Oligodendrocyte tethering effect on hyperelastic 3D response of axons in white matter

Abstract

A novel finite element model is proposed to study the mechanical response of axons embedded in extracellular matrix when subjected to tensile loads under purely non-affine kinematic boundary conditions. Ogden hyperelastic material model describes the axons and the extracellular matrix material characterizations. Two axon-glia tethering scenarios in white matter are studied a single oligodendrocyte (single-OL) with multiple connections a multi-oligodendrocyte (multi-OL) one. In the multi-OL tethering configuration, resultant forces are randomly oriented as distributed glial cells arbitrarily wrap around axons in their immediate vicinity. In the single-OL setup, a centrally located oligodendrocyte myelinates multiple axons nearby. Tethering forces are directed towards this oligodendrocyte, resulting in greater directionality and farther-reaching stress distribution. The oligodendrocyte connections to axons are represented by a spring-dashpot model. The material properties of myelin served as the upper limit for the parameterization of the oligodendrocyte stiffness (“K"). The proposed FE models enable realization of connection mechanisms and their influence on axonal stiffness to determine resultant stress states accurately. Root mean square deviation analysis of stress-strain plots of different connection scenarios reveal an increasing axonal stiffness with increasing tethering, indicating the role of oligodendrocytes in stress redistribution. In single-OL submodel, for the same number of connections per axons, RMSD values increased as “K" (the oligodendrocyte spring stiffness) values were set higher. RMSD calculations reveal that for a “K" value, single-OL model yielded slightly stiffer models compared to multi-OL. The current study also addresses the potential geometrical limitations of multi-OL model by randomizing and adding connections to ensure greater responsiveness. Cyclic bending stresses noticed in both submodels suggest the risk of axonal damage accumulation and repeated load failure.