ncku-talk2012-01-10

NCTS(South)/ NCKU Math Colloquium

DATE 2012-01-10　10:00-11:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Dr. Yu Jiang（Dept. of Applied Mathematics, Shanghai University of Finance and Economics, China）

TITLE Data analysis for Magnetic Resonance Elastography II: Recovery of Viscoelasticity

ABSTRACT MRE (Magnetic resonance elastography) is a new diagnostic modality to measure the stiff ness 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 sti ness 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 modffi ed Stokes system is a proper model. Further, by several numerical schemes for solving the inverse problem under this PDE model, we can recover the viscoelasticity of soft tissues.

NCTS(South)/ NCKU Math Colloquium

DATE	2012-01-10　10:00-11:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Dr. Yu Jiang（Dept. of Applied Mathematics, Shanghai University of Finance and Economics, China）

TITLE	Data analysis for Magnetic Resonance Elastography II: Recovery of Viscoelasticity

ABSTRACT	MRE (Magnetic resonance elastography) is a new diagnostic modality to measure the stiff ness 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 sti ness 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 modffi ed Stokes system is a proper model. Further, by several numerical schemes for solving the inverse problem under this PDE model, we can recover the viscoelasticity of soft tissues.