Requirements for accurate estimation of shear modulus by magnetic resonance elastography: A computational comparative study. (August 2020) - Hu, Liangliang
Highlights: This paper showed the difference between spatial domain method (algebraic inversion of the differential equation algorithm) and spatial frequency domain method (local frequency elastography algorithm). And we expounded the necessity of putting forward a robust complex local frequency estimation method for MRE. This paper demonstrated the method to ensure the measuring range of the selected reconstruction algorithm with selected parameters to cover the elasticity range of the target tissue. A previously published performance comparison of different algorithms declared that the finite element method was superior to the local frequency estimation method. However, this author found that not all cases are consistent with the previous research and they differ under certain conditions. Performance of the two classical algorithms was compared by selecting a range of parameters allowed by each algorithm from the perspective of calculation methods. It is concluded that the accuracy of finite element method is worse than that of local frequency estimation method in most cases. The measurement range of finite element method (spatial domain method) is much narrower than that of the local frequency estimation method (spatial frequency domain method). Thus, in the application of magnetic resonance elastography, researchers should pay special attention to the reasonable selection of parameters. In some in vivo studies of magnetic resonance elastography, the parameter setting leads to large errors in the results. However, in vivo measurements are difficult to verify by other means, so the results obtained by magnetic resonance elastography are deemed trustworthy. However, this assumption could lead to biased conclusions. To help the clinician choose the parameters reasonably, the author demonstrates a selection method of parameters required by 2 classical methods of magnetic resonance elastography experiment under the given precision criterion. Magnetic resonance elastography involves several parameters, such as size of field of view, sampling matrix size, and driving frequency, but true determining parameter of elasticity accuracy is the coordination of these parameters, which is simplified to the wavelength-to-pixel-size ratio. The experimental data list a specific selection range under the given precision limitation, and this range of parameters can be transferred to parameter setting in other magnetic resonance elastography experiments. This study summarized the widely used magnetic resonance elastography algorithm and the mainstream research ideas of developers. The local frequency estimation method is the first one applied to the magnetic resonance elastography. With further research, developers continued to weaken the assumptions of the mathematical model and gradually changed to the finite element method. This comparative study highlighted the advantages of the local frequency estimation method. Furthermore, the author described the shortcomings of the existing local frequency estimation method, which could only provide real value, but not the complex value. If the local frequency estimation method is directly extended to complex frequency estimation, the robustness of the algorithm will lead to abnormal results in some regions. The author suggested that the researchers should devote more time to introducing new spatial frequency domain methods for magnetic resonance elastography. Abstract: Background: 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. Objective: 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. Method: 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. Results: 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. Conclusion: 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.