神经系统轴突生长的数值模拟

Numerical simulation of axon growth in the nervous system

目的数值模拟神经系统在发育过程中轴突的生长情况。方法根据神经发育原理,建立具有一定刚性的非线性混合抛物型偏微分方程组,运用ADI差分格式和改进的欧拉法作数值分析。结果 (1)在一个正方形平面区域内有10个轴突以相等的间距围成圆形,当中心有1个靶细胞时,轴突生长路径的数值模拟结果与前人所做的有关结果一致;(2)轴突的初始位置同(1),当中央有4个两两上下并排分布的靶细胞时,数值模拟结果很好地反映了轴突生长时的趋化性;(3)在区域的近上、下边界分别有一串靶细胞和一串轴突时,数值模拟结果较好地反映了轴突结集生长时的成束和解束现象。结论本文给出的数学模型和数值主法能够较好地模拟有关实验所观测到的主要现象。

Objective To simulate the growth of axons in the developing nervous system numerically. Methods A set of mixed parabolic-gradient nonlinear equations was established based upon the principles of the developing neural biology, which was computed by the ADI scheme and the modified Euler＇ s method. Results （1） In the first case that one target was uniformly surrounded by ten axons in a square area, the pathway of the growing axons we simulated coincided with those obtained by the formers; （2） in the second case that a group of two-by-two-placed targets was surrounded by the same axons as in （1）, the results correctly reflected the ehemotaxis of the growing axons; （3） in the final case that a stream of targets lined near the upper edge of the square area and a stream of axons lined near the lower edge, the results ap- proximately displayed the bundling and debonding courses of the growing axons. Conclusion The mathematical model and the numerical method presented in this paper can simulate the main phenomenon observed in the related experiments.