In-vivo measurement of the mechanical properties of soft tissues is essential to provide necessary data in biomechanics and medicine (early cancer diagnosis, study of traumatic brain injuries, etc.). Imaging techniques such as Magnetic Resonance Elastography (MRE) can provide 3D displacement maps in the bulk and in vivo, from which, using inverse methods, it is then possible to identify some mechanical parameters of the tissues (stiffness, damping etc.). The main difficulties in these inverse identification procedures consist in dealing with the pressure waves contained in the data and with the experimental noise perturbing the spatial derivatives required during the processing. The Optimized Virtual Fields Method (OVFM) [1], designed to be robust to noise, present natural and rigorous solution to deal with these problems. The OVFM has been adapted to identify material parameter maps from Magnetic Resonance Elastography (MRE) data consisting of 3-dimensional displacement fields in harmonically loaded soft materials. In this work, the method has been developed to identify elastic and viscoelastic models. The OVFM sensitivity to spatial resolution and to noise has been studied by analyzing 3D analytically simulated displacement data. This study evaluates and describes the OVFM identification performances: different biases on the identified parameters are induced by the spatial resolution and experimental noise. The well-known identification problems in the case of quasi-incompressible materials also find a natural solution in the OVFM. Moreover, an a posteriori criterion to estimate the local identification quality is proposed. The identification results obtained on actual experiments are briefly presented.

中文翻译：

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优化虚拟场方法的扩展以从 3D 动态位移场估计粘弹性材料参数

软组织机械特性的体内测量对于提供生物力学和医学（早期癌症诊断、创伤性脑损伤研究等）必要数据至关重要。诸如磁共振弹性成像 (MRE) 之类的成像技术可以提供体积和体内的 3D 位移图，从中可以使用逆方法识别组织的一些机械参数（刚度、阻尼等）。这些逆识别程序的主要困难在于处理数据中包含的压力波以及干扰处理过程中所需空间导数的实验噪声。优化虚拟场方法 (OVFM) [1] 旨在对噪声具有鲁棒性，提出了自然而严谨的解决方案来处理这些问题。OVFM 已适应从磁共振弹性成像 (MRE) 数据中识别材料参数图，该数据由谐波加载的软材料中的 3 维位移场组成。在这项工作中，该方法已被开发用于识别弹性和粘弹性模型。通过分析 3D 解析模拟位移数据，研究了 OVFM 对空间分辨率和噪声的敏感性。本研究评估和描述了 OVFM 识别性能：识别参数的不同偏差是由空间分辨率和实验噪声引起的。在准不可压缩材料的情况下众所周知的识别问题也在 OVFM 中找到了一个自然的解决方案。此外，提出了一种后验标准来估计局部识别质量。