Biomedical Engineering Reference
In-Depth Information
Qin and Wang [2] argued that NO stimulates the production of OPG
expressed in OBA (see Section 7.2.2) while PTH downregulates OPG produc-
tion of OBA [24]. Therefore, based on the work of Pivonka et al. [3] and using
Equation (7.5), Qin and Wang obtained the expression of OPG concentration as
(
)
(
)
PTH
NO
=
β⋅
OBAk
⋅
⋅Π+
k
⋅Π
+
P
t
OPG
PTH
rep OBA
,
NO
actOBA
,
OPGd
,
OPG
( 7. 2 8)
(
)
β⋅
OBAk
⋅
⋅Π+
PTH
k
⋅Π
NO
OPG
PTH
rep OBA
,
NO
actOBA
,
+
D
OPG
OPG
max
where
β
OPG
is the production rate of OPG per OBA
k
PTH
is the relative influence of PTH binding in the production of OPG
in OBA
k
NO
is the relative influence of NO in the production of OPG in OBA
P
OPG, d
(
t
) is an external OPG administration term
D
OPG
is the rate of degradation of OPG
OPG
max
is the maximum possible OPG concentration
Further, NO inhibits RANKL expression in OBP and PTH upregulates the
RANKL “effective carrying capacity” of OBP [24]. Building on Pivonka et al.
[3], Qin and Wang obtained the concentration of RANKL as
PTH
ROBP
K
⋅
⋅
Π
RL
actOBP
,
RL
=
1
+
⋅
PG
+
KR
⋅
K
ARL
1
,
A
2
,
RL
( 7. 2 9)
()
NO
β
⋅
OBP
⋅
Π
+
P
t
RL
rep OBP
,
RL d
,
⋅
NO
PT
H
β
RL
⋅
OBP
⋅ +⋅
Π
D
ROBP
⋅
⋅
Π
rep OBP
,
RL
RL
actOBP
,
where
R
RL
is the maximum RANKL on OBP
K
A
1
, RL
is the association binding constant RANKL-OPG
K
A
2
, RL
is the association binding constant RANKL-RANK
β
RL
is the production rate of RANKL per OBP
P
RL, d
(
t
) is an external RANKL administration term
D
RL
is the rate of degradation of RANKL
Then, the activation function of RANKL on differentiation of osteoclast
precursor cells OCP can be obtained using Equations (7.3) and (7.29):
RL
RL
Π=
( 7. 3 0 )
actOCP
,
K
+
RL
DRL
8,
where
K
D
8, RL
is the activation coefficient related to RANKL binding on OCP.
