Biomedical Engineering Reference
In-Depth Information
The rate of bone resorption and formation is assumed to be proportional to
the numbers of osteoclasts and osteoblasts, respectively:
dZ
dt
=− ⋅+ ⋅
mC mB
1
(6.23)
2
where Z is the total bone mass, and m 1 and m 2 are normalized activities of
bone resorption and formation, respectively. Noting that at equilibrium,
where the simulation starts, the numbers of AOB, AOC, and ROB do not
change with time; solving the following three equations can determine the
initial values of B, C, and R:
1
=
DDR
⋅π −⋅
0
(6.24)
RC
B
I
π
C
1
−−π⋅ =
(
)
DR
⋅⋅ π
k
B
0
(6.25)
B
I
B
P
C
(
)
DD
⋅π −⋅ π−π⋅=
C
0
(6.26)
CL
AC L
Values of model parameters and initial conditions of variables are listed
in Table  6.1. Model equations (6.20)-(6.23) are then solved using numerical
integration by a fourth Runge-Kutta algorithm implemented in Matlab. This
is performed in the next section.
6.4 Results and Discussion
To demonstrate the tight coupling between osteoblast and osteoclast, Wang
et al. [2] computationally perturbed this system by adding or removing
specific cells. The results are displayed from Figures 6.2 to 6.7.
It is evident from Figures  6.2 and 6.3 that adding AOBs can initiate a
remodeling cycle from initial stable state as shown in Figure 6.2. Figure 6.2
also shows that the number of AOCs decreases for the first 7 days or so
and then increases back to the initial value, whereas the number of AOBs
increases as expected; this means that direct administration of AOBs does
not have a strong stimulatory effect on AOCs, consistent with experimental
observation [2]. Figure  6.3 clearly displays that bone mass increases with
administration of AOBs and rises a little more slowly after AOB injection
ceases.
Figure  6.4 shows that the administration of AOCs initiates a remodeling
cycle and their number remains almost unchanged from approximately the
7th day to the 60th day. There is also a strong and immediate stimulatory
 
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