Multi-Scale Modelling of Vascular Disease: Abdominal Aortic Aneurysm Evolution - Computational Modeling in Tissue Engineering - page 318

region and elevated values are observed in the aneurysm neck (1.08). The cyclic
stretch environment evolves from uniaxial (t ¼ 0) to almost equi-biaxial cyclic
stretching, i.e. in the aneurysm region v BSI ¼ 0 : 7 (see Fig. 5 f). Transition regions
occur in the upstream and downstream necks where the cyclic stretch environment
changes from almost uniaxial (v BSI ¼ 0 : 03) to equi-biaxial (v BSI ¼ 0 : 83). As with
case (i), as the aneurysm evolves, the proximal and distal regions of the artery
experience biaxial stretching. This is a consequence of proximal/distal regions of
the artery developing cyclic axial strain due to the axial expansion of the aneurysm
during the cardiac cycle.
4 Discussion
We have presented a fluid-solid-growth (FSG) model for evolution of AAA. The
model of the arterial wall accounts for the structural arrangement of collagen fibres
in the medial and adventitial layers, the natural reference configuration that
collagen fibres are recruited to load bearing and the concentrations (normalised
mass-densities) of the load bearing constituents. To simulate the development of
AAA we adopted two approaches: (i) we prescribed an axisymmetric degradation
of elastin; (ii) we linked degradation of elastin to local haemodynamic stimuli, i.e.
low WSS. In both examples, as the elastin degrades, the collagen fabric adapts (via
G&R) to restore its strain to the attachment strain E AT : The reference configura-
tions of the collagen fibres evolve to simulate the effect of fibre deposition (with
fibres attaching in a state of strain E AT Þ and fibre degradation in altered configu-
rations as the aneurysm enlarges; this simulates remodelling. The concentration of
collagen fibres evolves to compensate for the loss of load borne by the elastin; this
simulates growth. In the first example, we illustrated a AAA that stabilises in size
and develops tortuosity; to our knowledge, this is the first model of AAA evolution
to predict the formation of tortuosity. In the second example, we illustrated that
linking elastin degradation to low WSS predicts the evolution of enlarging fusi-
form aneurysms.
Computational fluid dynamic (CFD) studies of aneurysms often emphasise the
role of WSS (or WSSG) on pathogenesis of the disease, sometimes extrapolating
conclusions from other conditions, namely atherosclerosis However, in vivo,
vascular cells are also subject to cyclic stretching due to the pulsatility of the blood
pressure. Cell functionality [ 63 ] and vascular homeostasis [ 64 , 65 ] are influenced
by cyclic stretching. Hence, to address the G&R of the tissue that occurs during
aneurysm evolution, in addition to quantifying the haemodynamic stimuli that act
on the ECs, it is important to quantify the cyclic stretch environment of the
vascular cells. In this paper we propose a novel FSG computational framework:
rigid walls for the purpose of the CFD analysis combined with a quasi-static
analysis to determine the cyclic deformation of the arterial wall. Moreover, we
extended the existing G&R framework utilised to model AAA evolution [ 15 , 16 ]