A Mathematical Model of Regenerative Axon Growing along Glial Scar after Spinal Cord Injury.

Xuning Chen,Weiping Zhu

doi:10.1155/2016/3030454

Abstract

A major factor in the failure of central nervous system (CNS) axon regeneration is the formation of glial scar after the injury of CNS. Glial scar generates a dense barrier which the regenerative axons cannot easily pass through or by. In this paper, a mathematical model was established to explore how the regenerative axons grow along the surface of glial scar or bypass the glial scar. This mathematical model was constructed based on the spinal cord injury (SCI) repair experiments by transplanting Schwann cells as bridge over the glial scar. The Lattice Boltzmann Method (LBM) was used in this model for three-dimensional numerical simulation. The advantage of this model is that it provides a parallel and easily implemented algorithm and has the capability of handling complicated boundaries. Using the simulated data, two significant conclusions were made in this study: (1) the levels of inhibitory factors on the surface of the glial scar are the main factors affecting axon elongation and (2) when the inhibitory factor levels on the surface of the glial scar remain constant, the longitudinal size of the glial scar has greater influence on the average rate of axon growth than the transverse size. These results will provide theoretical guidance and reference for researchers to design efficient experiments.

Highlights

Spinal cord injury (SCI) is the damage to the spinal cord that results in a loss of function such as mobility or feeling
(1)–(4) were a set of coupled nonlinear partial differential equations which could only be solved numerically. The solution of this model contained three steps and three methods: the first step, using the Lattice Boltzmann Method (LBM) [26,27,28,29] to solve for the concentration field of various factors determined by the reaction-diffusion equations (1)–(3); the second step, using the central difference method to solve for gradients of various factors surrounding the growth cone, and axon growth rates would be solved when the solution for the gradient was inserted into (4); and, using Euler’s method to numerically integrate (4) and solving for the axonal growth path
The following hypothesis was tested through numerical simulation: glial scar exists, it does not affect the growth of regenerating axons as long as the inhibitor level on the surface of the glial scar is below a threshold

Summary

Introduction

Spinal cord injury (SCI) is the damage to the spinal cord that results in a loss of function such as mobility or feeling. The failure to regenerate is caused by a combination of factors, including neuroinflammation, axonal disruption, death of neurons, glial scar formation, the release of myelin-associated inhibitory molecules, and the lack of growth promoting molecules. Trauma or disease of a nerve in a mature mammal may result in a massive multiplication of glial cells around the damaged region, which eventually form a dense scar. This glial scar plays a dual role as chemical and mechanical barriers to the axonal regeneration of injured neurons [7,8,9,10]. The size, shape, and hardness of the glial scars represent the mechanical aspects that resist the extension of the regenerative axons

Methods

Results

Conclusion