Biomedical Engineering Reference
In-Depth Information
3
Multiield I
internal Bone Remodeling
3.1 Introduction
In the previous two chapters some fundamental concepts and basic
formulations for bone remodeling processes have been presented. We now
present applications of these formulations to multifield internal bone remod-
eling of inhomogeneous long cylindrical bone. Bone remodeling processes
are the mechanisms by which bone adapts its histological structure to
changes in long-term loading. As explained in Chapter 2, there are two kinds
of bone remodeling: internal and surface [1]. This chapter describes multi-
field internal bone remodeling; then, Chapter 4 gives the theory and solution
of multifield surface bone remodeling.
The capacity of bone remodeling has been investigated by many authors
[2-14]. Active research in the area of bone tissue such as living bone and
collagen has also shown these materials to be piezoelectric [15,16], and the
piezoelectric properties of bone play an important role in the development
and growth of remodeling of skeletons. Applications of piezoelectric theory to
bone remodeling have been the subject of fruitful scientific attention by many
distinguished researchers (e.g., references 17-19 and others). In particular,
Gjelsvik [20] presented a physical description of the remodeling of bone tissue
in terms of a very simplified form of linear theory of piezoelectricity. Williams
and Breger [21] explored the applicability of stress gradient theory for explain-
ing the experimental data for a cantilever bone beam subjected to constant end
load, showing that the approximate gradient theory was in good agreement
with the experimental data. Guzelsu [22] presented a piezoelectric model for
analyzing a cantilever dry bone beam subjected to a vertical end load.
Johnson, Williams, and Gross [23] further addressed the problem of a dry
bone beam by presenting some theoretical expressions for the piezoelectric
response to cantilever bending of the beam. Demiray [24] provided a theoreti-
cal description of electromechanical remodeling models of bones. Aschero
et al. [25] investigated the converse piezoelectric effect of fresh bone using a
highly sensitive dilatometer. They further investigated the piezoelectric prop-
erties of bone and presented a set of repeated measurements of coefficient
d
23
in 25 cow bone samples [26]. Fotiadis, Foutsitzi, and Massalas [27] studied
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