Biomedical Engineering Reference
In-Depth Information
TABLE 7.2
Initial Values of the Model Variables
Symbol
Unit
Value
OBA(0)
pM
0.2126991130e-3
OBP(0)
pM
0.8986869185e-5
OCA(0)
pM
0.2769166993e-3
OST(0)
pM
0.1029189256e-2
A mechanical stimulus not only can increase bone mass but also can
improve bone strength by influencing collagen alignment as new bone is
being formed by osteoblasts during bone turnover. A cortical bone tissue
located in regions subject to predominantly tensile stresses has a higher per-
centage of collagen fibers aligned along the long axis of the bone [6]. In regions
of predominantly compressive stresses, collagen fibers are more likely to be
aligned transverse to the long axis [67]. Evidently, this arrangement func-
tionally improves bone tensile properties with more collagen fibers oriented
in the longitudinal direction [68], whereas bone compressive properties are
improved by transversely oriented collagens [69].
In an experiment by Robling et al. [12], cyclic mechanical loads were
applied axially along the ulna of adult rats for 16 weeks. The results indi-
cated that the pattern of bone formation caused by loading resembled the
stress distribution, with more bone formation where the stresses were high-
est. Robling et al. tested the mechanical properties and BMC of the sample
before and immediately after the experiment stopped. They compared and
analyzed the data (before and after the experiment) and found that the bone
structure had improved, with a 69% increase in the second moment of area.
Bone strength increased by 64% and the energy absorbed before fracture
(BFE), which is of greater practical interest to clinical practice, increased by
94% while the BMC improved by only 7%.
The results demonstrate that BMC is only one of the factors that contribute
to bone strength, and it is the BFE that can evaluate the effect of mechani-
cal bone remodeling comprehensively. Thus, the use of BMC to characterize
bone remodeling, as done in existing mathematical models [3,23], is not suit-
able to measure the effect of bone remodeling under mechanical stimulus.
BMC is therefore replaced by BFE in this model.
In references 3 and 23, the BFE is used as a more appropriate standard to
assess the significance of bone remodeling under mechanical stimulus. The
BFE can be measured through experimentation; here, using the cell popula-
tion dynamics model, it is proposed that the formulation for calculating BFE is
dBFE
dt
(
)
(
)
(
)
(
)
=⋅
K
BA tOBA t
−
−⋅
KOCAt
−
OCAt
for
0
res
0
( 7. 4 7 )
)
)
(
(
+⋅
K
BA tOCA t
+
to
