This study presents a novel statistical volume element (SVE) for micromechanical modeling of the white matter structures, with histology-informed randomized distribution of axonal tracts within the extracellular matrix. The model was constructed based on the probability distribution functions obtained from the results of diffusion tensor imaging as well as the histological observations of scanning electron micrograph, at two structures of white matter susceptible to traumatic brain injury, i.e. corpus callosum and corona radiata. A simplistic representative volume element (RVE) with symmetrical arrangement of fully alligned axonal fibers was also created as a reference for comparison. A parametric study was conducted to find the optimum grid and edge size which ensured the periodicity and ergodicity of the SVE and RVE models. A multi-objective evolutionary optimization procedure was used to find the hyperelastic and viscoelastic material constants of the constituents, based on the experimentally reported responses of corpus callosum to axonal and transverse loadings. The optimal material properties were then used to predict the homogenized and localized responses of corpus callosum and corona radiata. The results indicated similar homogenized responses of the SVE and RVE under quasi-static extension, which were in good agreement with the experimental data. Under shear strain, however, the models exhibited different behaviors, with the SVE model showing much closer response to the experimental observations. Moreover, the SVE model displayed a significantly better agreement with the reports of the experiments at high strain rates. The results suggest that the randomized fiber architecture has a great influence on the validity of the micromechanical models of white matter, with a distinguished impact on the model's response to shear deformation and high strain rates. Moreover, it can provide a more detailed presentation of the localized responses of the tissue substructures, including the stress concentrations around the low caliber axonal tracts, which is critical for studying the axonal injury mechanisms.

中文翻译：

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用于组织学的三维统计体积元用于脑白质的微机械建模。

这项研究提出了一种新的统计体积元（SVE），用于白质结构的微机械建模，具有组织学信息的轴突束在细胞外基质内的随机分布。基于从扩散张量成像的结果以及扫描电子显微镜的组织学观察结果获得的概率分布函数，在易受脑部损伤的白质的两个结构即call体和电晕辐射处构造了模型。还创建了具有完全排列的轴突纤维对称排列的简化代表体积元素（RVE），作为比较的参考。进行了参数研究以找到最佳的网格和边缘尺寸，以确保SVE和RVE模型的周期性和遍历性。基于实验报道的call体对轴突和横向载荷的响应，使用了多目标进化优化程序来查找成分的超弹性和粘弹性材料常数。然后将最佳的材料特性用于预测call体和电晕辐射的均质化和局部化响应。结果表明，在准静态延伸下，SVE和RVE具有相似的均质响应，与实验数据吻合良好。然而，在剪切应变下，这些模型表现出不同的行为，而SVE模型则显示出与实验观察结果更为接近的响应。此外，在高应变率下，SVE模型与实验报告显示出明显更好的一致性。结果表明，随机纤维结构对白质微力学模型的有效性有很大影响，对模型对剪切变形和高应变率的响应有显着影响。此外，它可以提供组织亚结构的局部响应的更详细的表示，包括低口径轴突束周围的应力集中，这对于研究轴突损伤机制至关重要。