IEEE Trans Med Imaging. 2013 Dec;32(12):2189-99. doi: 10.1109/TMI.2013.2276060. Epub 2013 Aug 2.
In elasticity imaging, the shear modulus is obtained from measured tissue displacement data by solving an inverse problem based on the wave equation describing the tissue motion. In most inversion approaches, the wave equation is simplified using local homogeneity and incompressibility assumptions. This causes a loss of accuracy and therefore imaging artifacts in the resulting elasticity images. In this paper we present a new curl-based finite element method inversion technique that does not rely upon these simplifying assumptions. As done in previous research, we use the curl operator to eliminate the dilatational term in the wave equation, but we do not make the assumption of local homogeneity. We evaluate our approach using simulation data from a virtual tissue phantom assuming time harmonic motion and linear, isotropic, elastic behavior of the tissue. We show that our reconstruction results are superior to those obtained using previous curl-based methods with homogeneity assumption. We also show that with our approach, in the 2-D case, multi-frequency measurements provide better results than single-frequency measurements. Experimental results from magnetic resonance elastography of a CIRS elastography phantom confirm our simulation results and further demonstrate, in a quantitative and repeatable manner, that our method is accurate and robust.
在弹性成像中，通过求解基于描述组织运动的波动方程的反问题，从测量的组织位移数据中获得剪切模量。在大多数反演方法中，波动方程使用局部均匀性和不可压缩性假设进行简化。这会导致准确性的损失，从而导致弹性图像中的成像伪影。在本文中，我们提出了一种新的基于 curl 的有限元反演技术，该技术不依赖于这些简化假设。与以前的研究一样，我们使用 curl 算子消除波动方程中的扩张项，但我们不假设局部均匀性。我们使用假设组织呈时间谐变运动且具有线性各向同性弹性行为的虚拟组织体模的仿真数据来评估我们的方法。我们表明，与具有均匀性假设的以前基于 curl 的方法相比，我们的重建结果更优。我们还表明，在二维情况下，多频测量比单频测量提供更好的结果。CIRS 弹性体模的磁共振弹性成像实验结果证实了我们的仿真结果，并以定量和可重复的方式进一步证明了我们的方法是准确和稳健的。
