Multi-Scale Modelling of Vascular Disease: Abdominal Aortic Aneurysm Evolution - Computational Modeling in Tissue Engineering - page 321

collagen fabric plays an increasingly important load bearing role, it is important to
simulate how the collagen structure adapts to predict stress distributions. Imple-
menting more sophisticated models to represent the remodelling of fibre alignment
[ 82 - 84 ], collagen fibril distribution [ 85 ], fibre dispersion [ 86 ] or proteoglycan
cross-bridges [ 87 ] may prove useful in this respect. Furthermore, given that
VSMCs secrete connective tissue and matrix degrading enzymes [ 88 ] and are
subject to apoptosis during AAA evolution [ 89 ], explicitly modelling the VSM
cells with a suitable constitutive model [ 90 - 92 ] is needed to better understand the
aetiology of AAA evolution.
We modelled the abdominal aorta as a cylindrical nonlinearly elastic membrane
subject to an axial pre-stretch and uniform internal pressure. The distal and
proximal ends of the abdominal aorta are fixed to simulate vascular tethering by
the renal and iliac arteries. Formation and development of AAA is assumed to be a
consequence of the material constituents of the artery remodelling. At physio-
logical pressures the radius of a typical abdominal aorta is approximately 10 mm
and the thickness is 1 mm. Neglecting thrombus formation, the ratio of the
thickness of the wall to the diameter of the AAA will decrease as the aneurysm
enlarges, therefore the deformation of the three dimensional arterial wall of the
developing aneurysm is closely related to the deformation of its midplane. The
residual strain that is present in the unloaded configuration gives rise to an
approximately uniform strain field through the thickness of the arterial wall at
physiological pressures. If it is assumed that the physiological mechanism by
which collagen fibres attach to the artery is independent of both the current con-
figuration of the artery and the radial position in the arterial wall, then the
remodelling process may naturally maintain a uniform strain field (in the collagen
fibres) through the thickness of the arterial wall as the AAA develops. These
considerations thus support the suitability of a membrane model to model the
development of a AAA at physiological pressures. Nevertheless, the G&R
framework of Watton et al. [ 15 ] has recently been extended to consider transmural
variations of G&R for a thick-walled model of the artery [ 66 , 67 ]: the influence of
transmural variations in biochemomechanical stimuli on G&R and AAA evolution
will be explored in future studies.
We modelled the healthy abdominal aorta as cylindrical. However, in reality the
abdominal aorta is slightly tortuous and tapers. Although, most aneurysm evolu-
tion models to date have used conceptual geometrical models for the healthy
artery, recently, Zeinali-Davarani et al. [ 17 ] applied a stress-mediated constrained
mixture FEM approach [ 93 ] to model AAA evolution [ 18 ] using patient-specific
geometries with a nonlinear membrane formulation [ 65 , 94 ]. Modelling the exact
geometry of the healthy abdominal aorta would yield physiologically realistic
spatial distributions of haemodynamic stimuli and thus may enable more accurate
prediction of the evolution of AAA geometries. However, given that the abdom-
inal aorta is almost cylindrical, hypotheses can be explored and insight obtained
with (simpler) non-patient specific geometries. For instance, we observed that the
linking elastin degradation to low WSS gives rise to enlarging fusiform aneurysms.