Biomedical Engineering Reference
In-Depth Information
the remodelling processes. Any material parameter actually contributing to the
local bone stiffness will be subjected to a specific remodelling process which tries
to adapt the effective stiffness behaviour at the particular site under consideration
according to the local stresses and strains. In this approach the essential material
parameters governing the elastic material behaviour of bone tissue are given by the
apparent density, q
app
. The structural anisotropy is described by the orthotropic
parameters and the orientation of the principal material axes, with respect to the
global coordinate system, are described by a rotational vector. Negative values of
the stimulus lead to bone reabsorption whereas positive ones give rise to local bone
hypertrophy. Bone hypertrophy in the case of internal remodelling is interpreted as
an increase in bone apparent density. Each remodelling stimulus has to exceed a
specific threshold level to cause any actual adaptive changes at all, which means
that bone material is assumed to show a 'lazy-zone' behaviour in the vicinity of its
homeostatic state.
Within Carter's model, the effects of the nonlinearity in the equation of bone
remodelling was also studied [
50
] and developed [
51
]. This nonlinear development
of Carter's model begins with the work of Huiskes [
39
,
52
], Weinans et al. [
53
] and
Mullender et al. [
54
]. The Carter model was widely applied with the FEM [
55
], with
diverse variations in order to obtain the most accurate density distribution [
56
,
57
].
An interesting approach was proposed by Chen et al. [
58
], in which it is presented
an alternative way to obtain the density, very useful for the case of meshless
methods. The density is iteratively obtained in the nodes, and not in the integration
points, reducing in this manner the computational time and also the accuracy of the
process. More recently the Carter's model was extended to the micro-finite element
method [
59
,
60
], with stunning results. The bone adaptation and the inner remod-
elling processes were studied and the results show a very high correlation with the
actual density of the human proximal femur. Another conclusion was that bone
surface abnormalities contribute insignificantly to the bone global structural
integrity and generally tend to disappear during the remodelling process.
6.3.4 Rodrigues' Model
Rodrigues and co-workers presented a model [
61
] considering a global-local
hierarchical approach in which a global model of an entire bone supplies strain and
density information to a series of local models characterizing the trabecular
microstructure at each global model location. The process of bone adaptation is
described for two levels of the bone structure: the macroscopic level, where the
bone apparent density is determined; and a microscopic level, characterizing the
trabecular structure. The law of bone remodelling is obtained assuming that bone
adapts to functional demands in order to satisfy a multicriteria for structural
stiffness and metabolic cost of bone formation [
62
]. More recently the model was
successfully extended to the three-dimensional analysis [
63
], being the distribution
