Numerical simulation of stress states in white matter via a continuum model of 3D axons tethered to glia

A new finite element approach is proposed to study the propagation of stress in axons in the central nervous system (CNS) white matter. The axons are embedded in an extra cellular matrix (ECM) and are subjected to tensile loads under purely non-affine kinematic boundary conditions. The axons and the ECM are described by the Ogden hyperelastic material model. The effect of tethering of the axons by oligodendrocytes is investigated using the finite element model. Glial cells are often thought of as the “glue” that hold the axons together. More specifically, oligodendrocytes bond multiple axons to each other and create a myelin sheath that insulates and supports axons in the brainstem. The glial cells create a scaffold that supports the axons and can potentially bind 80 axons to a single oligodendrocyte. In this study, the microstructure of the oligodendrocyte connections to axons is modeled using a spring-dashpot approximation. The model allows for the oligodendrocytes to wrap around the outer diameter of the axons at various locations, parameterizing the number of connections, distance between connection points, and the stiffness of the connection hubs. The parameterization followed the distribution of axon-oligodendrocyte connections provided by literature data in which the values were acquired through microtome of CNS white matter. We develop two models: 1) multiple oligodendrocytes arbitrarily tethered to the nearest axons, and 2) a single oligodendrocyte tethered to all the axons at various locations. The results depict stiffening of the axons, which indicates that the oligodendrocytes do aid in the redistribution of stress. We also observe the appearance of bending stresses at inflections points along the tortuous path of the axons when subjected to tensile loading. The bending stresses appear to exhibit a cyclic variation along the length of the undulated axons. This makes the axons more susceptible to damage accumulation and fatigue. Finally, the effect of multiple axon-myelin connections in the central nervous system and the effect of the distribution of these connections in the brain tissue is further investigated at present.