Finite element analysis of trabecular bone microstructure using CT imaging and continuum mechanical modeling.
Finite element analysis of trabecular bone microstructure using CT imaging and continuum mechanical modeling.
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DOI：
10.1002/mp.15629
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发表时间：
2022-06
期刊：
影响因子：
3.8
通讯作者：
Saha, Punam K.
中科院分区：
文献类型：
--
作者：
Guha, Indranil;Zhang, Xiaoliu;Rajapakse, Chamith S.;Chang, Gregory;Saha, Punam K.
关键词：
骨质疏松症是一种与骨丢失增强、微结构变性和骨折风险相关的骨疾病。有限元（FE）建模用于通过高分辨率三维（3-D）成像模式（包括微计算机断层扫描（CT）、磁共振成像（MRI）和高分辨率外周定量CT（HR-pQCT））估计骨小梁（Tb）模量。本文验证了基于体素的连续有限元分析（FEA）的应用，通过与micro-CT和实验方法得出的测量结果进行比较，在类似于体内成像的条件下，从临床CT成像中预测Tb模量。使用线性和非线性模型实施了用于CT成像的基于体素的连续体FEA方法，并在类似于体内成像的条件下应用于胫骨远端扫描。首先，将CT扫描中的胫骨轴与150 μm各向同性体素处的坐标z轴对齐。有限元分析应用于一个直立的圆柱形体积的利益（VOI），其轴线与胫骨轴线重合。按照各向同性图像网格定义体素体积、边缘和顶点元素及其连接性。使用校准体模将Hounsfield单位的CT值校准为骨矿物质密度（BMD）值，然后将其转换为钙羟基磷灰石（CHA）密度。每个体素体积元素的机械性能使用其CT衍生CHA密度上定义的灰密度来定义。对于FEA，固定圆柱形VOI的底面，并在顶面上的每个顶点单元处沿z方向沿着施加恒定位移，以模拟物理轴向压缩载荷条件。最后，应用0.3的泊松比，并且Tb模量（MPa）被计算为顶表面上的体积元的平均冯米塞斯应力（MPa）与所施加的位移的比率。优化了有限元参数，包括网格单元尺寸、子步数和不同的公差值。使用连续有限元分析的CT衍生Tb模量值显示出与微观CT衍生参考值（r ∈ [0.87 0.90]）以及实验测量值（r ∈ [0.80 0.87]）的高度线性相关性。采用线性建模的连续有限元法计算的模量与其参考值的线性相关性与非线性建模获得的模量具有可比性。与线性连续体方法相比，基于非线性连续体有限元分析的模量值（平均值为1087.2 MPa）与其参考值（使用基于微CT的有限元分析的平均值为1498.9 MPa）的差异更大。对于使用线性和非线性连续FEA计算的模量值，观察到高重复CT扫描再现性（类内相关性[ICC] = 0.98）。据观察，高应力区符合Tb的微观结构，其特征在于BMD值模糊。Tb微结构和骨髓区的vonMises应力分布有显著性差异（p < 10-8）。基于体素的连续体FEA提供了在类似于体内成像的条件下来自CT成像的Tb模量的替代测量值，该条件证实了Tb和骨髓区域分割的需要，同时考虑了微观结构水平的骨分布。这种二进制分割的放松将扩展FEA应用范围，以评估相对低分辨率成像下骨微结构的力学性能。
Osteoporosis is a bone disease associated with enhanced bone loss, microstructural degeneration, and fracture‐risk. Finite element (FE) modeling is used to estimate trabecular bone (Tb) modulus from high‐resolution three‐dimensional (3‐D) imaging modalities including micro‐computed tomography (CT), magnetic resonance imaging (MRI), and high‐resolution peripheral quantitative CT (HR‐pQCT). This paper validates an application of voxel‐based continuum finite element analysis (FEA) to predict Tb modulus from clinical CT imaging under a condition similar to in vivo imaging by comparing with measures derived by micro‐CT and experimental approaches. Voxel‐based continuum FEA methods for CT imaging were implemented using linear and nonlinear models and applied on distal tibial scans under a condition similar to in vivo imaging. First, tibial axis in a CT scan was aligned with the coordinate z‐axis at 150 μm isotropic voxels. FEA was applied on an upright cylindrical volume of interests (VOI) with its axis coinciding with the tibial bone axis. Voxel volume, edge, and vertex elements and their connectivity were defined as per the isotropic image grid. A calibration phantom was used to calibrate CT numbers in Hounsfield unit to bone mineral density (BMD) values, which was then converted into calcium hydroxyapatite (CHA) density. Mechanical properties at each voxel volume element was defined using its ash‐density defined on CT‐derived CHA density. For FEA, the bottom surface of the cylindrical VOI was fixed and a constant displacement was applied along the z‐direction at each vertex element on the top surface to simulate a physical axial compressive loading condition. Finally, a Poisson's ratio of 0.3 was applied, and Tb modulus (MPa) was computed as the ratio of average von Mises stress (MPa) of volume elements on the top surface and the applied displacement. FEA parameters including mesh element size, substep number, and different tolerance values were optimized. CT‐derived Tb modulus values using continuum FEA showed high linear correlation with the micro‐CT‐derived reference values (r ∈ [0.87 0.90]) as well as experimentally measured values (r ∈ [0.80 0.87]). Linear correlation of computed modulus with their reference values using continuum FEA with linear modeling was comparable with that obtained by nonlinear modeling. Nonlinear continuum FEA‐based modulus values (mean of 1087.2 MPa) showed greater difference from their reference values (mean of 1498.9 MPa using micro‐CT‐based FEA) as compared with linear continuum methods. High repeat CT scan reproducibility (intra‐class correlation [ICC] = 0.98) was observed for computed modulus values using both linear and nonlinear continuum FEA. It was observed that high stress regions coincide with Tb microstructure as fuzzily characterized by BMD values. Distributions of von Mises stress over Tb microstructure and marrow regions were significantly different (p < 10–8). Voxel‐based continuum FEA offers surrogate measures of Tb modulus from CT imaging under a condition similar to in vivo imaging that alleviates the need for segmentation of Tb and marrow regions, while accounting for bone distribution at the microstructural level. This relaxation of binary segmentation will extend the scope of FEA application to assess mechanical properties of bone microstructure at relatively low‐resolution imaging.
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影响因子：
2
作者：
Chen, Chih-Li
通讯作者：
Chen, Chih-Li
DOI：
10.1097/01.blo.0000164400.37905.22
发表时间：
2005-08-01
影响因子：
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影响因子：
2.4
作者：
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