IEEE Trans Med Imaging. 2017 Aug;36(8):1686-1698. doi: 10.1109/TMI.2017.2686388. Epub 2017 Mar 22.
In quantitative elastography, maps of the mechanical properties of soft tissue, or elastograms, are calculated from the measured displacement data by solving an inverse problem. The model assumptions have a significant effect on elastograms. Motivated by the high sensitivity of imaging results to the model assumptions for in vivo magnetic resonance elastography of the prostate, we compared elastograms obtained with four different methods. Two finite-element method (FEM)-based methods developed by our group were compared with two other commonly used methods, local frequency estimator (LFE) and curl-based direct inversion (c-DI). All the methods assume a linear isotropic elastic model, but the methods vary in their assumptions, such as local homogeneity or incompressibility, and in the specific approach used. We report results using simulations, phantom, and ex vivo and in vivo data. The simulation and phantom studies show, for regions with an inclusion, that the contrast to noise ratio (CNR) for the FEM methods is about three to five times higher than the CNR for the LFE and c-DI and the rms error is about half. The LFE method produces very smooth results (i.e., low CNR) and is fast. c-DI is faster than the FEM methods but it is only accurate in areas where elasticity variations are small. The artifacts resulting from the homogeneity assumption in c-DI is detrimental in regions with large variations. The ex vivo and in vivo results also show similar trends as the simulation and phantom studies. The c-FEM method is more sensitive to noise compared with the mixed-FEM due to higher orders derivatives. This is especially evident at lower frequencies, where the wave curvature is smaller and it is more prone to such error, causing a discrepancy in the absolute values between the mixed-FEM and c-FEM in our in vivo results. In general, the proposed FEMs use fewer simplifying assumptions and outperform the other methods but they are computationally more expensive.
在定量弹性成像中，通过求解反问题，从测量的位移数据中计算软组织的力学性质图，即弹性图。模型假设对弹性图有重大影响。受体内磁共振弹性成像前列腺模型假设对成像结果高度敏感的启发，我们比较了四种不同方法得到的弹性图。我们小组开发的两种有限元方法（FEM）与两种其他常用方法，即局部频率估计器（LFE）和基于 curl 的直接反演（c-DI）进行了比较。所有方法都假设线性各向同性弹性模型，但方法在局部均匀性或不可压缩性等假设以及具体使用的方法上有所不同。我们报告了使用模拟、体模、离体和体内数据的结果。模拟和体模研究表明，对于包含区域，FEM 方法的对比度噪声比（CNR）比 LFE 和 c-DI 的 CNR 高约 3 到 5 倍，均方根误差约为一半。LFE 方法产生非常平滑的结果（即低 CNR）且速度很快。c-DI 比 FEM 方法快，但仅在弹性变化较小的区域准确。c-DI 中均匀性假设产生的伪影在弹性变化较大的区域是有害的。离体和体内结果也显示出与模拟和体模研究相似的趋势。与混合 FEM 相比，c-FEM 对噪声更敏感，因为它包含更高阶导数。这在较低频率下尤其明显，此时波曲率较小，更容易出现此类误差，导致我们的体内结果中混合 FEM 和 c-FEM 之间的绝对值存在差异。一般来说，所提出的 FEM 使用的简化假设较少，性能优于其他方法，但计算成本更高。
