**Page description appears here**

“Forward propagation of acoustic pressure pulses in 3D soft biological tissue”

Authors: Trond Varslot and Svein-Erik Måsøy,
Affiliation: NTNU
Reference: 2006, Vol 27, No 3, pp. 181-190.

     Valid XHTML 1.0 Strict

Keywords: Medical ultrasound, nonlinear acoustics, parabolic approximation, numerical simulation, operator splitting

Abstract: A simulation method for forward propagation of acoustic pressure pulses in a medium with three-dimensional (3D) spatially-variable acoustic properties is presented. The intended application is to study aspects of ultrasound imaging of soft biological tissue. The forward wave propagation is modelled by a one-way wave equation. The equation describes tissue exhibiting nonlinear elasticity and arbitrary frequency-dependent attenuation. A numerical solution to the equation is found by means of first-order accurate operator splitting and propagation along the spatial depth coordinate. Thus diffraction, nonlinearity and attenuation are solved independently at each propagation step, rendering their relative importance easy to monitor. The method is seen to yield an accurate simulation of the wave propagation when compared to numerical solutions of the full wave equation and experiments in a water tank. By this approach it is possible to simulate wave propagation over relatively large distances - typically several hundred wavelengths - at a modest computational complexity compared to solution of the full wave equation. It furthermore facilitates a high degree of parallelism, thus enabling efficient distribution of the required computations over multiple processors.

PDF PDF (220 Kb)        DOI: 10.4173/mic.2006.3.4

DOI forward links to this article:
  [1] Yun Jing (2012), doi:10.1121/1.3675967
  [2] Seung H. Ko, Sang G. Ryu, Nipun Misra, Heng Pan, Costas P. Grigoropoulos, Nick Kladias, Elias Panides and Gerald A. Domoto (2008), doi:10.1063/1.2980014
  [3] Seung Hwan Ko, Daeho Lee, Heng Pan, Sang-Gil Ryu, Costas P. Grigoropoulos, Nick Kladias, Elias Panides and Gerald A. Domoto (2010), doi:10.1007/s00339-010-5856-0
  [4] Thomas L. Szabo (2014), doi:10.1016/B978-0-12-396487-8.00012-4
  [5] Seung H. Ko, Sang G. Ryu, Nipun Misra, Heng Pan, Costas P. Grigoropoulos, Nick Kladias, Elias Panides and Gerald A. Domoto (2007), doi:10.1063/1.2768192
