Annals of Biomedical Engineering

, Volume 29, Issue 9, pp 781–790

Ultrasonic Wave Propagation in Trabecular Bone Predicted by the Stratified Model

  • Wei Lin
  • Yi-Xian Qin
  • Clinton Rubin
Article

Abstract

The objective of this study was to investigate ultrasound propagation in trabecular bone by considering the wave reflection and transmission in a multilayered medium. The use of ultrasound to identify those at risk of osteoporosis is a promising diagnostic method providing a measure of bone mineral density (BMD). A stratified model was proposed to study the effect of transmission and reflection of ultrasound wave within the trabecular architecture on the relationship between ultrasound and BMD. The results demonstrated that ultrasound velocity in trabecular bone was highly correlated with the bone apparent density (r=0.97). Moreover, a consistent pattern of the frequency dependence of ultrasound attenuation coefficient has been observed between simulation using this model and experimental measurement of trabecular bone. The normalized broadband ultrasound attenuation (nBUA) derived from the simulation results revealed that nBUA was nonlinear with respect to trabecular porosity and BMD. The curve of the relationship between nBUA and BMD was parabolic in shape, and the peak magnitude of nBUA was observed at ∼60% of bone porosity. These results agreed with the published experimental data and demonstrated that according to the stratified model, reflection and transmission were important factors in the ultrasonic propagation through the trabecular bone. © 2001 Biomedical Engineering Society.

PAC01: 4380Vj, 4380Qf, 8763Df, 8710+e, 4325Ed, 8719-j

Ultrasound Ultrasound velocity Broadband ultrasound attenuation Bone Stratified model Bone mineral density Osteoporosis Bone porosity Trabecular bone Strength 

