标题： 微管驱动的轴突生长的高效模拟 显示英文标题

标题： Efficient simulations of tubulin-driven axonal growth

摘要： 这项工作涉及对微管驱动轴突生长的移动边界模型动态行为的高效且可靠的数值模拟。 该模型是非线性的，由一组耦合的偏微分方程（PDE）和两个常微分方程组成。 PDE 定义在一个具有移动边界的计算域上，该边界是解的一部分。 基于标准显式时间步进方法的数值模拟由于需要小的时间步长以保证数值稳定性而过于耗时。 另一方面，标准隐式格式由于在每一步都需要求解非线性方程而过于复杂。 相反，我们建议使用 Peaceman--Rachford 分裂方案，并结合模型的时间和空间缩放。 基于此方案的模拟已被证明是高效、准确和可靠的，这使得可以评估该模型，例如其对生物和物理模型参数的依赖性。 这些评估表明，轴突的初始生长非常迅速，主动运输是影响生长速度的主要因素，而非扩散，而且生长锥中的聚合速率不影响最终的轴突长度。 显示英文摘要

摘要： This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation (PDE) and two ordinary differential equations. The PDE is defined on a computational domain with a moving boundary, which is part of the solution. Numerical simulations based on standard explicit time-stepping methods are too time consuming due to the small time steps required for numerical stability. On the other hand standard implicit schemes are too complex due to the nonlinear equations that needs to be solved in each step. Instead, we propose to use the Peaceman--Rachford splitting scheme combined with temporal and spatial scalings of the model. Simulations based on this scheme have shown to be efficient, accurate, and reliable which makes it possible to evaluate the model, e.g.\ its dependency on biological and physical model parameters. These evaluations show among other things that the initial axon growth is very fast, that the active transport is the dominant reason over diffusion for the growth velocity, and that the polymerization rate in the growth cone does not affect the final axon length.