Biomedical Engineering Reference
In-Depth Information
five differentiation and apoptosis rate parameters, whereby the exponent
ex
ranged from -10 to 10 with a step increase of 0.5. The assessment of the effect
of each of the parameter combinations to the system behavior was chosen as
the responses of bone volume, which were sampled on the 90th day to indicate
the maximum change. Using Matlab, all 242 graphs were plotted. Then, sum-
marizing all the plots of bone volume versus variation of exponent
ex,
Wang
and Qin [1] found three subsets of curves, which are plotted in Figure 8.6.
Figure 8.6(a) and 8.6(b) demonstrates an exponential increase and decrease
of bone volume, respectively, for increasing the model parameter exponen-
tially (exponent
e
x
from -10 to 10). This type of behavior is considered physio-
logically unrealistic from a biological perspective and was obtained for quite
a large range of model parameter combinations. Conversely, Figure 8.6(c)
101.8
101.8
BV-90th day
BV-90th day
101.6
101.4
101.6
101.4
101.2
101
101.2
101
100.8
100.8
100.6
100.6
100.4
100.2
100.4
100.2
100
100
-10
-5
0
5
10
-10
-5
0
5
10
Exponent
Exponent
(a)
(b)
100
80
60
40
20
BV-90th day
0
-10
-5
0
5
Exponent
(c)
FIGURE 8.6
Physiologically unrealistic changes of BMC (bone mineral content) and BFE (bone fracture
energy) versus combined changes of model parameter [1.5
-10
- 1.5
+10
]
p:
(a) exponential bone
growth; (b) exponential bone decrease; and (c) slight changes of bone. (
p
is the parameter value.)
