Multi-Scale Modelling of Vascular Disease: Abdominal Aortic Aneurysm Evolution - Computational Modeling in Tissue Engineering - page 301

Fibroblasts continually maintain the collagen fabric by synthesising structural
proteins and matrix degrading enzymes [ 25 ]. They work on the collagen, crawling
over it and tugging on it in order to compact it into sheets and draw it out into
cables [ 26 ]. In doing this, the fibroblasts attach the collagen fibres to the ECM in a
state of stretch. Each fibroblast can synthesise approximately 3.5 million procol-
lagen molecules per day. However, the amount a fibroblast secretes is regulated:
between 10 and 90 % of all procollagen molecules are degraded intracellularly
prior to secretion [ 27 ]. This provides a mechanism for rapid adaptation of the
amount of collagen secreted and thus enables the artery to rapidly adapt in
response to altered environmental conditions.
During the evolution of an AAA, it is observed that there is an accompanying
loss of elastin [ 28 ] due to increased elastolysis [ 29 ]. However, the highly nonlinear
mechanical response of the collagen implies that the degradation of elastin alone is
insufficient to explain the large dilatations that arise as the aneurysm evolves. In
fact, the collagen fabric continually remodels: collagen has a half-life of 2 months
[ 30 ] whereas elastin is a relatively stable protein with a long half-life (approxi-
mately 40 years [ 31 ]). Consequently, models of AAA evolution must address both
the degradation of elastin and the G&R of collagen [ 15 ].
Watton et al. [ 15 ] proposed the first mathematical model of AAA evolution.
The model utilises a realistic structural model for the arterial wall [ 32 ] which is
adapted to incorporate variables which relate to the normalised mass density
(hereon referred to as concentration) of the elastinous and collagenous constituents
and the reference configurations in which the collagenous constituents are
recruited to load bearing. This enables the G&R of the tissue to be simulated as an
aneurysm evolves. A key assumption of the model is that collagen fibres, which
are in a continual state of deposition and degradation [ 30 ], attach to the artery in a
state of stretch, denoted the attachment stretch, which is independent of the current
configuration of the tissue. A degradation of elastin is prescribed and differential
equations are employed to evolve the reference configurations and concentrations
of collagen fibres to maintain the stretch of the collagen to homeostatic levels, i.e.
the attachment stretch. The model predicts evolution of AAA mechanical
parameters and growth-rates consistent with clinical observations [ 16 ]. The G&R
framework has subsequently been applied to consider conceptual 1D models of
intracranial aneurysm (IA) evolution, i.e. enlarging (and stabilising) cylindrical
and spherical membranes [ 33 ] and the evolution of saccular IAs of the internal
carotid artery [ 34 ]. It has been implemented into a novel Fluid-Solid-Growth
(FSG) framework to couple the G&R of aneurysmal tissue to local haemodynamic
stimuli [ 35 , 36 ] and applied to model patient-specific IA aneurysm evolution [ 37 ].
Watton et al. [ 15 ] and Watton and Hill [ 16 ] simulated AAA evolution by
prescribing the loss of elastinous constituents. However, local aortic hemodynamic
conditions may influence the risk for, and the progression of, aneurysm disease [ 38 ].
Experimental models of AAA suggest an inverse relationship between WSS and
aneurysm expansion [ 39 , 40 ]. In fact, expansion of AAA is believed to be related to
increasing macrophage infiltration secondary to low WSS in the aneurysms
recirculation region [ 41 ]. Hence, spatial and temporal

changes in the WSS