Rheological characterization of human brain tissue.

The rheology of ultrasoft materials like the human brain is highly sensitive to regional and temporal variations and to the type of loading. While recent experiments have shaped our understanding of the time-independent, hyperelastic response of human brain tissue, its time-dependent behavior under various loading conditions remains insufficiently understood. Here we combine cyclic and relaxation testing under multiple loading conditions, shear, compression, and tension, to understand the rheology of four different regions of the human brain, the cortex, the basal ganglia, the corona radiata, and the corpus callosum. We establish a family of finite viscoelastic Ogden-type models and calibrate their parameters simultaneously for all loading conditions. We show that the model with only one viscoelastic mode and a constant viscosity captures the essential features of brain tissue: nonlinearity, pre-conditioning, hysteresis, and tension-compression asymmetry. With stiffnesses and time constants of μ∞=0.7kPa, μ1=2.0kPa, and τ1=9.7s in the gray matter cortex and μ∞=0.3kPa, μ1=0.9kPa and τ1=14.9s in the white matter corona radiata combined with negative parameters α∞ and α1, this five-parameter model naturally accounts for pre-conditioning and tissue softening. Increasing the number of viscoelastic modes improves the agreement between model and experiment, especially across the entire relaxation regime. Strikingly, two cycles of pre-conditioning decrease the gray matter stiffness by up to a factor three, while the white matter stiffness remains almost identical. These new insights allow us to better understand the rheology of different brain regions under mixed loading conditions. Our family of finite viscoelastic Ogden-type models for human brain tissue is simple to integrate into standard nonlinear finite element packages. Our simultaneous parameter identification of multiple loading modes can inform computational simulations under physiological conditions, especially at low to moderate strain rates. Understanding the rheology of the human brain will allow us to more accurately model the behavior of the brain during development and disease and predict outcomes of neurosurgical procedures. STATEMENT OF SIGNIFICANCE While recent experiments have shaped our understanding of the time-independent, hyperelastic response of human brain tissue, its time-dependent behavior at finite strains and under various loading conditions remains insufficiently understood. In this manuscript, we characterize the rheology of human brain tissue through a family of finite viscoelastic Ogdentype models and identify their parameters for multiple loading modes in four different regions of the brain. We show that even the simplest model of this family, with only one viscoelastic mode and five material parameters, naturally captures the essential features of brain tissue: its characteristic nonlinearity, pre-conditioning, hysteresis, and tension-compression asymmetry. For the first time, we simultaneously identify a single parameter set for shear, compression, tension, shear relaxation, and compression relaxation loading. This parameter set is significant for computational simulations under physiological conditions, where loading is naturally of mixed mode nature. Understanding the rheology of the human brain will help us predict neurosurgical procedures, inform brain injury criteria, and improve the design of protective devices.