Biomedical Engineering Reference
In-Depth Information
interpolator (RPI) technique. The construction of the meshless shape functions is
explicitly presented and the most important properties are demonstrated.
The fifth chapter is dedicated to the two-dimensional and the three-dimensional
linear analysis. First, the RPIM and NNRPIM patch test are presented. From the
patch test results, the optimal values of the most important parameters of the RPI
shape functions are obtained, allowing to improve and stabilize the meshless
method. Afterwards, static and dynamic benchmark examples are solved with the
RPIM and the NNRPIM. The obtained results validated the meshless method and
prompted advances and improvements in the RPI formulation.
The mechanobiolgy analysis can be found in the sixth chapter, first the basic
concepts of the bone biology are introduced. Then, bone tissue phenomenological
laws are presented, which permit to correlate the bone tissue local apparent density
with the bone tissue local mechanical properties. The mathematical law proposed
by the author is presented in detail. This chapter ends with an extensive presen-
tation of the most relevant numerical approaches for the prediction of the bone
tissue remodelling. Additionally, the bone tissue remodelling algorithm used in
this topic is presented explicitly.
In the seventh chapter it is possible to find mechanobiologic applications, where
the proposed phenomenological bone tissue material law and the used remodelling
algorithm are applied. Two-dimensional and three-dimensional benchmark
examples are studied to validate the bone trabecular remodelling algorithm. The
maxillary central incisor, the calcaneus bone and the femoral bone are analysed. In
all bone examples, the obtained trabecular bone architecture is in very good
agreement with the real bone X-ray images. This chapter ends with bone tissue
remodelling studies in which the remodelling is triggered by the insertion of an
implant. The bone tissue remodelling analysis of the mandibular bone due to the
insertion of a dental implant is analysed. Trabecular distributions are obtained and
the osseointegration process is studied. A similar study is performed to study the
bone tissue remodelling of the femur bone when a stem is inserted in the femur
head along the diaphysis.
References
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