Biomedical Engineering Reference
In-Depth Information
Fig. 2 A patient-specific iliac bifurcation artery is attached downstream of the AAA structural
model; a connecting patch is created to join two geometries together. A cylindrical extension is
attached upstream (not depicted)
incompressible Navier-Stokes equations using a finite volume formulation [ 48 , 49 ].
The solver is based on a coupled approach (i.e. velocities and pressure are cast and
solved as a single system) and a fully implicit time discretisation, where needed. An
algebraic multigrid variant is used for convergence acceleration [ 50 ]. Blood is
modelled as a Newtonian fluid [ 51 , 52 ] with constant density q ¼ 1 ; 069 kgm 3 [ 53 ,
54 ] and constant viscosity g ¼ 0 : 0035 Pa s. At the arterial wall, no slip, no-flux
conditions are applied. We adopted a steady flow analysis to reduce the cost of the
computational simulations. The mean flow and pressure boundary conditions are
taken from a 1D model of the arterial tree [ 55 ] which has been integrated into the
software suite @neufuse which was developed for the European project @neuIST
[ 56 ] (www.aneurist.org: 'Integrated Biomedical Informatics for the Management of
Cerebral Aneurysms'). It solves the 1D form of the Navier-Stokes equation in a
distributed model of the human systemic arteries, accounting for the ventricular-
vascular interaction and wall viscoelasticity; it was recently validated through a
comparison with in vivo flow measurements [ 57 ]. A flow rate of 24 cm 3 = s is applied
at the inlet and the pressure at the illiac arteries is set to 12760 Pa.
2.3 Growth and Remodelling
To model AAA evolution, we simulate the G&R of the load bearing constituents of
the arterial wall, i.e. elastin and collagen. Remodelling is associated with changes in
the natural reference configurations that constituents are recruited to load bearing
whereas growth is associated with changes in the mass of the constituents.
2.3.1 Elastin Degradation
To simulate the degradation of elastin that occurs during AAA evolution, two
approaches are considered. Firstly, the degradation of elastin is prescribed ([ 15 ])
and secondly it is linked to the haemodynamic environment (see [ 35 ]).
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