Biomedical Engineering Reference
In-Depth Information
expansion in the constitutive Eq. (3.272) fit the experimental data with sufficient
accuracy. Restrictions regarding material stability (polyconvexity, D
RUCKERS
'
criterion etc.) were additionally included in the optimization procedure and are
The results of the parameter identification for the skin/fat model (Fig.
5.24
a)
and the muscle-bone model (Fig.
5.24
b) compared with the evaluated force-dis-
placement data show correlation factors of R
2
= 0.957 (skin/fat) and R
2
= 0.998
(muscle). The steep ascent of the experimental skin/fat data at high compression
could not be captured precisely, even after running several optimization runs with
different start parameter sets. An agreeable verification was achieved, Fig.
5.24
c
by combining both parameter sets into the fat-muscle compound model and
simulating the exact experimental scenario of tissue indentation.
In Table
5.3
the long-term parameter values for human gluteal skin/fat and
muscle tissues from a 35 year old male subject and, additionally from a 42 year
old female subject are shown (Table
5.4
). The parameter values for skin/fat and
muscle tissue exhibited stable material behaviour within the maximum nominal
strain range reached when simulating the maximum indenter displacement. Further
tissue parameter sets are supplied at the end of this subsection.
The long-term shear moduli for human gluteal skin/fat and muscle tissue can be
calculated from the optimized parameters. For the male volunteer, using (3.273)
1
and (3.273)
2
these moduli read for skin/fat G
1;
S
=
F
¼
l
1
;
S
=
F
þ
l
2
;
S
=
F
¼
1182 Pa
and for muscle G
1;
M
¼
l
1
;
M
þ
l
2
;
NM
¼
1025 Pa
:
The equivalent parameters for
the female volunteer can be derived accordingly.
Compared to the derived long-term value for human gluteal muscle tissue,
(Gefen et al. 2005) has reported that values for G
1
for transversally loaded rat
muscle tissue lay in the range of 538 ± 193 Pa. These authors deduced that long-
term transverse shear moduli of human skeletal muscle should be in the order of
250-1,200 Pa. This deduction relied on ex vivo tensile tests of fresh human muscle
fibers extracted during surgical treatment and in vivo elastography of human
muscle. Both tests provided short-term shear moduli which are, according to
(Bosboom et al. 2001), who employed rat tibialis anterior muscles, 1.6-2.0 times
the long-term shear moduli. (Palevski et al. 2006) found long-term shear modulus
values in the range of 700 ± 300 Pa, by performing transversal ex vivo indenta-
tion testing on porcine gluteal muscle. Similarly to Bosboom et al., Palevski et al.
have stated that for porcine gluteal muscle the instantaneous shear modulus is 7-14
times its long-term counterpart. (Van Loocke et al. 2008) reported values for
skeletal muscle long-term properties in the transverse direction of 523 Pa. Derived
material parameters for fully relaxed human gluteal muscle compare well with
long-term shear modulus data of gluteal porcine muscle and estimations for human
skeletal muscle. Comparable values for long-term shear moduli representing in
vivo human gluteal skin and fat could not be found in the literature.
Furthermore, the corresponding long-term elastic moduli for human gluteal
skin/fat and muscle soft tissue can be derived using the calculated long-term shear
moduli as well as the relation E
1
¼
2
ð
1
þ
m
Þ
G
1
for gluteal skin/fat to E
1;
S
=
F
¼
