论文标题
轴突中信号传播问题的PML方法
A PML method for signal-propagation problems in axon
论文作者
论文摘要
这项工作的重点是髓鞘轴突中信号传播的建模，以表征髓鞘在神经结构中的功能。基于对介质特性的合理假设，我们从时光谐波麦克斯韦方程中得出了圆柱坐标中的二维神经信号模型。在神经结构的两端和辐射条件下，在结构的径向方向上建立了模型的适当性。使用完美匹配的层（PML）方法，我们截断了无限的背景介质，并提出了截断域上的近似问题。建立了PML问题的适当性和近似解决方案与精确溶液的指数收敛性。提出了基于有限元离散化的数值实验，以证明理论结果和我们的方法的效率，以模拟轴突中的信号传播。
This work is focused on the modelling of signal propagations in myelinated axons to characterize the functions of the myelin sheath in the neural structure. Based on reasonable assumptions on the medium properties, we derive a two-dimensional neural-signaling model in cylindrical coordinates from the time-harmonic Maxwell's equations. The well-posedness of model is established upon Dirichlet boundary conditions at the two ends of the neural structure and the radiative condition in the radial direction of the structure. Using the perfectly matched layer (PML) method, we truncate the unbounded background medium and propose an approximate problem on the truncated domain. The well-posedness of the PML problem and the exponential convergence of the approximate solution to the exact solution are established. Numerical experiments based on finite element discretization are presented to demonstrate the theoretical results and the efficiency of our methods to simulate the signal propagation in axons.
