A diffusion-reaction model of nerve regeneration.

The process of peripheral nerve regeneration has been modeled using 5 populations of mathematical variables to represent the biological activities of Wallerian degeneration, fibrin matrix development, Schwann cell activity, elongating neurites, and neovascularization. The mathematical model provided simulations of nerve regeneration following transection and crush injuries that correspond with growth behaviors quantified in biological experiments. Neovascularization was spatiotemporally quantified in nerve regeneration chambers and following nerve crush injury in order to test the simulations of the mathematical model. The vasculature in both the chamber and following nerve crush responded as predicted by the model, increasing beyond normal levels to a peak only to decrease back to normal. This behavior appeared as a traveling wave in the proximal-distal direction preceeding the major thrust of neuritic outgrowth suggesting that development of the vasculature is a rate-limiting step in nerve regeneration.