School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology, Tunxi Road 193, Hefei, China.
Comput Methods Programs Biomed. 2020 Aug;192:105437. doi: 10.1016/j.cmpb.2020.105437. Epub 2020 Mar 5.
Magnetic resonance (MR) elastography is a non-destructive method of measuring biological tissue and is conducive to the early detection of tumors. Researchers usually set different assumptions according to different research objects, then establish and solve wave equations to estimate the shear modulus. Establishing a more reasonable model for a measured object estimates a more accurate shear modulus. Different assumptions of the mathematical model, and the method used to solve the wave equation causes deviation of the estimation.
This study focused on shear modulus deviations caused by differences in calculation methods. The author demonstrated a method to ensure that the measuring range of the selected reconstruction algorithm with selected drive frequency covers the elasticity range of the target tissue. It is hoped to arouse the interest of researchers to introduce new transform domain methods to the field of MR elastography.
In linear, isotropic and local homogeneity assumptions, the typical representative of two different calculation methods are algebraic inversion of the differential equation (AIDE) algorithm and local frequency elastography (LFE) algorithm. To compare the accuracy of these calculation methods, the author adopted a digital phantom that can set the parameter values accurately. It is assumed that the phantom tissue was linear and isotropic, and that the driving wave was sinusoidal. The displacement distribution of waves in the tissue was calculated by the finite element simulation method in two different resolutions with the signal-to-noise ratio (SNR) set to 40 dB and the threshold of relative mean error (RME) no more than 10%. The wavelength-to-pixel-size ratios of the two methods under the setting threshold of RME were compared.
The lower threshold of wavelength-to-pixel-size ratio for AIDE was close to 10, while that for LFE was nearly 2 (the limitation of Shannon's law) under the setting precision. Thus, the measuring range of the AIDE method was less than that of LFE at the same experimental conditions.
The driving frequency selection range of the spatial frequency domain method is wider than that of the spatial domain method. It is worthwhile for researchers to devote more time to introducing new transformation domain method for MR elastography.
磁共振弹性成像是一种非破坏性的测量生物组织的方法，有利于肿瘤的早期检测。研究人员通常根据不同的研究对象设置不同的假设，然后建立和求解波动方程来估计剪切弹性模量。为被测对象建立更合理的模型可以估计出更准确的剪切弹性模量。不同的数学模型假设和求解波动方程的方法都会导致估计的偏差。
本研究重点关注计算方法差异引起的剪切弹性模量偏差。作者展示了一种方法，以确保所选重建算法的测量范围与所选驱动频率的覆盖范围相匹配，该算法的弹性范围是目标组织的弹性范围。希望引起研究人员的兴趣，将新的变换域方法引入磁共振弹性成像领域。
在线性、各向同性和局部均匀性假设下，采用两种不同计算方法的典型代表：微分方程代数反演（AIDE）算法和局部频率弹性成像（LFE）算法。为了比较这些计算方法的准确性，作者采用了一种可以准确设置参数值的数字体模。假设组织为线性各向同性，驱动波为正弦波。采用有限元模拟方法，在两种不同的分辨率下计算组织中波的位移分布，设置信噪比（SNR）为 40dB，相对均方误差（RME）阈值不超过 10%。比较两种方法在 RME 阈值设置下的波长与像素尺寸比。
在设定的精度下，AIDE 的波长与像素尺寸比的下限接近 10，而 LFE 的下限接近 2（Shannon 定律的限制）。因此，在相同的实验条件下，AIDE 方法的测量范围小于 LFE 方法。
空间频率域方法的驱动频率选择范围比空间域方法更宽。值得研究人员投入更多时间将新的变换域方法引入磁共振弹性成像。
