A linearized and incompressible constitutive model for arteries

Y. Liu, W. Zhang, C. Wang, G.S. Kassab
2011 Journal of Theoretical Biology  
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 logarithmicexponential strain. This strain tensor absorbs the material nonlinearity and its trace is zero for volume-preserving
more » ... ons. 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.
doi:10.1016/j.jtbi.2011.05.005 pmid:21605567 pmcid:PMC3164528 fatcat:msmxnztmfrdafjut5qb43eqs7q