Data-driven modeling on anisotropic mechanical behavior of brain tissue with internal pressure

Abstract

Brain tissue is one of the softest parts of the human body, composed of white matter and grey matter. The mechanical behavior of the brain tissue plays an essential role in regulating brain morphology and brain function. Besides, traumatic brain injury (TBI) and various brain diseases are also greatly influenced by the brain's mechanical properties. Whether white matter or grey matter, brain tissue contains multiscale structures composed of neurons, glial cells, fibers, blood vessels, etc., each with different mechanical properties. As such, brain tissue exhibits complex mechanical behavior, usually with strong nonlinearity, heterogeneity, and directional dependence. Building a constitutive law for multiscale brain tissue using traditional function-based approaches can be very challenging. Instead, this paper proposes a data-driven approach to establish the desired mechanical model of brain tissue. We focus on blood vessels with internal pressure embedded in a white or grey matter matrix material to demonstrate our approach. The matrix is described by an isotropic or anisotropic nonlinear elastic model. A representative unit cell (RUC) with blood vessels is built, which is used to generate the stress-strain data under different internal blood pressure and various proportional displacement loading paths. The generated stress-strain data is then used to train a mechanical law using artificial neural networks to predict the macroscopic mechanical response of brain tissue under different internal pressures. Finally, the trained material model is implemented into finite element software to predict the mechanical behavior of a whole brain under intracranial pressure and distributed body forces. Compared with a direct numerical simulation that employs a reference material model, our proposed approach greatly reduces the computational cost and improves modeling efficiency. The predictions made by our trained model demonstrate sufficient accuracy. Specifically, we find that the level of internal blood pressure can greatly influence stress distribution and determine the possible related damage behaviors.

Keywords

• Data driven
• Constitutive law
• Anisotropy
• Brain tissue
• Internal pressure