Biomedical Engineering Reference
In-Depth Information
Table 5.8 Established material parameters w.r.t. (3.300) representing long-term gluteal skin/fat
tissue and passive muscle tissue behaviour with loading direction transversal to muscle fibre
orientation
D(M -1 Pa -1 )
c 1 (MPa)
k 1 (MPa)
k 2 (-)
k(-)
Skin/Fat
9.27942E-004
2.78050E+000
6.56340E-009
1.50920E+002
1/3
Passive muscle
4.40712E-004
2.58623E+001
1.30769E-002
4.68772E+001
1/3
which is based on relaxation testing. Gluteal fat and muscle tissue geometries are,
however, different. These tissue geometries used in the finite element modelling
process were MR-recorded after the ramp phases of indentation deformation and at
times of constant indenter position (cf. Sect. 5.2.4.2 ). In addition to the previous
assumption, potential transient displacement of material points of the fat-muscle
interface boundary were assumed to be negligible during the relaxation process
after the ramp. Cine MR-scanning of the interface region during relaxation
revealed no noticeable position change at given spatial and transient MR-image
resolution (pixel dimension: 1.5 9 1.5 mm; Dt = 0.675 s).
Identification of Long-Term Parameters: The H OLZAPFEL -G ASSER -O GDEN
model was used for long-term elastic tissue property evaluation (according to
guidelines given in Sect. 5.2.3.2 ) for an actualized FE-model of the anatomical
structure of the gluteal region (cf. beginning of Sect. 5.2.5 ). Assuming slight
compressibility as well as isotropy the H OLZAPFEL -G ASSER -O GDEN -form (3.300) reads
ð 4 Þ B :
I þ 2 c 1 þ k 1
9
s ¼ 1
D
Þ e k 9
B I 3
Þ 2
B I 3
J 2 1
ð
ð
In the long-term elastic material parameter optimization process, material sta-
bility was ensured by making use of the B AKER -E RICKSEN inequalities (cf. Sect. 3.4
), and the material model from (Balzani et al. 2006)
Slight tissue compressibility was assumed, and P OISSON 's ratio was thus
restricted to the range 0 : 495 m 0 : 499 in the optimization process. Established
long-term elastic tissue material parameters are provided in Table 5.8 .
Identification of the P RONY Series Parameters: To describe the viscoelastic
(time-dependent) behaviour of gluteal adipose and passive transversally loaded
muscle tissue the H OLZAPFEL -G ASSER -O GDEN -model, in the form (3.342) as well as
in the form (3.345) was used.
A FE-model was generated based on the anatomy of the MR-scanned inden-
tation region (cf. Fig. 5.29 ) at the initially undeformed state to achieve a Prony
series parameter optimization. From this (compound) model, two separate models,
i.e. one model containing the fat anatomy and a second model containing the
muscle and bone anatomy, similar to the models presented in Figs. 5.21 and 5.22 ,
were created. Second-order tetrahedral continuum elements with an average edge
length of 3 mm were used for tissue representation. Both models were equipped
with the corresponding displacement boundary conditions obtained from the MR-
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