Biomedical Engineering Reference
In-Depth Information
or microstructure. These materials include living bones, living wood, and
certain saturated porous geological materials. The ability of a bone to adapt
to mechanical loads is brought about by continuous bone resorption and bone
formation. If these processes occur at different locations, the morphology of
the bone is altered. This process was defined as “modeling” by Frost [12]. In
a homeostatic equilibrium, resorption and formation are balanced. In that
case, old bone is continuously replaced by a new tissue. This ensures that the
mechanical integrity of the bone is maintained without any global change in
morphology. Frost defined this as “remodeling” [13].
To model these processes mathematically, Cowin and Hegedus [14],
Hegedus and Cowin [15], and Cowin and Nachlinger [16] developed a the-
ory of adaptive elasticity for modeling these complex stress or strain adap-
tation processes with a simple continuum model. The theoretical model is
composed of a porous anisotropic linear elastic solid perfused with and
surrounded by a fluid. The chemical reactions of the stress (or strain) adap-
tation process are modeled by the transfer of mass from the fluid to the
porous solid matrix, and vice versa. As a result of the chemical reactions,
mass is transferred to (from) the solid matrix so that it increases (decreases)
either the overall size of the body or the mass density of the body. The rate
of change of the overall size and shape of the body is controlled by the sur-
face strain, and the rate of change of mass density at a point is controlled by
the local matrix strain. Details of this adaptive model are described in the
following subsections.
2.2.1 Two Kinds of Bone Remodeling
Remodeling is fundamental to bone biology. It is a two-stage process car-
ried out by teams of BMUs. Resorption of a packet of bones by osteoclasts is
followed by refilling of the resorption cavity by osteoblasts. This sequence
typically requires 3-4 months to complete at each locus, and the resorption
and refilling cavities, while individually small, may collectively add sub-
stantial temporary porosity or “remodeling space” to the bone. If the pur-
pose of elevated remodeling is to remove bone mass, the remodeling space
is inconsequential, but if the goal is damage removal or tissue rearrange-
ment, the porosity involved in remodeling can weaken the bone structure.
It is therefore essential that remodeling be understood not simply as a funda-
mental biological process, but also in the context of the load-bearing function
of bone.
Generally, there are two major theories of bone remodeling: internal and
surface [17]. The distinction between them is as follows. Internal remodel-
ing refers to the resorption or reinforcement of the bone tissue internally by
changing the bulk density of the tissue. In a cortical bone, internal remodel-
ing occurs via changes in the diameter of the lamina of the osteons and by
the total replacement of osteons. Surface (external) remodeling refers to the
resorption or deposition of bone material on the external surface of the bone.
