Biomedical Engineering Reference
In-Depth Information
The details of the process of deposition of new lamina on the surface of a
bone were described by Currey [18].
Surface remodeling can be induced in the leg bones of animals by super-
posing axial and/or bending loads. Woo et al. [19] showed that increased
physical activity in pigs can cause the periosteal surface of the leg bone to
move out and the endosteal surface to move in. Surface remodeling can
also be induced in the leg bones of animals by reducing the loads on the
limb. In two studies, Uhthoff and Jaworski [20] and Jaworski, Liskovakiar,
and Uhthoff [21] immobilized one of the forelimbs of beagles. In the study
of Uhthoff and Jaworski [20], young beagles were used and it was found
that the endosteal surface showed little movement, whereas there was much
resorption on the periosteal surface.
As mentioned in Cowin [11], the theories of both internal and surface
remodeling use a simple two-constituent model for bone tissues. The bone
matrix—that is, the solid extracellular material and the bone cells—is
modeled as a solid structure with interconnected pores, a porous solid. Since
bone is adaptively modeled as a linear anisotropic elastic solid, it is assumed
that the bone matrix can be modeled as a porous anisotropic linear elastic
solid. The extracellular fluid and blood are modeled as a single fluid. Thus,
the basic model of bone is a porous, anisotropic linear elastic solid perfused
with a fluid.
The chemical reactions that convert body fluids into solid porous bone
matrices and vice versa are mediated by the bone cells. Mass, momentum,
energy, and entropy are transferred to or from the solid porous bone matrix
as a result of the chemical reactions. The rates of these chemical reactions
depend on strain and are very slow. The distinction between the two theo-
ries lies in the locations at which the chemical reactions occur and the way in
which mass is added or removed from the solid porous bone matrix. In the
theory of surface remodeling, the chemical reactions occur on the external
surfaces only of the bone, and mass is added to or removed from the bone
by changing the external shape of the bone. During surface remodeling,
the interior of the bone remains at a constant bulk density. In the theory of
internal remodeling, the chemical reaction occurs everywhere in the solid
porous bone matrix, and mass is added by changing the bulk density of the
bone matrix without changing its exterior dimensions. In both cases, the rate
and direction of the chemical reaction at a point are determined by the strain
at that point.
Cowin [11] mentioned that the surface remodeling theory acknowledges
the observed fact that external changes in bone shape are induced by
changes in the loading environment of the bone. This theory postulates a
causal relationship between the rate of surface deposition or resorption and
the strain on the surface of the bone. Bone is considered an open system
with regard to mass transport, and the mass of the bone will vary as the
external shape of the bone varies. (The theory of external remodeling is dis-
cussed in detail in Section 2.3.) In contrast, the theory of internal remodeling
