摘要
从血液流动、血管壁运动、血液 血管壁耦合运动三方面出发 ,建立了粘弹性血管发展流动的数学模型。导出了一组血液流动的速度分布、压力分布公式以及管壁位移公式。并结合一组狗的胸主动脉参数进行分析与讨论。结果表明 :(1)入口区域内血液流动的速度分布、压力分布公式与管壁的粘弹性无关 ;(2 )导得的管壁运动公式反映了定常、非定常、入口流动、充分发展流动等不同流动时态和形态下血流压力、速度变化对血管壁运动的影响。 (3)定常、非定常状态下粘弹性血管的运动呈现一定的规律 :当x/RnR <0 .16时 ,管壁位移变化显著 ;当x/RnR >0 .16时 ,管壁位移变化平稳。在相同条件下 ,弹性血管的位移变化幅值大于粘弹性血管。 (4)粘弹性血管的运动不仅与它的径向、轴向位置有关 ,而且与血液对血管的作用力有关。 (5 )
A mathematical model is developed to describe the developing flow of a viscoelastic vessel in consideration of three factors, blood flow, vessel wall motion and coupling motion between blood and vessel wall. A set of formulae for velocity distribution, pressure distribution and displacement of vessel were derived. Parameters of the dog thoracic aorta were used as an example to conduct analysis and discussion. The results showed that (1) the velocity distribution and pressure distribution of blood flow in the entrance region were not related to the viscoelasticity of the vessel wall. (2) the formula of vessel wall motion derived in this paper reflected the effects of different states such as steady flow or unsteady flow, and different types of entrance flow or fully developed flow on the motion of vessel wall. (3) the displacement of viscoelastic vessel wall showed a fixed pattern whether in condition of steady flow or unsteady flow: in the near region where x/RnR 0. 16, the displacement curves changed rather slowly. At the same time, the changing amplitude of the elastic vessels was bigger than that of the viscoelastic vessels. (4) the wall displacement related not only to the radical and axial directions but also to thestress exerted by the blood flow. Hence, points at different radii displaced differently. (5) the case of perfect elasticity can be considered as one of special conditions in this paper.
出处
《中国生物医学工程学报》
EI
CAS
CSCD
北大核心
2002年第5期385-392,共8页
Chinese Journal of Biomedical Engineering
基金
国家自然科学基金 (3 983 0 110 )(10 10 2 0 12 )
中国博士后科学基金联合资助项目
关键词
血管
粘弹性
发展流动
耦合运动
血管壁
Blood
Elasticity
Mathematical models
Pressure distribution
Steady flow
Unsteady flow
Viscoelasticity
