Biomedical Engineering Reference
In-Depth Information
Table 1
Geometry, physiological data used for modelling the human abdominal aorta artery
Length
In vivo
L
120 mm
Reference configuration
L
1
L
=
k
z
Radii
At systole
r
s
5.7 mm
Reference configuration
R
r
s
=
k
s
Wall thickness
Total
H
R
=
5
Media
H
M
2H
=
3
Adventitia
H
A
H
=
3
Fibre orientation
Media
c
M
þ
;
c
M
þ
30
;
30
Adventitia
c
A
þ
;
c
A
þ
60
;
60
Applied pressure, kinematics
Systolic pressure
p
s
16 kPa
Diastolic pressure
p
d
10.67 kPa
Axial pre-stretch
k
z
1.3
Systolic circumferential stretch at t
¼
0
k
s
1.25
Diastolic circumferential stretch at t
¼
0
k
d
1.13
Attachment stretch
k
AT
1.07
Recruitment stretches (t
¼
0)
Media
k
M
þ
;
k
M
1.18
Adventitia
k
A
þ
;
k
A
1.20
2.1.3 Cyclic Deformations of Aneurysmal Tissue
To quantify the cyclic deformation we determine the geometry of the aneurysm at
systolic (p
¼
p
s
= 16 kPa) and diastolic pressures (p
¼
p
d
= 10.67 kPa) as it
evolves. Initially, the artery has a cylindrical configuration. It can be shown (see
[
15
]) that the governing force-balance equation for a cylindrical membrane subject
to fixed axial stretch k
z
and radial inflation is
(
!
p
¼
1
Rk
z
1
k
z
k
4
ð
h
M
k
M
þ
h
A
k
A
Þ
1
=
2h
J
k
J
A
C
E
J
p
exp
f
A
C
E
J
p
2
g
cos
2
c
J
p
k
J
p
2
X
þ
;
ð
5
Þ
;
J
¼
M
;
A;p
¼
:E
J
p
[ 0
where the first and second terms on the right of (
5
) correspond to the contribution of
load bearing from the elastinous and collagenous constituents, respectively. Equa-
tion (
5
) is derived from the governing variational equation, i.e. (
1
), the functional form
the of the SEFs (
2
) and considerations of the displacement field for a cylindrical
membrane. It can be solved numerically to obtain the radius as a function of the pressure.
At t
¼
0
;
the diastolic and systolic displacement fields to satsify (
1
) are known, i.e.
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