We propose a new finite element approach to study the propagation of stress in axons in 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 the oligodendrocytes is also investigated by incorporating them into 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, we have modelled the microstructure of the oligodendrocyte connections to axons using a spring-dashpot approximation. We have allowed the oligodendrocytes to wrap around the outer diameter of the axons at various locations, parametrizing the number of connections, the distance among connection points, and the length of the connection hubs. The parametrization 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) a single oligodendrocyte tethered to all the axons at various locations, and 2) multiple oligodendrocytes arbitrarily connecting to the nearest axons. The impact of the oligodendrocyte connection on stress distribution is studied. The results depict reduced stress in the axons, which indicates that the oligodendrocytes do aid in the redistribution of stress. Specifically, at inflections points formed by the tortuous path of the axons, the bending stresses appear to undergo full stress reversal when the tissue is subjected to cyclic tensile and/or compressive loads. Bending stresses were also recorded multiple times on a single axon during various loading scenarios (stretch, repetitive low cycle loads of variable loading and dwell times, and variable amplitude impulse loads), thus increasing the probability of fatigue damage. Although the stress responses vary according to the loading conditions, the stress patterns in the axons exhibit a cyclic variation along the length of the undulated axons. This makes the axons more susceptible to damage accumulation. 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.


Numerical Simulation of Stress States in White Matter via a Continuum Model of 3D Axons Tethered to Glia

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Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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