Biomedical Engineering Reference
In-Depth Information
C
0
(
C
0
=
f
0
·
C
S
) represents the basal concentration of the AOCs in the system
with
f
0
being a fixed proportion
The outgoing flow from the ROB compartment is also the feeding flow to
the AOB compartment. Under the influence of TGF-β and IGF, which inhibit
and stimulate AOB production, respectively,
s
1
=⋅
CC
CC
+
+
DR
⋅⋅
π
+π
DR
⋅
+π
(6.16)
B
I
B
I
0
C
where
D
B
is a proportionality factor associated with AOB production.
RANK-RANKL binding promotes the differentiation of mesenchy-
mal stem cells into AOC [2]; the differentiation rate is proportional to the
RANK occupancy ratio π
L
. This ratio is equal to
K
•
L
/
K
in the case under
consideration:
P
KL
K
•
=⋅
k
k
KB
π
I
r
3
L
P
L
⋅ +
1
(6.17)
P
kK
k
k
kk
K
4
L
3
1
O
1
++⋅
RI
+
O
π
4
2
O
P
The flow of differentiation precursors entering the AOC compartment is
then given by
DD
KL
K
•
(6.18)
⋅π =⋅
CL
C
where
D
C
is the differentiation rate of the osteoclasts' precursors.
TGF-β induces osteoclast apoptosis via binding to specific receptors and
also under the influence of RANKL. This phenomenon is then represented as
0
CC
CC
C
+
+
⋅π−π ⋅= ⋅
)
D
C
D
⋅
(6.19)
AC L
A
s
The equations governing the evolution of the number of cells in each
compartment are simply balance equations [21], which means that each cell
compartment is fed by an entering flow and is emptied by the outgoing flow
of differentiated or apoptotic cells [2]:
dR
dt
1
=⋅π− ⋅⋅
π
DDR
+π
(6.20)
RC
B
I
C
dB
dt
1
−−π⋅
(
)
=⋅
DR
⋅
+π
k
B
(6.21)
B
I
B
P
π
C
dC
dt
)
(
=⋅π− ⋅π−π ⋅
DD
C
(6.22)
CL
AC L
