Biomedical Engineering Reference
In-Depth Information
Table 1 Optimum time constants and coefficients of exponential fits to hold-relaxation stress
history data for the Adaptive QLV model
e
s
0
= ? (Pa)
s
1
= 5.5 s (Pa)
s
2
= 66 s (Pa)
s
3
= 699 s (Pa)
0.0667
r
o
= 0.8
c
1
= 0.2
c
2
= 0.4
c
3
= 0.6
0.1333
r
o
= 6.0
c
1
= 1.6
c
2
= 2.8
c
3
= 4.1
0.2000
r
o
= 18.3
c
1
= 6.6
c
2
= 8.4
c
3
= 10.7
0.2667
r
o
= 36.9
c
1
= 23.2
c
2
= 20.7
c
3
= 23.2
Table 2 Fitted values of k
i
for the Adaptive QLV model at the final strains of incremental ramp-
and-hold tests
e
s
1
= 5.5 s (Pa)
s
2
= 66 s (Pa)
s
3
= 699 s (Pa)
0.0667
k
1
= 12
k
2
= 7
k
3
= 9
0.1333
k
1
= 91
k
2
= 49
k
3
= 62
0.2000
k
1
= 371
k
2
= 146
k
3
= 163
0.2667
k
1
= 1300
k
2
= 361
k
3
= 354
4.2.2 Generalized Fung QLV Model
As with the Adaptive QLV model, fitting of the Generalized Fung QLV model
began with function r
o
. This, again, has values of 1, 6, 19 and 38 Pa at strains of
0.0667, 0.1333, 0.2000 and 0.2667, respectively. Calibration of the values of the
functions A
1
(e), A
2
(e), and A
3
(e) at each strain level required calculation of the
model predictions of the hold stresses. Substituting the strain and shape functions
from Eqs. (
53
) and (
51
) into Eq. (
49
), the hold relaxation stress in Generalized
Fung model is:
r
Hn
ð
t
Þ¼
r
o
0
:
0667n
ð
Þ
e
t
ð =
s
i
ds
Z
T
X
3
ð
58
Þ
þ
0
:
0667
20
0
:
0667
ð
n
1
Þþ
0
:
0667
20
A
i
s
i
¼
1
0
To simplify the calibration we assumed a piecewise linear approximation of the
unknown A
i
(e) functions as given in Eq. (
50
). For piecewise linear A
i
(e) functions
the hold stress can be rewritten as:
r
Hn
ð
t
Þ¼
r
o
0
:
0667n
ð
Þ
e
t
ð =
s
i
ds
Z
T
X
3
ð
59
Þ
þ
0
:
0667
20
Þ þ
m
ni
0
:
0667
20
A
i
0
:
0667
ð
n
1
Þ
ð
s
i
¼
1
0
or, equivalently, as:
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