A linearized and incompressible constitutive model for arteries

JOURNAL OF THEORETICAL BIOLOGY

卷:286

Article

Liu, Y.¹  Zhang, W.¹  Wang, C.²  Kassab, G. S.^1,3,4 

[1] Indiana Univ Purdue Univ Indianapolis, Dept Biomed Engn, Indianapolis, IN 46202 USA

[2] Univ Virginia, Robert M Berne Cardiovasc Res Ctr, Charlottesville, VA 22908 USA

[3] Indiana Univ Purdue Univ Indianapolis, Dept Surg, Indianapolis, IN 46202 USA

[4] Indiana Univ Purdue Univ Indianapolis, Dept Cellular & Integrat Physiol, Indianapolis, IN 46202 USA

关键词: Hooke's law;    Large deformation;    Strain measure;    Blood vessel;   

DOI  :  10.1016/j.jtbi.2011.05.005

来源: Elsevier

【 摘 要 】

In many biomechanical studies, blood vessels can be modeled as pseudoelastic orthotropic materials that are incompressible (volume-preserving) under physiological loading. To use a minimum number of elastic constants to describe the constitutive behavior of arteries, we adopt a generalized Hooke's law for the co-rotational Cauchy stress and a recently proposed logarithmic-exponential strain. This strain tensor absorbs the material nonlinearity and its trace is zero for volume-preserving deformations. Thus, the relationships between model parameters due to the incompressibility constraint are easy to analyze and interpret. In particular, the number of independent elastic constants reduces from ten to seven in the orthotropic model. As an illustratory study, we fit this model to measured data of porcine coronary arteries in inflation-stretch tests. Four parameters, n (material nonlinearity), Young's moduli E-1 (circumferential), E-2 (axial), and E-3 (radial) are necessary to fit the data. The advantages and limitations of this model are discussed. (C) 2011 Elsevier Ltd. All rights reserved.

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