Biomedical Engineering Reference
In-Depth Information
Table 5.7 In vivo Prony series parameters for human gluteal skin/fat and muscle tissue of a
35 year old male subject in conjunction with long-term parameters provided in Table
5.5
for the
male volunteer (35 years, 82 kg, 182 m)
i
g
i
(-)
k
i
(-)
s
i
(s)
Skin/Fat
1
8.40641E-001
6.29429E-002,
9.47773E-003
2
4.08043E-002
3.84088E-001
8.78817E-002
3
9.17867E-003
1.73360E-003
4.11343E-001
4
1.01018E-002
2.38561E-001
8.04298E-001
5
4.52944E-005
1.15129E-003
9.88915E+001
Passive muscle
1
8.99379E-001
7.34513E-002
1.53840E-002
2
-6.96537E-002
4.00930E-001
6.74479E-001
3
4.51427E-003
-1.45672E-003
1.40283E+000
4
1.12330E-002
4.27225E-001
4.18451E+001
5
8.38142E-005
1.12759E-003
6.71585E+002
on the indenter axis, were selected. For each point an individual displacement-
time relation was established, which then together served as boundary conditions
in the parameter optimization process.
Parameter optimization was performed employing an exact analysis solver
method using A
BAQUS
(S
IMULA
,D
ASSAULT
S
YSTÈMES
S
IMULIA
C
ORP
., Providence,
RI, USA) to provide the particular model functions. The parameter fits on the
separated skin/fat and muscle data showed sufficient agreement, Fig.
5.31
, and in
Table
5.7
the derived parameters are shown.
Considering (3.273) and (3.330) and l
0
G
0
and using (3.336)
3
, derivation of
in vivo instantaneous shear moduli based on the long-term values provided in
Table
5.5
(male volunteer: 35 years, 82 kg, 182 m) and Prony series parameters
provided in Table
5.7
leads to G
0
;
S
=
F
¼
11
:
9 kPa for gluteal skin/fat and G
0
;
M
¼
6
:
6 kPa for passive muscle tissue (where the latter values depend on the employed
compressive strain rate and the ambient temperature).
5.2.5.2 Relaxation-Behaviour
Modelling Assumptions: As described previously, a basic assumption regarding
tissue indentation following the principle of force equilibrium, was that the
indenter force is transmitted through both tissue layers (mainly gluteal fat and
muscle) to be captured at the pelvic bone, which acts as a counter bearing. This
assumption allowed establishment of individual force-displacement characteristics
for both tissue types in the elastic long-term tissue characterization process.
Similarly, the same assumption entails one identical force-time relation for fat and
muscle tissue used as a target function to be fitted in the material parameter
estimation process in the viscoelastic tissue material characterization process
