To analyze the fractal form of the vascular network in the human circulatory system, the optimal transport effect has been achieved from the point of view of biological evolution. The blood flow mathematical models based on the fractal theory for capillary network and arteriole–capillary vascular fractal network were established using theory derivation, and the blood flow characteristics, dynamic flow resistance effects, and vascular fractal physiology property based on the fractal porous medium theory for the coronary artery circulatory network were analyzed under the consideration of some influencing factors, namely, non-Newtonian fluid characteristics of blood, hemocoagulation and embolization effect in capillaries, and plasma mass flow effects. Moreover, the Poiseuille flow equation is modified by introducing the correction function, and the flow model of blood in the vascular network is established. Obviously, the relationship characteristics between blood flow and bifurcation grade in fractal vascular, fractal dimension in the arteriole–capillary vascular network, fractal dimensions of the diameter of capillary tubular diameter, fractal dimensions of capillary blood vessels, blood Casson yield stress, and ratio of red blood cell radius to capillary diameter can be obtained. And the relationship characteristics between blood flow resistance and ratio of erythrocyte radius to capillary diameter, ratios of the distance between adjacent red blood cells to the radius of red cells, and bifurcation grade can be obtained. Finally, the clinical verification tests were accomplished to verify the theory is worthy of authenticity and rationality where the curve tendencies are very similar with those obtained by numerical simulations based on the theoretical models and experimental test showed that the theoretical calculation and simulation analysis of blood circulation system of fractal vascular network were reasonable and applicable by means of experimental relative method because of the maximum relative error is less than 10%, whatever fractal dimension m changes under different conditions.

为了分析人体循环系统中血管网络的分形形式，从生物进化的观点出发，已经获得了最佳的运输效果。利用理论推导建立了基于分形理论的毛细血管网络和小动脉-毛细血管-血管分形网络的血流数学模型，并基于分形多孔介质理论建立了血流特征，动态流阻效应和血管分形生理特性。在考虑一些非牛顿流体的血液特性，毛细血管的凝血和栓塞作用以及血浆质量流量影响等因素的影响下，对冠状动脉循环网络进行了分析。此外，通过引入校正函数来修改Poiseuille流动方程，建立了血管网络中的血液流动模型。显然，分形血管的血流与分叉程度，小动脉-毛细血管网络的分形维数，毛细血管直径的分形维数，毛细血管的分形维数，血液卡森屈服应力，以及可获得红细胞半径至毛细血管直径。并且可以获得血流阻力与红细胞半径与毛细管直径之比，相邻红细胞之间的距离与红细胞半径之比以及分叉等级之间的关系特性。最后，m在不同条件下变化。