On the elasticity of transverse isotropic soft tissues (L)

Quantitative elastography techniques have recently been developed to estimate the shear modulus μ of soft tissues in vivo. In the case of isotropic and quasi-incompressible media, the Young's modulus E is close to 3 μ, which is not true in transverse anisotropic tissues such as muscles. In this letter, the transverse isotropic model established for hexagonal crystals is revisited in the case of soft solids. Relationships between elastic constants and Young's moduli are derived and validated on experimental data found in the literature. It is shown that 3 μ(⊥) ≤ E(⊥) ≤ 4 μ(⊥) and that E(//) cannot only be determined from the measurements of μ(//) and μ(⊥).