A Microstructurally Driven Model for Pulmonary Artery Tissue

Abstract

A new constitutive model for elastic, proximal pulmonary artery tissue is presented here, called the Total Crimped Fiber Model. This model is based on the material and micro-structural properties of the two main, passive, load-bearing components of the artery wall, elastin and collagen. Elastin matrix proteins are modeled with an orthotropic neo-Hookean material. High stretch behavior is governed by an orthotropic crimped fiber material, modeled as a planar sinusoidal linear elastic beam, which represents collagen fiber deformations. Collagen-dependent artery orthotropy is defined by a structure tensor representing the effective orientation distribution of collagen fiber bundles. Therefore, every parameter of the total crimped fiber model is correlated with either a physiologic structure or geometry or is a mechanically-measured material property of the composite tissue. Further, by incorporating elastin orthotropy, this model better represents the mechanics of arterial tissue deformation. These advancements result in a micro-structural total crimped fiber model of pulmonary artery tissue mechanics which demonstrates good quality of fit and flexibility for modeling varied mechanical behaviors encountered in disease states.

Simulation of planar soft tissues using a structural constitutive model: Finite element implementation and validation

“…Later, Sacks demonstrated that with the use of only an equi-biaxial test and the experimentally measured fiber orientation distribution, the complete in-plane biaxial response could be simulated (Sacks, 2003). More recently, structural approaches have been used for a wide range of native and engineered tissue applications, such as elastomeric tissue engineering scaffolds (Courtney et al, 2006), urinary bladder wall (Wognum et al, 2009), and many others (Fata et al, 2014; Hansen et al, 2009; Hollander et al, 2011; Kao et al, 2011). …”

Validation of an arterial constitutive model accounting for collagen content and crosslinking

“…Unfortunately, we have neither mechanical data nor three-dimensional microscopic images directly showing collagen fibers’ two-dimensional behavior. Nevertheless, previous studies have suggested that collagen fibers have a planar distribution in human cerebral arteries, calf proximal PAs and rabbit carotid arteries [21,60–62], and several modeling studies have adopted a planar distribution of collagen fibers previously with good results [26,35,41]. The zero value for the material parameter, C r , is thus believed to be reasonable.…”

“…This indicates that PA is stiffer in the circumferential direction than all other directions in this circumferential-longitudinal plane if all the collagen fibers have exactly the same mechanical properties and that the parameter C θ should be larger than C z . Nevertheless, previous modeling studies on calf and rat proximal PAs suggested nearly transversely isotropic behavior [21]. Since axial force-length data were not available, we assumed that the PA is transversely isotropic, i.e., the mechanical properties in the circumferential and longitudinal directions are the same, which forces the parameters C θ = C z .…”

“…Many mechanical testing methods including uniaxial, planar biaxial and pressure-inflation tests have been used to characterize the extrinsic and intrinsic, or more generally, mechanical properties of proximal PAs and their components [1,3,4,6,21–23]. The role of smooth muscle cell activity in proximal PA remodeling, without experimental or pharmacological activation, appears minimal [23,24].…”

“…The phenomenological approach with polynomial, exponential or logarithmic function [36–39] captures hyperelastic behavior, but does not provide information about arterial material and structure. Structural strain-energy functions (SEFs) with terms representing elastin and collagen have been used as well [21,26,40,41], but none of these models has material parameters related to collagen crosslinking. One model that does effectively capture the effects of fiber crosslinking is an eight-chain isotropic element model that uses statistical mechanics to model the hyperelastic behavior of macromolecules [42].…”