Muller Alexandre, Clarke Richard, Ho Harvey
a Bioengineering Institute, University of Auckland , Auckland , New Zealand.
b ENSEEIHT , National Polytechnic Institute of Toulouse , Toulouse , France.
Comput Methods Biomech Biomed Engin. 2017 Feb;20(2):160-170. doi: 10.1080/10255842.2016.1207170. Epub 2016 Jul 4.
Blood flow modelling has previously been successfully carried out in arterial trees to study pulse wave propagation using nonlinear or linear flow solvers. However, the number of vessels used in the simulations seldom grows over a few hundred. The aim of this work is to present a computationally efficient solver coupled with highly detailed arterial trees containing thousands of vessels. The core of the solver is based on a modified transmission line method, which exploits the analogy between electrical current in finite-length conductors and blood flow in vessels. The viscoelastic behaviour of the arterial-wall is taken into account using a complex elastic modulus. The flow is solved vessel by vessel in the frequency domain and the calculated output pressure is then used as an input boundary condition for daughter vessels. The computational results yield pulsatile blood pressure and flow rate for every segment in the tree. This solver is coupled with large arterial trees generated from a three-dimensional constrained constructive optimisation algorithm. The tree contains thousands of blood vessels with radii spanning ~1 mm in the root artery to ~30 μm in leaf vessels. The computation takes seconds to complete for a vasculature of 2048 vessels and less than 2 min for a vasculature of 4096 vessels on a desktop computer.
此前，利用非线性或线性流动求解器，已经成功地在动脉树中进行了血流建模，以研究脉搏波传播。然而，模拟中使用的血管数量很少能超过几百个。这项工作的目的是提出一种计算效率高的求解器，并结合包含数千个血管的高度详细的动脉树。该求解器的核心基于一种改进的传输线方法，该方法利用有限长度导体中的电流与血管中血流之间的相似性。使用复弹性模量来考虑动脉壁的粘弹性行为。在频域中逐个血管地求解流动，然后将计算得到的输出压力用作子血管的输入边界条件。计算结果给出了树中每个节段的脉动血压和流速。该求解器与通过三维约束构造优化算法生成的大型动脉树相结合。该树包含数千条血管，根动脉的半径约为1毫米，叶血管的半径约为30微米。在台式计算机上，对于2048个血管的脉管系统，计算需要几秒钟完成，对于4096个血管的脉管系统，计算不到2分钟。
