We introduce two model-based iterative methods to obtain shear modulus images of tissue using magnetic resonance elastography. The first method jointly finds the displacement field that best fits tissue displacement data and the corresponding shear modulus. The displacement satisfies a viscoelastic wave equation constraint, discretized using the finite element method. Sparsifying regularization terms in both shear modulus and displacement are used in the cost function minimized for the best fit. The second method extends the first method for multifrequency tissue displacement data. The formulated problems are bi-convex. Their solution can be obtained iteratively by using the alternating direction method of multipliers. Sparsifying regularizations and the wave equation constraint filter out sensor noise and compressional waves. Our methods do not require bandpass filtering as a preprocessing step and converge fast irrespective of the initialization. We evaluate our new methods in multiple in silico and phantom experiments, with comparisons with existing methods, and we show improvements in contrast to noise and signal-to-noise ratios. Results from an in vivo liver imaging study show elastograms with mean elasticity comparable to other values reported in the literature.

中文翻译：

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使用 ADMM 进行基于模型的定量弹性重建

我们介绍了两种基于模型的迭代方法，以使用磁共振弹性成像获取组织的剪切模量图像。第一种方法联合找到最适合组织位移数据的位移场和相应的剪切模量。位移满足粘弹性波动方程约束，使用有限元方法离散化。剪切模量和位移中的稀疏化正则化项用于为最佳拟合而最小化的成本函数。第二种方法扩展了用于多频组织位移数据的第一种方法。制定的问题是双凸的。它们的解可以用乘子的交替方向法迭代求得。稀疏正则化和波动方程约束滤除传感器噪声和压缩波。我们的方法不需要带通滤波作为预处理步骤，并且无论初始化如何都可以快速收敛。我们在多个计算机和模型实验中评估了我们的新方法，并与现有方法进行了比较，并且我们展示了与噪声和信噪比相比的改进。体内肝脏成像研究的结果显示弹性图的平均弹性与文献中报道的其他值相当。