  [6] Fabrice Prieur, Tonni Franke Johansen, Sverre Holm and Hans Torp (2012), doi:10.1121/1.4714773
  [7] Nathan Albin, Oscar P. Bruno, Theresa Y. Cheung and Robin O. Cleveland (2012), doi:10.1121/1.4742722
  [8] A.E. Malcolm, F. Reitich, J. Yang, J.F. Greenleaf and M. Fatemi (2008), doi:10.1016/j.ultras.2008.04.006
  [9] Lixiang Yang, Yung-Yu Chen and Sheng-Tao John Yu (2013), doi:10.1016/j.wavemoti.2012.09.002
  [10] Jochen M. Rau, Svein-Erik Ma so y, Rune Hansen, Bjo rn Angelsen and Thor Andreas Tangen (2013), doi:10.1121/1.4817900
  [11] Francois Varray, Christian Cachard, Alessandro Ramalli, Piero Tortoli and Olivier Basset (2011), doi:10.1186/1687-5281-2011-17
  [12] Rune Hansen, Svein-Erik Ma so y, Thor A. Tangen and Bjo rn A. Angelsen (2011), doi:10.1121/1.3518753
  [13] M.D. Verweij, B.E. Treeby, K.W.A. van Dongen and L. Demi (2014), doi:10.1016/B978-0-444-53632-7.00221-5
  [14] P. V. Yuldashev, L. M. Krutyansky, V. A. Khokhlova, A. P. Brysev and F. V. Bunkin (2010), doi:10.1134/S106377101004010X
  [15] R. Velasco-Segura and P.L. Rendón (2015), doi:10.1016/j.wavemoti.2015.05.006
  [16] M.E. Frijlink, H. Kaupang, T. Varslot and S.-E. Masoy (2008), doi:10.1109/ULTSYM.2008.0310
  [17] T. Hergum, S. Langeland, E.W. Remme and H. Torp (2009), doi:10.1109/TUFFC.2009.1158
  [18] T. Hergum, T.R. Skaug, K. Matre and H. Torp (2009), doi:10.1109/TUFFC.2009.1129
  [19] T. Varslot, S.-E. Masoy, T.F. Johansen and B. Angelsen (2007), doi:10.1109/TUFFC.2007.271
  [20] Francois Varray, Christian Cachard, Piero Tortoli and Olivier Basset (2010), doi:10.1109/ULTSYM.2010.5935538
  [21] F. Varray, A. Ramalli, C. Cachard, P. Tortoli and O. Basset (2011), doi:10.1109/TUFFC.2011.1956
  [22] B.A.J. Angelsen and R. Hansen (2007), doi:10.1109/ULTSYM.2007.140
  [23] Fabrice Prieur, Bastien Denarie, Andreas Austeng and Hans Torp (2013), doi:10.1109/TUFFC.2013.2868
  [24] Tasnim Azad Abir, Md. Rashedul Islam and A.B.M. Aowlad Hossain (2014), doi:10.1109/SKIMA.2014.7083530
  [25] Yigang Du, Rui Fan, Yong Li, Siping Chen and Jørgen Arendt Jensen (2016), doi:10.1016/j.ultras.2016.03.015
  [26] Nusrat Zahan, A. B. M. Aowlad Hossain and Sakib Mostafa (2015), doi:10.1109/WIECON-ECE.2015.7443957
  [27] Rokhsan Ara Hemel and Hiroyuki Hirahara (2017), doi:10.1007/s12650-017-0422-x
  [28] Oliver Mattausch, Maxim Makhinya and Orcun Goksel (2017), doi:10.1111/cgf.13260

