动脉壁非线性弹性的理论和实验研究

THEORETICAL AND EXPERIMENTAL INVESTIGATIONSOF NONLINEAR ELASTIC PROPERTIES OFARTERIAL WALLS

在理论方面,作者提出了一个三维理论模型分析动脉壁的非线性力学性质。该模型假设动脉壁是各向异性、局部正交对称、不可压缩和非线性弹性的。引进了一个含有七个物理参数的三维指数型应变能函数,并由该函数详细地推导了动脉壁非线性弹性本构方程及增量形式的应力和应变关系。在实验方面,本文讨论了研究大血管力学特性的实验方法,对六只狗的胸主动脉离体血管段进行了测量研究,得出了主动脉的应力和应变关系曲线及七个参数的值,并由这些参数,根据本文的理论计算出主动脉的增量弹性模量。结果比较表明,本文理论模型是能很好地描述动脉壁的力学行为。

<ABSTRACT> Mechanical characterization of the blood vessels is an important pre- requisite for the wave propagation phenomena of arteries. This paper de- als with nonlinear elastic properties of large arteries. To establish nonli- near constitutive relationships of arterial walls, a detailed study on this subject was made experimentally and theoretically. In this experimental study, the arteries of dogs were taken as the sp- ecimen. The testing process is divided into three procedures: (1) prete- st; (2 ) P procedure: fixed length of vessel and increasing pressure; (3) L procedure: fixed pressure and increasing length of wall. From the experimental results, the authors proposed a theoretical model to analyze the nonlinear elastic properties of arterial walls. The artery was modeled to be a locally anisotropic, elastic, incompressible and axisymmetric vessel. On these assumptions a new pseudo strain energy function of exponential type was introduced to establish the constitutive relationship of nonlinear elasticity of arterial walls. In this pseudo strain eneray function there are 7 constants. These co- nstants are determined by the experimental data. In this paper, the non- linear constitutive relationship for the descending aorta of dogs were st- udied. It was shown that the mechanical behaviors of caqine arteries pr- edicted by the present theory were satisfactorily similar with the experi- men tal data.