Hyper-Viscoelastic 3D Response of Axons Subjected to Repeated Tensile Loads in Brain White Matter

Abstract

A novel finite element method (FEM) is developed to study mechanical response of axons embedded in extra cellular matrix (ECM) when subjected to harmonic uniaxial stretch under purely non-affine kinematic boundary conditions. The proposed modeling approach combines hyper-elastic (such as Ogden model) and time/frequency domain viscoelastic constitutive models to evaluate the effect of parametrically varying oligodendrocyte-axon tethering under harmonic stretch at 50Hz. A hybrid hyper-viscoelastic material (HVE) model enabled the analysis of repeated uniaxial load on stress propagation and damage accumulation in white matter. In the proposed FEM, oligodendrocyte connections to axons are depicted via a spring-dashpot model. This tethering technique facilitates contact definition at various locations, parameterizes connection points and varies stiffness of connection hubs. Results from a home-grown FE submodel configuration of a single oligodendrocyte tethered to axons at various locations are presented. Root mean square deviation (RMSD) are computed between stress-strain plots to depict trends in mechanical response. Steady-state dynamic (SSD) simulations show stress relaxation in axons. Gradual axonal softening under repetitive loads is illustrated employing Prony series - HVE models. Representative von-Mises stress plots indicate that undulated axons experience bending stresses along their tortuous path, suggesting greater susceptibility to damage accumulation and fatigue failure due to repeated strains.