Archives of Acoustics, 47, 1, pp. 81–88, 2022

Calculation for Acoustic Radiation Force from Rectangular Weakly Focusing Transducer Using the Ray Acoustic Model

Lili YU
Merchant Marine College, Shanghai Maritime University

Shuchang QIAO
Merchant Marine College, Shanghai Maritime University

Wende SHOU
Merchant Marine College, Shanghai Maritime University; Shanghai Institute of Ultrasound in Medicine,

Junhua LI
College of Ocean Science and Engineering, Shanghai Maritime University

Based on the ray acoustic model, a new relationship between the radiation force and the acoustic power is studied for a rectangular weakly focusing transducer. The effect of pressure reflection coefficient on this model is discussed. For a totally absorbing target, an approximate closed-form expression is also derived and the performance of this model is compared with that of the far-field integration model. The numerical results show that the agreement is excellent with these two models, which can be both used for correction of measured results, but the formula based on the ray acoustic model can be applied more widely in practice because of its simpler expression. The experimental results show further the effectiveness of the relationship between radiation force and acoustic power for rectangular weakly focusing transducer based on the ray acoustic model. The results presented in this paper are important for application of ultrasound transducers in therapy.
Keywords: radiation force calculation; ray acoustic model; rectangular weakly focusing transducer; far-field integration.
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).


Beissner K. (1987), Radiation force calculations, Acta Acustica united with Acustica, 62(4): 255–263.

Beissner K. (2008), Radiation force calculations for ultrasonic fields from rectangular weakly focusing transducers, The Journal of the Acoustical Society of America, 124(4): 1941–1949, doi: 10.1121/1.2968687.

Beissner K. (2010), Minimum radiation force target size for power measurements in focused ultrasonic fields with circular symmetry, The Journal of the Acoustical Society of America, 128(6): 3355–3362, doi: 10.1121/1.3505105.

Beissner K., Oosterbaan W.A., Hekkenberg R.T., Shaw A. (1996), European intercomparision of ultrasonic power measurements, Acta Acustica united with Acustica, 82(3): 450–458.

Civale J., Rivens J., Shaw A., Ter Haar G. (2018), Focused ultrasound transducer spatial peak intensity estimation: a comparison of methods, Physics in Medicine and Biology, 63(5): 055015, doi: 10.1088/ 1361-6560/aaaf01.

Gélat P., Shaw A. (2015), Relationship between acoustic power and acoustic radiation force on absorbing and reflecting targets for spherically focusing radiators, Ultrasound in Medicine and Biology, 41(3): 832– 844, doi: 10.1016/j.ultrasmedbio.2014.09.021.

Hekkenberg R.T., Beissner K., Zeqiri B., Bezemer R.A., Hodnett M. (2001), Validated ultrasonic power measurements up to 20 W, Ultrasound in Medicine and Biology, 27(3): 427–438, doi: 10.1016/S03015629(00)00344-6.

IEC61161 (2013), Ultrasonics – Power measurementRadiation force balances and performance requirements, 3rd ed., International Electrotechnical Commission.

IEC TS 62903 (2018), Ultrasonics – Measurements of electroacoustical parameters and acoustic output power of spherically curved transducers using the selfreciprocity method, 1st ed., International Electrotechnical Commission.

Muruvada S., Harris G.R., Herman B.A. (2007),

Acoustic power calibration of high-intensity focused ultrasound transducers using a radiation force technique, The Journal of the Acoustical Society of America, 121(3): 1434–1439, doi: 10.1121/1.2431332.

Qian Z.W., Zhu Z.M., Ye S.G., Jiang W.H., Zhu H.Q., Yu J.S. (2010), Radiation force on absorbing targets and power measurements of a high intensity focused ultrasound (HIFU) source, Science China Physics, Mechanics and Astronomy, 53(10): 1780–1787, doi: 10.1007/s11433-010-4117-8.

Shaw A., Hodnett M. (2008), Calibration and measurement issues for therapeutic ultrasound, Ultrasonics, 48(4): 234–252, doi: 10.1016/j.ultras.2007.10.010.

Shaw A., Martin E., Haller J., Ter Haar G. (2016), Equipment, measurement and dose – a survey for therapeutic ultrasound, Journal of Therapeutic Ultrasound, 4(1): 7, doi: 10.1186/s40349-016-0051-1.

Shaw A., Ter Haar G., Haller J., Wilkens V. (2015), Towards a dosimetric framework for therapeutic ultrasound, International Journal of Hyperthermia, 31(2): 182–192, doi: 10.3109/02656736.2014.997311.

Shou W.D. et al. (1998), Radiation force calculation of focused ultrasound and its experiment in high intensity focused ultrasound [in Chinese], Technical Acoustics, 17(4): 145–147.

Shou W.D. et al. (2006), Acoustic power measurement of high intensity focused ultrasound in medicine based

on radiation force, Ultrasonics, 44(Supplement): e17– e20, doi: 10.1016/j.ultras.2006.06.034.

Xu J.X., Gui Y.F., Ma J.M. (2019), Calculation and optimization of acoustic radiation force produced by a two-dimensional transducer array, Journal of Applied Physics, 125(13): 134905, doi: 10.1063/1.5055362.

Yu L.L., Shou W.D., Hui C., Hu B. (2012), Radiation force calculation and acoustic power measurement for a cylindrical concave transducer based on the ray acoustic model, Journal of the Korean Physical Society, 61(4): 544–550, doi: 10.3938/jkps.61.544.

DOI: 10.24425/aoa.2022.140734