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

6. THE DETERMINISTIC STRESS ANALYSIS
The validation of the model needs to be done by comparing the stress results from the
deterministic stress analysis with that in the literature since there is not any study in the
literature, to our knowledge, regarding the probabilistic analysis of the knee implant in
which the material properties and loads applied were considered as random variables.
Therefore, a static structural analysis was carried out, and the results have been
compared with the previous studies.
As seen from Fig. 7, the contact area on the UHMWPE is larger compared to that in the
literature, thus the contact stress is less than given in the similar studies. However, the
stress patterns given in Fig. 7 are similar, which can be yielded that the model
developed in this study is valid.
7. THE PROBABILISTIC ANALYSIS
The inherent variability in both material properties and loading affect the performance
of the knee implant. Therefore, the design variables having variations are considered as
random variables. Their statistical properties are determined using statistical methods
based on the experiments. For femur and tibia cortical, the statistical values obtained
from the literature, which are assumed to be lognormal distributed with GPa
and GPa. For trabecular bone, HU values from the CT images were grouped in
30. Then, the Lognormal distribution and statistical values for the rabecular bones of
both the femur and tibia were obtained using MATLAB (Mathworks Inc., Natrick,
USA) statistical toolbox as given in Fig. 8, which results in MPa and
MPa for the femur trabecular bone, and MPa and MPa for the tibia
trabecular bone.
Probabilistic analyses, which utilize simulation methods such as the Monte Carlo or
Importance Sampling, take considerable time. Therefore, some limitations such as
reducing the random variables affecting the model or simplifying the FE models are
common practices in such analyses.
(a) (b)
Figure 8. Distribution of Young’s Modulus of the femur trabecular (a) and tibia
trabecular (b).
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