A constitutive model for fibrous tissues considering collagen fiber crimp

Abstract

A micromechanically-based constitutive model for fibrous tissues is presented. The model considers the randomly crimped morphology of individual collagen fibers, a morphology typically seen in photomicrographs of tissue samples. It describes the relationship between the fiber endpoints and its arc-length in terms of a measurable quantity, which can be estimated from image data. The collective mechanical behavior of collagen fibers is presented in terms of an explicit expression for the strain-energy function, where a fiber-specific random variable is approximated by a Beta distribution. The model-related stress and elasticity tensors are provided. Two representative numerical examples are analyzed with the aim of demonstrating the peculiar mechanism of the constitutive model and quantifying the effect of parameter changes on the mechanical response. In particular, a fibrous tissue, assumed to be (nearly) incompressible, is subject to a uniaxial extension along the fiber direction, and, separately, to pure shear. It is shown that the fiber crimp model can reproduce several of the expected characteristics of fibrous tissues.

Experimental investigation of collagen waviness and orientation in the arterial adventitia using confocal laser scanning microscopy

“…The straightening stretch is the stretch to be applied along the fiber to get it straightened. Therefore, P s distribution is of particular interest for developing structural models of arterial tissue, which take into account the waviness of fibers (Zulliger et al 2004;Cacho et al 2007). These studies are mainly influenced by an earlier framework proposed by Lanir (1983).…”

Constitutive modeling of crimped collagen fibrils in soft tissues

“…Lanir used a statistical distribution in either the stretch of the fibrils or their length. Recently, Cacho et al (2007) presented a model, where a randomly crimped morphology of individual collagen fibrils is assumed. Traditionally applied to model the DNA double helix, the wormlike chain model (Kratky and Porod, 1949;Flory, 1969) was also successfully applied to describe the constitutive behavior of crimped collagen fibrils (Bischoff et al, 2002;Garikipati et al, 2004;Kuhl et al, 2005).…”

Impact of transmural heterogeneities on arterial adaptation

“…This could be addressed by implementing other constitutive model for the collagen, see e.g. Horgan and Saccomandi (2003); Vito and Dixon (2003); Wulandana and Robertson (2005);Cacho et al (2007); Tsamis and Stergiopulos (2007). It could also be simulated by polyconvex constitutive equations with a damage parameter (Ehret and Itskov 2008), which promise more robust FE calculations.…”