Multi-Scale Modelling of Vascular Disease: Abdominal Aortic Aneurysm Evolution - Computational Modeling in Tissue Engineering - page 320

mechanism for generating tortuosity is incompletely understood [ 72 ]. However, it
appears to be partly attributed to failure of elastin: in an experimental study on
canine carotid arteries, Dobrin et al. [ 73 ] observed that degradation of elastin
caused aneurysmal dilatation and a marked decrease in longitudinal retractive
force which permitted the development of tortuosity; failure of collagen causes
vessels to rupture but it was observed not to facilitate the development of tortu-
osity. These findings are consistent with our computational model: we observed
that elastin degradation gave rise to aneurysmal expansion and a reduced axial
stretch of the proximal section of artery; coupling with a model of spinal contact
and collagen G&R, tortuosity naturally develops. Hence, we suggest tortuosity is
influenced by several factors: elastin degradation, remodelling of collagen and
interaction with perivascular structures.
The structural arrangement of the cells is influenced by their local mechanical
environment. For instance, ECs align with the mean direction of flow and if they
are grown on a deformable substrate and subjected to cyclic uniaxial stretching,
they reorient away from the stretching direction [ 74 , 75 ]; in fact, it is observed that
the alignment of ECs subjected to WSS appears to be significantly enhanced by the
addition of cyclic stretching [ 76 ]. VSMCs align in the direction of cyclic stretching
and it is observed that in 2D monolayers they align perpendicular to the applied
haemodynamic WSS [ 77 ]. Fibroblasts align perpendicular to the direction of
interstitial flow [ 78 ] and their orientation may be influenced by the direction of
maximum principal stress or strain [ 79 ] or cyclic stretch [ 80 ]. Recently, a novel
parameter was proposed to characterise the biaxial cyclic stretch environment [ 36 ],
i.e. the biaxial stretch index v BSI : v BSI ¼ 0 denotes 1D cyclic stretch and v BSI ¼ 1
denotes equi-biaxial stretching. In this study, it was observed that as the AAA
evolved, the BSI distribution changed significantly: within the aneurysm, the tissue
experiences almost equi-biaxial cyclic stretching; however, in certain regions of
the tissue, e.g. the necks, rapid transition regions were observed. If it is assumed
that the AAA should evolve to achieve a particular distribution of v BSI then
analysing the evolving distributions of v BSI could be used to test competing
hypotheses for remodelling of cell/fibre alignment and dispersion. Elucidating the
relationship between the mechanical environment of vascular cells and their ori-
entation and functionality will pave the way for more sophisticated computational
models.
Following Watton et al. [ 15 ] we do not explicitly remodel the collagen fibre
orientations. However, it is important to appreciate that the collagen fibre orien-
tations are defined relative to the undeformed reference configuration. Conse-
quently, the fibres reorientate in the loaded configuration towards directions of
increasing principal stretch as the aneurysm evolves; Zeinali-Davarani et al [ 17 ]
use an identical approach, i.e. in the vivo configuration, newly deposited collagen
fibres align along the direction of the exisiting collagen fibres. There is some
justification for this approach. Fibroblasts crawl along the existing ECM matrix
thus the orientation in which they deposit and degrade collagen is partly dependent
on the existing ECM structure [ 81 ]. However, given that as an AAA evolves, the