Quantitative elasticity imaging: what can and cannot be inferred from strain images
Quantitative elasticity imaging: what can and cannot be inferred from strain images
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DOI：
10.1088/0031-9155/47/12/310
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发表时间：
2002-06-21
影响因子：
3.5
通讯作者：
Bamber, JC
中科院分区：
文献类型：
--
作者：
Barbone, PE;Bamber, JC
我们研究与定量弹性模量成像相关的反演问题：给定二维不可压缩弹性材料中的平衡应变场，确定弹性刚度（剪切模量）。我们通过分析表明，除非先验地知道边界的足够部分的刚度信息，否则反问题的直接公式没有唯一的解。这意味着基于恒定边界刚度假设构建的相对刚度图像是错误的，除非刚度在边界上确实是恒定的。我们进一步表明，在正向不可压缩弹性问题中使用位移边界条件会导致非唯一的逆问题。事实上，我们给出的例子表明，在位移边界条件下，不同的弹性模量分布会产生完全相同的应变场。我们还表明，在某些配置中，了解边界上的应力可以导致弹性刚度的适定反问题。这些结果表明，如果要从应变图像可靠且定量地重建弹性模量，则必须获取哪些数据。
We examine the inverse problem associated with quantitative elastic modulus imaging: given the equilibrium strain field in a 2D incompressible elastic material, determine the elastic stiffness (shear modulus). We show analytically that a direct formulation of the inverse problem has no unique solution unless stiffness information is known a priori on a sufficient portion of the boundary. This implies that relative stiffness images constructed on the assumption of constant boundary stiffness are in error, unless the stiffness is truly constant on the boundary. We show further that using displacement boundary conditions in the forward incompressible elasticity problem leads to a nonunique inverse problem. Indeed, we give examples in which exactly the same strain field results from different elastic modulus distributions under displacement boundary conditions. We also show that knowing the stress on the boundary can, in certain configurations, lead to a well-posed inverse problem for the elastic stiffness. These results indicate what data must be taken if the elastic modulus is to be reconstructed reliably and quantitatively from a strain image.