Transformation Elastography

弹性成像是指使用非侵入性光学、声学或磁共振成像方法，基于测量材料中的波动来映射材料中的机械特性。例如，增加刚度将增加波长。刚度和粘度可以取决于位置和方向。具有对齐的纤维或层的材料可沿沿着纤维或层相对于横跨它们具有不同的刚度和粘度值。将波测量转换成机械特性图或图像被称为重建。在各向同性材料中重建，无论方向如何都具有相同的机械性能，比在各向异性材料中更容易，其性能随方向而变化。变换弹性成像基于将材料变形作为重建算法的一部分的想法，以使各向异性问题变为各向同性。这种策略，这已被证明是简单的二维重建问题的工作，将被扩展到更复杂的三维问题。弹性成像是一种潜在的变革性测量技术，用于材料力学的基础研究。将其扩展到各向异性材料对于推进其在地球物理勘探，纤维复合材料分析以及大脑，骨骼肌，心脏和其他器官疾病的医学诊断中的应用至关重要，这些器官具有对齐的纤维，其刚度和粘度的变化已被证明与疾病相关。这项研究支持NSF的使命，以促进科学的进步和提高国民健康。研究进展将被整合到课程和多媒体教育材料中，为不同层次的学生提供从K-12到研究生水平的工程。弹性成像依赖于粘弹性材料中机械波动的本构模型来解释非侵入性测量。为了使建模问题易于分析，通常假设各向同性和均匀性，并忽略有限边界的影响。但是，无限各向同性的均匀性是不是在大多数情况下感兴趣的情况下，当有病理条件，材料故障或隐藏的异常，不均匀分布在纤维或层状结构的有限尺寸。引入各向异性、不均匀性和有限边界使分析复杂化，迫使放弃分析驱动的策略，而采用计算昂贵且产生较少物理见解的数值近似。一种新的策略，变换弹性成像，计划涉及空间失真，以使各向异性的问题成为各向同性。这一新策略的开发和实验验证需要反转算法，并将初始开发从二维扩展到三维非均匀性问题。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Elastography refers to mapping mechanical properties in a material based on measuring wave motion in it using noninvasive optical, acoustic or magnetic resonance imaging methods. For example, increased stiffness will increase wavelength. Stiffness and viscosity can depend on both location and direction. A material with aligned fibers or layers may have different stiffness and viscosity values along the fibers or layers versus across them. Converting wave measurements into a mechanical property map or image is known as reconstruction. Reconstruction in isotropic materials, with the same mechanical properties regardless of direction, is easier than in anisotropic materials, whose properties vary with direction. Transformation Elastography is based on the idea of distorting the material as part of the reconstruction algorithm to make the anisotropic problem become isotropic. This strategy, which has been shown to work in simple two-dimensional reconstruction problems, will be extended to more complex three-dimensional problems. Elastography is a potentially transformative measurement technology for basic research into material mechanics. Extending it to anisotropic materials is essential to advance its application in geophysical exploration, fiber composite analysis, and medical diagnosis of diseases of the brain, skeletal muscle, heart and other organs with aligned fibers for which changes in stiffness and viscosity have been proven to correlate with disease. This research supports NSF's mission to promote the progress of science and advance national health. Research developments will be integrated into courses and multimedia educational materials for a diverse group of students at multiple levels, from K-12 through graduate level engineering.Elastography relies on a constitutive model of mechanical wave motion in the viscoelastic material to interpret the noninvasive measurements. To make the modeling problem analytically tractable, isotropy and homogeneity are often assumed, and the effects of finite boundaries are ignored. But, infinite isotropic homogeneity is not the situation in most cases of interest, when there are pathological conditions, material faults or hidden anomalies that are not uniformly distributed in fibrous or layered structures of finite dimension. Introduction of anisotropy, inhomogeneity and finite boundaries complicates the analysis forcing the abandonment of analytically-driven strategies, in favor of numerical approximations that are computationally expensive and yield less physical insight. A new strategy, Transformation Elastography, is planned that involves spatial distortion in order to make an anisotropic problem become isotropic. Development and experimental validation of this new strategy requires inverting the algorithm and extending initial developments from two- to three-dimensional problems with inhomogeneity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.