Anisotropy of soft biological tissues and its consideration in constitutive models of arteries

Abstract

Biomechanical computational models used more and more in medical research as well as in clinical applications need mathematical description of soft tissues with their very complex mechanical behaviour. They show large deformations with stress softening during cyclic loading, being moreover time-dependent due to their viscoelasticity, anisotropic due to fibrous structure and dependent on tissue excitation in case of muscular tissues, including smooth muscle cells in arterial walls. They are capable to adapt to the acting load (tissue remodelation) and to self-repair (healing) in case of damage or failure (rupture of fibres, etc.) This paper deals with constitutive description of passive elastic response of soft tissues to the acting load and with the ways, how the anisotropic structure of the tissue can be reflected. For this purpose, the spatial arrangement of fibres in the tissue needs to be detected and mathematically described. Lack of data on fibre arrangement in soft tissues and their interpatient variability is a major limiting factor for anisotropic constitutive description of soft tissues. Some problems related to transformation of results of mechanical tests and histological analyses of arterial tissues into parameters applicable in constitutive models are addressed as well.

Experimental analysis and biaxial biomechanical behaviour of ex-vivo sheep trachea

“…Like its name, this model is hyperelastic anisotropic material model whose strain energy function is expressed as a polynomial series of isotropic and anisotropic strain invariants given as (Bursa et al, 2008).…”