Oligodendrocyte Tethering Effect on Hyperelastic 3D Response of Injured Axons in Brain White Matter

Abstract

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.