A passive strain-energy function for elastic and muscular arteries: correlation of material parameters with histological data

Abstract

A plethora of phenomenological and structure-motivated constitutive models have thus far been used as pseudoelastic descriptors in arterial biomechanics, but their parameters have not been explicitly correlated with histology. This study associated biaxial histological data with strain-energy function (SEF) parameters derived from uniaxial tension data of arteries from different topographical sites (carotid artery vs. thoracic aorta vs. femoral artery). A two-term SEF fitted the passive stress-strain data of healthy porcine tissue, justified by the biphasic response characterizing elastin-rich tissues. Selection of a quadratic (orthotropic) over the neo-Hookean (isotropic) term was dictated by the directional dissimilarities in low-stress mechanical response, consistent with our histological data indicating orthotropic symmetry for unstressed elastin. Use of the exponential term was dictated by mechanical dissimilarities at high stresses and variations in unstressed collagen composition and orientation. Accurate fits were attained; topographical variations and anisotropy in material parameters were accounted by respective variations in histomorphometrical data.

Differential histomechanical response of carotid artery in relation to species and region: mathematical description accounting for elastin and collagen anisotropy

“…These models and their variants, postulating isotropic contribution for elastin and anisotropic for collagen, via two [1,8,16,46] or four-fiber families [12,15,43], have met with considerable success in characterizing elastic-type arteries, but it is unclear how well they manage muscular vessels and they have been correlated with histology in merely qualitative terms, owing to the paucity of relevant observations. Exceptions are the recent studies from Wicker et al [43] and our group [31,32], wherein emphasis was laid upon associating material with histological parameters, e.g., fiber waviness and orientation, on the same specimen.…”

“…Serial 5-lm sections were cut and treated with hematoxylin-eosin for nucleus, orcein for elastin, and picro-Sirius red stain for collagen differentiation. As in our recent studies [31,32], the color images were segmented with Image-Pro Plus (v4.5; Media Cybernetics Inc.) and the area density occupied by elastin and collagen fibers, except those with orientation normal to the plane of section, was measured with respect to total area. The lengths of fiber contours were hand-traced and quantitated by the software, together with the straight distance between the fiber ends, and their ratios were considered as waviness indices.…”

“…Toward this end, we have found that only the combined quadratic and exponential SEF, originated by Tong and Fung [38] for skin, whose terms are anisotropic, captures the differing directional dissimilarities in the low and highstress response of porcine elastic, transitional, and muscular arteries, authenticated by the structural anisotropy of elastin and collagen present [32]. This study was, however, limited in that simple elongation data were considered that may not allow a robust identification of a material law [19] and only phenomenological formulations were considered that may not have the advantages of state-of-the-art microstructure-motivated SEFs.…”

Microstructural quantification of collagen fiber orientations and its integration in constitutive modeling of the porcine carotid artery

“…Most importantly, structural SEFs allocate macroscopic stress to different micro-structural components, and are able to link the macroscopic loading to potential cellular responses. Structural SEFs for the vessel wall are based on fiber-reinforced composite concepts, which assume straight and parallel-aligned [16,33,40], straight and orientation-dispersed [1,13], undulated and parallelaligned [39,40], or undulated and orientation-dispersed [19,23] (families of) fibers. Despite the fact that considerable work has been dedicated to develop and numerically implement structural SEFs, only very few studies consistently validated structural SEFs, i.e.…”

Biomechanical Behavior of Atherosclerotic Plaque

“…Some protocols use rings of arterial tissue hooked onto grips and pulled to measure mechanical response in uniaxial tension (Oxlund and Andreassen 1980). Other protocols for uniaxial tension tests use strips or dog-bone-shaped specimens of arterial tissue secured into clamping grips (Sokolis et al 2002(Sokolis et al , 2006Lally et al 2004;Jhun and Criscione 2008;Sokolis 2010). Dog bones are generally used for tensile testing of plaque specimens.…”