We introduce and analyze a discontinuous Galerkin method for the numerical modelling 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 $\theta$-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.

翻译：本文提出并分析了一种用于动态公式化多网络多孔弹性理论（MPET）方程数值建模的间断伽辽金方法。MPET模型能够综合考虑多尺度流体对脑功能变化的全面描述。在空间离散化方面，我们采用多边形和多面体网格上的高阶间断伽辽金方法，并推导了稳定性与先验误差估计。时间离散化基于动量方程的Newmark $\beta$ 方法与压力方程的 $\theta$ 方法的耦合。在展示若干验证性数值测试后，我们利用一个脑切片几何的聚合网格进行了收敛性分析。最后，我们展示了一项基于磁共振图像重建的三维患者特异性脑部模拟。本文提出的模型可视为对脑灌注建模的初步尝试。