Many blood vessels exist in brain tissue. Their internal blood pressure plays a crucial role in physiological disorders, such as brain edema, stroke, or traumatic brain injury (concussion). Homogenized continuum mechanics-based brain tissue models can provide an attractive approach to rapidly simulate blood-pressure related physiological disorders, and traumatic brain injury. These homogenized models are much easier and faster to apply compared to finite element models that detail the microstructure. This paper thus presents a homogenized constitutive model for brain tissue in which the vascular networks and blood pressure are taken into account. The proposed model is microstructurally motivated and derived, in which the matrix of the brain tissue (gray/white matter) is modeled as hyperelastic material, while the blood vessels with their inner pressure define the microstructure. The proposed constitutive model is implemented in finite element software. Despite the simplicity of the model, we show it predicts strains and stresses comparable to finite element models with detailed microstructural representations under different loading conditions, demonstrating the potential usefulness of the model in rapidly estimating brain injury risk, hematoma formation, as well as brain tissue expansion/shrinkage.

中文翻译：

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具有内压的脑组织基于管的本构模型


脑组织中有许多血管。他们的内部血压在生理疾病中起着至关重要的作用，例如脑水肿、中风或创伤性脑损伤（脑震荡）。基于连续体力学的均质化脑组织模型可以提供一种有吸引力的方法来快速模拟与血压相关的生理疾病和创伤性脑损伤。与详细描述微观结构的有限元模型相比，这些均质模型更容易、更快速地应用。因此，本文提出了一个脑组织的均质化组成型模型，其中考虑了血管网络和血压。所提出的模型是微结构驱动和推导的，其中脑组织基质（灰/白质）被建模为超弹性材料，而血管及其内部压力定义了微观结构。所提出的本构模型是在有限元软件中实现的。尽管该模型很简单，但我们表明它预测的应变和应力可与有限元模型相媲美，并在不同的载荷条件下具有详细的微观结构表示，证明了该模型在快速估计脑损伤风险、血肿形成以及脑组织扩张/收缩方面的潜在有用性。