Theory Of Acoustic Radiation Force Research Articles

Acoustic Radiation Force: A Review of Four Mechanisms for Biomedical Applications.

Radiation force is a universal phenomenon in any wave motion where the wave energy produces a static or transient force on the propagation medium. The theory of acoustic radiation force (ARF) dates back to the early 19th century. In recent years, there has been an increasing interest in the biomedical applications of ARF. Following a brief history of ARF, this article describes a concise theory of ARF under four physical mechanisms of radiation force generation in tissue-like media. These mechanisms are primarily based on the dissipation of acoustic energy of propagating waves, the reflection of the incident wave, gradients of the compressional wave speeds, and the spatial variations of energy density in standing acoustic waves. Examples describing some of the practical applications of ARF under each mechanism are presented. This article concludes with a discussion on selected ideas for potential future applications of ARF in biomedicine.

Force on a compressible sphere and the resonance of a bubble in standing surface acoustic waves

In this paper, the theory for acoustic radiation force exerted by standing surface acoustic waves (SSAWs) is extended to a compressible sphere in inviscid fluids. The conventional theory, developed in plane standing waves, fails to predict the radiation force incident on particles in the SSAW. Our extended formulas reveal that, in the direction normal to the piezoelectric substrate, the acoustic radiation force cannot only push the sphere away, but also pull it back towards the substrate. In the direction parallel to the substrate, both the magnitude of the radiation force and the equilibrium positions for particles can be actively tuned by changing the Rayleigh angle. This is exceedingly meaningful for particle positioning by tilted angle SSAWs and SSAWs. Furthermore, the Rayleigh angle can also be used to actively regulate the resonance point and peak for bubbles acted on by SSAWs. The extended theory can thus be used in the design of SSAWs for manipulating particles and bubbles.

The radiation force on a rigid sphere in standing surface acoustic waves

In this paper, the theory of acoustic radiation force exerted by standing surface acoustic waves (SSAWs) on a rigid sphere in ideal fluids is extended to account for the Rayleigh angle. The conventional theory used to calculate the radiation force acting on spheres in SSAWs is developed for plane standing waves (PSWs). PSWs exclude the dependence on the Rayleigh angle, causing significant limitations in the SSAW-based application settings. The radiation force on a cylinder in SSAWs is calculated based on which spherical structure is to be further considered. The Rayleigh angle effects can amplify the force of acoustic radiation in the direction normal to the piezoelectric substrate. In addition, the Rayleigh angle plays a notable role in both the magnitude and sign of the acoustic radiation force in the direction parallel to the substrate, which is significant for manipulating spherical particles in SSAWs. Thus, our formulas have great potential in the SSAW-based applications.

Nonlinear large deformation of acoustomechanical soft materials

An acoustomechanical theory of soft materials is proposed to account for the nonlinear large deformation of soft materials triggered by both the ultrasound waves and mechanical forces. This theory is formulated by employing the nonlinear elasticity theory of the soft material and the theory of acoustic radiation force, which takes into consideration of the combination loading of mechanical forces and acoustic inputs. While the propagation of acoustic wave depends on material configuration, the radiation force generated by wave propagation deforms the material configuration. This complex interaction reaches a steady state when the mechanical stress and the acoustic radiation stress are able to balance with the elastic deformation stress. The acoustomechanical theory is employed to characterize the acoustomechanical behaviors of thin soft material layers under different boundary conditions (e.g., equal-biaxial forces, uniaxial force, and uniaxial constraint). Prestretches arising from these boundary conditions are shown to play significant roles in affecting the acoustomechanical repsonse of soft material: the same material actuated from different prestretches and boundary conditions exhibits different stretch-stress relations. This novel functionality enables innovative design of acoustic sensors and actuators based on soft materials.

Scattered shear wave contribution to acoustic radiation force on spheres in soft tissue

A theory for acoustic radiation force on a sphere in soft tissue was developed for arbitrary incident compressional wave fields [Ilinskii et al., Proc. Meet. Acoust. 19, 045004 (2013)]. This theory includes two contributions to the radiation force. The first depends only on the incident and scattered compressional waves, whereas the second depends on the scattered shear waves as well. Each contribution in turn has two parts, one due to direct integration of the time-averaged Piola-Kirchhoff stress tensor over the surface of the sphere, and the other due to the irrotational component of the body force on the sphere. While both parts are known analytically for the compressional waves, only the first part has been obtained analytically for the contribution involving shear waves. The irrotational portion associated with shear waves and its effect on the total radiation force is the subject of this presentation. The analysis is conducted via Helmholtz decomposition of the body force associated with shear waves and subsequent integration of the irrotational portion over the surface of the sphere. Simplifying analytical approximations based on numerical calculations are examined for various elastic properties of the sphere and soft tissue. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.]

