Inversion analysis for magnetic resonance elastography

We will propose a new reconstruction scheme to identify the viscoelasticity of a living body from MRE measurements. The reconstruction scheme consists of application of the oscillating–decaying solution, Taylor expansion, complex geometric optics solutions, and an iterative method for solving the Cauchy problem for elliptic equations.

[1]  溝畑 茂,et al.  The theory of partial differential equations , 1973 .

[2]  M. Potier-Ferry.  On the mathematical foundations of elastic stability theory. I. , 1982 .

[3]  J. Sylvester,et al.  A global uniqueness theorem for an inverse boundary value problem , 1987 .

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

[5]  R. Sinkus,et al.  High-resolution tensor MR elastography for breast tumour detection. , 2000, 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]  Joyce R. McLaughlin,et al.  Interior elastodynamics inverse problems: shear wave speed reconstruction in transient elastography , 2003 .

[8]  Joyce R. McLaughlin,et al.  Unique identifiability of elastic parameters from time-dependent interior displacement measurement , 2004 .

[9]  Joyce R. McLaughlin,et al.  Recovery of the Lamé parameter μ in biological tissues , 2003 .

[10]  T. Johansson.  An iterative procedure for solving a Cauchy problem for second order elliptic equations , 2004 .

[11]  G. Nakamura.  Applications of the Oscillating-Decaying Solutions to Inverse Problems , 2004 .

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

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

[14]  Joyce R. McLaughlin,et al.  Shear wave speed recovery in transient elastography and supersonic imaging using propagating fronts , 2006 .

[15]  J. McLaughlin,et al.  Using level set based inversion of arrival times to recover shear wave speed in transient elastography and supersonic imaging , 2006 .

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

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