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

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.

[1]  Armando Manduca,et al.  Spatio-temporal Directional Filtering for Improved Inversion of MR Elastography Images , 2002, MICCAI.

[2]  L. Hörmander.  The Analysis of Linear Partial Differential Operators III , 2007 .

[3]  Habib Ammari,et al.  A method of biological tissues elasticity reconstruction using magnetic resonance elastography measurements , 2007 .

[4]  Identification of viscoelastic properties by magnetic resonance elastography , 2007 .

[5]  I. Sack,et al.  Algebraic Helmholtz inversion in planar magnetic resonance elastography , 2008, Physics in medicine and biology.

[6]  J. F. Greenleaf,et al.  Magnetic resonance elastography: Non-invasive mapping of tissue elasticity , 2001, Medical Image Anal..

[7]  J. D. de Certaines,et al.  MR imaging of viscoelastic properties , 1995, Journal of magnetic resonance imaging : JMRI.

[8]  J. Shirron,et al.  On the noninvasive determination of material parameters from a knowledge of elastic displacements theory and numerical simulation , 1998, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[9]  R. Sinkus,et al.  High-resolution tensor MR elastography for breast tumour detection. , 2000, Physics in medicine and biology.

[10]  L. Hörmander.  The analysis of linear partial differential operators , 1990 .

[11]  Dieter Klatt,et al.  The impact of aging and gender on brain viscoelasticity , 2009, NeuroImage.

[12]  D B Plewes,et al.  Visualizing tissue compliance with MR imaging , 1995, Journal of magnetic resonance imaging : JMRI.

[13]  A. Manduca,et al.  Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. , 1995, Science.

[14]  Diego Murio,et al.  Mollification and space marching , 2002 .

[15]  Joyce R. McLaughlin,et al.  An error estimate on the direct inversion model in shear stiffness imaging , 2009 .

[16]  A. Maniatty,et al.  Shear modulus reconstruction in dynamic elastography: time harmonic case , 2006, Physics in medicine and biology.

[17]  P. Carson,et al.  Magnetic-resonance imaging techniques for detection of elasticity variation. , 1995, Medical physics.

[18]  Gen Nakamura,et al.  Inversion analysis for magnetic resonance elastography , 2008 .

[19]  Jun Okamoto,et al.  Measurement of in vivo local shear modulus using MR elastography multiple-phase patchwork offsets , 2003, IEEE Transactions on Biomedical Engineering.

[20]  K J Parker,et al.  Imaging of the elastic properties of tissue--a review. , 1996, Ultrasound in medicine & biology.

[21]  M Fink,et al.  Imaging anisotropic and viscous properties of breast tissue by magnetic resonance‐elastography , 2005, Magnetic resonance in medicine.

[22]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[23]  Mickael Tanter,et al.  Viscoelastic shear properties of in vivo breast lesions measured by MR elastography. , 2005, Magnetic resonance imaging.

[24]  J. M. Muñoz Rivera,et al.  Decay rates of solutions of an anisotropic inhomogeneousn-dimensional viscoelastic equation with polynomially decaying kernels , 1996 .

[25]  P. Asbach,et al.  Noninvasive assessment of the rheological behavior of human organs using multifrequency MR elastography: a study of brain and liver viscoelasticity , 2007, Physics in medicine and biology.

[26]  J. McLaughlin,et al.  Log-elastographic and non-marching full inversion schemes for shear modulus recovery from single frequency elastographic data , 2009 .