Numerical characterization of regenerative axons growing along a spherical multifunctional scaffold after spinal cord injury.

Spinal cord injury (SCI) followed by extensive cell loss, inflammation, and scarring, often permanently damages neurological function. Biomaterial scaffolds are promising but currently have limited applicability in SCI because after entering the scaffold, regenerating axons tend to become trapped and rarelyre-enter the host tissue, the reasons for which remain to be completely explored. Here, we propose a mathematical model and computer simulation for characterizing regenerative axons growing along a scaffold following SCI, and how their growth may be guided. The model assumed a solid, spherical, multifunctional, biomaterial scaffold, that would bridge the rostral and caudal stumps of a completely transected spinal cord in a rat model and would guide the rostral regenerative axons toward the caudal tissue. Other assumptions include the whole scaffold being coated with extracellular matrix components, and the caudal area being additionally seeded with chemoattractants. The chemical factors on and around the scaffold were formulated to several coupled variables, and the parameter values were derived fromexisting experimental data. Special attention was given to the effects of coating strength, seeding location, and seeding density, as well as the ramp slope of the scaffold, on axonal regeneration. In numerical simulations, a slimmer scaffold provided a small slope at the entry "on-ramp" area that improved the success rate of axonal regeneration. If success rates are high, an increased number of regenerative axons traverse through the narrow channels, causing congestion and lowering the growth rate. An increase in the number of severed axons (300-12000) did not significantly affect the growth rate, but it reduced the success rate of axonal regeneration. However, an increase in the seeding densities of the complexes on the whole scaffold, and that in the seeding densities of the chemoattractants on the caudal area, improved both the success and growth rates. However, an increase in the density of thecomplexes on the whole scaffold risks an over-eutrophic surface that harms axonal regeneration.Although theoretical predictions are yet to be validated directly by experiments, this theoretical tool can advance the treatment of SCI, and is also applicable to scaffolds with other architectures.