Abstract：
:We consider several inverse problems motivated by elastography. Given the (possibly transient) displacement field measured everywhere in an isotropic, compressible, linear elastic solid, and given density rho, determine the Lamé parameters lambda and mu. We consider several special cases of this problem: (a) for mu known a priori, lambda is determined by a single deformation field up to a constant. (b) Conversely, for lambda known a priori, mu is determined by a single deformation field up to a constant. This includes as a special case that for which the term [see text]. (c) Finally, if neither lambda nor mu is known a priori, but Poisson's ratio nu is known, then mu and lambda are determined by a single deformation field up to a constant. This includes as a special case plane stress deformations of an incompressible material. Exact analytical solutions valid for 2D, 3D and transient deformations are given for all cases in terms of quadratures. These are used to show that the inverse problem for mu based on the compressible elasticity equations is unstable in the limit lambda --> infinity. Finally, we use the exact solutions as a basis to compute non-trivial modulus distributions in a simulated example.
journal_name
Phys Med Bioljournal_title
Physics in medicine and biologyauthors
Barbone PE,Oberai AAdoi
10.1088/0031-9155/52/6/003subject
Has Abstractpub_date
2007-03-21 00:00:00pages
1577-93issue
6eissn
0031-9155issn
1361-6560pii
S0031-9155(07)31691-6journal_volume
52pub_type
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