A tube-based constitutive model of brain tissue with inner pressure

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.