动脉血流作为人体血液循环系统中的重要环节，其动力学调节机制一直是力学、医学、生理学等各个学科所关注的关键问题。近年来，分数阶动力学在物理、力学等各学科中引起了热门讨论，动脉血流动力学的分数阶行为便是其中新起的重要分支。不同于经典欧式空间中的整数阶连续介质力学描述法，本文从一种新的研究角度，建立了动脉物理分形空间结构形式与分数阶血流动力学之间的相互关联性。 动脉血流动力学中，除了运用Navier-Stokes方程描述动脉流固耦合动力学问题以外，还有被广泛应用于血液系统整体分析的弹性腔模型。它基于力电比拟法，将影响血流的力学因子，比拟为电学元件，组成结构电路模型，模拟动力学问题。为了拓展增加有限级弹性腔数量改变模型结构形式的研究模式，本文提出了一种无穷级动脉弹性腔物理电路模型，克服了有限级弹性腔电路模型在无穷小假设下与真实有限长动脉不等价的问题。正是无穷级模型的提出，使问题从量变发生了质变，由此动脉血流动力学引入了一种新的物理分形空间结构形式。 借助分形胞元和分形算子概念，本文提出了决定物理分形电路整体响应的分形导纳算子。研究表明，这类空间结构形式的分形导纳算子，调控着动脉时间分数阶微分响应特征。基于算子级数展开收敛法，发现分形导纳算子以Bessel型特殊函数为卷积核，调节动脉呈现出生命体中重要的血液回流和迟滞回环现象。利用对偶性，进一步提出了动脉物理分形结构的分形阻抗算子，发现主动脉和小动脉分形阻抗特性分别在低频和高频段有效，而在中动脉段，利用改性元件，可实现全频段有效模拟真实动脉阻抗特性。本文还运用另一种求解算子卷积核函数的逆Laplace变换法，推广了具有物理分形结构背景的分数阶分形算子卷积核函数运算规则。 通过多分支物理分形结构的算子代数分析，发现物理分形结构呈现分数阶特征的数学来源及结构基础为分形拓扑不变量。研究表明，多分支物理分形树与环结构之间具有对偶性，其算子代数解与物理元件算子之间还存在着乘积不变性。 物理分形结构是一个普适性的概念，除了生物纤维、神经、动脉血流，最新研究进展表明，血管外组织液流动也具有物理分形结构及分数阶动力学特征。物理分形结构则可作为仿生材料制备、医学临床诊疗等实际工程应用的结构设计蓝本。

As an important part of the human blood circulation system, the dynamic regulation mechanism of arterial blood flow has always been the key problem concerned by mechanics, medicine, physiology and other disciplines. In recent years, fractional dynamics has aroused a hot discussion in physics, mechanics and other disciplines, among which the fractional behavior of arterial blood flow mechanics is a new and important branch. Different from the integer order continuum mechanical description in classical Euclidean space, this paper establishes the correlation between the physics fractal spatial structure of arterial and fractional hemodynamics from a new perspective. In arterial hemodynamics, in addition to the Navier-Stokes equations to describe the dynamics of arterial fluid-solid coupling, there is also an elastic cavity model which is widely used in the overall analysis of blood system. It is based on the mechanoelectric analogy, which compares the mechanical factors that affect blood flow to electrical components to form a structural circuit model and simulate dynamics problems. In order to expand the research mode of increasing the number of finite order elastic cavities to change the model structure, a physical circuit model of infinite order elastic cavity is proposed in this paper, which overcomes the problem that the circuit model of finite order elastic cavity is not equivalent to the real finite long artery under the infinitesimal assumption. It is the proposal of infinite model that makes the problem change from quantitative to qualitative. Therefore, arterial blood flow mechanics introduces a new physical fractal spatial structure form. Based on the concept of fractal cell and fractal operator, the fractal admittance operator which determines the global response of physical fractal circuit is proposed. The results show that the fractal admittance operators of this spatial structure regulate the fractional differential response characteristics of arterial time. Based on the operator series expansion convergence method, it is found that the fractal admittance operator takes the Bessel type special function as the convolution kernel, and the regulating artery presents the important phenomenon of blood return and hysteresis loop in the living body. Based on the duality, the fractal impedance operator of the physical fractal structure of the artery is proposed. It is found that the fractal impedance characteristics of the aorta and arteriole are effective in the low frequency and high frequency bands respectively, while in the middle artery segment, the modified element can effectively simulate the real impedance characteristics of the artery in the full frequency band. The inverse Laplace transform method for solving convolution kernel functions of fractional-order fractal operators with the background of physical fractal structure is also applied in this paper. Through the operator algebraic analysis of the multi-branch physical fractal structure, it is found that the mathematical source and structural basis of the fractional-order response characteristics are the fractal topological invariants. The results show that there is duality between the multi-branch physical fractal tree and the ring structure, and there is product invariance between the algebraic solution of the operator and the physical element operator. Physical fractal structure is a universal concept. In addition to biological fiber, nerve and arterial blood flow, the latest research progress shows that the flow of fluid in the extracapsular tissue also has physical fractal structure and fractional dynamics characteristics. Physical fractal structure can be used as a structural design blueprint for biomimetic material preparation, medical clinical treatment and other practical engineering applications.