Stress-Modulated Growth, Residual Stress, and Vascular Heterogeneity

Abstract

A simple phenomenological model is used to study interrelations between material properties, growth-induced residual stresses, and opening angles in arteries. The artery is assumed to be a thick-walled tube composed of an orthotropic pseudoelastic material. In addition, the normal mature vessel is assumed to have uniform circumferential wall stress, which is achieved here via a mechanical growth law. Residual stresses are computed for three configurations: the unloaded intact artery, the artery after a single transmural cut, and the inner and outer rings of the artery created by combined radial and circumferential cuts. The results show that the magnitudes of the opening angles depend strongly on the heterogeneity of the material properties of the vessel wall and that multiple radial and circumferential cuts may be needed to relieve all residual stress. In addition, comparing computed opening angles with published experimental data for the bovine carotid artery suggests that the material properties change continuously across the vessel wall and that stress, not strain, correlates well with growth in arteries.

A theoretical model for fibroblast-controlled growth of saccular cerebral aneurysms

“…Baek et al (2006); Humphrey and Rajagopal (2002); Kroon and Holzapfel (2007a,b); Rachev et al (1996); Ryan and Humphrey (1999); Taber and Humphrey (2001); Watton et al (2004)). In the present paper, we propose a new theoretical model for the growth of human cerebral saccular aneurysms.…”

Modeling the coupled mechanics, transport, and growth processes in collagen tissues.

“…4.1 and is analogous to the classical decomposition of multiplicative plasticity first applied by Lee (1969). Similar decompositions of the deformation gradient have been applied by Taber and Humphrey (2001), Ambrosi and Mollica (2002), and Klisch et al (2003) to describe growth of biological tissues. The total elastic deformation gradient arising both from internal stresses caused by growth and externally applied stresses, is defined as,…”

Mechano-regulation of mesenchymal stem cell differentiation and collagen organisation during skeletal tissue repair

“…Collagen remodelling has been extensively studied in the context of cardiovascular tissues. In these studies collagen fibres have been assumed to align with respect to a local mechanical regulator such as stress (Taber and Humphrey, 2001;Gleason and Humphrey, 2004;Hariton et al, 2007b,a) or strain (Driessen et al, 2003b,a;Kuhl and Holzapfel, 2007;Driessen et al, 2008). The strain driven remodelling algorithm proposed by Driessen et al (2005) has also been successfully used to predict the collagen architecture in articular cartilage (Wilson et al, 2006a).…”