Numerical study of axonal outgrowth in grooved nerve conduits

Nerve conduits with grooved inner texture, working as a topographical guidance cue, have been experimentally proved to play a significant role in axonal alignment. How grooved conduits guide axonal outgrowth is of particular interest for studying nerve regeneration. A viscoelastic model of axonal outgrowth in a conduit with a defined grooved geometry characterized by its width in the circumferential direction and its height in the radial direction is developed in this work. In this model, the axon is considered as an elastic beam and the axonal deformation and motion, including stretching, bending and torsion, are described using a Cosserat rod theory. The friction between axon and substrate is also considered in this model as well as the tip outgrowth. It is found that the directional outgrowth of the axon can be significantly improved by the grooved texture: when the groove width decreases or the groove height increases, the axonal elongation in the longitudinal direction of the conduit can be increased, which is in good agreement with experimental observations. This work is the first numerical model to study the effect of the substrate geometry on axonal outgrowth.