[1] U. Haberkorn, G. Layer, V. Rudat, I. Zuna, A. Lorenz, G. van Kaick, (1993). Ultrasound image properties influenced by abdominal wall thickness and composition, J. Clin. Ultrasound, vol. 21, pp. 423-429 doi:10.1002/jcu.1870210704
[2] L. Hinkelman, D.-L. Liu, L. A. Metlay, R. C. Waag, (1994). Measurements of ultrasonic pulse arrival time and energy level variations produced by propagation through abdominal wall, J. Acoust. Soc. Am., vol. 95, no. 1, pp. 530-541 doi:10.1121/1.408347
[3] G. E. Trahey, P. D. Freiburger, L. F. Nock, D. C. Sullivan, (1991). In-vivo measurements of ultrasonic beam distortion in the breast, Ultrason. Imaging, vol. 13, no. 1, pp. 71-90 doi:10.1016/0161-7346(91)90071-O
[4] P. D. Freiburger, D. Sullivan, B. H. LeBlanc, G. E. Trahey, (1992). Two-dimensional ultrasonic beam distortion in the breast: in-vivo measurements and effects, Ultrason. Imaging, vol. 14, pp. 398-414 doi:10.1016/0161-7346(92)90080-F
[5] Q. Zhu B. D. Steinberg, (1994). Wavefront amplitude distribution in the female breast, J. Acoust. Soc. Am., vol. 96, no. 1, pp. 1-9 doi:10.1121/1.410466
[6] M. Tabei, T. D. Mast, R. C. Waag, (2003). Simulation of ultrasonic focus aberration and correction through human tissue, J. Acoust. Soc. Am., vol. 113, no. 2, pp. 1166-1176 doi:10.1121/1.1531986
[7] S. E. Måsøy, T. F. Johansen, B. Angelsen, (2003). Correction of ultrasonic wave aberration with a time delay and amplitude filter, J. Acoust. Soc. Am., vol. 113, no. 4, pp. 2009-2020 doi:10.1121/1.1559174
[8] A. I. Nachman, J. F. Smith, R. C.Waag, (1990). An equation for acoustic propagation in inhomogeneous media with relaxation losses, J. Acoust. Soc. Am., vol. 88, pp. 1584-1595 doi:10.1121/1.400317
[9] P. T. Christopher K. J. Parker, (1991). New approaches to nonlinear diffractive fields propagation, J. Acoust. Soc. Am., vol. 90, no. 1, pp. 488-499 doi:10.1121/1.401274
[10] A. P. Berkhoff J. M. Thijssen, (1996). Correction of concentrated and distributed aberrations in medical ultrasound imaging, In Proc. 1996 IEEE-UFFC Ultrasonics Symposium, pp. 1405-1410.
[11] G. Wojcik, J. Mould, F. Ayter, L. Carcione, (1998). A study of second harmonic generation by focused medical transducer pulses, In Proc. 1998 IEEE-UFFC Ultrasonics Symposium, pp. 1583-1588.
[12] T. D. Mast, (2002). Two- and three-dimensional simulations of ultrasonic propagation through human breast tissue, Acoust. Res. Lett. Online, vol. 2, no. 3, pp. 53-58 doi:10.1121/1.1447722
[13] G. Taraldsen, (2001). Derivation of a generalized Westervelt equation for nonlinear medical ultrasound, J. Acoust. Soc. Am., vol. 109, no. 4, pp. 1329-1333 doi:10.1121/1.1344157
[14] B. A. Angelsen, (2000). Ultrasound imaging: Waves, signals and signal processing, Trondheim, Norway: Emantec, vol. 2, http://www.ultrasoundbook.com.
[15] M. F. Hamilton D. T. Blackstock, (1997). Nonlinear Acoustics, San Diego: Academic Press.
[16] T. D. Mast, L. Hinkelman, M. Orr, R. C. Waag, (1998). The effect of abdominal wall morphology on ultrasonic pulse distortion: part II- simulations, J. Acoust. Soc. Am., vol. 104, no. 6, pp. 3651-3664, December doi:10.1121/1.423947
[17] F. Tappert, (1977). The parabolic approximation method in wave propagation and underwater acoustics, In Lectures in Physics, J. B. Keller and J. S. Papadakis, Eds. New York: Springer, pp. 224-287.
[18] E. A. Zabotskaya R. V. Khoklov, (1969). Quasi-plane waves in the non-linear acoustics of confined beams, Sov. Phys. Acoust., vol. 15, pp. 35-40.
[19] V. P. Kuznetsov, (1971). Equations of nonlinear acoustics, Sov. Phys. Acoust., vol. 16, pp. 467-470.
[20] J. F. Claerbout, (1976). Fundamentals of Geophysical Data Processing, New York: McGraw-Hill.
[21] J.-P. Berenger, (1994). A perfectly matched layer for the absorption of electromagnetic waves, J. Comp. Phys., vol. 114, no. 2, pp. 185-200 doi:10.1109/TUFFC.2003.1209563
[22] F. Collino, (1997). Perfectly matched absorbing layers for the paraxial equations, J. Comp. Phys., vol. 131, no. 1, pp. 164-180 doi:10.1006/jcph.1996.5594
