Research On The Blood Flow Characteristics Of Fractal Vascular Network Based On Fractional Order Theory

The biofractal network is a very common fractal structure in the biological nature,such as the fractal of the branches of the tree,the veins of the leaves,the fractal of the vascular network of the human circulatory system,etc.The fractal structure has a whole and part,part and part of the self-similarity Sex,applying statistical and mathematical iterative methods can describe the characteristics of its fractals.In the human circulatory system,studies have shown that blood vessels are distributed in the form of fractal networks,which have self-similarity.From the perspective of biological evolution,the transportation mode of this fractal network is optimal.This study reveals the transport mechanism of blood in fractal vascular networks,analyzes the effects of vascular physiological parameters on blood,and mathematically characterizes the blood flow characteristics of vascular fractal networks in the intersection of biomedical and fluid mechanics.Medical research,while providing theoretical support for the optimization of pipeline design for bionic fractals.Fractional calculus is a mathematical theory that has been developed in recent years.It shows superiority in describing phenomena that cannot be accurately described by integer orders such as anomalous diffusion,viscoelasticity,and non-Newtonian fluid flow.In this study,the theory of time fractional differential is applied to establish the governing equation of blood flow and describe the mechanical properties of its non-Newtonian fluid.This paper is divided into six chapters.The first chapter mainly expounds the background and research significance of the topic,introduces the research status of fractal theory and fractional theory,and discusses the innovation and difficulty of the research work.The second chapter introduces the fractal theory.Considering the red blood cell embolization effect and plasma agglomeration effect in capillaries,the blood flow model in fractal vascular network was established based on fractal theory,and the influence of blood vessel fractal parameters and blood physiological parameters on blood flow was analyzed.Finally,the medical data of coronary coronary artery network was collected.The results are verified.The third chapter first introduces the fractional order theory.Based on the theory of time fractional differential,the flow model of blood in straight tube is established,and the influence of fractional order and blood flow parameters on blood velocity field is analyzed.Based on the second chapter fractal theory and the third chapter fractional theory research results,the flow model based on fractional differential and fractal theory blood is established,and the influence of fractional parameters and fractal parameters on blood flow characteristics is analyzed,and the fractional differential is proved in fractal theory.Applicability in the modeling of blood flow;Chapter 5 Design Peristaltic pump-Bionic Fractal pipeline experiment,simulation mode of transport fractal blood vessels,collecting experimental data and theoretical results were compared to verify;sixth chapter summarizes the main contents of this paper,the study of blood flow characteristics of fractal vascular network proposed some prospects.