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References

  1. 1.
    Alves, J. M., J. T. Ryaby, J. J. Kaufman, F. P. Magee, and R. S. Siffert. Influence of marrow on ultrasonic velocity and attenuation in bovine trabecular bone. Calcif. Tissue Int.58:362–367, 1996.Google Scholar
  2. 2.
    Ashman, R. B., J. D. Corin, and C. H. Turner. Elastic properties of cancellous bone: Measurement by an ultrasonic technique. J. Biomech.20:979–986, 1987.Google Scholar
  3. 3.
    Ashman, R. B., and J. Y. Rho. Elastic modulus of trabecular bone material. J. Biomech.21:177–181, 1988.Google Scholar
  4. 4.
    Biot, M. A.Generalized theory of acoustic propagation in porous dissipative media. J. Acoust. Soc. Am.34:1254–1264, 1962.Google Scholar
  5. 5.
    Bouxsein, M. L., B. S. Coan, and S. C. Lee. Prediction of the strength of the elderly proximal femur by bone mineral density and quantitative ultrasound measurements of the heel and tibia. Bone (N.Y.)25:49–54, 1999.Google Scholar
  6. 6.
    Brouard, B., D. Lafarge, and J. F. Allard. A general method of modeling sound propagation in layered media. J. Sound Vib.183:129–142, 1995.Google Scholar
  7. 7.
    Cowin, S. C. Bone Mechanics. Boca Raton: 1989.Google Scholar
  8. 8.
    Gluer, C. C., C. Y. Wu, M. Jergas, S. A. Goldstein, and H. K. Genant. Three quantitative ultrasound parameters reflect bone structure. Calcif. Tissue Int.55:46–52, 1994.Google Scholar
  9. 9.
    Haire, T. J., and C. M. Langton. Biot theory: A review of its application to ultrasound propagation through cancellous bone. Bone (N.Y.)24:291–295, 1999.Google Scholar
  10. 10.
    Han, S., J. Medige, and I. Ziv. Combined models of ultrasound velocity and attenuation for predicting trabecular bone strength and mineral density. Clin. Biomech.11:348–353, 1996.Google Scholar
  11. 11.
    Han, S., J. Rho, J. Medige, and I. Ziv. Ultrasound velocity and broadband attenuation over a wide range of bone mineral density. Osteoporosis Int.6:291–296, 1996.Google Scholar
  12. 12.
    Hosokawa, A., and T. Otani. Ultrasonic wave propagation in bovine cancellous bone. J. Acoust. Soc. Am.101:558–562, 1997.Google Scholar
  13. 13.
    Hosokawa, A., and T. Otani. Acoustic anisotropy in bovine cancellous bone. J. Acoust. Soc. Am.103:2718–2722, 1998.Google Scholar
  14. 14.
    Hughes, E. R., T. G. Leighton, G. W. Petley, and P. R. White. Ultrasonic propagation in cancellous bone: A new stratified model. Ultra. Med. Biol.25:811–821, 1999.Google Scholar
  15. 15.
    Langton, C. M., C. F. Njeh, R. Hodgskinson, and J. D. Currey. Prediction of mechanical properties of the human calcaneus by broadband ultrasonic attenuation. Bone (N.Y.)18:495–503, 1996.Google Scholar
  16. 16.
    Langton, C. M., S. B. Palmer, and R. W. Porter. The measurement of broadband ultrasonic attenuation in cancellous bone. Eng. Med.13:89–91, 1984.Google Scholar
  17. 17.
    Lin, W., Y. X. Qin, and C. T. Rubin. Frequency specific scanning of ultrasound attenuation of bone properties. Trans. 46th Annual Meeting of Orthopaedic Res. Soc.46:750, 2000.Google Scholar
  18. 18.
    McKelvie, M. L., and S. B. Palmer. The interaction of ultrasound with cancellous bone. Phys. Med. Biol.36:1331–1340, 1991.Google Scholar
  19. 19.
    Nicholson, P. H., R. Strelitzki, R. O. Cleveland, and M. L. Bouxsein. Scattering of ultrasound in cancellous bone: Predictions from a theoretical model. J. Biomech.33:503–506, 2000.Google Scholar
  20. 20.
    Njeh, C. F., D. Hans, T. Fuerst, C. C. Gluer, and H. K. Genant. Quantitative Ultrasound: Assessment of Osteoporosis and Bone Status. London: 1999.Google Scholar
  21. 21.
    Prins, S. H., H. L. Jorgensen, L. V. Jorgensen, and C. Hassager. The role of quantitative ultrasound in the assessment of bone: A review. Clin. Physiol.18:3–17, 1998.Google Scholar
  22. 22.
    Schoenberg, M.Wave propagation in alternating solid and fluid layers. Wave Motion6:303–321, 1984.Google Scholar
  23. 23.
    Serpe, L., and J. Y. Rho. The nonlinear transition period of broadband ultrasound attenuation as bone density varies. J. Biomech.29:963–966, 1996.Google Scholar
  24. 24.
    Strelitzki, R., J. A. Evans, and A. J. Clarke. The influence of porosity and pore size on the ultrasonic properties of bone investigated using a phantom material. Osteoporosis Int.7:370–375, 1997.Google Scholar
  25. 25.
    Tavakoli, M. B., and J. A. Evans. Dependence of the velocity and attenuation of ultrasound in bone on the mineral content. Phys. Med. Biol.36:1529–1537, 1991.Google Scholar
  26. 26.
    Turner, C. H., J. Rho, Y. Takano, T. Y. Tsui, and G. M. Pharr. The elastic properties of trabecular and cortical bone tissues are similar: Results from two microscopic measurement techniques. J. Biomech.32:437–441, 1999.Google Scholar
  27. 27.
    Wear, K. A.Frequency dependence of ultrasonic backscatter from human trabecular bone: Theory and experiment. J. Acoust. Soc. Am.106:3659–3664, 1999.Google Scholar
  28. 28.
    Wear, K. A. Anisotropy of ultrasonic backscatter and attenuation from human calcaneus: Implications for relative roles of absorption and scattering in determining attenuation. J. Acoust. Soc. Am.107:3474–3479, 2000.Google Scholar
  29. 29.
    Wear, K. A.The effects of frequency-dependent attenuation and dispersion on sound speed measurement: Applications in human trabecular bone. IEEE Trans. Ultrason. Ferroelectr. Freq. Control47:265–273, 2000.Google Scholar
  30. 30.
    Williams, J. L.Ultrasonic wave propagation in cancellous and cortical bone: Prediction of some experimental results by Biot's theory. J. Acoust. Soc. Am.91:1106–1112, 1992.Google Scholar

Copyright information

© Biomedical Engineering Society 2001

Authors and Affiliations

  • Wei Lin
    • 1
  • Yi-Xian Qin
    • 1
  • Clinton Rubin
    • 1
  1. 1.Department of Biomedical EngineeringState University of New York at Stony BrookStony Brook

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