Biomedical Engineering Reference
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distribution could influence the G&R of the tissue and thus the rate at which an AAA
enlarges. In this study, we apply a novel FSG framework [ 35 ] to model AAA evo-
lution. Furthermore, we sophisticate the G&R formulation (as utilised by all previous
published studies with this modelling approach [ 15 , 16 , 33 - 37 ]) to explicitly link
both the growth and remodelling of the collagen fabric to cyclic deformation of the
arterial wall. Two novel examples of AAA development are illustrated: firstly, we
prescribe the degradation of elastin secondly, we assume that the degradation of
elastin is driven by low magnitudes of WSS. In both cases, collagen remodelling and
collagen growth are linked to the magnitude of the local cyclic deformation of the
arterial wall.
2 Fluid-Solid-Growth Model for Aneurysm Evolution
In this section, we describe our FSG computational framework for modelling AAA
evolution. Figure 1 depicts the methodology. The computational modelling cycle
begins with a structural analysis of the aneurysm to solve the systolic and diastolic
equilibrium deformation fields for given pressure and boundary conditions (Fig. 1 i).
The structural analysis quantifies the stress and stretch, and the cyclic deformation,
of the ECM components and the cells (each of which may have different natural
reference configurations). The geometry of the aneurysm is subsequently exported
to be prepared for computational fluid dynamics (CFD) analysis (Fig. 1 ii): the
aneurysm geometry is integrated into a physiological geometrical domain; the
domain is automatically meshed; physiological flow rate and pressure boundary
conditions are applied. The flow is solved assuming rigid boundaries for the hae-
modynamic domain. The haemodynamic quantities of interest, for example, WSS,
are then exported and interpolated onto the nodes of the structural mesh: each node
of the structural mesh contains information regarding the mechanical stimuli
obtained from the haemodynamic and structural analyses. G&R algorithms simulate
cells responding to the mechanical stimuli and adapting the tissue (Fig. 1 iii).
Following G&R, the constitutive model of the aneurysmal tissue is updated and the
structural analysis is re-executed to calculate the new equilibrium deformation
fields. The updated geometry is exported for haemodynamic analysis. The cycle
continues and as the tissue adapts an aneurysm evolves. The stages of the FSG
framework, i.e. the structural modelling (Fig. 1 i), CFD (Fig. 1 ii) and G&R meth-
odology (Fig. 1 iii) are detailed in the subsequent subsections, i.e. Sects. 2.1 , 2.2 and
2.3 , respectively. Note that whilst we are considering the development of an
aneurysm, we could equivalently apply such a computational framework to simulate
the evolving mechanical, biological and morphological properties of a tissue
engineered construct. Moreover, if the mechanobiology was clearly understood and
accurately modelled, such a computational framework could guide and optimise the
design of a tissue-engineered construct.
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