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Phase Velocity of Cancellous Bone: Negative Dispersion Arising from Fast and Slow Waves, Interference, Diffraction, and Phase Cancellation at Piezoelectric Receiving Elements

  • Christian C. Anderson
  • Adam Q. Bauer
  • Karen R. Marutyan
  • Mark R. Holland
  • Michal Pakula
  • G. Larry Bretthorst
  • Pascal Laugier
  • James G. MillerEmail author
Chapter

Abstract

Frequency-dependent phase velocity measurements may prove useful in bone quality assessment. However, the physical mechanisms of ultrasonic wave propagation in cancellous bone that govern phase velocity are not yet fully understood, particularly the phenomena that lead to the observed anomalous negative dispersion. This chapter provides an overview of phase velocity studies of cancellous bone, especially negative dispersion, and proposals for resolving the apparent conflict with the causality-imposed Kramers-Kronig relations.

Keywords

Artifact Bayesian Negative dispersion Phase cancellation Phase velocity 

Notes

Acknowledgments

Work presented in this chapter was supported by NIH grants R01HL40302 and R01AR057433 and by NSF grant CBET-0717830.

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Copyright information

© Springer Netherlands 2011

Authors and Affiliations

  • Christian C. Anderson
    • 1
  • Adam Q. Bauer
    • 1
  • Karen R. Marutyan
    • 1
  • Mark R. Holland
    • 1
  • Michal Pakula
    • 2
  • G. Larry Bretthorst
    • 1
  • Pascal Laugier
    • 3
  • James G. Miller
    • 1
    Email author
  1. 1.Department of PhysicsWashington UniversitySaint LouisUSA
  2. 2.Kazimierz Wielki UniversityBydgoszczPoland
  3. 3.CNRS, Laboratoire d’Imagerie ParametriqueUniversité Pierre et Marie CurieParisFrance

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