Computer Vision Laboratory, Swiss Federal Institute of Technology (ETH), 8092 Zürich, Switzerland.
IEEE Trans Med Imaging. 2013 Feb;32(2):408-18. doi: 10.1109/TMI.2012.2228664. Epub 2012 Nov 21.
The finite element method is commonly used to model tissue deformation in order to solve for unknown parameters in the inverse problem of viscoelasticity. Typically, a (regular-grid) structured mesh is used since the internal geometry of the domain to be identified is not known a priori. In this work, the generation of problem-specific meshes is studied and such meshes are shown to significantly improve inverse-problem elastic parameter reconstruction. Improved meshes are generated from axial strain images, which provide an approximation to the underlying structure, using an optimization-based mesh adaptation approach. Such strain-based adapted meshes fit the underlying geometry even at coarse mesh resolutions, therefore improving the effective resolution of the reconstruction at a given mesh size/complexity. Elasticity reconstructions are then performed iteratively using the reflective trust-region method for optimizing the fit between estimated and observed displacements. This approach is studied for Young's modulus reconstruction at various mesh resolutions through simulations, yielding 40%-72% decrease in root-mean-square reconstruction error and 4-52 times improvement in contrast-to-noise ratio in simulations of a numerical phantom with a circular inclusion. A noise study indicates that conventional structured meshes with no noise perform considerably worse than the proposed adapted meshes with noise levels up to 20% of the compression amplitude. A phantom study and preliminary in vivo results from a breast tumor case confirm the benefit of the proposed technique. Not only conventional axial strain images but also other elasticity approximations can be used to adapt meshes. This is demonstrated on images generated by combining axial strain and axial-shear strain, which enhances lateral image contrast in particular settings, consequently further improving mesh-adapted reconstructions.
有限元法常用于模拟组织变形，以便求解粘弹性反问题中的未知参数。通常使用（规则网格）结构化网格，因为要识别的域的内部几何形状事先未知。在这项工作中，研究了特定于问题的网格的生成，并且表明这种网格可以显著改善反问题弹性参数重建。从轴应变图像生成改进的网格，这些图像使用基于优化的网格自适应方法提供对基础结构的近似值。这种基于应变的自适应网格即使在粗网格分辨率下也能适应基础几何形状，从而在给定的网格大小/复杂性下提高重建的有效分辨率。然后使用反射信任区域方法进行弹性重建，以优化估计位移和观测位移之间的拟合。通过模拟研究了各种网格分辨率下的杨氏模量重建，在模拟具有圆形包含物的数值幽灵的情况下，重建误差的均方根减少了 40%-72%，对比噪声比提高了 4-52 倍。噪声研究表明，具有噪声的常规结构化网格的性能明显不如具有噪声水平高达压缩幅度 20%的建议自适应网格。一项幻影研究和来自乳腺癌病例的初步体内结果证实了该技术的优势。不仅可以使用常规的轴向应变图像，还可以使用其他弹性近似值来自适应网格。这在结合轴向应变和轴向剪切应变生成的图像上得到了证明，这特别增强了横向图像对比度，从而进一步改善了网格自适应重建。
