Biomedical Engineering Reference
In-Depth Information
Fig. 1
Left
: skin data segmented from prone MRI were fitted to a prone FE model.
Right
:
segmented muscle (
red/dark grey
), fibroglandular (
yellow/light grey
) and fat tissues (
transparent
)
3 Modelling Mechanics of the Breast
Finite elasticity theory [
8
] was used to model the large deformations of the
volunteer's breast from the prone to supine position (45.3 mm nipple displacement).
FEM [
9
,
10
] was used to numerically solve the equations governing tissue biome-
chanics. The mechanical response of the breast tissues was modelled using an ideally
incompressible hyperelastic neo-Hookean constitutive relation. This relation
contains a single stiffness parameter
c
. The strain energy density function is defined
as
W
3)
, where
I
1
is the first invariant of the right Cauchy-Green deforma-
tion tensor. The different breast tissues can each be described with a different
stiffness parameter, namely
c
fat
,
c
fibro
, and
c
muscle
, for fat, fibroglandular and muscle
tissue, respectively. These parameters were incorporated into the geometric model
by applying a weighted combination of them to each of the FE Gauss quadrature
points. This was achieved using a kd-tree algorithm, which paired each segmented
tissue point with its geometrically closest Gauss point, thereby allowing the
weighted contribution of each of the three tissues to be determined at each Gauss
point. The result of the allocation of muscle tissue to the breast model's Gauss points
is shown in Fig.
2
. Densities of 928 Kg/m
3
, 1,035 Kg/m
3
[
11
], and 1,060 Kg/m
3
[
12
]
were used for fat, fibroglandular and muscle tissue, respectively, and were weighted
at each Gauss point in a similar manner to the constitutive parameters.
For the homogeneous breast simulations a density of 1,000 Kg/m
3
was used and
a homogenous stiffness,
c
homog
, determined. Displacement converged models with
3,084 degrees of freedom were used in the simulation, with four Gauss points along
each element coordinate.
c(I
1
ΒΌ
