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Numerical simulations using non-linear hyper-elastic material models to describe interactions between brain white matter (axons and extra cellular matrix (ECM)) have enabled high-fidelity characterization of stress-strain response. In this paper, a novel finite element model (FEM) has been developed to study mechanical response of axons embedded in ECM when subjected to tensile loads under purely non-affine kinematic boundary conditions. FEM leveraging Ogden hyper-elastic material model is deployed to understand impact of parametrically varying oligodendrocyte-axon tethering and analyze influence of aging material characteristics on stress propagation. In proposed FEM, oligodendrocyte connections to axons are represented via spring-dashpot model, such tethering technique facilitates contact definition at various locations, parameterize connection points and vary stiffness of connection hubs. Two FE submodels are discussed: 1) multiple oligodendrocytes arbitrarily tethered to the nearest axons, and 2) single oligodendrocyte tethered to all axons at various locations. Root mean square deviation (RMSD) were computed between stress-strain plots to depict trends in mechanical response. Axonal stiffness was found to rise with increasing tethering, indicating role of oligodendrocytes in stress redistribution. Finally, stress state results for aging axon material, with varying stiffnesses and number of connections in FEM ensemble have also been discussed to demonstrate gradual softening of tissues.

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.