Vascular networks possess properties of self-similarity, which allows one to consider them as stochastic fractals. The box-counting method based on calculations along the vessel centerlines is traditionally used to evaluate the parameters of the fractal structure. Such an algorithm does not allow one to consider structural differences between different bifurcation levels of the system, characterized by the natural property of changing the blood vessel caliber. In this case, the discrepancy between the values of the fractal dimension may exceed 20%. In this paper, an approach that allows one to avoid underestimating the complexity of the system for low bifurcation orders and large vessels is proposed. Based on the constructed arterial tree of the rat brain, it was shown that the fractal dimension increases with an increase in the values of both bifurcation exponent and length coefficient. The obtained values most fully reflect the properties of the arterial tree considering the real geometry of the vessels; they are proposed for use in estimating three-dimensional vascular networks.

中文翻译：

---

分形分析在大鼠脑动脉系统评价中的应用

血管网络具有自相似性，这使得人们可以将它们视为随机分形。基于沿血管中心线计算的盒计数方法传统上用于评估分形结构的参数。这种算法不允许考虑系统不同分叉层级之间的结构差异，其特征是改变血管口径的自然属性。在这种情况下，分形维数值之间的差异可能会超过 20%。在本文中，提出了一种方法，可以避免低估低分叉阶数和大血管的系统复杂性。基于构建的大鼠大脑动脉树，结果表明，分形维数随着分岔指数和长度系数的增加而增加。考虑到血管的真实几何形状，获得的值最充分地反映了动脉树的特性；它们被提议用于估计三维血管网络。