ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

information. Based on the indentation data together with the corresponding tissue
displacement, individual force-displacement characteristics were established for both
tissue types. The test scenario was modelled based on MR images of the undeformed
gluteal anatomy. Based on the long-term elastic material properties, material parameter
identification was performed. In the optimization process, the employed finite element
models were equipped with specific boundary and transitional conditions as outlined in
Then et al. (2007). Individual adipose and muscle tissue material parameters were thus
established, describing the long-term elastic material behaviour subject to respective
loading conditions.
To evaluate the transient tissue material behaviour, displacement-controlled ramp-andhold
indentation testing at the buttocks was performed. Specifically, tissue indentation
with ramp displacements of 10-, 20-, 30-, 40-mm at a constant ramp speed of
0.68mm / s (being equivalent to an (engineering) strain rate of 0.75% / s along the
indenter axis) followed by a hold phase of 180-s were performed and corresponding
tissue deformations after the ramp phases were MR scanned, Figure-1a. Indenter force
was recorded with a time resolution of 0.05-s, Figure-1b. Both, the recorded force-time
relation at 40 mm ramp displacement, together with the individually MR scanned
deformed tissue geometries after the ramps served as constraints in the Prony series
parameter optimization process.
(a) (b)
Figure-1 (a) Transversal MR-image of the indentation region showing gluteal adipose (white)
and skeletal muscle (dark) tissue deformation at a constant indenter displacement of 40 mm, (b)
experimental in vivo gluteal tissue compound force-relaxation curves at various ramp
displacements and corresponding simulation output
4. CONSTITUTIVE MODELLING
The Holzapfel-Gasser-Ogden strain-energy function (Holzapfel et al., 2000; Gasser et
al., 2006) was used to model tissue mechanical properties. With the isotropic
assumption κ = 1/
3 it is given by
T
-2/3
where C : F ⋅ F ≡ J C
2 2
( 1 )
( ) ( )
( )
3
k
k ⎡ I − ⎤
1 w C = c 9
1 C1I − 3 + ⎢e − 1⎥
+ f J
(1)
2k2
⎢⎣ ⎥⎦
f J is
= is the modified right CAUCHY strain tensor and ( )