Biomedical Engineering Reference
In-Depth Information
131.6% increases of BFE for the 360 × 1 and 90 × 4 loading schemes, respec-
tively, after a 16 week loading (see the small circles and squares with words
“Present model” on the solid and dotted curves). This closely resembles the
measured changes in the experiment, in which the BFE increased by 94%
and 165%, respectively [12] (see the small circles and squares with words
“Experiment [12]”), in Figure 7.5.
Comparing the increases of BMC in Figure 7.5(a) and BFE in Figure 7.5(b),
the present study shows that these small gains in BMC (around 10%) impart
very large increases in BFE (72%-131%) because the new bone formation is
localized to the most mechanically needed sites. Consequently, it is pos-
sible to enhance fracture resistance significantly through mechanical load-
ing such as exercises, even though most exercise intervention studies yield
increases in BMC of only a few percent at most. There might be a significant
difference between pharmacologically induced bone formation and loading-
induced bone formation. For example, intermittent administration of PTH
adds new bone mainly to the endocortical and trabecular surfaces, which
makes relatively little contribution to resistance to bending [70]. Mechanical
loading, on the other hand, appears to be able not only to increase bone mass
but also, more importantly, to optimize the new bone formation spatially to
obtain maximal bone strength.
7.4 Parametric Study of the Control Mechanism
In this section, results in Wang and Qin [71] are presented and discussed. In
the analysis, perturbations are applied to the mechanical bone remodeling
system in a steady state, by down- and upregulating its six differentiation
and apoptosis rate parameters
DF
obu
,
DF
ocp
,
DF
obp
,
A
oba
,
A
oca
, and
A
ost
.
In this
case, there are six different parameters and each parameter may be either
up-or downregulated. Using a simple combination theory, the number of
permutations is calculated as
6
∑
i
i
728
=
C
⋅
2
6
i
=
1
To investigate the system behavior for a wide range of changes, the expo-
nentially changed factor is applied (1.5
ex
) to each of the six differentiation
and apoptosis rate parameters, whereby the exponent
ex
ranges from -10 to
10 in step increases of 0.5. The assessment of the contribution of each of the
parameter combinations to the system's behavior is chosen as the responses
of BMC and BFE, which are sampled on the 100th day, to stand for the maxi-
mum change. After analysis of all the combinations of 728 permutations in six
model parameters, a small number of parameter combinations were identified
