Hyper-viscoelastic mechanical behavior of cranial pia mater in tension

Cranial pia mater, the innermost layer of the meninges, protects the central nervous system by tightly wrapping the brain and damping the external impact force to the brain. Accurate experimental data of the mechanical property of the cranial pia mater can enhance the theoretical prediction of traumatic brain injury or the scientific surgery design for brain disease. The aim of this study is to characterize the mechanical behavior of the cranial pia mater.

In vitro tensile and stress-relaxation experiments of ovine cranial pia mater specimens were conducted at eight strain rates to characterize the rate-dependent viscoelastic property. The tensile and stress-relaxation experimental data were fitted by an Ogden hyper-viscoelastic model with a strain rate function to describe the mechanical behavior of the cranial pia mater.

The elastic modulus and the ultimate stress are significantly increased from 5.545 MPa and 0.535 MPa at 0.00167 s^-1 to 18.345 MPa and 2.547 MPa at 0.83 s^-1 (p < .0001), respectively. The initial stress and the long-term stress (300 s) are also increased significantly with the increasing strain rates (p < .0001). A good fit of the experimental data with the Ogden hyper-viscoelastic model incorporated with a strain rate function was achieved (R² > 0.93).

The cranial pia mater exhibits as a rate-dependent hyper-viscoelastic material in the tensile and stress-relaxation experiments. Compared with the brain, the stiffer nature of the cranial pia mater indicates its essential role in brain protection. The rate-dependent constitutive model provides a proper description of the hyper-viscoelastic characteristics of the cranial pia mater in tension and may provide a basic constitutive relationship for numerical simulations of traumatic brain injury.