ABSTRACT Neuronal models based on the Hodgkin–Huxley equation form a fundamental framework in the field of computational neuroscience. While the neuronal state is often modelled deterministically, experimental recordings show stochastic fluctuations, presumably driven by molecular noise from the underlying microphysical conditions. In turn, the firing of individual neurons gives rise to an electric field in extracellular space, also thought to affect the firing pattern of nearby neurons. We develop a multiscale model which combines a stochastic ion channel gating process taking place on the neuronal membrane, together with the propagation of an action potential along the neuronal structure. We also devise a numerical method relying on a split-step strategy which effectively couples these two processes and we experimentally test the feasibility of this approach. We finally also explain how the approach can be extended with Maxwell’s equations to allow the potential to be propagated in extracellular space.

中文翻译：

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通过神经放电中的分步方法进行多尺度建模

摘要 基于霍奇金-赫胥黎方程的神经元模型构成了计算神经科学领域的基本框架。虽然神经元状态通常是确定性建模的，但实验记录显示随机波动，大概是由来自潜在微物理条件的分子噪声驱动的。反过来，单个神经元的放电会在细胞外空间产生电场，也被认为会影响附近神经元的放电模式。我们开发了一个多尺度模型，该模型结合了发生在神经元膜上的随机离子通道门控过程，以及沿神经元结构传播的动作电位。我们还设计了一种基于分步策略的数值方法，该方法有效地将这两个过程结合起来，并通过实验测试了这种方法的可行性。我们最后还解释了如何使用麦克斯韦方程扩展该方法，以允许在细胞外空间中传播潜力。