Identification of uniaxial deformation behavior and its initial tangent modulus for atheromatous intima in the human carotid artery and thoracic aorta using three-parameter isotropic hyperelastic models

Uniaxial stretching tests are used for mechanical identification of small fibrous regions of atheromatous arteries. Material constants in isotropic hyperelastic models are determined to minimize the fitting error for the stress-strain curve. We developed a novel method to better characterize the material constants in typical forms of Yeoh, Ogden, Chuong-Fung (CF) and Gasser-Ogden-Holzapfel (GOH) isotropic hyperelastic models for fibrous caps and normal intimal layers from human carotid artery and thoracic aorta by incorporating Young's modulus, i.e., the initial tangent modulus of uniaxial stress-strain relationships, as one of three material constants. We derived a unified, isotropic form for the anisotropic exponential-Type strain energy density functions of CF and GOH models. The uniaxial stress-strain relationship equations were expanded to Maclaurin series to identify Young's modulus as a coefficient of the linear term of the strain and to examine the roles of the material constants in the nonlinear function. The remaining two material constants were determined by curvefitting. The incorporation of Young's modulus into the CF and GOH models gave reasonable curvefitting, with errors <10%, whereas large errors (>10%) were observed in one case for the Yeoh model and in two cases for the Ogden model.