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 timeindependent, 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 l1 ¼ 0:7 kPa, l1 ¼ 2:0 kPa, and s1 ¼ 9:7 s in the gray matter cortex and l1 ¼ 0:3 kPa, l1 ¼ 0:9 kPa and s1 ¼ 14:9 s in the white matter corona radiata combined with negative parameters a1 and a1, 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.