Soft tissues are inhomogeneous, anisotropic materials which show viscoelastic and nonlinear properties. Morover, even under physiological conditions they undergo large deformations. For instance, in arteries, the in vivo longitudinal stretch ratio may pass more than 1.6. ( in vivo length/ unloaded length=1.6) These properties make the continuum approach suitable for the purpose of analyzing material properties of soft tissue. Therefore, knowledge of nonlinear solid mechanics by a continuum approach seems essential.
Identification of an appropriate strain energy function (SEF) is the preferred method to describe the complex nonlinear elastic properties of vascular tissues. Once the strain energy function is known, the constitutive stress-strain relationships can be directly obtained from the SEF.
Early formulations of SEFs were purely phenomenological, in the sense that parameters involved in the mathematical expression of SEF bared little physiological meaning. Lately, significant effort has been put into developing structure-based or constituent-based SEF, where the parameters of the strain energy function represent some identifiable physical or structural characteristics of the different components of the vessel wall, such as elastic constants of elastin and collagen, fiber structural characteristics of the collagen network, volume fraction of elastin, collagen and vascular smooth muscle cells, etc.
An example of a constituent -based SEF which considers some structural properties, i.e. the orientation of the collagen fibers relative to the arterial wall’s circumferential direction is the model by Holzapfel and colleagues. The Holzapfel et al. model has been subsequently modified and extended by Zulliger et al. take the waviness of collagen fibers into the account and later to include vascular tone.
The structure-based SEFs did provide a significant improvement over the previous phenomenological SEFs. Furthermore, they supplied scientists more powerful tools to relate morpholoy with mechanical properties of soft tissue. Pa
