Univ Lyon, INSA Lyon, CNRS, LaMCoS, UMR5259, 69621 Villeurbanne, France.
Université de Lyon, INSA Lyon, Université Claude Bernard Lyon 1, Ecole Centrale de Lyon, CNRS, Ampère UMR5005, Villeurbanne, France.
J Acoust Soc Am. 2022 May;151(5):3481. doi: 10.1121/10.0011392.
Magnetic resonance elastography (MRE) is an elasticity imaging technique for quantitatively assessing the stiffness of human tissues. In MRE, finite element method (FEM) is widely used for modeling wave propagation and stiffness reconstruction. However, in front of inclusions with complex interfaces, FEM can become burdensome in terms of the model partition and computationally expensive. In this work, we implement a formulation of FEM, known as the eXtended finite element method (XFEM), which is a method used for modeling discontinuity like crack and heterogeneity. Using a level-set method, it makes the interface independent of the mesh, thus relieving the meshing efforts. We investigate this method in two studies: wave propagation across an oblique linear interface and stiffness reconstruction of a random-shape inclusion. In the first study, numerical results by XFEM and FEM models revealing the wave conversion rules at linear interface are presented and successfully compared to the theoretical predictions. The second study, investigated in a pseudo-practical application, demonstrates further the applicability of XFEM in MRE and the convenience, accuracy, and speed of XFEM with respect to FEM. XFEM can be regarded as a promising alternative to FEM for inclusion modeling in MRE.
磁共振弹性成像（MRE）是一种用于定量评估人体组织硬度的弹性成像技术。在 MRE 中，有限元方法（FEM）广泛用于建模波传播和刚度重建。然而，在面对具有复杂界面的夹杂时，FEM 在模型分区和计算成本方面变得很繁琐。在这项工作中，我们实现了一种称为扩展有限元法（XFEM）的 FEM 公式，该方法用于模拟裂纹和非均匀性等不连续性。使用水平集方法，它使界面与网格无关，从而减轻了网格划分的工作。我们在两项研究中研究了这种方法：波在倾斜线性界面上的传播和随机形状夹杂的刚度重建。在第一项研究中，通过 XFEM 和 FEM 模型的数值结果揭示了线性界面处的波转换规则，并成功与理论预测进行了比较。第二项研究在伪实际应用中进行了进一步研究，进一步证明了 XFEM 在 MRE 中应用的适用性，以及 XFEM 在 FEM 中具有方便、准确和快速的优点。XFEM 可以被视为 MRE 中夹杂建模的一种有前途的替代 FEM 方法。
