex and trigonometric (nonvortex) beams are provided. The scattered pressure is expressed using a generalized partial-wave series expansion involving the beam-shape coefficients (BSCs), the scattering coefficients of the spherical shell, and the half-cone angle of the beam. The BSCs are evaluated using the numerical discrete spherical harmonics transform (DSHT). The far-field acoustic resonance scattering directivity diagrams are calculated for an albuminoidal shell immersed in water and filled with perfluoropropane gas, by subtracting an appropriate background from the total far-field form function. The properties related to the arbitrary scattering are analyzed and discussed. The results are of particular importance in acoustical scattering applications involving imaging and beam-forming for transducer design. Moreover, the GTRS method can be applied to investigate the scattering of any beam of arbitrary shape that satisfies the source-free Helmholtz equation, and the method can be readily adapted to viscoelastic spherical shells or spheres.

Vibroacoustography imaging of kidney stones in vitro.

Vibroacoustography (VA) is an ultrasound-based modality sensitive to stiffness and free from speckle and possesses some advantages over conventional ultrasound imaging in terms of image quality. The primary objective here is to show its feasibility in detecting/imaging kidney stones (KSs) in vitro . In VA, two intersecting ultrasound beams driven at two different frequencies f (1) and f (2), respectively, are focused within a freshly excised porcine kidney attached to a solid frame with elastic rubber bands, while the amplitude of the acoustic emission pressure field produced at the difference frequency Δf = | f(1) - f(2) | is detected by a low-frequency hydrophone. The received low-frequency signal is bandpass filtered and amplified, then digitized by a 14-bits/sample digitizer. The data are then recorded on a computer and processed numerically to construct the images. 2-D magnitude VA images are obtained at different depths within the kidney before and after stone implantation, showing kidney features and stones shapes. Experiments conducted in a water tank on a chalk sphere as well as a series of excised kidneys in which stones are artificially embedded show that all the implanted stones are detected at all chosen depths, when compared with an X-ray fluoroscopy taken to be the reference image. The resulting VA images, obtained from a nonionizing type of radiation (i.e., ultrasound waves) as compared to fluoroscopy, are speckle free unlike conventional ultrasound images. The results presented in this preliminary feasibility study show that VA allows imaging KSs in vitro, and provide the impetus to further develop and investigate VA imaging in a clinical setting for in vivo applications.

Difference-frequency generation in vibro-acoustography.

Vibro-acoustography (VA) is a medical imaging method based on the nonlinear interaction of two or more distinct ultrasound beams whose frequencies differ by several kHz. In turn, the interacting waves produce a difference-frequency signal which carries the information of the imaged tissue region. Two mechanisms are responsible for the difference-frequency generation (DFG) in VA, namely the dynamic (oscillatory) radiation force and the scattering of sound-by-sound. The role and importance of each phenomenon in VA is assessed here. A theoretical model based on Westervelt's equation for the DFG in the nonlinear scattering of two incident ultrasound waves by a small rigid sphere (compared to the incident wavelengths) is presented. Furthermore, a scattering experiment using VA is devised and the data show very good agreement with the proposed theory. The results reveal that the effect of scattering of sound-by-sound is the dominant component in the DFG in VA rather than the dynamic radiation force.

Acoustic radiation force on a spherical contrast agent shell near a vessel porous wall--theory.

Contrast agent microshells (CAMSs) are under intensive investigation for their wide applications in biomedical imaging and drug delivery. In drug delivery applications, CAMSs are guided to the targeted site before fragmentation by high-intensity ultrasound waves leading to the drug release. Prediction of the acoustic radiation force used to nondestructively guide a CAMS to the suspected site is becoming increasingly important and gaining attention particularly because it increases the system efficiency. The goal of this work is to present a theoretical model for the time-averaged (static) acoustic radiation force experienced by a CAMS near a blood vessel wall. An exact solution for the scattering of normal incident plane acoustic waves on an air-filled elastic spherical shell immersed in a nonviscous fluid near a porous and nonrigid boundary is employed to evaluate the radiation force function (which is the radiation force per unit energy density per unit cross-sectional surface). A particular example is chosen to illustrate the behavior of the time-averaged (static) radiation force on an elastic polyethylene spherical shell near a porous wall, with particular emphasis on the relative thickness of the shell and the distance from its center to the wall. This proposed model allows obtaining a priori information on the static radiation force that may be used to advantage in related as drug delivery and contrast agent imaging. This study should assist in the development of improved models for the evaluation of the time-averaged acoustic radiation force on a cluster of CAMSs in viscous and heat-conducting fluids.

Nonlinear acoustics in higher-order approximation: Comment.

Some useful expressions for the second- and third-order equations for harmonic generation of infinite plane acoustic waves in a nonlinear non-viscous fluid are corrected. The concern addressed in the present comment is to point out some typographical errors in the first-order velocity and pressure expressions intervening in the calculation of the secondorder nonlinear equations, as well as a miscalculation of the axial component of the third-order Lighthill tensor term and the resulting third-order velocity and pressure equations presented in that paper.

Interaction of a nondiffracting high-order Bessel (vortex) beam of fractional type alpha and integer order m with a rigid sphere: linear acoustic scattering and net instantaneous axial force.

