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.[1][2][3]

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

${\displaystyle F={\frac {2\alpha I}{c}}}$

where

• α is the absorption coefficient
• I is the ultrasound intensity, and
• c is the longitudinal wave speed in the medium.[4]

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 [5] 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.[6] 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.[7]

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.[8] 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.[9]

## Medical imaging applications

The widest area of biomedical applications of ARF is related to medical diagnostics, to assessing viscoelastic properties of biological tissues and fluids, and more specifically to elasticity imaging. Acoustic radiation force of focused ultrasound became the basis of numerous emerging diagnostic imaging techniques such as Shear Wave Elasticity Imaging (SWEI), Acoustic Radiation Force Impulse Imaging (ARFI), Supersonic Shear Imaging (SSI), Shearwave Dispersion Ultrasound Vibrometry (SDUV), Harmonic Motion Imaging (HMI), Comb-push Ultrasound Shear Elastography (CUSE), and Spatially Modulated Ultrasound Radiation Force (SMURF).[10][11][12][13][14][15][16] One of the most advanced modalities of the ARF-based elastography is Supersonic Shear Imaging (SSI). SSI uses ARF to induce a 'push' inside the tissue of interest generating shear waves and the tissue's stiffness is computed from how fast the shear wave travels through the tissue. Shear wave elasticity imaging has been developed into a clinical imaging modality over the last two decades and the radiation force-based methods are currently implemented in the commercial devices: SuperSonic Imagine Aixplorer, in the Siemens Acuson S2000 and S3000 as Virtual Touch Quantification, and in the General Electric Logiq E9.

## References

1. ^ Nyborg WL. Physical principles of ultrasound. In: Ultrasound: its applications in medicine and biology, ed. Fry FJ. Elsevier, Amsterdam 1978;1:1-75.
2. ^ Graff KF. A history of ultrasonics, Physical Acoustics, Principles and Methods, ed. Mason WP, Thurston RN. Academic Press, v XV, 1981, 1-98.
3. ^ Sarvazyan AP, Rudenko OV, and Nyborg WL, Biomedical applications of radiation force of ultrasound: historical roots and physical basis. Ultrasound Med. Biol. 2010; 36: 1379-1394.
4. ^ Palmeri ML, Sharma AC, Bouchard RR, Nightingale RW, and Nightingale KR. "A finite-element method model of soft tissue response to impulsive acoustic radiation force". IEEE Trans Ultrason Ferroelectr Freq Control 52 (10): 1699–712. October 2005. PMC 2818996. PMID 16382621.
5. ^ William T. Richards W.T., An Intensity Gauge for Supersonic Radiation in Liquids., Proc. Natl. Acad. Sci. U S A., April 15, 15(4), 310–314, 1929.
6. ^ Ostrovsky L., Sutin A., Il’inskii Y., Rudenko O., Sarvazyan.A., Non - dissipative mechanism of acoustic radiation force generation., JASA, 121(3), 1324-1331, 2007.
7. ^ Wu JR., Acoustical tweezers., Acoust Soc Am., May, 89(5), 2140-2143, 1991.
8. ^ Kundt A. and Lehmann O., Longitudinal vibrations and acoustic figures in cylindrical columns of liquids, Ann. Phys. Chem., 1874, 153, 1.
9. ^ Coakley WT, Hawkes JJ, Sobanski MA, Cousins CM, Spengler J. Analytical scale ultrasonic standing wave manipulation of cells and microparticles. Ultrasonics 2000;38:638-641.
10. ^ Sarvazyan AP, Rudenko OV, Swanson SD, Fowlkes JB, and Emelianov SY, Shear wave elasticity imaging: a new ultrasonic technology of medical diagnostics. Ultrasound Med. Biol. 1998; 24: 1419-35.
11. ^ Nightingale KR, Palmeri ML, Nightingale RW, and Trahey GE, On the feasibility of remote palpation using acoustic radiation force. J. Acoust. Soc. Am. 2001; 110: 625-34.
12. ^ Bercoff J, Tanter M, and Fink M, Supersonic shear imaging: a new technique for soft tissue elasticity mapping. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2004; 51: 396-409.
13. ^ Chen S, Urban MW, Pislaru C, Kinnick R, Zheng Y, Yao A, and Greenleaf JF, Shearwave dispersion ultrasound vibrometry (SDUV) for measuring tissue elasticity and viscosity. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2009; 56: 55-6.
14. ^ Vappou J, Maleke C, and Konofagou EE, Quantitative viscoelastic parameters measured by harmonic motion imaging. Phys. Med. Biol. 2009; 54: 3579-3594.
15. ^ Song P, Zhao H, Manduca A, Urban M W, Greenleaf J F, and Chen S, "Comb-push ultrasound shear elastography (CUSE): a novel method for two-dimensional shear elasticity imaging of soft tissues," IEEE Trans. Med. Imaging, vol. 31, pp. 1821-1832, 2012.
16. ^ McAleavey S. A., Menon M., and Orszulak J., "Shear-modulus estimation by application of spatially-modulated impulsive acoustic radiation force," Ultrason. Imaging, vol. 29, pp. 87-104, 2007.