Biomedical Engineering Reference
In-Depth Information
a
b
100
3
ε
0
= 0.1
ε
0
= 0.5
ε
0
= 0.9
2
50
1
0
0
0
1
2
3
4
0
1
2
3
4
time (weeks)
time (weeks)
c
d
0.2
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
0
0
1
2
3
4
0
1
2
3
4
time (weeks)
time (weeks)
Fig. 4
Sensitivity analysis of the phase-change model in both layers to the porosity of the polymer
ʵ
0
. Temporal evolution of
a
the solid-phase drug concentration
c
e
;
b
the liquid-phase drug concen-
tration
c
0
;
c
the free drug concentration
c
1
;
d
the bound drug concentration
c
b
, each averaged over
the entirety of their respective layers
implicitly in our model through the continuity condition between polymer and wall
Eq. (
10
) and in the unbinding rate constant
ʲ
0
. As the fraction of polymer is reduced
and the liquid space is increased, drug release is faster since less drug is stored in the
coating (Fig.
4
a). However, since we kept the volume-averaged initial concentration
constant, the intrinsic drug concentration in the solid phase increases
c
e
=
.
This leads to higher liquid phase concentrations in the coating (Fig.
4
b). The elevated
mean free drug concentration levels in the wall occurring at relatively high porosi-
ties indicate that the wall is “overloaded” with free drug causing some drug not to
be bound (Fig.
4
c). The uptake of drug in the wall is accelerated and the receptors
rapidly occupied (Fig.
4
d). Due to the sufficiently fast binding kinetics in the wall,
virtually all the receptors can be occupied. Nevertheless, since drug supply from the
coating reduces quickly, the concentration levels in the wall drop faster.
Figure
5
shows the temporal evolution of the averaged concentrations for varying
drug unbinding times
t
1
. Figure
5
a, b indicate that the drug release in the coating
is unaffected by the variations in the drug dynamics in the wall (the three curves
overlap). Thus, there is no feedback from the wall to the coating. Figure
5
cshows
that the faster the unbinding time (which also implies a faster binding time, since
K
1
is held constant) the higher the overall concentration levels in the wall, as more
drug gets bound to the receptors. Also, the mean peak concentration occurs earlier for
c
e
ʵ
0