Closed-form analytical solutions for the acoustic scattering and net axial force of a new class of Bessel beams, termed nondiffracting Bessel vortex beams of fractional type alpha, are derived. This new class of Bessel beams preserves the same nondiffracting feature of conventional high-order Bessel beams of integer order. The far-field acoustic scattering field by a rigid sphere centered on the beam axis is expressed as a partial wave series involving the real number alpha, the scattering angle relative to the beam axis theta, and the half-conical angle beta of the wave number components of the beam. Unlike the acoustic scattering properties of conventional high-order Bessel beams, the acoustic forward scattering (theta = 0 degrees) and backscattering (theta = 180 degrees) of Bessel vortex beams of fractional type alpha by a rigid sphere do not vanish unless alpha becomes an integer number. Furthermore, an expression for the net instantaneous axial force is derived for the case of progressive, stationary, and quasi-stationary waves. These results provide new insights into the acoustic scattering theory in the context of nondiffracting beams. The properties of nondiffracting Bessel vortex beams of fractional type alpha may lead to the development of an "acoustic blender" with possible applications in particle rotation, mixing, and manipulation. Imaging and other related applications may also benefit from this new type of acoustic beams.

Vibro-acoustography imaging applications for the prostate.

Vibro-acoustography (VA) is a novel modality that has shown significant features in imaging hard inclusions and inhomogeneities within biological tissue. Here we focus on its applications for prostate imaging as well as some of its related feasibility studies to guide minimally-invasive therapies such as brachytherapy and cryosurgery.

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.

Equivalence of expressions for the acoustic scattering of a progressive high-order Bessel beam by an elastic sphere.

The exact analytical solution for the acoustic scattering of a high-order (commonly known as generalized) Bessel beam (HOBB) by an elastic sphere immersed in an ideal fluid and centered along the beam axis is revisited. The far-field acoustic scattering field is expressed as a partial wave series involving the scattering angle relative to the beam axis, the order, and the half-conical angle of the wave number components of the generalized Bessel beam. Using an appropriate grouping of terms, the expressions for the incident and scattered pressures, as well as the scattering (complex) form function provided in a recent work are transformed into expressions involving the partial wave series starting from the order m of the generalized Bessel beam. In this new formulation, the scattering coefficients for a HOBB are found to equal those obtained from the study of sound scattering of plane progressive waves by an elastic sphere. This suggests that the (complex) form function presented here may be used to advantage toward studying the acoustic scattering of a HOBB by spherical shells, coated spheres, and coated spherical shells using their corresponding scattering partial wave coefficients available in standard and recent literature texts.

Theory of the acoustic radiation force exerted on a sphere by standing and quasistanding zero-order Bessel beam tweezers of variable half-cone angles.

A rigorous theory is developed to predict the radiation force (RF) exerted on a sphere immersed in an ideal fluid by a standing or quasistanding zero-order Bessel beam of different half-cone angles. A standing or a quasistanding acoustic field is the result of counter propagating 2 equal or unequal amplitude zero-order Bessel beams, respectively, along the same axis. Each Bessel beam is characterized by its halfcone angle beta(l);l = 1, 2 of its plane wave components, such that beta(l) = 0 represents a plane wave. Analytical expressions of RF are derived for a homogeneous viscoelastic sphere chosen as an example. RF calculations for a polyethylene sphere immersed in water are performed. Particularly, the half-cone angle dependency on the RF is analyzed for standing and quasistanding waves. Changing the half-cone angle is equivalent to changing the beamwidth. Potential applications include particle manipulation in microfluidic lab-on-chips as well as in reduced gravity environments.

Prostate cryotherapy monitoring using vibroacoustography: preliminary results of an ex vivo study and technical feasibility.

The objective of this research is to prospectively evaluate the feasibility of vibroacoustography (VA) imaging in monitoring prostate cryotherapy in an ex vivo model. Baseline scanning of an excised human prostate is accomplished by a VA system apparatus in a tank of degassed water. Alcohol and dry ice mixture are used to freeze two prostate tissue samples. The frozen prostates are subsequently placed within the water tank at 27 degrees C and rescanned. VA images were acquired at prescribed time intervals to characterize the acoustic properties of the partially frozen tissue. The frozen prostate tissue appears in the images as hypoemitting signal. Once the tissue thaws, previously frozen regions show coarser texture than prior to freezing. The margin of the frozen tissue is delineated with a well-defined rim. The thawed cryolesions show a different contrast compared with normal unfrozen prostate. In conclusion, this pilot study shows that VA produces clear images of a frozen prostate at different temperature stages. The frozen tissue appears as a uniform region with well-defined borders that are readily identified. These characteristic images should allow safer and more efficient application of prostatic cryosurgery. These results provide substantial motivation to further investigate VA as a potential modality to monitor prostate cryotherapy intraoperatively.

Theory of dynamic acoustic radiation force experienced by solid cylinders.

A body insonified by a sound field is known to experience a steady force that is called the acoustic radiation force. This force can also be dynamic or oscillatory, knowing that the intensity of the incident sound field changes over time (amplitude modulation). The present paper develops the theory of dynamic radiation force experienced by a solid cylinder immersed in an ideal fluid. Analytical solutions of the equations for the dynamic force are derived. The equations provide analytical radiation force dependencies on the acoustic field and medium parameters. The case of compressional and shear waves' absorption in the solid material of the cylinder is also discussed. It is shown here that radiation force is no longer static and cannot be treated as a steady-state phenomenon.

Frequency dependence of the acoustic radiation force acting on absorbing cylindrical shells.

The frequency dependence of the radiation force function Y(p) for absorbing cylindrical shells suspended in an inviscid fluid in a plane incident sound field is analysed, in relation to the thickness and the content of their interior hollow region. The theory is modified to include the effect of hysteresis type absorption of compressional and shear waves in the material. The results of numerical calculations are presented for two viscoelastic (lucite and phenolic polymer) materials, with the hollow region filled with water or air indicating how damping and change of the interior fluid inside the shell's hollow region affect the acoustic radiation force. The acoustic radiation force acting on cylindrical lucite shells immersed in a high density fluid (in this case mercury) and filled with water in their hollow region, is also studied.