References
- Ammari , H , Garapon , P , Kang , H and Lee , H . A method of biological tissues elasticity reconstruction using magnetic resonance elastography measurements . Quarterly Journal of Applied Mathematics , (in press)
- Ji , L , McLaughlin , JR , Renzi , D and Yoon , JR . 2003 . Interior elastodynamics inverse problems: shear wave speed reconstruction in transient elastography . Inverse Problems , 19 : S1 – S29 .
- Ji , L and McLaughlin , JR . 2004 . Recovery of the Lamé parameter μ in biological tissues . Inverse Problems , 20 ( 1 ) : 1 – 24 .
- Higashimori , N . 2007 . Identification of viscoelastic properties by magnetic resonance elastography . Journal of Physics: Conference Series , 73 : 012009 (6pp) online
- Johansson , T . 2004 . An iterative procedure for solving a Cauchy problem for second order elliptic equations . Mathematische Nachrichten , 272 : 46 – 54 .
- Manduca , A , Oliphant , TE , Dresner , MA , Mahowald , JL , Kruse , SA , Amromin , E , Felmlee , JP , Greenleaf , JF and Ehman , RL . 2001 . Magnetic resonance elastography: noninvasive mapping of tissue elasticity . Medical Image Analysis , 5 : 237 – 254 .
- McLaughlin , JR and Yoon , JR . 2004 . Unique identifiability of elastic parameters from time dependent interior displacement measurement . Inverse Problems , 20 ( 1 ) : 25 – 45 .
- McLaughlin , JR and Daniel , R . 2006 . Shear wave speed recovery in transient elastography and supersonic imaging using propagating fronts . Inverse Problems , 22 : 681 – 706 .
- McLaughlin , JR and Daniel , R . 2006 . Using level set based inversion of arrival times to recover shear wavespeed in transient elastography and supersonic imaging . Inverse Problems , 22 : 707 – 725 .
- Mizohata , S . 1973 . The Theory of Partial Differential Equations , Edited by: Miyahara , K . New York : Cambridge University Press . (Transl.)
- Muthupillai , R , Lomas , DJ , Rossman , PJ , Greenlead , JF , Manduca , A and Ehman , RL . 1995 . Magnetic resonance elastography by direct visualization of propagating acoustic strain waves . Science , 269 : 1854 – 1857 .
- Nakamura , G . 2004 . “ Applications of the oscillating–decaying solutions to inverse problems ” . In New Analytic and Geometric Method in Inverse Problems , Edited by: Bingham , K , Kurylev , VY and Somersalo , E . 353 – 365 . Berlin : Springer .
- Potier-Ferry , M . 1982 . On the mathematical foundations of elastic stability theory. I . Archive for Rational Mechanics and Analysis , 78 ( 1 ) : 55 – 72 .
- Sinkus , R , Lorenzen , J , Schrader , D , Lorenzen , M , Dargatz , M and Holz , D . 2000 . Highresolution tensor MR elastography for breast tumour detection . Physics in Medicine and Biology , 45 : 1649 – 1664 .
- Sinkus , R , Tanter , M , Catheline , S , Lorenzen , J , Kuhl , C , Sondermann , E and Fink , M . 2005 . Imaging anisotropic and viscous properties of breast tissue by magnetic resonanceelastography . Magnetic Resonance in Medicine , 53 : 372 – 387 .
- Sinkus , R , Tanter , M , Xydeas , T , Catheline , S , Bercoff , J and Fink , M . 2005 . Viscoelastic shear properties of in vivo breast lesions measured by MR elastography . Magnetic Resonance Imaging , 23 : 159 – 165 .
- Sylvester , J and Uhlmann , G . 1987 . A global uniqueness theorem for an inverse boundary value problem . Annals of Mathematics (2) , 125 ( 1 ) : 153 – 169 .