In this paper, we introduce a one-dimensional model for analyzing the cerebrospinal fluid dynamics within the fourth ventricle and the spinal subarachnoid space (SSAS). The model has been derived starting from an original model of Linninger et al. and from the detailed mathematical analysis of two different reformulations. We show the steps of the modelization and the rigorous analysis of the first-order nonlinear hyperbolic system of equations which rules the new CSF model, whose conservative-law form and characteristic form are required for the boundary conditions treatment. By assuming sub-critical flows, for the particular dynamics we are dealing with, the most desirable option is to employ the nonreflecting boundary conditions, that allow the simple wave associated with the outgoing characteristic to exit the computational domain with no reflections. Finally, we carry out some numerical simulations related to different cerebral physiological conditions.

中文翻译：

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第四脑室 CSF 模型的非反射边界条件：脊柱 SAS 动力学

在本文中，我们介绍了一种用于分析第四脑室和脊髓蛛网膜下腔 (SSAS) 内脑脊液动力学的一维模型。该模型源自 Linninger 等人的原始模型。并来自对两种不同重新表述的详细数学分析。我们展示了建模的步骤和对控制新 CSF 模型的一阶非线性双曲方程组的严格分析，边界条件处理需要其保守律形式和特征形式。通过假设亚临界流动，对于我们正在处理的特定动力学，最理想的选择是采用非反射边界条件，允许与传出特性相关的简单波在没有反射的情况下退出计算域。最后，我们进行了一些与不同大脑生理条件相关的数值模拟。