Biomedical Engineering Reference
In-Depth Information
the application of PEMF. Then, the inhibitory effect of PEMF on the OBP takes
over and this overall trend is maintained until the end of the simulation.
The cell population dynamics of OBA, OCA, and OBP can be observed in
Figure 8.4. As expected, the OBA and OBP populations rise and OCA decreases
in the first 2 weeks of the simulation, which is consistent with experimental
observations. Due to the coupling effect between OCA and OBA, the OBA
population starts to decrease after it peaks and continues to decrease until the
end of the simulation, while maintaining a higher concentration than OCA,
which accounts for the continuing growth of bone volume in Figure 8.5.
8.4 Parametric Study of Control Mechanism
of Bone Remodeling under PEMF
Based on the mathematical model presented before, an extensive paramet-
ric study was performed [1]. Model parameters related to fundamental cell
behaviors such as differentiation and apoptosis were investigated, in order
to identify putative control mechanisms for physiologically reasonable bone
remodeling under PEMF.
The functional outputs of the bone remodeling system, such as bone loss or
gain, or homeostasis, are executed by BMUs whereby osteoclasts absorb bone
mineral in bone matrix and activated osteoblasts lay down the newly formed
bone. The BMU acts as a mediator mechanism, bridging individual cellular
activity to whole bone morphology [21], and that mechanism is sensitive to any
changes in its microenvironment. It is expected, therefore, that modification to
any component of the BMU will have a significant effect on its output behavior.
From a control theory perspective, one can always argue that there must
be several control mechanisms working simultaneously in the complex
bone remodeling system under PEMF, governing the response of a BMU to
changes in its microenvironment by modifying the differentiation or apop-
tosis rates of bone cells. Wang and Qin [1] applied perturbations to the bone
remodeling system under PEMF (which is in a steady state) by down- and
upregulating its parameters in random combination groups of five differen-
tiation and apoptosis rate parameters:
DF
obu
,
DF
ocp
,
DF
obp
,
A
oba
, and
A
oca
.
Each
parameter in each group (groups of one, two, three, four, and finally all five
parameters at one time) could be up- or downregulated. Using simple com-
bination theory, the total number of permutation could be calculated and is
5
∑
i
i
242
=
C
⋅
2
5
i
=
1
Then, in order to investigate the system behavior for a wide range of
changes, the exponentially changed factor (1.5
ex
) was applied to each of the
