A transverse-plane hyperelastic micromechanical model of brain white matter tissue was developed using the embedded element technique (EET). The model consisted of a histology-informed probabilistic distribution of axonal fibers embedded within an extracellular matrix, both described using the generalized Ogden hyperelastic material model. A correcting method, based on the strain energy density function, was formulated to resolve the stiffness redundancy problem of the EET in large deformation regime. The model was then used to predict the homogenized tissue behavior and the associated localized responses of the axonal fibers under quasi-static, transverse, large deformations. Results indicated that with a sufficiently large representative volume element (RVE) and fine mesh, the statistically randomized microstructure implemented in the RVE exhibits directional independency in transverse plane, and the model predictions for the overall and local tissue responses, characterized by the normalized strain energy density and Cauchy and von Mises stresses, are independent from the modeling parameters. Comparison of the responses of the probabilistic model with that of a simple uniform RVE revealed that only the first one is capable of representing the localized behavior of the tissue constituents. The validity test of the model predictions for the corona radiata against experimental data from the literature indicated a very close agreement. In comparison with the conventional direct meshing method, the model provided almost the same results after correcting the stiffness redundancy, however, with much less computational cost and facilitated geometrical modeling, meshing, and boundary conditions imposing. It was concluded that the EET can be used effectively for detailed probabilistic micromechanical modeling of the white matter in order to provide more accurate predictions for the axonal responses, which are of great importance when simulating the brain trauma or tumor growth.

使用嵌入式元素技术（EET）建立了脑白质组织的横断面超弹性微力学模型。该模型由组织学知悉的，嵌入细胞外基质中的轴突纤维的概率分布组成，均使用广义的Ogden超弹性材料模型进行描述。提出了一种基于应变能密度函数的校正方法，以解决大变形状态下EET的刚度冗余问题。然后使用该模型预测准静态，横向，大变形下轴突纤维的均质组织行为和相关的局部响应。结果表明，在具有足够大的代表体积元素（RVE）和精细网格的情况下，RVE中实现的统计随机微观结构在横向平面上表现出方向独立性，以归一化应变能密度以及Cauchy和von Mises应力为特征的整体和局部组织反应的模型预测与建模参数无关。比较概率模型的响应与简单统一的RVE的响应，发现只有第一个能够代表组织成分的局部行为。针对电晕辐射的模型预测相对于来自文献的实验数据的有效性测试表明了非常接近的一致性。与传统的直接啮合方法相比，该模型在校正刚度冗余后提供了几乎相同的结果，但是，大大降低了计算成本，并促进了几何建模，网格划分和边界条件的施加。结论是，EET可以有效地用于白质的详细概率微力学建模，从而为轴突反应提供更准确的预测，这在模拟脑部创伤或肿瘤生长时非常重要。