Biomedical Engineering Reference
In-Depth Information
Fig. 8.6 a Histological image of white adipose tissue with adipose cells and extracellular matrix
(image adopted from
www.mhhe.com/biosci/ap/histology_mh/
)
, b superimposed finite element
mesh (only adipose cells for clarity)
degrees of freedom and/or higher gradients must be introduced. Another approach
is to separately model relevant tissue structures based on continuum mechanical
methods on the microscopic level. This approach was used for subcutaneous
adipose tissue employing histological section cut images of white adipocytes and
modelling the lipid-filled cell structures and the adjacent extracellular matrix (i.e. a
framework of collagen fibres) on a scaled level (total model size:
In Fig.
8.6
b the finite element modelled structures of Fig.
8.6
a are depicted
(extracellular matrix excluded for clarity). The meshed in-plane structures are
extruded to obtain a volume model, Fig.
8.7
a.
To obtain exclusively geometrical effects in the FE simulation, the nonlinear
contributions of the employed O
GDEN
model (3.272) were reduced by fitting the
material parameters (over a sufficient strain range) to linear-elastic stress-strain
curves, assumed for both adipose and extracellular matrix. The corresponding
Y
OUNG
'
S
modulus of the force-displacement curve used for extracellular matrix
parameter fitting was assumed to be much smaller than that of adipose cell
material, specifically: E
ct
= 0.01 kPa (extracellular matrix) and E
ac
= 3.52 kPa
(adipose cells) and geared to the initial value for adipose tissue established in
Sect.
5.2.3.2
. The employed linear elastic parameters rely on values previously estab-
lished,
the
ratio
between
matrix
material
and
lipid
cell
material,
however,
is assumed.
Images of simulated tissue compression at different stages of densification are
depicted in Fig.
8.8
.
Simulated compressive force and prescribed tissue displacement were recorded.
The force values strongly increase at higher compression at a stage where the
