Biomedical Engineering Reference
In-Depth Information
2
Basic Bone
Remodeling Theory
2.1 Introduction
Living bone is a remarkable and extremely adaptable substance in the
human body. It continuously undergoes processes of growth, reinforcement,
and resorption. These processes are collectively termed
remodeling.
The
concept of stress- or strain-induced bone remodeling was first proposed by
the German anatomist Julius Wolff [1]. In 1892, Wolff found that the orienta-
tion of trabecular bone coincides with the direction of the stress trajecto-
ries. He proposed that bone loading is somehow sensed and that the bone
adapts its structure accordingly. This principle of functional adaptation is
often known as Wolff's law. It occurs in conditions of disuse, such as during
immobility, space flight, and long-term bed rest, when bone is lost [2,3], and
in overloading, which causes a gain in bone mass [4].
Wolff's law was first described in vitro in 1939 by Glucksmann [5]. Bassett
and Becker [6], Shamos, Shamos, and Lavine [7], Justus [8], Cowin [9], and
Qin and Ye [10] have proposed various mechanisms for bone remodeling in
terms of certain thermal, mechanical, electrical, and chemical properties of
bone. In this chapter, we begin with a brief description of adaptive elastic
theory [9], followed by a discussion of two typical types of bone remodeling:
internal and surface remodeling. A simple theory and its solution related to
these two kinds of bone remodeling are presented.
2.2 Adaptive Elastic Theory
An adaptive elastic theory developed by Cowin [9,11] for analyzing the
adaptive behavior of living bone under thermal and mechanical loading is
briefly reviewed in this section.
As indicated in Cowin [9], certain natural living materials can adjust to
their ambient environmentally applied thermal, mechanical, and electrical
loads by slowly changing their overall shape and their local mass density
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