Shear wave speed in pressurized soft tissue

Shear wave elastography is a non-invasive measurement technique to infer mechanical properties of soft tissue. A shear wave is propagated inside a region of interest. The medium perturbations caused by the wave are measured using an imaging modality, e.g., ultrasound, or NMR. The shear wave speed in the medium is thus inferred. Recent studies reported different shear wave speeds in pressurized soft tissue when measured in constrained versus unconstrained conditions, i.e., the volume of the body is free to change or not. Acoustoelasticity theory, which accounts for prestress in elastic materials, does not explain this phenomenon. We model this phenomenon by examining incremental waves in a pressurized poroelastic medium with incompressible phases. We derive a simple formula for the shear wave speed in an isotropic poroelastic medium, with the solid phase modeled by an arbitrary strain energy function. We discuss necessary constraints on the form of the strain energy function that are evident in this context. Interestingly, these constraints exclude all decoupled strain energy functions. We then specialize to a specific exponential model that yields shear wave speeds consistent with previously published measurements.