RECONSTRUCTION OF A FULLY ANISOTROPIC ELASTICITY TENSOR FROM KNOWLEDGE OF DISPLACEMENT FIELDS

被引：14

作者：

Bal, Guillaume ^{[1
]}

Monard, Francois ^{[2
]}

Uhlmann, Gunther ^{[2
,3
,4
]}

机构：

[1] Columbia Univ, Dept Appl Phys & Appl Math, New York, NY 10027 USA

[2] Univ Washington, Dept Math, Seattle, WA 98195 USA

[3] Univ Helsinki, Dept Math & Stat, FI-00014 Helsinki, Finland

[4] Hong Kong Univ Sci & Technol, IAS, Hong Kong, Hong Kong, Peoples R China

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2015年 / 75卷 / 05期

基金：

美国国家科学基金会;

关键词：

inverse problems; anisotropic elasticity tensors; elastography; Runge approximation; hybrid methods; MAGNETIC-RESONANCE ELASTOGRAPHY; LAME PARAMETERS; STABILITY; TISSUE; UNIQUENESS; EQUATIONS; MODELS;

D O I：

10.1137/151005269

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present explicit reconstruction algorithms for fully anisotropic unknown elasticity tensors from knowledge of a finite number of internal displacement fields, with applications to transient elastography. Under certain rank-maximality assumptions satisfied by the strain fields, explicit algebraic reconstruction formulas are provided. A discussion ensues on how to fulfill these assumptions, describing the range of validity of the approach. We also show how the general method can be applied to more specific cases such as the transversely isotropic one.

引用

页码：2214 / 2231

页数：18

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