三维动脉血管树的模拟与分析

Simulation and Analysis of Three-Dimensional Arterial Trees

进行血液动力学模拟和血液传热计算需要先建立血管网络,为此,借鉴强制结构优化(CCO)方法,提出了基于分支法则、Poiseuilles’law及质量守恒原则,直接在模拟区域上生成动脉血管树的新方法及相应的半径比计算公式和分支点确定步骤.模型采用根血管半径已知和末端压力未知作为定解条件,并使用了变化的分支指数.根据该方法建立了球形血管树;分析了搜索数组最佳大小随末端数的变化规律;计算了变化的分支指数对生成血管树直径分布的影响.结果表明:末端数越多,需要的搜索数组越大;由变指数得到的血管直径分布优于常指数的结果.

It is necessary to generate a three-dimensional model of arterial tree for hemodynamic simulation and heat transfer analysis of blood. Referring to the method of constrained constructive optimization （ CCO ） , a new method based on bifurcation law, Poiseuille＇s law and mass conservation was proposed to model arterial trees directly in simulation objects. The formulas for calculating the bifurcation ratios and the way to determine the location of bifurcation point were presented. In this model, the radius of the root segment was constant, the terminal pressure was unknown and the bifurcation exponent was variable. In order to demonstrate the feasibility of this method, an arterial tree was constructed in a spherical tissue. The variation trend of the size of searching array with the number of terminal segments was analyzed. The larger the number of terminal segments was, the bigger the size of searching array was. The influence of the bifurcation exponent on the distribution of vascular diameters was also studied. The results show that the distribution of diameters of the model with variable bifurcation exponent is better than that of the model with constant exponent.