McGarry Matthew D J, Van Houten Elijah E W
Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8020, New Zealand.
Med Biol Eng Comput. 2008 Aug;46(8):759-66. doi: 10.1007/s11517-008-0356-5. Epub 2008 Jun 3.
A Rayleigh damping model applied to magnetic resonance elastography incorporates attenuation behavior proportionally related to both elastic and inertial forces, and allows two damping parameters to be extracted from an MRI motion dataset. Under time-harmonic conditions, the model can be implemented by the use of complex shear modulus and density, whereas viscoelastic damping models commonly used in elastography consist of only a complex shear modulus, and model only a single damping effect. Simulation studies reveal that the differences between damped elastic behavior resulting from a purely complex shear modulus (CSM damping) and from a purely complex density (CD damping) become larger as the overall level of damping present (indicated by the damping ratio) increases. A plot of results generated from the finite element (FE) model indicate the relative motion differences estimated for a range of damping ratios and CSM/CD damping combinations increase with damping ratio, and can be up to 15% at a damping ratio of 50% and therefore using the correct model for a Rayleigh damped material becomes increasingly important as damping levels increase. Resonance-related effects cause values from this plot to vary by as much as 3% as parameters such as wave speed, frequency, and problem size are altered. These motion differences can be compared to expected noise levels to estimate the parameter resolution achievable by a reconstruction algorithm. An optimization-based global property reconstruction algorithm was developed, and used for testing Rayleigh damping parameter reconstructions with gaussian noise added to the simulated motion input data. The coherent motion errors resulting from altering the combination of the two damping parameters are large enough to allow accurate determination of both of the Rayleigh damping parameters with incoherent noise levels comparable to MR measurements. The accuracy achieved by the global reconstructions was significantly better than would be predicted by examining the motion differences for differing CSM/CD damping combinations, which is likely to be due to the low ratio between number of reconstructed parameters and number of noisy measurements.
应用于磁共振弹性成像的瑞利阻尼模型纳入了与弹性力和惯性力成比例相关的衰减行为，并允许从MRI运动数据集中提取两个阻尼参数。在时谐条件下，该模型可通过使用复剪切模量和密度来实现，而弹性成像中常用的粘弹性阻尼模型仅由复剪切模量组成，且仅模拟单一的阻尼效应。模拟研究表明，随着存在的阻尼总体水平（由阻尼比表示）增加，由纯复剪切模量（CSM阻尼）和纯复密度（CD阻尼）导致的阻尼弹性行为之间的差异会变得更大。有限元（FE）模型生成的结果图表明，对于一系列阻尼比和CSM/CD阻尼组合估计的相对运动差异随阻尼比增加，在阻尼比为50%时可达15%，因此随着阻尼水平增加，为瑞利阻尼材料使用正确的模型变得越来越重要。与共振相关的效应会导致该图中的值随着诸如波速、频率和问题规模等参数的改变而变化高达3%。这些运动差异可与预期噪声水平进行比较，以估计重建算法可实现的参数分辨率。开发了一种基于优化的全局特性重建算法，并用于测试在模拟运动输入数据中添加高斯噪声的瑞利阻尼参数重建。改变两个阻尼参数的组合所产生的相干运动误差足够大，能够在与MR测量相当的非相干噪声水平下准确确定两个瑞利阻尼参数。通过全局重建实现的精度明显优于通过检查不同CSM/CD阻尼组合的运动差异所预测的精度，这可能是由于重建参数数量与噪声测量数量之间的比例较低。