[23] A. Bouakaz, C. Lancée, N. de Jong, (2003). Harmonic ultrasonic field of medical phased arrays: Simulations and measurements, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 50, no. 6, pp. 730-735 doi:10.1109/TUFFC.2003.1209563
[24] A. Bamberg, B. Engqvist, L. Halpern, P. Joly, (1988). Parabolic wave equation approximations in heterogeneous media, SIAM J. Appl. Math., vol. 48, no. 1, pp. 99-128 doi:10.1137/0148005
[25] T. Varslot G. Taraldsen, (2005). Computer simulation of forward wave propagation in soft tissue, IEEE Trans. Ultrason. Ferroelectr. Freq. Control,.Accepted for publication doi:10.1109/TUFFC.2005.1516019
[26] T. Varslot, (2004). Wavefront aberration in medical ultrasound imaging, Dr.ing. thesis, Institutt for matematiske fag, NTNU, Trondheim.
[27] L. Brekhovskikh O. Godin, (1999). Acoustics of Layered Media I-II, 2nd ed. Springer.
[28] F. A. Duck, (1990). Physical properties of tissue, London: Academic Press.
[29] I. Kappel, (1997). Evolution equations and Approximations, San Diego: Academic Press.
[30] J. Dollard C. Friedman, (1979). Product Integration with Applications to Differential Equations, Ser. Encyclopædia of mathematics and its applications, G.-C. Rota, Ed. Reading, Massachusetts: Addison-Wesley.
[31] G. Strang, (1968). On the construction and comparison of difference schemes, Numer. Anal., vol. 5, pp. 506-517 doi:10.1137/0705041
[32] H. Engl, M. Hanke, A. Neubauer, (2000). Regularization of inverse problems, Netherlands: Kluwer Academic Publishers.
[33] T. L. Szabo, (1994). Time domain wave equations for lossy media obeying a frequency power law, J. Acoust. Soc. Am., vol. 96, pp. 491-500 doi:10.1121/1.410434
[34] H. Holden N. H. Risebro, (2002). Front Tracking for Hyperbolic Conservation Laws, Ser. Applied Mathematical Sciences. New York: Springer Verlag, vol. 152.
[35] A. Bamberg, B. Engqvist, L. Halpern, P. Joly, (1988). Higher order paraxial wave equation approximations in heterogeneous media, SIAM J. Appl. Math., vol. 48, no. 1, pp. 129-154 doi:10.1137/0148006
[36] E. Bécache, F. Collino, P. Joly, (1998). Higher-order numerical schemes and operator splitting for solving 3D paraxial wave equations in heterogeneous media, INRIA, Technical Report 3497.
[37] G. B. Whitham, (1974). Linear and Nonlinear Waves, Wiley.
[38] G. L. Wojcik, B. Fornberg, R. C. Waag, L. Carcione, J. Mould, L. Nikodym, T. Driscoll, (1997). Pseudospectral methods for large-scale bioacoustic models, In Proc. 1997 IEEE-UFFC Ultrasonics Symposium, pp. 1501-1506.
[39] M. E. Anderson, (2000). A 2D nonlinear wave propagation solver written in open-source matlab code, In Proc. IEEE-UFFC Ultrasonics Symposium, [Online]. Available: http://www.seas.rochester.edu, maanders/sps2d.html.
[40] J. F. Baldomero, (2005). MPI toolbox for matlab, http://atc.ugr.es/javier-bin/mpitb eng.

  title={{Forward propagation of acoustic pressure pulses in 3D soft biological tissue}},
  author={Varslot, Trond and Måsøy, Svein-Erik},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}


Oct 2018: MIC reaches 3000 DOI Forward Links. The last 1000 took 2 years and 5 months.

May 2016: MIC reaches 2000 DOI Forward Links. The first 1000 took 34 years, the next 1000 took 2.5 years.

July 2015: MIC's new impact factor is now 0.778. The number of papers published in 2014 was 21 compared to 15 in 2013, which partially explains the small decrease in impact factor.

Aug 2014: For the 3rd year in a row MIC's impact factor increases. It is now 0.826.

Dec 2013: New database-driven web-design enabling extended statistics. Article number 500 is published and MIC reaches 1000 DOI Forward Links.

Jan 2012: Follow MIC on your smartphone by using the RSS feed.


July 2011: MIC passes 1000 ISI Web of Science citations.

Mar 2010: MIC is now indexed by DOAJ and has received the Sparc Seal seal for open access journals.

Dec 2009: A MIC group is created at LinkedIn and Twitter.

Oct 2009: MIC is now fully updated in ISI Web of Knowledge.