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Micro Finite Element models of the vertebral body: Validation of local displacement predictions

机译：椎体的微有限元模型：局部位移预测的验证

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The estimation of local and structural mechanical properties of bones with micro Finite Element (microFE) models based on Micro Computed Tomography images depends on the quality bone geometry is captured, reconstructed and modelled. The aim of this study was to validate microFE models predictions of local displacements for vertebral bodies and to evaluate the effect of the elastic tissue modulus on model’s predictions of axial forces. Four porcine thoracic vertebrae were axially compressed in situ, in a step-wise fashion and scanned at approximately 39μm resolution in preloaded and loaded conditions. A global digital volume correlation (DVC) approach was used to compute the full-field displacements. Homogeneous, isotropic and linear elastic microFE models were generated with boundary conditions assigned from the interpolated displacement field measured from the DVC. Measured and predicted local displacements were compared for the cortical and trabecular compartments in the middle of the specimens. Models were run with two different tissue moduli defined from microindentation data (12.0GPa) and a back-calculation procedure (4.6GPa). The predicted sum of axial reaction forces was compared to the experimental values for each specimen. MicroFE models predicted more than 87% of the variation in the displacement measurements (R2 = 0.87–0.99). However, model predictions of axial forces were largely overestimated (80–369%) for a tissue modulus of 12.0GPa, whereas differences in the range 10–80% were found for a back-calculated tissue modulus. The specimen with the lowest density showed a large number of elements strained beyond yield and the highest predictive errors. This study shows that the simplest microFE models can accurately predict quantitatively the local displacements and qualitatively the strain distribution within the vertebral body, independently from the considered bone types.
机译：使用基于微型计算机断层扫描图像的微型有限元（microFE）模型估计骨骼的局部和结构力学性能取决于捕获，重建和建模的骨骼质量。这项研究的目的是验证microFE模型对椎体局部位移的预测，并评估弹性组织模量对模型对轴向力的预测的影响。四个猪胸椎椎骨被逐步轴向压缩，并在预加载和加载条件下以约39μm的分辨率扫描。全局数字体积相关性（DVC）方法用于计算全场位移。均质，各向同性和线性弹性microFE模型是根据从DVC测量的内插位移场分配的边界条件生成的。对标本中部的皮质和小梁隔室的测量和预测的局部位移进行了比较。使用由微压痕数据（12.0GPa）和反算程序（4.6GPa）定义的两个不同的组织模量运行模型。将轴向反作用力的预计总和与每个样品的实验值进行比较。 MicroFE模型预测位移测量值的变化超过87％（R 2 = 0.87–0.99）。但是，对于12.0GPa的组织模量，轴向力的模型预测在很大程度上被高估了（80–369％），而对于反向计算的组织模量，发现的范围在10–80％之间。密度最低的样品显示出大量超出屈服的元素，且预测误差最高。这项研究表明，最简单的microFE模型可以准确地定量预测椎体内的局部位移和定性的应变分布，而与所考虑的骨骼类型无关。

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