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

The coupled SQA model and the conventional ETS model are shown in Fig.1, in which
the dimensions of the graft diameter (DG), coronary artery diameter (DA), length of the
STS anastomosis (LSTS), distance between the two anastomoses (d), length of the ETS
anastomosis (LETS), and length of the distal section of the host artery (LD) are,
respectively, 4, 2, 9, 30, 10, and 48 mm. The length of the proximal section of the host
artery, located between the stenosis and the anastomosis (LP) is 6.5 and 10 mm in the
SQA model (Fig.1a) and the conventional ETS model (Fig.1b), respectively. Both the
SQA model (Fig.1a) and the conventional ETS anastomosis model (Fig.1b) have an
ETS anastomotic angle of 30°, and are designed to be planar, with smooth graft inner
walls [9] and the proximal segment of the coronary artery fully occluded.
3.1 Vessel wall model
A small strain (large deformation) approximation of blood vessel mechanics is utilized
in this study. The transient structural equilibrium equation is
(1)
Where {F} is the load vector, [M] is the structural mass matrix, [K] is the structural
stiffness matrix, {u} is the nodal displacement vector, and is the nodal acceleration
vector.
The vessel walls are assumed to be isotropic, incompressible, and homogeneous with a
density of 1060 kg/m 3 , and modeled as a linearly elastic, geometrically non-linear shell
structure [5, 10]. Poisson’s ratio is regarded as ν0.5 to express the incompressibility of
the isotropic vessel wall material. The Young’s modulus and the thickness of the
isotropic vessel walls are taken to be Eθ=2.2 MPa and 2 mm, respectively, in this
investigation [11, 12] .
3.2 Blood flow model
Blood flow through the CABG is assumed to be a three-dimensional, time-dependent,
incompressible, isothermal, and laminar flow. In distensible models, the modified
equations of motion for fluid mechanics computations (with corrected convective
velocity due to moving boundaries [13]), which are obtained by applying the Leibnitz
Rule on the integral conservation equations, are as follows.
0 (2)
where Uj and Wj are the components of the flow velocity and the velocity of the control
volume boundary (mesh velocity), respectively, ρ is density (assumed to be 1050 kg/m 3
for blood in this study), P is pressure, and η is the dynamic viscosity of the fluid. V and
S denote volume and surface regions of integration, respectively, and dnj are the
differential Cartesian components of the outward normal surface vector.
To model the shear thinning behavior of blood, the Carreau-Yasuda model [14, 15] is
(3)