Biomedical Engineering Reference
In-Depth Information
Ta b l e 1
Model parameters of the reference model
Parameter
Coating (0)
Arterial wall (1)
ʵ
0
.
1
0
.
25
k
1
1
D
m
2
s
−
1
1
×
10
−
14
5
×
10
−
12
V
ms
−
1
10
−
8
-
5
×
ʴ
s
−
1
10
−
6
10
−
8
1
.
2
×
2
.
8
×
3
×
10
−
3
mol m
−
3
K
9
mol m
−
3
c
max
b
-
0
.
2
C
e
mol m
−
3
100
-
polymer and wall tissue as accessible and thus
k
0
=
k
1
=
1. The values for
ʴ
0
and
ʴ
1
correspond to a characteristic solid-liquid transfer time
t
0
=
1 day and an unbinding
time scale
t
1
=
100 h, respectively.
2.4 Numerical Simulation
The governing equations are discretized using a finite element method with second-
order Lagrangian elements, implemented in the commercial software package
COMSOL Multiphysics 4.3a (COMSOL AB, Burlington, MA, USA). The relative
tolerance is set to 10
−
5
and the absolute tolerance to 10
−
10
. The time advancing
scheme is a backward difference formulation with variable order and time step size.
The domain is discretized by 2,000 equally spaced elements. Mesh independence
of the solution was confirmed using a coarse, medium and fine meshes with 1,000,
2,000 and 4,000 elements, respectively, with a relative difference of less than 0
.
1%
between solutions of progressively more refined meshes.
3 Results and Discussion
We present the mean concentration of each phase of the eluted drug in each of the
layers of the model. The time considered in our simulations was 4 weeks. Figure
3
illustrates the temporal evolution of the averaged concentrations for three charac-
teristic values of the solid-fluid transfer time
t
0
. For the smallest transfer time of
t
0
=
1 days, all drug is released from the solid phase in the polymer within 1 week
(Fig.
3
a) which leads to a spike in the fluid phase drug concentration at
0
.
≈
2 days at
an average concentration of
2 (Fig.
3
b).
Slower release of the drug from the solid phase entails significantly lower peak
concentrations (Fig.
3
b). For
t
0
=
≈
1 day, the coating is almost entirely depletedwithin
