Laboratory of Applied Mathematics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, I-38100 Trento, Italy.
Int J Numer Method Biomed Eng. 2013 Dec;29(12):1388-411. doi: 10.1002/cnm.2580. Epub 2013 Jul 31.
We present a well-balanced, high-order non-linear numerical scheme for solving a hyperbolic system that models one-dimensional flow in blood vessels with variable mechanical and geometrical properties along their length. Using a suitable set of test problems with exact solution, we rigorously assess the performance of the scheme. In particular, we assess the well-balanced property and the effective order of accuracy through an empirical convergence rate study. Schemes of up to fifth order of accuracy in both space and time are implemented and assessed. The numerical methodology is then extended to realistic networks of elastic vessels and is validated against published state-of-the-art numerical solutions and experimental measurements. It is envisaged that the present scheme will constitute the building block for a closed, global model for the human circulation system involving arteries, veins, capillaries and cerebrospinal fluid.
我们提出了一种平衡良好、高精度的非线性数值方案，用于求解一个用于描述血管中一维流动的双曲型系统，该系统具有沿其长度变化的机械和几何特性。我们使用一组具有精确解的合适测试问题，严格评估了方案的性能。特别是，我们通过经验收敛率研究评估了方案的平衡性质和有效精度阶数。我们实现并评估了空间和时间上最高达五阶精度的方案。然后，将数值方法扩展到弹性血管的实际网络，并将其与已发表的最先进的数值解和实验测量结果进行验证。我们设想，目前的方案将构成一个包含动脉、静脉、毛细血管和脑脊液的人类循环系统的封闭、全局模型的构建块。
