A constitutive formulation of arterial mechanics including vascular smooth muscle tone

Abstract

A pseudo-strain energy function (pseudo-SEF) describing the biomechanical properties of large conduit arteries under the influence of vascular smooth muscle (VSM) tone is proposed. In contrast to previous models that include the effects of smooth muscle contraction through generation of an active stress, in this study we consider the vascular muscle as a structural element whose contribution to load bearing is modulated by the contraction. This novel pseudo-SEF models not only arterial mechanics at maximal VSM contraction but also the myogenic contraction of the VSM in response to local increases in stretch. The proposed pseudo-SEF was verified with experimentally obtained pressure-radius curves and zero-stress state configurations from rat carotid arteries displaying distinct differences in VSM tone: arteries from normotensive rats displaying minimal VSM tone and arteries from hypertensive rats exhibiting significant VSM tone. The pressure-radius curves were measured in three different VSM states: fully relaxed, maximally contracted, and normal VSM tone. The model fitted the experimental data very well (r2 > 0.99) in both the normo- and hypertensive groups for all three states of VSM activation. The pseudo-SEF was used to illustrate the localized reduction of circumferential stress in the arterial wall due to normal VSM tone, suggesting that the proposed pseudo-SEF can be of general utility for describing stress distribution not only under passive VSM conditions, as most SEFs proposed so far, but also under physiological and pathological conditions with varying levels of VSM tone.

Electrospinning of Nanocomposite Fibrillar Tubular and Flat Scaffolds with Controlled Fiber Orientation

“…Natural biomaterials close to the materials of natural arteries are ideal to avoid thrombosis and gelatine in this study fits this requirement as it is collagen-derived, collagen being the main material component of natural arteries. The second specification set in this study is to fabricate gelatine fibrillar, tubular scaffolds with axial fibre orientation to mimic the collagen fibre orientation in the tunica media of the walls of natural arteries [6,19,40].…”

Constitutive modelling of arteries

“…Based on the threeelement Hill model several models have been developed; here, however, we mention in particular the papers by Ettema & Meijer (2000), Lloyd & Besier (2003) and Lichtwark & Wilson (2005), which collectively provide an overview of the literature although they do not particularly focus on the contraction of smooth muscle cells. Papers which capture smooth muscle contractions and related models, also based on the Hill model, are those by Gestrelius & Borgström (1986), Yang et al (2003a) and Zulliger et al (2004b), which are now summarized briefly. Gestrelius & Borgström (1986) proposed a one-dimensional dynamic model of smooth muscle contraction.…”

“…A different approach to modelling the vascular smooth muscle tone was proposed by Zulliger et al (2004b). Their phenomenological model is based on three-dimensional continuum mechanics and uses a pseudo-strain-energy function that incorporates parameters describing the mechanical properties.…”

Statistical characterization of the anisotropic strain energy in soft materials with distributed fibers

“…In particular, Zulliger et al (2004) considered a log-logistic PDF for the progressive engagement of the fibers, while more recently Rodríquez et al (2006) introduced a stochastic structural model describing the waviness of a fiber bundle. The material model described in Rodríquez et al (2006), derived from the wormlike chain model of Arruda and Boyce (1993), adopts a PDF of Beta type, calculated using Bayesian statistics but assuming a deterministic orientation of the fibers.…”