Viscoelastic properties of soft tissues in a living body measured by MR elastography

Abstract

MRE (Magnetic resonance elastography) is a new diagnostic modality to measure the stiffness of soft tissues in a living body. It measures the displacements of waves propagating in the tissues and then this measured data is linked to the stiffness via a proper model for wave propagation in the tissues and by solving some inverse problem under this model. We will show why we can only see transverse waves inside soft tissues even if we inject longitudinal vibrations into the tissues from their surfaces by modeling the soft tissues of a living body as a nearly incompressible isotropic viscoelastic medium. We interpret the nearly incompressibility by an asymptotic analysis. As a consequence, we show that the so-called modified Stokes system is a proper model. Further, by a modified numerical integral method for solving the inverse problem under this PDE model, we can recover the viscoelasticity of soft tissues.