血液动力学中血管流激波与驻波的相互作用

血液动力学问题是生物力学心血管系统中的重要研究课题.血管内斑块处,血管截面和血管壁的材质发生变化,对血液流动产生重要影响.血液流动中基本波及其相互作用对探究血液流动的规律、生理学意义及与疾病的关系有着重要的意义.本文研究血液动力学血液流动简化数学模型的基本波的相互作用.血管流模型是3×3非严格双曲型方程组.构造性地得到了初值为三段常状态时,血管流问题的解,即解决了激波与驻波的相互作用问题.特别地,给出四种后前激波与驻波的相互作用的结果.

Interaction of Shock Waves with Stationary Waves for a Blood Flow in Hemodynamics

Hemodynamics is an important research topic in biomechanical cardiovascular system. The changes of blood vessel cross section and the material of vascular wall in the plaque have important effects on blood flow. It is of great significance to study on the interaction of elementary waves in the blood flow for the law of blood flow, physiological significance and the relationship between blood flow and disease. In this paper, the authors study the simplified mathematical model of the blood flow in hemodynamics and interactions of its elementary waves. Vascular flow model is 3 × 3 nonstrictly hyperbolic equations. The solutions of the vascular flow problem are obtained constructively when the initial data are three pieces constant states, i.e., the interactions of shock waves with stationary wave are solved. In particular, the results of four kinds of interactions of backward shock waves with stationary wave are given.