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

living [13, 14].
Table 1. Load weight factors for the motions of abduction and anterior flexion.
10º 30º 50º 70º 90º 110º
Abduction 0.145735 0.069027 0.064054 0.031480 0.006265 0.001621
Anterior flexion 0.312289 0.147916 0.137258 0.067456 0.013425 0.003474
Starting from a uniform density distribution of 0.4, several values for the parameters κ
and m are tested to reproduce the bone density of the scapula, which is taken from the
CT scan images by relating the intensity of the image pixels with the bone apparent
density [15]. The predictions from the bone remodeling model are evaluated by
qualitative and quantitative comparisons. For the latter, the Pearson’s correlation
coefficient r and the root-mean-square error (rms), based on a relative and an absolute
difference, denoted as r
and a
, respectively, are computed. Mathematically, r
and a
are expressed as
%
i
r
i i
BR CT
i
CT
i i
BR
CT
i
g
a
cc
(2)
i
i
where BR and CT is the bone apparent density taken from the bone remodeling
simulation and the CT scan images for node i, respectively.
4. RESULTS
4
4
Bone remodeling simulations are performed considering values of 1
10 , 2 10 ,
4
4
4
4
4
4
4
3
3
3
10 , 4 10 , 5
10 , 6 10 , 7 10 , 8 10 , 9 10 , 1
10 , 1.
2 10 and
3
1.
4 10 for the parameter κ and 1, 2, 3, 4, 5, 6, 7 and 8 for the parameter m. Given that
the rms of the absolute and relative differences point towards different best solutions, an
average error is considered instead by taking into account both criteria. It is important to
note that the rms of each criterion is normalized by its maximum so that the contribution
to the average error is dimensionless and, at most, unitary. Figures 2a and 2b present the
average errors and the Pearson’s coefficients for the performed simulations,
respectively. The results present the solutions with parameter m of 4 and 5 as the most
suitable. Furthermore, if the mean bone density of the whole scapula and its standard
4
deviation is analyzed, the solution with parameter κ of 4 10 appears to stand out as it
compares well with the actual mean bone density and standard deviation. In particular,
the analyzed scapula presents a mean bone density and standard deviation of 1.01 and
0.39 g/cc, while this solution presents 1.01 and 0.33 g/cc, respectively. Also, regarding
the absolute difference, the rms is only 0.379 g/cc and almost 70% and 90% of the
nodes present an absolute error lower than 0.4 and 0.6 g/cc, respectively. Based on the
4
above reasoning, the solution with parameter κ of 4 10 and parameter m of 5 appears
to be the most suitable to reproduce the bone density distribution of the specimen’s
scapula. The visual comparison between the predicted bone densities and the CT scan
images show, in general, a rather good similarity.
5. DISCUSSION
Finite element analysis can provide an important insight into the long-term effects of the
glenoid prostheses on the bone adaptation process and thus enable a continuous