Acoustic radiation force is a physical phenomenon resulting from the interaction of an acoustic wave with an obstacle placed along its path. Generally, the force exerted on the obstacle is evaluated by integrating the acoustic radiation pressure (due to the presence of the sonic wave) over its time-varying surface.

The magnitude of the force exerted by an acoustic plane wave at any given location can be calculated as:[1][2]

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

where

• F is the force in kg/(s2cm2),
• α is the absorption coefficient in Np/cm,
• I is the temporal average intensity of the acoustic wave at the given location in W/cm2, and
• c is the speed of sound in the medium in cm/s.

The effect of frequency on acoustic radiation force is taken into account via intensity (higher pressures are more difficult to attain at higher frequencies) and absorption (higher frequencies have a higher absorption rate). As a reference water has an acoustic absorption of 0.002 dB/(MHz2cm).[3]

## Medical imaging applications

Acoustic radiation force is currently being used in medical ultrasonic imaging to generate images based on the mechanical properties; the discipline of creating these images is called elastography. Modalities include Acoustic Radiation Force Impulse (ARFI) Imaging,[4] Shearwave Dispersion Ultrasound Vibrometry,[5] Harmonic Motion Imaging (HMI),[6] Supersonic Shear Imaging (SSI),[7] and Spatially Modulated Ultrasound Radiation Force (SMURF).[8]

## References

1. ^ "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.
2. ^ "Estimates of echo correlation and measurement bias in acoustic radiation force impulse imaging". IEEE Trans Ultrason Ferroelectr Freq Control 50 (6): 631–41. June 2003. PMID 12839175.
3. ^ Diagnostic ultrasound imaging : inside out. ISBN 9780126801453.
4. ^ Palmeri, M.L.; Wang, M.H.; Dahl, J.J.; Frinkley, K.D.; Nightingale, K.R. (2008). "Quantifying Hepatic Shear Modulus in Vivo Using Acoustic Radiation Force". Ultrasound in Medicine & Biology 34 (4): 546–58. doi:10.1016/j.ultrasmedbio.2007.10.009. PMC 2362504. PMID 18222031.
5. ^ Chen, Shigao; Urban, Matthew W.; Pislaru, Cristina; Kinnick, Randall; Zheng, Yi; Yao, Aiping; Greenleaf, James F (2009). "Shearwave Dispersion Ultrasound Vibrometry (SDUV) for Measuring Tissue Elasticity and Viscosity". IEEE Trans Ultrason Ferroelectr Freq Control. 56 (1): 55–62. doi:10.1109/TUFFC.2009.1005. PMC 2658640. PMID 19213632.
6. ^ http://orion.bme.columbia.edu/ueil/research.php?id=hmi
7. ^ Bercoff, J; Tanter, M; Fink, M (2004). "Supersonic shear imaging: A new technique for soft tissue elasticity mapping". IEEE transactions on ultrasonics, ferroelectrics, and frequency control 51 (4): 396–409. doi:10.1109/TUFFC.2004.1295425. PMID 15139541.
8. ^ http://www.urmc.rochester.edu/bme/people/faculty/bio/project.cfm?id=246&projectId=116