Ultrasound Elastography for Biomedical Applications and Medicine

6 Transverse Wave Propagation in Anisotropic Media

Jean‐Luc Gennisson

Imagerie par Résonance Magnétique Médicale et Multi‐Modalités, Université Paris‐Saclay, Orsay, France

6.1 Introduction

In science and technology elastic properties of solids have considerable significance. This information is of fundamental importance in interpreting and understanding the nature of bonding in the solid state, because the elastic properties describe the mechanical behavior of materials. When a material is subjected to a stress it will experience strain. Within the elastic limit, strain varies linearly with the applied stress and leads to the definition of the common elastic material properties, which are the Young's modulus (E), bulk modulus (κ), shear modulus (μ), and Poisson's ratio (υ). Additional to these elastic constants there is the longitudinal modulus and transverse modulus that can be determined from the velocity of propagation of longitudinal waves and transverse waves through a solid. The number of elastic constants for anisotropic solids such as crystals that have been discussed previously [1–5]. Anisotropy has also long been studied in geophysics [6, 7] or in nondestructive testing with ultrasound [8, 9]. In biological media ex vivo, Hoffmeister [10] and Kuo [11] on tendon, Yoon [12] on bone, or Levinson [13] and Andersen [14] on muscle quantify the anisotropic longitudinal elastic moduli. The first technique that tried to quantify shear elastic anisotropy was the ...