Transformation Elastography

弹性成像是指基于使用非侵入性光学、声学或磁共振成像方法测量材料中的波动来绘制材料的力学属性。例如，增加刚度将增加波长。刚性和粘度可以同时取决于位置和方向。具有对齐的纤维或层的材料沿纤维或层与跨纤维或层的材料可能具有不同的硬度和粘性值。将波的测量结果转换为力学特性图或图像称为重建。在各向同性材料中的重建比在各向异性材料中更容易，因为各向同性材料的性能随方向变化。变换弹性成像是基于将材料变形作为重建算法的一部分，以使各向异性问题变为各向同性的思想。这一策略已被证明适用于简单的二维重建问题，并将扩展到更复杂的三维问题。弹性成像是材料力学基础研究的一种潜在的变革性测量技术。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，这些疾病的纤维排列已被证明其硬度和粘度的变化与疾病相关。这项研究支持了美国国家科学基金会促进科学进步和增进国民健康的使命。研究开发将被整合到课程和多媒体教材中，供不同层次的学生使用，从K-12到研究生水平的工程学。弹性学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处理，通常假定各向同性和均质性，而忽略了有限边界的影响。但是，在大多数感兴趣的情况下，当存在不均匀分布在有限维的纤维或层状结构中的病理条件、材料断层或隐藏的异常时，无限各向同性均质不是一种情况。各向异性、非均质性和有限边界的引入使分析变得复杂，迫使放弃分析驱动的策略，转而采用计算昂贵且产生的物理洞察力较少的数值近似。为了使各向异性问题变得各向同性，计划了一种新的策略，即变换弹性成像，该策略涉及到空间失真。这一新策略的开发和实验验证需要颠倒算法，并将最初的开发从具有非均质性的二维问题扩展到三维问题。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.