Abstract
Shear wave elastography measures shear wave speed in soft tissues for diagnostic purposes. In Rotemberg et al. [J. Biomech. 46(11), (2013), pp. 1875-1881] and Rotemberg et al. [Phys. Med. Biol. 57(2), (2012), pp. 329-341], shear wave speed measurements were shown to depend on prestrain, but not necessarily prestress, in a perfused canine liver. We model this phenomenon by examining incremental waves in a pressurized poroelastic medium with incompressible phases. For a poroelastic material with strain energy function W, which due to pressurization undergoes a volume expansion of Δ, we find the following general expression for the shear wave speed: c2/c02=(W1(Δ) + W2(Δ) Δ2/3)/Δ2/3 (W1(1) + W2(1)). Here, c0 is the shear wave speed in the unpressurized material, Wj = ∂ W/∂ Ij, and Ij is an invariant of the Cauchy-Green strain tensor. We also find important restrictions on the form of the strain energy function, which are typically not satisfied by strain energy functions commonly assumed for soft tissues.
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