Biomedical Engineering Reference
In-Depth Information
forces acting on the endothelial layer of the arterial wall; a normal hydrostatic
pressure and interstitial fluid forces due to movement of fluid through the ECM.
Mechanosensors convert the mechanical stimuli into chemical signals which lead to
activation of genes that regulate cell functionality. The physiological mechanisms
that give rise to the development of an aneurysm involve the complex interplay
between the local mechanical forces acting on the arterial wall and the biological
processes occurring at the cellular level. Consequently, models of aneurysm evolu-
tion must take into consideration: (i) the biomechanics of the arterial wall; (ii) the
biology of the arterial wall and (iii) the complex interplay between (i) and (ii), i.e.
the mechanobiology of the arterial wall. Humphrey and Taylor (
2008
) recently em-
phasized the need for a new class of fluid-solid-growth models to study aneurysm
evolution and proposed the terminology FSG models. These combine fluid and solid
mechanics analyzes of the vascular wall with descriptions of the kinetics of biolog-
ical growth and remodeling (G&R).
12.3.1 Methodology
In this section, we describe our FSG computational framework for modeling IA evo-
lution. It utilizes and extends the novel abdominal aortic aneurysm (AAA) evolution
model developed by Watton et al. (
2004
) and Watton and Hill (
2009
) which was later
adapted to model IA evolution (Watton et al.,
2009b
; Watton and Ventikos,
2009
)
and extended to consider transmural variations in G&R (Schmid et al.,
2010
,
2011
).
The aneurysm evolution model incorporates microstructural G&R variables into a
realistic structural model of the arterial wall (Holzapfel et al.,
2000
). These describe
the
normalized mass-density
and
natural reference configurations
of the load bear-
ing constituents, and enable the G&R of the tissue to be simulated as an aneurysm
evolves. More specifically, the natural reference configurations that collagen fibers
are recruited to load bearing remodels to simulates the mechanical consequences
of: (i) fiber deposition and degradation in altered configurations as the aneurysm
enlarges; (ii) fibroblasts configuring the collagen to achieve a maximum strain dur-
ing the cardiac cycle, denoted the attachment strain. The normalized mass-density
evolves to simulate growth/atrophy of the constituents (elastin and collagen). The
aneurysm evolution model has been integrated into a novel FSG framework (Watton
et al.,
2009a
) so that G&R can be explicitly linked to hemodynamic stimuli. More
recently, the G&R framework has been extended to link both
growth
and
remodeling
to cyclic deformation of vascular cells (see Watton et al.,
2012
).
Figure
12.4
depicts the FSG methodology. The computational modeling cycle
begins with a structural analysis to solve the systolic and diastolic equilibrium defor-
mation fields (of the artery/aneurysm) for given pressure and boundary conditions.
The structural analysis quantifies the stress, stretch, and the cyclic deformation, of
the constituents and vascular cells (each of which may have different natural ref-
erence configurations). The geometry of the aneurysm is subsequently exported to
be prepared for hemodynamic analysis: first the geometry is integrated into a phys-
iological geometrical domain; the domain is automatically meshed; physiological
