Graduate School of Science and Engineering, Chiba University, 1-33 Yayoicho, Inage, Chiba, Chiba, 263-8522, Japan.
Graduate School of Informatics, Kyoto University, Kyoto, Japan.
Int J Comput Assist Radiol Surg. 2021 Nov;16(11):1947-1956. doi: 10.1007/s11548-021-02517-8. Epub 2021 Oct 25.
The viscoelasticity (storage modulus and loss modulus) of living tissues is known to be related to diseases. Magnetic resonance elastography (MRE) is a quantitative method for non-invasive measuring viscoelasticity. The viscoelasticity is calculated from the elastic wave images using an inversion algorithm. The estimation accuracy of the inversion algorithm is degraded by background noise. This study aims to propose novel inversion algorithms that are applicable for noisy elastic wave images.
The proposed algorithms are based on the Voigt-type viscoelastic equation. The algorithms are designed to improve the noise robustness by avoiding direct differentiation of measurement data by virtue of Green's formula. Similarly, stabilization is introduced to the curl-operator which works to eliminate the compression waves in measurement data. To clarify the characteristics of the algorithms, the proposed algorithms were compared with the conventional algorithms using isotropic and anisotropic voxel numerical simulations and phantom experimental data.
From the results of the numerical simulations, normalized errors of stiffness of proposed algorithms were 3% or less. The proposed algorithms mostly showed better results than the conventional algorithms despite noisy elastic wave images. From the gel phantom experiment, we confirmed the same tendency as the characteristics of the algorithms observed in the numerical simulation results.
We have developed a novel inversion algorithm and evaluated it quantitatively. The results confirm that the proposed algorithms are highly quantitative and noise-robust methods for estimating storage and loss modulus regardless of noise, voxel anisotropy, and propagation direction. Therefore, the proposed algorithms will appropriate to various three-dimensional MRE systems.
已知活体组织的粘弹性（储能模量和损耗模量）与疾病有关。磁共振弹性成像（MRE）是一种用于无创测量粘弹性的定量方法。粘弹性通过反演算法从弹性波图像中计算得出。反演算法的估计精度会因背景噪声而降低。本研究旨在提出适用于弹性波图像噪声的新型反演算法。
所提出的算法基于 Voigt 型粘弹性方程。这些算法旨在通过格林公式避免直接对测量数据进行微分，从而提高噪声鲁棒性。同样，在用于消除测量数据中压缩波的 curl 算子中引入了稳定性。为了阐明算法的特性，使用各向同性和各向异性体素数值模拟和体模实验数据对所提出的算法与传统算法进行了比较。
从数值模拟的结果来看，所提出算法的刚度归一化误差为 3%或更小。尽管存在弹性波图像噪声，但所提出的算法大多比传统算法表现出更好的结果。从凝胶体模实验中，我们证实了与在数值模拟结果中观察到的算法特性相同的趋势。
我们开发了一种新型的反演算法，并对其进行了定量评估。结果证实，所提出的算法是一种高度定量且抗噪的方法，可用于估计存储模量和损耗模量，而与噪声、体素各向异性和传播方向无关。因此，所提出的算法将适用于各种三维 MRE 系统。
