Analysis of constitutive laws of vascular walls by finite deformation theory

Kozaburo Hayashi, Masaaki Sato, Hideyuki Niimi, Hajime Handa, Kouzo Moritake, Atsushi Okumura

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)


There is an urgent need for determining the correct constitutive laws of vascular walls because their mechanical properties have been recognized to be closely related to the cardiovascular disease. Accurate knowledge of vascular rheology is also required for an intelligent design of artificial blood vessels. The mechanical properties of arteries have been studied extensively using infinitesimal strain theory, and they have recently been determined on the basis of finite deformation theory. However, few research works have been done for evaluating them in the triaxial condition. The purpose of the present paper is to modify the stress-strain relation of vascular walls in the circumferential direction, which was proposed by Hayashi et al. in 1974, and to extend it to a triaxial form. Static analysis of large elastic deformation was carried out for an axisymmetric cylinde r on the assumption of homogeneity and incompressibility. The final relations between stresses σγ, σθ σz and extension ratios λθ, λzbecame: [formula omitted] where A, B, C and D are materials constants. These values of A, B, C and D were determined by using the iterative calculation for excised common carotid arteries and femoral arteries. The calculated results of force-displacement relations agreed well with the experimental data. The calculated distribution of three components of stress through the wall thickness showed that the radial component of stress was negligibly small in comparison with the other two stress components. In such a case, the relations between stress and extension ratio were simplified in the following form: [formula omitted] These equations are practically useful because each of them includes only two materials parameters.

Original languageEnglish
Pages (from-to)293-298
Number of pages6
Journaljapanese journal of medical electronics and biological engineering
Issue number5
Publication statusPublished - 1975
Externally publishedYes

ASJC Scopus subject areas

  • Biomedical Engineering


Dive into the research topics of 'Analysis of constitutive laws of vascular walls by finite deformation theory'. Together they form a unique fingerprint.

Cite this