Analysis of blood flow characteristics in fractal vascular network based on the time fractional order

Abstract

Fractional calculus has shown good adaptability in describing the mechanical properties of viscoelastic materials. Based on fractional order theory, the characteristics of blood flow in the fractal network of blood vessels are analyzed, and experiments are carried out by using a mixed solution to prove the results of simulation analysis that contains glycerol, gelatin, sodium chloride, etc. Under different time of fractional order conditions, the effects of Reynolds number, vascular network fractal dimension, and bifurcation series conditions, the blood flow characteristics in fractal vascular network are analyzed. The analysis results show that the blood flow increases with the increase in time fractional order and the flow resistance decreases with the increase in time fractional order. The blood flow law curve based on the equivalent Casson fluid theory has the same trend between the orders α = 0.9 and α = 1.0 of the time fractional order curve, so the order of time fractional order can describe the blood flow characteristics of equivalent Casson fluid. The experimental data are distributed on both sides of the theoretical calculation curve and the relative error is small, which is in good agreement with the effect of vascular fractal parameters obtained by integer order on blood.