Elasticity of transverse isotropic soft tissues

Abstract : Quantitative elastography techniques such as Supersonic Shear Imaging (SSI) have recently been developed to estimate non-invasively the mechanical properties of soft tissues in vivo. Based on the measurement of shear wave velocity Vs, SSI techniques allow to estimate the shear modulus µ from the relation µ = \rho (Vs)². In the case of soft isotropic media, this quantity can be related to the Young’s modulus E, which corresponds to the physician’s palpation or mechanical testing results, as E = 3µ. In more complex tissues such as muscles, which exhibit a strong transverse anisotropy, two shear moduli (µ// and µ\perp) and two Young’s moduli (E// and E\perp) are defined. Moreover, the simple relationship E = 3µ doesn’t hold anymore. Transverse isotropic medium are commonly described by a stiffness tensor having five coefficients. This model, established for hexagonal crystals, is revisited in the case of soft anisotropic solids. Relationships between elastic constants and Young’s moduli are derived and these relations are validated on experimental data found in the literature. It is shown that 3µ\perp \leq E\perp \leq 4µ\perp and that E// cannot be determined from the measurements of µ// and µ\perp alone. The limits of ultrasonic testing for the mechanical characterization of soft anisotropic media are discussed.
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Daniel Royer, Jean-Luc Gennisson, Thomas Deffieux, Mickaël Tanter. Elasticity of transverse isotropic soft tissues. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810693⟩

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