A novel procedure for micromechanical characterization of white matter constituents at various strain rates

Optimal hyperplastic coefficients of the micromechanical constituents of human brain stem were investigated. An evolutionary optimization algorithm was combined with a Finite Element (FE) model of a Representative Volume Element (RVE) to find the optimal material properties of axon and Extra Cellular Matrix (ECM). The tension and compression test results of a previous experiment were used for optimizing the material coefficients and the shear experiment was used for validation of the resulting constitutive model. Periodic Boundary Conditions (PBC) were applied to ensure the symmetry of displacements on the opposite faces of the RVE. The optimization algorithm searched for optimal shear moduli and fiber stiffness of axon and ECM by fitting the average stress in axonal direction. The resulting constitutive model was validated against the shear stress results of the same experiment. The results were in strong agreement with those of the shear test. In addition, we concluded that the instantaneous shear moduli and fiber stiffness of both axon and ECM rise at higher strain rates, and more importantly, the shear modulus ratio of axon to ECM decreases from the value of 10 at low strain rate of 0.5/s to the value of 5 at the strain rate of 30/s.