Multiple Scattering Contribution to Trabecular Bone Backscatter

  • J. Wójcik
  • J. Litniewski
  • A. Nowicki
Conference paper
Part of the Acoustical Imaging book series (ACIM, volume 30)


Integral equations that describe scattering on the structure with stependly changing physical parameters, have been numerically solved on example of the trabecular bone model. The model consists of several hundred elements with randomly selected parameters. The spectral distribution of scatter coefficients in subsequent orders of scattering has been presented.


Multiple scattering Absorbing medium Complex random structure Back scatter coefficients Trabecular bone 



This work is supported by Ministry of Science and Higher Education (grant No. 0219/T02/2007/32)


  1. 1.
    Wear, K.: Frequency dependence of ultrasonic backscatter from human trabecular bone: theory and experiments. J. Acoust. Soc. Am. 106(6), 3659–3664 (1999)ADSCrossRefGoogle Scholar
  2. 2.
    Bossy, E., Padilla, F., Peyrin, F., Laugier, P.: Three-dimensional simulation of ultrasound propagation through trabecular bone structures measured by synchrotron micro-tomography. Phys. Med. Biol. 50, 5545–5556 (2005)CrossRefGoogle Scholar
  3. 3.
    Wear, K.: Ultrasonic scattering from cancellous bone: A review. IEEE Trans. Ultrason. Freq. Contr. 55(7), 1432–1441 (2008)CrossRefGoogle Scholar
  4. 4.
    Brekhovskikh, L.M., Godin, O.A.: Acoustics of layered media I, ISBN 3-540-51038-9, pp. 1–14. Springer-Verlag Berlin Haidelberg, New York (1990)Google Scholar
  5. 5.
    Wójcik, J.: Conservation of energy and absorption in acoustic fields for linear and nonlinear propagation. J. Acoust. Soc. Am. 104(5), 2654–2663 (1998)ADSCrossRefGoogle Scholar
  6. 6.
    Hosokawa, A.: Development of numerical cancellous bone model for finite-difference time-domain simulations of ultrasound propagation. IEEE Trans. Ultrason. Ferro. Freq. Contr. 55(6), 1219–1233 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • J. Wójcik
    • 1
  • J. Litniewski
    • 1
  • A. Nowicki
    • 2
  1. 1.Institute of Fundamental Technological Research, Polish Academy of SciencesWarsawPoland
  2. 2.Polish Academy of SciencesInstitute of Fundamental Technological ResearchWarsawPoland

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