肺气管树分形结构的数学描述

Mathematical Description of Fractal Structure of Bronchial Tree

根据人体气管树内部复杂的自相似的结构,收集气管树的解剖学资料,在二维平面上建立了人体气管树完全二叉分支的分形结构数学模型。拟合出右肺的外形边界曲线,根据进出气体以最小能量损失到达分布目的的思想,借鉴血管分支形态的优化分析对前几级支气管的几何形态进行数学模拟,在此基础上建立边界控制气管树分叉控制概率模型,模拟了人体右肺气管树的分形结构。计算结果表明,该模型能很好的模拟支气管形态优化及管径确定,并能对复杂的气管树几何形态进行描述。

Based on the understanding of the complicated anatomical structure of human bronchial tree, the length ratio of the immediate bronchia, the change of bronchus diameters, and the bifurcation angles were analyzed. A bifurcation mathematical model that is used to simulate the fractal structure of human right bronchial tree was proposed using computer graphic method. According to the minimum energy loss principle and the optimal analysis of blood vessel bifurcation, The bifurcation angles and the diameters of the first three graded bifurcations of bronchia was determined. The bronchial three of right lung was depicted figuratively. The calculation results showed that the model could simulate the bronchial optimal structure and determine the diameters well, and it can describe the complex geometrical structure of human bronchial tree. 