Acoustic radiation force

Acoustic radiation force (ARF), as a well-defined scientific subject, emerged in 1902, after publication of classical work by Lord Rayleigh on the theory of sound. Rayleigh introduced the concept of acoustic radiation pressure which he named “the pressure of vibrations”. The detailed history of ARF, its physical basis and biomedical applications can be found in the reviews.

The ARF is, in general, defined as a period-averaged force exerted on the medium by a sound wave. The mechanisms of acoustic radiation force generations include: (1) change in the density of energy of the propagating wave due to absorption and scattering; (2) reflection from inclusions, walls or other interfaces; and (3) spatial variations in propagation velocity, and (4) spatial variations of energy density in standing acoustic waves.

The first of these mechanisms is the basis of biomedical applications of ARF related to assessing viscoelastic properties of biological tissues and fluids, and specifically to elasticity imaging. The simplified equation for the ARF, F, generated due to absorption and scattering in tissue is given as

where

The second of the listed mechanisms is the basis of one of the oldest applications of ARF, proposed by Wood and Loomis in the 1920s to measure total power in ultrasonic beams which later was implemented in radiation balances that were widely used to measure the power output from physiotherapy ultrasound units. Until now, it is the standard method of measuring output power for physiotherapy systems.

The third mechanism presents generation of ARF in media without attenuation or acoustic wave reflection. Gradients of acoustic properties of medium, such as variations of sound velocity, cause gradients of the energy density in the propagating acoustic wave. As a result, radiation force is generated. Displacement produced by such non-dissipative acoustic radiation force in inhomogeneous media can be in both directions (outward and inward toward the transducer) depending on the sign of the gradient of energy density of the propagating wave. Non-dissipative radiation force, in contrast to the dissipative radiation force, can be generated in tissue at low sub-MHz frequencies despite the low attenuation coefficient of the media. This mechanism is currently used for development of acoustic tweezers.

The fourth mechanism of generation of ARF is related to an actively explored area of manipulation of biological cells and particles in standing ultrasonic wave fields. It has been known since the 19th century that an object in a sound field is affected by a steady-state acoustic radiation force. In a classical experiment, Kundt and Lehman trapped dust particles in a tube by applying a standing-wave field. However, it is only in the last decades the phenomenon has found widespread application ranging from manipulation of cells in suspension, increasing the sensitivity of biosensors and immunochemical tests.

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