We introduce and analyze a discontinuous Galerkin method for the numerical modeling of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes in the brain considering multiple scales of fluids. Concerning the spatial discretization, we employ a high-order discontinuous Galerkin method on polygonal and polyhedral grids and we derive stability and a priori error estimates. The temporal discretization is based on a coupling between a Newmark $\beta$-method for the momentum equation and a $𝜃$-method for the pressure equations. After the presentation of some verification numerical tests, we perform a convergence analysis using an agglomerated mesh of a geometry of a brain slice. Finally, we present a simulation in a three-dimensional patient-specific brain reconstructed from magnetic resonance images. The model presented in this paper can be regarded as a preliminary attempt to model the perfusion in the brain.

我们介绍并分析了一种不连续伽辽金方法，用于动态公式中多网络多孔弹性理论（MPET）方程的数值模拟。MPET模型可以综合描述考虑多种流体尺度的大脑功能变化。关于空间离散化，我们在多边形和多面体网格上采用高阶不连续伽辽金方法，并得出稳定性和先验误差估计。时间离散化基于 Newmark 之间的耦合$\beta$-动量方程的方法和$𝜃$-压力方程的方法。在进行了一些验证数值测试之后，我们使用脑切片几何形状的聚集网格进行收敛分析。最后，我们提出了根据磁共振图像重建的三维患者特定大脑的模拟。本文提出的模型可以被视为模拟大脑灌注的初步尝试。