Constitutive Modeling of Brain Tissue: Current Perspectives

Abstract

Modeling the mechanical response of the brain has become increasingly important over the past decades. Although mechanical stimuli to the brain are small under physiological conditions, mechanics plays a significant role under pathological conditions including brain development, brain injury, and brain surgery. Well calibrated and validated constitutive models for brain tissue are essential to accurately simulate these phenomena. A variety of constitutive models have been proposed over the past three decades, but no general consensus on these models exists. Here, we provide a comprehensive and structured overview of state-of-the-art modeling of the brain tissue. We categorize the different features of existing models into time-independent, time-dependent, and history-dependent contributions. To model the time-independent, elastic behavior of the brain tissue, most existing models adopt a hyperelastic approach. To model the time-dependent response, most models either use a convolution integral approach or a multiplicative decomposition of the deformation gradient. We evaluate existing constitutive models by their physical motivation and their practical relevance. Our comparison suggests that the classical Ogden model is a well-suited phenomenological model to characterize the time-independent behavior of the brain tissue. However, no consensus exists for mechanistic, physics-based models, neither for the time-independent nor for the time-dependent response. We anticipate that this review will provide useful guidelines for selecting the appropriate constitutive model for a specific application and for refining, calibrating, and validating future models that will help us to better understand the mechanical behavior of the human brain.