基于默里定律的微血管网络中剪切应力的数值模拟

Numerical Simulation of Shear Stress in Microvascular Networks Based on Murray’s Law

微血管的结构特征密切影响血液流动行为,体外构建微血管网络模型是研究微血管血流动力学的有效方法。本文基于计算流体力学及有限元理论基本原理,结合默里定律,设计不同结构的微血管网络,研究包括血管直径、分叉角度、血管长度在内的关键结构参数与微血管网络中剪切应力分布情况之间的关系。结果表明,分支参数,即相邻两层血管管径之间的关系,是决定剪切应力分布的主要因素。分叉角度的变化可能引起分叉处剪切应力大小的显著变化。本文的研究结果是对基于默里定律的体外微血管网络设计原则的补充,为构建不同的生理、病理情况下的剪切应力模型提供理论依据,为基于微流控芯片等技术在体外构建微血管网络提供理论支持。

The structural characteristics of microvasculature closely affect the flow behavior of the blood.The in vitro reconstruction of microvascular network model is an effective method to study microvascular hemodynamics.In this paper,based on the basic principles of computational fluid dynamics and finite element theory,microvascular networks with different structures are designed under the guidance of Murray’s law to study the relationship between the distribution of shear stress and the key structural parameters,including vascular diameter,bifurcation angle,and vascular length in the microvascular network.The results show that the branch parameter,which is,the relationship between the diameters of the adjacent two layers of blood vessels,is the main factor that determine the distribution of shear stress.The change of the bifurcation angle may cause a significant change in the shear stress at the bifurcation.The results of this paper could be helpful for future design of in vitro microvascular network based on Murray’s law,while provide the theoretical basis for the construction of various models with multiple shear stress distribution mimicking different physiological and pathological conditions.This study also provides the theoretical support for the design of microvascular network towards future in vitro microvasculature construction based on microfluidic techniques.