Biomedical Engineering Reference
In-Depth Information
Fig. 5.31 Fit of the experimental data of human gluteal skin/fat tissue and muscle tissue:
a 0-270 s and b detailed: 0-5 s
ðÞþ
s
0
ðÞ
Z
t
X
N
K
t
0
s
K
k
i
s
i
s
ðÞ¼
s
H
ðÞþ
s
D
ðÞ¼
s
0
i
s
0
t
t
0
Þ
dt
0
ð
e
i
¼
1
t
0
¼
0
2
3
Z
t
X
N
G
t
0
s
i
F
1
t
g
i
s
i
ð
4
Þ
4
t
t
0
Þ
s
0
t
t
0
Þ
F
T
t
t
t
0
Þ
dt
0
5
e
ð
ð
ð
i
¼
1
t
0
¼
0
5.2.5.1 Creep-Behaviour
Using the creep data derived in
Sect. 5.2.4.1
, the viscoelasticity parameters, as
apparent in (3.334) (i.e. relative moduli k
i
and g
i
as well as relaxation times s
i
and
s
i
), can be established in conjunction with the Ogden model. Long-term Ogden
material parameters of fat and muscle tissue of the human gluteal region can be
identified by employing the K
IRCHHOFF
stress tensor (3.272) for equilibrium elas-
ticity and steady state elasticity (
Sect. 5.2.3.2
). The volumetric and deviatoric parts
s
H
ðÞ
and s
D
ðÞ
of the K
IRCHHOFF
stress tensor (3.334) were used in accordance
with (3.336) and (3.337). Hereby, the identification of the Prony series coefficients
k
i
;
g
i
;
s
i
and s
i
was done employing the optimization algorithm as described in
Sect. 3.4
. Since cine-MRI provided image data in the indenter axis plane only,
information of the deformed 3D fat/muscle interface surface did not exist.
To compensate, an attempt was made to sufficiently capture in-plane deformation.
Hence, two additional material points in the fat/muscle interface, besides the one
