On the Transversely Isotropic, Hyperelastic Response of Central Nervous System White Matter Using a Hybrid Approach

Abstract

A numerical and experimental hybrid approach is developed to study the constitutive behavior of the central nervous system white matter. A published transversely isotropic hyperelastic strain energy function is reviewed and used to determine stress–strain relationships for three idealized, simple loading scenarios. The proposed constitutive model is simplified to a three-parameter hyperelastic model by assuming the white matter's incompressibility. Due to a lack of experimental data in all three loading scenarios, a finite element model that accounts for microstructural axons and their kinematics is developed to simulate behaviors in simple shear loading scenarios to supplement existing uniaxial tensile test data. The parameters of the transversely isotropic hyperelastic material model are determined regressively using the hybrid data. The results highlight that a hybrid numerical virtual test coupled with experimental data, can determine the transversely isotropic hyperelastic model. It is noted that the model is not limited to small strains and can be applied to large deformations.