Biomedical Engineering Reference
In-Depth Information
Table 2 Values of age-dependent model parameters for aortic media employed in numerical
applications and relevant references (when available) for physiological ranges
Age
(years)
kk
cl
ð
pN
=
nm
Þ
H
o
=
L
o
ð
-
Þ
r
F
=
L
o
ð
-
Þ
V
f
=ð
1
V
o
Þ
ð
%
Þ
V
o
(%)
E
e
ð
kPa
Þ
h
e
ð
lm
Þ
h
a
(mm)
r
i
j
p
¼
0
ð
mm
Þ
20-24
5
0.425
0.065
15
10
30
1.4
0.588
5.6
36-42
10
0.295
0.032
20
30
80
1.5
0.630
6.2
71-78
15
0.225
0.022
25
50
120
1.65
0.693
7.4
Ref.
[
36
]
[
36
]
[
66
]
[
66
]
35
]
[
35
]
[
35
]
34
]
Experience-based age-dependent aortic features are reported in the following,
together
with
the
corresponding
evolution
trends
for
the
physically-based
parameters introduced in the present model:
• Unloaded aortic radius [
34
,
65
] and media thickness [
65
] increase with age.
Physiological ranges are about 5
:
5-8
:
65 mm and 0
:
44-0
:
76 mm, respectively.
Accordingly, r
i
j
p
¼
0
and h
a
increase with age.
• Elastin stiffness increases in men, due to increasing glycation with age [
35
], in
the range 30-280 kPa. Thereby, E
e
increases with age.
• The stiffness of collagenous constituents at high pressure (when the collagen
fibers are straightened) increases with age [
35
], indicating a higher stiffness of
the collagen fibrils, that is E
f
. Since the genetic pattern of healthy people is
practically constant in time, it is unlikely to believe that this stiffening behavior
is related to variations in the nanoscale structure of collagen molecules.
Thereby, variations in E
f
are associated with the alteration of cross-link stiffness
and/or occurrence, that is with the variation of kk
cl
, which increases with age.
This is fully in agreement with the experimental results from [
57
].
• With increasing age, collagen-induced stiffening effects occur at lower pressure
levels during the cardiac cycle [
35
]. In agreement with present microscale results
(see Fig.
10
), this evidence can be associated with a reduced aspect ratio H
o
=
L
o
of
the collagen fibers, which then results to be inversely proportional to age.
• The stiffness of collagenous constituents at very low physiological pressure
decreases with age [
65
]. As shown in Fig.
10
, a reduction in stiffness of
collagenous constituents at small strains can be associated with either more
crimped or thinner fibers. In agreement with the previous evidences, the occur-
rence of fibers more crimped has been excluded, associating the present finding to a
reduced value of the collagen fiber radius. Thereby, ratio r
F
=
L
o
decreases with age.
• Dry weight of the aortic wall decreases with age (about four or five times, [
66
])
despite of the increase of the aortic thickness [
65
]. Therefore, aortic water
content (non-solid matter) increases with age, leading to the decrease of the
absolute amount of elastin and collagen. On the other hand, the increase (about
three times) of the relative amount of collagen with respect to the non-collag-
enous solid matter has been reported [
66
]. Accordingly, V
o
increases with age,
as well as also V
f
=ð
1
V
o
Þ
.
In agreement with previous considerations, parameters employed in proposed
numerical applications are chosen as summarized in Table
2
.
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