Biomedical Engineering Reference
In-Depth Information
1
√
3
,
1
√
3
,
W
3
=
ξ
3
=
η
3
=
1
−
1
√
3
,
1
√
3
,
W
4
=
1.
ξ
4
=
η
4
=
16.8
Example
One of the treatments for coronary occlusions that may lead to an infarct is to put a
stent at the location of the occlusion. One of the problems with this intervention is
that the blood vessels often occlude again quite soon after the stent is placed. One
of the solutions may be to design a stent that gradually releases drugs to prevent
such an occlusion from occurring again, see Fig.
16.6
. How these drugs propagate
through the vascular tree is a convection-diffusion problem.
Consider the domain as sketched in Fig.
16.7
. It represents a section of a long
channel. For reasons of simplicity the three-dimensional problem is modelled as a
two-dimensional problem: the relevant fields in the configuration are assumed to
be independent of the coordinate perpendicular to the
xy
-plane. A so-called New-
tonian fluid (modelling blood in a first approximation) flows through the channel
as indicated in the figure.
Let
u
denote the concentration of a certain drug. Along the entrance of the
domain the drug concentration is zero. Along the small part of the wall indicated
Figure 16.6
Schematic of a stent in a blood vessel.
y
2
1
0
-1
-2
-2
0
2
4
6
8
10
12
x
Figure 16.7
Specification of the convection-diffusion problem.
