Biomedical Engineering Reference
In-Depth Information
x
10
4
2
1.5
1
0.5
0
−0.5
−1
−1.5
−2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
d(m)
x 10
−5
Fig. 5
p
YL
of (
2
)), dry
contact in
dashed-dot line
(p
c
,(
5
)) and the constitutive equation of surface tension adhesive contact
in
continuous line
(p
,(
3
)). The parameters of the equations are:
Graphs showing the pressure of Young-Laplace's Law in
dashed line
(
Q
10
3
N=m, d
1
D
7:5
D
10
6
m, d
2
D
10
6
m, p
c
0
10
4
Pa
3
7
D
2
3.3
Viability Test
Because the significance of capilarity effects relies on the length scale, the proposed
constitutive equation have to be evaluated on a structure with the length scale of an
alveolus. In order to reduce the test's numerical complexity, a simple approximate
geometry was used. The human alveoli have an average diameter of D
0:3 mm
[
19
]. Simplifying to 2D, a central section of a sphere of this diameter is a circle
with perimeter P
D
D
0:9 mm. A rectangle with the same perimeter can then
be taken P
0:15/ mm, as shows Fig.
7
.Thisisafairly
reasonable approximation since some portions of the lung tend to deform in a non-
uniform way.
The membrane of the inter-alveolar septum is simulated with non-linear first-
order isoparametric truss elements [
20
], with the Kirchhoff material model [
21
]as
constitutive equation. The value of Young's modulus for collagen, E
D
2.l
1
C
l
2
/
2.0:30
C
10
9
Pa [
8
],
was chosen as material constant. Despite the Young's modulus (E) and Kirchhoff
material's constant (C
SE
) relate different strain measures, they differ very little
for small uniaxial strains. That is, at small strains the first Piola-Kirchhoff stress
D
