9789400700161-c2 - Chapter 2 Introduction to the Physics of...

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Chapter 2 Introduction to the Physics of Ultrasound Pascal Laugier and Guillaume Ha¨ ıat Abstract From an acoustical point of view, bone is a complex medium as it is heterogeneous, anisotropic and viscoelastic. This chapter reviews the basic notions of physical acoustics which are necessary to tackle the problem of the ultrasonic propagation in bone, in the perspective of the application of quantitative ultrasound (QUS) techniques to bone characterization. The ±rst section introduces the basic phenomena related to the ±eld of medical ultrasound. Basic description of wave propagation is introduced. Mechanical bases are necessary to understand the elas- todynamic nature of the interaction between bone and ultrasound. The physical determinants of the speed of sound of the different types of waves corresponding to the propagation in a liquid and in a solid are considered. The effects of bound- ary conditions (guided waves) are also detailed. The second section describes the physical interaction between an ultrasonic wave and bone tissue, by introducing re²ection/refraction, attenuation and scattering phenomena. Keywords Absorption · Anisotropy · Attenuation · Compression wave · Diffrac- tion · Elastic modulus · Elastic solid · Group velocity · Guided wave · Impedance · Kramers Kr¨onig · Lamb waves · Phase velocity · Poisson’s ratio · Re²ection · Refraction · Scattering · Shear wave · Snell’s law · Speckle · Speed of sound · Stiffness · Strain · Stress · Young’s modulus 2.1 Fundamentals of Ultrasound In analogy to visible and ultraviolet light, the terms sound and ultrasound are used to describe the propagation of a mechanical perturbation in different frequency ranges. Ultrasound corresponds to a mechanical wave propagating at frequencies P. Laugier ( ± ) Universit´e Pierre et Marie Curie, CNRS, Laboratoire d’Imagerie Parametrique, 15, rue de L’Ecole de Medecine, 75006 Paris, France e-mail: pascal.laugier@upmc.fr G. Ha¨ ıat CNRS, B2OA UMR 7052, 10, avenue de Verdun, 75010 Paris, France e-mail: guillaume.haiat@univ-paris-est.fr P. Laugier and G. Ha¨ ıat (eds.), Bone Quantitative Ultrasound , DOI 10.1007/978-94-007-0017-8 2, c ± Springer Science+Business Media B.V. 2011 29
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30 P. Laugier and G. Ha¨ ıat above the range of human hearing (conventionally 20 kHz). Ultrasound and sound waves propagate in Fuids (gases and liquids) and solids. The mechanical perturba- tion provokes tiny disturbances of the medium particles from their resting position. These disturbances induce a displacement of these particles and are transmitted step by step to other parts of the medium. The interaction between the particles can be schematically described using a mechanical spring analogy. In particular the wave propagation depends on the intrinsic elastic properties of the medium as well as on its mass density. ±or tiny perturbations (linear propagation regime), no mass is trans- ported as the wave propagates from point to point: the medium as a whole remains stationary. In depth analysis of some aspects of non-linear propagation regimes will
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9789400700161-c2 - Chapter 2 Introduction to the Physics of...

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