基于DLA模型的人体血管生长模拟方法

摘要

Currently the generating methods of blood vessel structure are from the trunk to the branch, which is incompatible with the blood vessels growth in natural state and leads to some differences in the construction of human blood vessel model. This paper proposes a fractal algorithm for simulation of human blood vessel growth, namely diffusion-limited aggregation model (DLA) based simulation of human blood vessel growth. Firstly, combining fractal algorithm with constrained optimization, the paper establishes a natural growth method of blood vessel curves with directed motion and Brownian motion; and then generates blood vessel curve structure by using the deterministic zero-sided L system (D0L), simulates, in the manner from branch to trunk, the fractal graphics condensed mostly in the natural state, which makes the generated blood vessel model more realistic in structure compared with the blood vessel in natural growth. The experiment and analysis with simulated blood vessel growth show that the algorithm is feasible and the precision is guaranteed.%针对现有研究血管曲线结构生成方法均是从主干到支干的形式,与血管自然生长不符,导致构建的人体血管模型与实际生长结构存在一定差异的局限性的问题,提出一种模拟人体血管生长的分形算法,即基于受限扩散凝聚(DLA)模型的人体血管生长模拟算法.首先结合分形算法与约束构建优化方法的特点,建立兼具布朗运动与定向运动的血管曲线自然生长方法;然后运用分形算法中的确定型林氏无关系统(D0L)生成血管曲线结构,以支干生成主干的方式模拟大量自然状态下凝聚而成的分形图形,使构建的血管模型逼真自然血管的生长结构特性.对模拟血管的生长实验与分析结果表明,该算法具有可行性且精度得到保证.