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

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.