Biomedical Engineering Reference
In-Depth Information
experiments as possible to see if it is valid in a statistical sense. The reality,
however, is that due to the complexity of such experiments and suitability
of the specific model, there are few experiments available for comparison.
In this section, the results presented in Wang [1] and Qin and Wang [2] for
simulating five experiments of two different types in Saxon et al. [58] and
Robling et al. [12] are briefly reviewed.
First, Qin and Wang [2] simulated the three experiments conducted in Saxon
et al. [58], in which 57 female Sprague-Dawley rats were randomized to three
groups: group I loading was applied for 5 weeks followed by 10 weeks of time
off (1 × 5); group II loading was applied for 5 weeks followed by 5 weeks of
time off and loading again for 5 weeks (2 × 5); group III loading was applied
continuously for 15 weeks (3 × 5). An axial load was applied to the right ulna
for 360 cycles per day, at 2 Hz, 3 days per week at 15 N. Qin and Wang simu-
lated the effects of the three different loading schemes on BFE and compared
them with the experimental results, which are shown in Figure 7.3.
The trends of BMC of loading schemes 1 × 5 and 3 × 5 are shown in Figure 7.3(a).
From the dotted curve, we can see that for the 1 × 5 loading scheme, the BMC
retains its initial value for the first 4 ~ 5 days of loading, which is in agreement
with bone remodeling theory, and then it begins to increase almost linearly
under the mechanical stimulus until the loading stops on the 35th day. After
that, because of the accumulated NO and PGE
2
, the BMC continues to increase
but the BFR (bone formation rate) drops until BMC reaches its peak value
when BFR becomes zero on the 50th day; the bone remodeling then maintains
its new equilibrium and the BMC remains unchanged.
During the 3 × 5 loading scheme, the BMC follows the same pattern as in
the 1 × 5 scheme for the first 5 weeks. The mechanical stimulus continues
for another 10 weeks, when the BFR decreases slowly toward the end of the
experiment (15 weeks' loading). By the end of the experiment, each rat's BMC
was measured and compared with that before the experiment. The measured
BMC increases (in percentage) are shown in the graph by the small circles and
squares with the word “Experiment [58]” and are 7.6% and 10.4% for the 1 × 5
and 3 × 5 schemes, respectively—closely matching the simulation results that
are shown by the small circles and squares with the words “Present model”
predicting 5.7% and 11.1% increases for the 1 × 5 and 3 × 5 schemes, respectively.
The pattern of BMC with respect to time (days) for the 2 × 5 loading scheme
is plotted in Figure 7.3(b). From day 0 to day 70 (5 weeks' loading plus 5
weeks' rest), the BMC demonstrates exactly the same pattern as in the 1 × 5
scheme. After the 5 weeks' break, the bone cells regain some mechano-
sensitivity and start to respond to the mechanical loading from day 71 as
predicted, but the graph shows clearly that the BFR is less than that in the
first 5 weeks, implying that the bone mechanosensitivity has not recovered
fully after 5 weeks' rest. Eventually, the experiment shows a 9.8% increase,
which compares well with the 7.4% from our simulation results (see the small
squares with words “Experiment [58]” and “Present model” representing
experimental and current simulation results).
