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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.

Blood physiological and flow characteristics within coronary artery circulatory network for human heart based on vascular fractal theory