The paper presents a hierarchical series of computational models for myelinated axonal compartments. Three classes of models are considered, either with distributed parameters (2.5D EQS–ElectroQuasi Static, 1D TL-Transmission Lines) or with lumped parameters (0D). They are systematically analyzed with both analytical and numerical approaches, the main goal being to identify the best procedure for order reduction of each case. An appropriate error estimator is proposed in order to assess the accuracy of the models. This is the foundation of a procedure able to find the simplest reduced model having an imposed precision. The most computationally efficient model from the three geometries proved to be the analytical 1D one, which is able to have accuracy less than 0.1%. By order reduction with vector fitting, a finite model is generated with a relative difference of 10^− 4 for order 5. The dynamical models thus extracted allow an efficient simulation of neurons and, consequently, of neuronal circuits. In such situations, the linear models of the myelinated compartments coupled with the dynamical, non-linear models of the Ranvier nodes, neuronal body (soma) and dendritic tree give global reduced models. In order to ease the simulation of large-scale neuronal systems, the sub-models at each level, including those of myelinated compartments should have the lowest possible order. The presented procedure is a first step in achieving simulations of neural systems with accuracy control.

中文翻译：

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髓鞘轴突室的降阶模型。

本文提出了有髓的轴突区室的一系列计算模型。考虑三类模型，要么具有分布式参数（2.5D EQS–ElectroQuasi静态，一维TL传输线），要么具有集总参数（0D）。使用分析和数值方法对它们进行系统地分析，主要目标是确定每种情况下减少订单的最佳程序。为了评估模型的准确性，提出了合适的误差估计器。这是能够找到具有强制精度的最简单的简化模型的过程的基础。三种几何中计算效率最高的模型被证明是解析一维模型，其精度低于0.1％。通过向量拟合减少阶数^{− 4}为阶数5。由此提取的动力学模型可以有效地模拟神经元，进而模拟神经元回路。在这种情况下，有髓隔室的线性模型与Ranvier结，神经元体（树突）和树突树的动态，非线性模型相结合，给出了整体简化模型。为了简化大型神经系统的仿真，每个级别的子模型（包括有髓隔室的子模型）应具有最低的顺序。所介绍的过程是实现具有精确控制的神经系统仿真的第一步。