ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

Fluid model. The final configuration of the structural domain was converted into a finite
volume domain using Ansys ICEM CFD (v13.0) in preparation for CFD simulations
(figure 1). The final Octree mesh consisted of 3804294 tetrahedral elements and 744370
nodes (figure 1b).
3.2 Flow and mass transport conditions
Flow boundary conditions. The finite-volume commercial code Fluent (v13.0) was used
to solve the steady three-dimensional flow and mass transport within the geometry
shown in Figure 1a. The SIMPLE formulation was used for pressure-velocity coupling,
and the second-order upwind discretisation scheme was used for the momentum and
species transport equations. Convergence was achieved when the maximum mass,
momentum, and species residuals fell below 10 -6 . Blood was modeled as an
incompressible fluid (ρ = 1060 kg/m 3 ), while viscosity was defined according to the
Carreau’s model using the following parameters: µ∞= 0.0035 kg/m·s, µ0= 0.25 kg/m·s,
λ=25.00 s and n = 0.25. Simulations were run in the steady state using a parabolic inlet
velocity waveform (peak velocity = 0.255 m/s) appropriate for flow within the porcine
coronary artery [8]. The relative pressure on the outlet was set to 0 Pa. The artery and
stent were considered a rigid wall boundary with no-slip boundary conditions.
Mass transport boundary conditions. Oxygen was assumed to be dissolved within the
blood plasma with diffusivity DO2 = 1.2×10 -9 m 2 s -1 , yielding an inlet Schmidt number Sc
= μ/ρDO2 ~ 2750 relative to the thickness of the mass transfer boundary layer. For the
given inlet velocity the Reynolds number Re = ρvd/μ = 225 indicates that the flow is
laminar. Oxygen conditions were based on the work of Coppola and Caro 2009 [6], the
fully developed inlet flow carried a uniform oxygen mass fraction, 0.002125, while
outlet flow maintained zero flux condition for the species as assumed for a stress-free
condition. For simplicity, the walls were defined by a fixed oxygen mass fraction,
0.0015.
Haemodynamic quantities of interest and oxygen profile patterns along the stented
vessel were then evaluated in terms of WSS, helicity, and Sherwood number at the
identified locations (proximal, middle and distal, as indicated in Figure 1a). For
quantitative evaluation, the WSS is calculated from the product of the dynamic viscosity
and the shear rate. Shear rate is calculated by the Fluent solver from the strain rate
tensor. Helicity is described as the scalar product of vorticity and the velocity vector.
Sherwood number (Sh) represents the non-dimensional mass flux through the arterial
wall,
Sh = k ∙ l / DO2 (1),
and is calculated from the oxygen mass transfer coefficient (k), the average
characteristic diameter of the model section (l), and the oxygen diffusion coefficient
(DO2).
4. RESULTS
Results are reported at three locations (proximal, middle, and distal) in the axial
direction for which corresponding histology and numerical data is available. Figures 2a