有髓神经元动作电位传播的空间分数阶电缆方程
A space-fractional cable equation for the propagation of action potentials in myelinated neurons
摘要：
有髓神经元的特征在于存在髓磷脂，髓磷脂是由专门的神经胶质细胞形成的轴突周围的多层包裹物。髓鞘充当电绝缘体，因此，在有髓鞘神经元中，动作电位不在轴突内传播，而仅发生在作为轴突髓鞘形成中的间隙的朗维尔结处。脑科学的最新进展表明，这些所谓的跳跃动作电位的形状，时间和传播速度是由神经元，神经胶质细胞和细胞外空间之间的各种生化相互作用控制的。鉴于大脑结构和加工过程的复杂性，本文提出了动作电位最佳传播过程中存在非局部效应的工作假设。提出了一个空间分数电缆方程的有髓神经元的动作电位传播，涉及分数阶的空间导数。利用数值模拟研究了非局域性对膜电位分布的影响。
英文摘要：
Myelinated neurons are characterized by the presence of myelin, a multilaminated wrapping around the axons formed by specialized neuroglial cells. Myelin acts as an electrical insulator and therefore, in myelinated neurons, the action potentials do not propagate within the axons but happen only at the nodes of Ranvier which are gaps in the axonal myelination. Recent advancements in brain science have shown that the shapes, timings, and propagation speeds of these so-called saltatory action potentials are controlled by various biochemical interactions among neurons, glial cells, and the extracellular space. Given the complexity of brain's structure and processes, the work hypothesis made in this paper is that non-local effects are involved in the optimal propagation of action potentials. A space-fractional cable equation for the action potentials propagation in myelinated neurons is proposed that involves spatial derivatives of fractional order. The effects of non-locality on the distribution of the membrane potential are investigated using numerical simulations.
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