动脉壁零应力状态和材料参数的无损识别  

A non-destructive approach to identify the stress-free state and material properties of arteries

作　　者：赵学峰 钱璟 ZHAO XueFeng;QIAN Jing(Department of Mechanical and Industrial Engineering, University of Iowa, Iowa 52242, USA;Shenzhen Dehaze Technology Ltd, Shenzhen 518112, China)

机构地区：[1]爱荷华大学机械与工业工程系,美国爱荷华52242 [2]深圳浥清环保科技有限公司,深圳518112

出　　处：《中国科学：物理学、力学、天文学》2018年第5期28-38,共11页Scientia Sinica Physica,Mechanica & Astronomica

摘　　要：动脉的材料参数识别在现代生物医学工程领域有着重要的意义.不同于传统的切割实验方法,本文提出了一种新的无损识别的方法来识别动脉壁的零应力状态,即其内半径和张开角,并由此来确定动脉壁中残余应力的分布.该方法的本质是从优化的角度定义了一个逆问题,利用动脉壁的一系列负载构型来确定表征其零应力状态的两个几何参数.本文采用数值模拟的实验对该方法的可行性进行了验证,并同时讨论了实验误差对逆向分析精确性的影响,进而提出了一个利用动脉壁的压力-半径关系对具有误差的实验数据进行修正的方法.另外,本文还通过应用平均拉伸比和平均应力的概念,提出了一种无损识别的方法来识别动脉的Fung本构模型中的材料参数,并且利用识别所得到的材料参数来识别动脉壁的零应力状态.Residual strains and stresses in arteries play a significant role in homogenizing the stress field in the arterial wall and make arteries more compliant. The stress-free state of the artery needs to be identified in order to determine the residual stresses or strains in the unloaded and loaded states of the artery. The stress-free state of an artery can be characterized by two geometric parameters of the open sector achieved after a short artery segment is cut open radially, i.e., the inner radius and the opening angle. A traditional method to determine the stress-free state of arteries is to cut a short artery segment radially and measure the inner radius and the opening angle of the open sector, which is destructive by nature. In this paper, we propose a novel non-destructive method to identify the stress-free state of arteries, i.e., its inner radius and the opening angle, without the need to make the physical cut to the artery. The essence of this method is an inverse problem to identify the inner radius and the opening angle of the stress-free state by applying optimization algorithms based on a series of loaded states of the artery under different intraluminal pressures. Numerical simulations were conducted to generate a series of deformed states of an artery from which the inner radius and the opening angle of the stress-free state were identified thereafter. In addition, the effect of experimental error was investigated, and a method to modify the experimental data with error based on the pressure-radius relation of the artery was proposed. Furthermore, a non-destructive method was proposed to identify the material parameters in Fung’s constitutive model by applying the notion of average stretch ratios and stresses, from which the stress-free state can be further identified.

关 键 词：动脉血管 材料参数 逆问题 无损伤 

分 类 号：TB302.5[一般工业技术—材料科学与工程]