Biomedical Engineering Reference
In-Depth Information
unstressed tissue, we apply a strain that increases in steps of 10 % until it reaches
100 %. The new length can be calculated as
new
=
(
1
+
ε)
old
(6.14)
with the subscript
old
denoting the characteristics before applying the strain step.
Assuming a constant tissue volume
V
t
, the radius will decrease:
V
t
2
π
new
h
=
R
old
·
old
new
R
new
=
(6.15)
with
R
new
and
R
old
the new and old airway radius, respectively. We neglect the
changes in the thickness
h
of the tube wall with changes in the strain. Applying
a typical value for the oscillatory flow
Q
=
0
.
5 l/s at the oscillatory frequency of
5 Hz, the velocity
v
can be calculated as
10
−
4
A
new
5
·
v
new
=
(6.16)
Since the
B
's and
K
's are time-invariant material properties, the transfer function
H(s)
from (
6.12
) will be independent of the strain. The elongation
of the airway
tube will have an effect on the pipeline equation (
4.13
) which can be expressed as
K
A
h
B
A
dε
dt
p
+
ε
+
=
0
(6.17)
ν
p
)
R(
1
−
with
ν
p
the Poisson coefficient. The new values for the pressure and the stress are
given by
F
new
A
new
=
v
new
H
πR
new
P
new
=
(6.18)
ν
p
)
R
new
(
1
−
σ
new
=−
P
new
(6.19)
h
Hence, in this representation, the stress and strain properties can be evaluated using
(
6.14
)-(
6.19
), leading to the stress-strain curves depicted in Fig.
6.10
. The strain is
increased in steps of 10 % from 10 to 100 %. Starting from level 24, one can then
calculate the stress-strain curve at the input of each level. This then will give rheo-
logical information in the context that all parenchymal levels are interconnected.
As expected, the stress increases with the degree of elongation applied to the en-
tire structure. The more levels we have in our structure, the higher the values of the
stress-strain curve, due to higher amount of cartilage tissue (collagen). The latter
observation has been illustrated in Fig.
6.8
. The obtained results are qualitatively
similar to those reported in literature [
18
,
96
,
143
]. Quantitatively, it is not possi-
ble to make an evaluation of our model, since the values reported hitherto in the
literature are based on excised tissue strips.
