Biomedical Engineering Reference
In-Depth Information
new tissue, thus increasing the rate at which fracture heals [35, 36]. In contrast,
excessive interfragmentary movement delays the healing process and may result in
nonunion of bone fragments causing, in some cases, pseudoarthrosis [37]. Another
important mechanical factor is the type of load to which the fracture site is subjected
(shear [38, 39], torsion [40], compresion, or tension [41]) which results in different
fracture healing outcomes.
4.3
Phenomenological Models of Bone Remodeling
For many years, many theoretical models have been proposed to explain how the
mechanical environment influences bone remodeling, the ''Wolff's law'' being the
most well-known [42]. In fact, Wolff proposed that there is a dependence between
bone structure and the load that it supports. However, he did not provide any idea
about the possible processes responsible of this effect. It was Roux in 1881 who
proposed that ''bone adapted itself in order to support stresses in an optimal way
with minimum mass'' [43]. Both theories in combination with the development
of computational tools and a huge battery of experimental results have motivated
the current tremendous development of computational remodeling models. These
models may be classified into two main categories depending on the assumptions
on which they are based: phenomenological and mechanistic.
Phenomenological models are able to predict bone remodeling through direct
relationships between mechanical stimulus and bone response, following known
experimental and clinical evidences, but no actual cell processes are considered. At
the same time, we can classify this kinds of models into three types:
•
Models based on global optimality criteria, in which different mechanical criteria
are proposed to be optimal [22, 23, 44].
•
Models based on achieving a homeostatic value for a certain mechanical stimulus.
These models admit the existence of a certain mechanical stimulus that produces
bone apposition or resorption such that, by this process, the stimulus tends to a
certain uniform physiological level (homeostasis) in the whole tissue [45-50].
•
Models based on damage repair, based on the assumption that bone tries to
optimize its strength and stiffness regulating the local damage generated by
fatigue or creep [16, 17].
These mathematical models are particularly useful to predict the adaptative bone
changes regulated by mechanical factors to improve implant design or treat some
patients, as it is shown in Section 4.5.
4.4
Mechanistic Models of Bone Remodeling
Mechanistic models are more complex since they try to characterize, understand,
and unravel the role of the mechanical environment in the biological mechanisms
involved in bone remodeling. These models are interested not only in the prediction
