Potential of in vivo MRI-based nonlinear finite-element analysis for the assessment of trabecular bone post-yield properties.
Potential of in vivo MRI-based nonlinear finite-element analysis for the assessment of trabecular bone post-yield properties.
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DOI：
10.1118/1.4802085
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发表时间：
2013-05
期刊：
影响因子：
3.8
通讯作者：
Ning Zhang;J. Magland;C. Rajapakse;Y. Bhagat;F. Wehrli
中科院分区：
文献类型：
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作者：
Ning Zhang;J. Magland;C. Rajapakse;Y. Bhagat;F. Wehrli
目的骨强度是影响骨折风险的关键因素。从高分辨率（HR）图像中评估骨强度在很大程度上依赖于线性微有限元分析（μFEA），尽管破坏总是发生在屈服点之外，这是在线性范围之外。因此，非线性μFEA可以在预测失效行为方面提供更多信息。然而，现有的用于小梁骨（TB）的非线性模型在很大程度上局限于微计算机断层扫描（μCT）和最近的HR外围定量计算机断层扫描（HR- pqct）图像，并且通常忽略了对屈服后行为的评估。这项工作的主要目的有三个：(1)提供一种改进的算法和程序来评估结核产量和产后特性；(2)探索非线性μFEA相对于线性μFEA的潜在优势；(3)评估基于患者体内微磁共振（μMR）图像在台式计算机上进行非线性分析的可行性和实用性。方法设计了一种TB屈服和屈服后行为的非线性μFE建模方法，根据线性分析得到的组织级有效应变，采用计算优化算法，通过迭代调整组织模量来捕捉材料非线性。该软件允许体内μMRI分辨率的图像作为输入，并保留灰度信息。利用胫骨远端（N = 20，年龄：58-84）和桡骨（N = 20，年龄：50-75）的体内μMR图像，研究线性分析估计的轴向刚度与屈服及非线性分析后屈服参数之间的关系。结果所有模拟均在1 h或更短时间内完成，采用台式计算机（双四核Xeon 3.16 GHz cpu，配置40gb RAM）。虽然屈服应力和极限应力与轴向刚度相关性强（R(2) = 0.95, p < 0.001），但韧性在胫骨远端相关性中等（R(2) = 0.81, p < 0.001），在桡骨远端相关性较弱（R(2) = 0.34, p = 0.007）。此外，对于轴向刚度非常相似（<2%）的骨，发现韧性变化高达16%。结论：该研究证明了在体内μMRI分辨率下非线性μFE模拟的实用性，以及它提供线性分析之外的额外信息的潜力。数据表明，对韧性的直接评估可以提供刚度所不能获得的信息。
PURPOSE Bone strength is the key factor impacting fracture risk. Assessment of bone strength from high-resolution (HR) images have largely relied on linear micro-finite element analysis (μFEA) even though failure always occurs beyond the yield point, which is outside the linear regime. Nonlinear μFEA may therefore be more informative in predicting failure behavior. However, existing nonlinear models applied to trabecular bone (TB) have largely been confined to micro-computed tomography (μCT) and, more recently, HR peripheral quantitative computed tomography (HR-pQCT) images, and typically have ignored evaluation of the post-yield behavior. The primary purpose of this work was threefold: (1) to provide an improved algorithm and program to assess TB yield as well as post-yield properties; (2) to explore the potential benefits of nonlinear μFEA beyond its linear counterpart; and (3) to assess the feasibility and practicality of performing nonlinear analysis on desktop computers on the basis of micro-magnetic resonance (μMR) images obtained in vivo in patients. METHODS A method for nonlinear μFE modeling of TB yield as well as post-yield behavior has been designed where material nonlinearity is captured by adjusting the tissue modulus iteratively according to the tissue-level effective strain obtained from linear analysis using a computationally optimized algorithm. The software allows for images at in vivo μMRI resolution as input with retention of grayscale information. Associations between axial stiffness estimated from linear analysis and yield as well as post-yield parameters from nonlinear analysis were investigated from in vivo μMR images of the distal tibia (N = 20; ages: 58-84) and radius (N = 20; ages: 50-75). RESULTS All simulations were completed in 1 h or less for 61 strain levels using a desktop computer (dual quad-core Xeon 3.16 GHz CPUs equipped with 40 GB of RAM). Although yield stress and ultimate stress correlated strongly (R(2) > 0.95, p < 0.001) with axial stiffness, toughness correlated moderately at the distal tibia (R(2) = 0.81, p < 0.001) and only weakly at the distal radius (R(2) = 0.34, p = 0.007). Further, toughness was found to vary by up to 16% for bone of very similar axial stiffness (<2%). CONCLUSIONS The work demonstrates the practicality of nonlinear μFE simulations at in vivo μMRI resolution, as well as its potential for providing additional information beyond that obtainable from linear analysis. The data suggest that a direct assessment of toughness may provide information not captured by stiffness.