Biomedical Engineering Reference
In-Depth Information
TABLE 7.1 (
Continued
)
Parameter Values and Description
s
Symbol
Unit
Value
Description
K
A
2,
RL
pM
-1
3.412 × 10
−2
Association binding constant RANKL-RANK
OPG
max
pM
2 × 10
8
Maximum possible OPG concentration
α
%
1
TGF-β content stored in bone matrix
K
res
Day
-1
1
Relative rate of bone resorption
K
for
Day
-1
1.571
Relative rate of bone formation
K
to
Day
-1
1.552 × 10
Relative rate of bone turnover [20,21]
K
OBA
pM/day
0.15
Rate of trapped OBA in bone matrix [20,21]
K
NO
pM/day
2 × 10
4
Secretion rate of NO by osteocytes [20,21]
K
P
2
pM/day
1 × 10
2
Secretion rate of PGE
2
by osteocytes [20,21]
T
acc
Day
24
Time constant describing the rate at which
accommodation takes place [56]
τ
h
6
A time constant [57]
Sources:
Most parameter values are from Pivonka P. et al.
Bone
43 (2): 249-263 (2008), and
Lemaire V. et al.
Journal of Theoretical Biology
229 (3): 293-309 (2004), except where
otherwise indicated.
much faster than changes in the number of active osteoclasts. Using the short
time scale and a quasisteady-state assumption in Equation (7.10), the expres-
sion of TGF-β can be given by [3]
β=
α⋅
KOCA
+
S
res
T
β
T
( 7.11)
D
T
β
Consequently, the activation and repression forms of TGF-β can be obtained
by substituting Equation (7.11) into Equations (7.3) and (7.4) as
T
β
T
β
Π=
( 7.1 2)
actOBU
,
K
+β
T
D1,T
β
1
T
β
Π=
( 7.1 3)
rep OBP
,
1+
T
β
K
D2,T
β
T
β
T
β
Π=
(7.14)
actOCA
,
K
+β
T
D3,T
β
Applying the law of mass action [23] used to describe the reactions of
receptors and corresponding ligands, the formulations including PTH with
its receptor, RANKL with OPG, and RANKL with RANK can be found based
on the mathematical model presented in Chapter 6 or in Wang, Qin, and
Kalyanasundaram [24]. The model presented in Pivonka et al. [3] included
