Biomedical Engineering Reference
In-Depth Information
Fig. 5.3
Porcine tissue strip
dissected from an artery. The
strip has the dimensions
l/w/t
a
/t
m
=
3
.
0
/
3
.
0
/
0
.
1
/
0
.
1mm
the contractible media (
t
m
=
0
.
1mm,
dark grey). In the proposed example we are interested in the tissue response when a
completely deactivated strip with an extracellular calcium concentration being ini-
tially zero is exposed to an environment with an external calcium concentration of
[
0
.
1 mm, light grey) and the adventitia (
t
a
=
Ca
2
+
]=
500 mMol. This example is closely related to the experimental work of
Arner (
1982
).
In order to analyze the contraction process the main variables, i.e. the calcium
concentration
Ca
2
+
]
n
D
)
, and the equivalent
von Mises stress
σ
vM
have been tracked during contraction. In doing so, Fig.
5.4
illustrated the results for four discrete time steps
t
[
, the chemical concentrations
(n
C
+
10
/
30
/
80
/
250 s. Focusing on
the calcium concentration (first line) a converged state is achieved in dependence on
the choice of the diffusion coefficients, here this situation occurs at time
t
=
=
80 s.
The chemical states
(n
C
+
n
D
)
in the second line display a small delay with respect
to the calcium concentration, see, e.g., at time
t
=
30 s. Also here, the converged
state arises after 80 seconds. In the third line the distribution of the equivalent von
Mises stress is illustrated. Small stresses can be detected for the first time step (10 s).
As the media differs from the adventitia by a higher stiffness also the stress values
a higher. This is impressively documented at time
t
30 s where the maximum
stress is achieved. The stress increases continuously until at 80 seconds a decrease
can be observed. During further activation the stress again increases. Focusing on
the overall deformation of the strip a clear bending deformation can be seen that
continuously increases. This bending arises from the fact that the layers are aligned
asymmetrical and that the media contracts, only.
=
