Biomedical Engineering Reference
In-Depth Information
between the acquired prone and supine scans, the anterior rib surface of the prone
model was aligned to digitised anterior rib data of the reference supine MRI scan
using a non-linear least-squares closest point to surface fit [
14
].
4
Identification of Subject-Specific Mechanical Properties
In order to assess the importance of modelling the muscle, the subject-specific
mechanical properties were identified for the volunteer considered in this study.
The non-linear optimisation algorithm used to identify these parameters was the
fmincon
function in the Matlab
1
Optimisation toolbox. For the purposes of this
study, the fat and fibroglandular tissues within the breast were treated as a single
combined compartment separate to the pectoral muscle. A two parameter
optimisation framework was developed to identify the neo-Hooekan parameters
of the two compartments, namely
c
muscle
for muscle and
c
breast-tissue
for the
remaining breast tissues (fibroglandular tissue was assumed to have the same
density as fat). The results from these simulations were compared with those
based on a homogeneous representation of the breast tissues (where fat,
fibroglandular and muscle tissue were all assumed to have the same mechanical
properties, namely
c
homog
). The objective function
, was constructed by combin-
ing information digitised from reference supine MRI as described below.
In order to facilitate the identification of the
c
muscle
parameter, the muscle's
surface was segmented from the prone MRI. These segmented data were embedded
into the prone FE model and tracked to the supine position using the modelling
procedure outlined in Fig.
3
. A closest point-to-point search was then used to define
the mean squared error (
F
F
muscle
) using a kd-tree algorithm, between the model
tracked muscle data and the supine muscle reference data (obtained from
segmenting the reference supine MRI). In order to facilitate the identification of
the
c
breast-tissue
parameter, the mean squared error, from the closest point-to-surface
projection between digitised skin data of the reference supine MRI and the surface of
the model (
F
skin
), was also determined [
14
]. The displacement error between the
predicted supine nipple location and the reference nipple location (
F
nipple
) was also
included in the objective function. The sum of these individual mean squared error
objective functions was used to define a combined objective function used in the
optimisation procedure (
F
nipple
).
The optimisation procedure was implemented in Matlab and the objective
function was evaluated by solving an FE model from the prone to supine positions
as summarised in Fig.
3
using the CMISS
2
biological modelling package. To aid
interpretation of
F
ΒΌ
F
muscle
+
F
skin
+
the results,
the RMSE of each of
the objective function
constituents were used to assess the quality of fit.
1
Matlab Version 2010a, The MathWorks, Inc., USA:
www.mathworks.com
.
2
CMISS Version 2.1, Auckland Bioengineering Institute, New Zealand:
www.cmiss.org
.
