A method of biological tissues elasticity reconstruction using magnetic resonance elastography measurements
Authors:
Habib Ammari, Pierre Garapon, Hyeonbae Kang and Hyundae Lee
Journal:
Quart. Appl. Math. 66 (2008), 139175
MSC (2000):
Primary 35R30, 35B20; Secondary 74B05, 35Q30
Published electronically:
December 7, 2007
MathSciNet review:
2396655
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Abstract: Magnetic resonance elastography (MRE) is an approach to measuring material properties using external vibration in which the internal displacement measurements are made with magnetic resonance. A variety of simple methods have been designed to recover mechanical properties by inverting the displacement data. Currently, the remaining problems with all of these methods are that, in general, the homogeneous Helmholtz equation is used and therefore it fails at interfaces between tissues of different properties. The purpose of this work is to propose a new method for reconstructing both the shape and the shear modulus of a small anomaly with Lamé parameters different from the background ones using internal displacement measurements.
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 H. Ammari and H. Kang, Polarization and Moment Tensors with Applications to Inverse Problems and Effective Medium Theory, Applied Mathematical Sciences, Volume 162, SpringerVerlag, New York, 2007.
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 H. Ammari, H. Kang, G. Nakamura, and K. Tanuma, Complete asymptotic expansions of solutions of the system of elastostatics in the presence of an inclusion of small diameter and detection of an inclusion, J. Elasticity, 67 (2002), 97129. MR 1985444 (2004c:74005)
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Additional Information
Habib Ammari
Affiliation:
Laboratoire Ondes et Acoustique, CNRS & ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France
Email:
habib.ammari@polytechnique.fr
Pierre Garapon
Affiliation:
Laboratoire Ondes et Acoustique, CNRS & ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France
Email:
Pierre.Garapon@espci.fr
Hyeonbae Kang
Affiliation:
School of Mathematical Sciences, Seoul National University, Seoul 151747, Korea
Email:
hbkang@snu.ac.kr
Hyundae Lee
Affiliation:
School of Mathematical Sciences, Seoul National University, Seoul 151747, Korea
Email:
hdlee@math.snu.ac.kr
DOI:
http://dx.doi.org/10.1090/S0033569X07010898
PII:
S 0033569X(07)010898
Keywords:
Elastic imaging,
reconstruction,
quasiincompressible elasticity,
layer potentials,
Stokes system,
small volume asymptotic expansions,
level set method
Received by editor(s):
March 26, 2007
Published electronically:
December 7, 2007
Additional Notes:
The first author was supported in part by the Brain Pool Korea Program at Seoul National University and by the project ANR06BLAN0089.
The second and fourth authors were supported in part by the BK21 Math. division at Seoul National University.
The third author was supported in part by the grant KOSEF R012006000100020.
Article copyright:
© Copyright 2007 Brown University
The copyright for this article reverts to public domain 28 years after publication.