Direction of acoustic radiation force on spherical scatterers in soft tissue

A theory for acoustic radiation force on a viscoelastic sphere of arbitrary size in soft tissue has been reported previously for a nonaxisymmetric incident field described via spherical harmonic expansion [Ilinskii et al., POMA 19, 045004 (2013)]. At the Fall 2014 ASA meeting, the model was used to compute the radiation force on scatterers with different sizes and properties at various positions relative to the focus of an axisymmetric incident beam. For a particle located away from the focus, the model predicts a change in the direction of the axial or the transverse component of the radiation force depending on properties of both the particle and the host medium. The focus of the present contribution is this change in direction. Scatterers with various sizes and mechanical properties are considered, and small particles are found to be more prone to this phenomenon. Additionally, the reversal in direction is found to be sensitive to variations in the shear modulus of the host medium. Comparisons are made with liquid as the shear modulus of the host medium spans the range of values encountered in soft tissue. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.]

Acoustic radiation force due to nonaxisymmetric sound beams incident on spherical viscoelastic scatterers in tissue

The theory for acoustic radiation force on a viscoelastic sphere of arbitrary size in tissue was extended recently to account for nonaxisymmetric incident fields [Ilinskii et al., POMA 19, 045004 (2013)]. A spherical harmonic expansion was used to describe the incident field. This work was specialized at the spring 2014 ASA meeting to focused axisymmetric sound beams with various focal spot sizes and a scatterer located at the focus. The emphasis of the present contribution is nonaxisymmetric fields, either through moving the scatterer off the axis of an axisymmetric beam or through explicitly defining a nonaxisymmetric beam. This is accomplished via angular spectrum decomposition of the incident field, spherical wave expansions of the resulting plane waves about the center of the scatterer, Wigner D-matrix transformations to express these spherical waves in a coordinate system with the polar axis aligned with the desired radiation force component, and finally integration over solid angle to obtain spherical wave amplitudes as required in the theory. Various scatterer sizes and positions relative to the focus are considered, and the effects of changing properties of both the scatterer and the surrounding tissue are examined. [Work supported by the ARL:UT McKinney Fellowship in Acoustics.]

Effects of diffraction on acoustic radiation force produced by sound beams incident on spherical viscoelastic scatterers in tissue

The theory for acoustic radiation force on a viscoelastic sphere of arbitrary size in tissue was extended at the spring 2013 ASA meeting to account for nonaxisymmetric fields incident on the scatterer [Ilinskii et al., POMA 19, 045004 (2013)]. The results were presented in a form that permits inclusion of as many spherical harmonics as needed to describe the field structure. At the fall 2013 ASA meeting, it was shown that for spheres having sizes up to about one wavelength, only four or five spherical harmonics are required for convergence of the solution when plane waves are incident on the scatterer. At the present meeting, the model is applied to diffracting sound beams incident on the scatterer. The analysis is based on angular spectrum decomposition of the incident field, expansion of the resulting plane waves in spherical waves, then a Wigner transformation of the latter back into spherical coordinates with polar axis coinciding with the beam axis, and finally integration over solid angle to obtain the spherical wave amplitudes used in the theory. Results are presented for different radiation patterns illustrating dependence of the radiation force both on beamwidth and on wavelength relative to the size of the scatterer.

Dependence of acoustic trapping capability on the orientation and shape of particles

This paper presents an experimental and theoretical investigation of the dependence of acoustic trapping capability on the orientation and shape of particles to be trapped in different media. In the experimental investigation, two sharp edges of metal strips in ultrasonic vibration are used to trap particles in air. Experimental particles are made of clay, having the same mass and volume but different shapes. In the theoretical investigation, a method which combines the analysis of finite element method and theory of acoustic radiation force is used to calculate the acoustic radiation force acting on particles with different shapes and orientations. Both the experimental and theoretical results show that the acoustic trapping capability depends on the orientation and shape of particles. It is found that both in air and in water, for a particle with a given shape, the trapping capability is different at different orientations; for some commonly shaped particles, such as rectangular cuboid, cylinder, cone, cube, sphere, and hollow cylinder; the trapping capability for each particle shape at its best trapping orientation decreases in the listed sequence of shapes.