Biomedical Engineering Reference
In-Depth Information
and defined by Equations (7.12)-(7.14). The corresponding PTH concentra-
tion and its relevant activation and repression functions are also defined by
E q u a t i o n s ( 7. 2 5 ) - ( 7. 2 7 ) .
As stated previously, it has already been concluded that PEMF stimulates
the production of OPG expressed in OBA and inhibits the expression of
RANKL in OBP, based on experimental observations (see Section 8.2.1). OPG
and RANKL are the only two factors that are considered to be regulated by
PEMF stimulation in the model. The systemic hormone PTH downregulates
OPG production in OBA. Therefore, based on Pivonka et al. [25], the OPG
concentration can be expressed as
(
(
)
)
()
PTH
=
β⋅
OBA
⋅Π +
F
Iftw
,,,
,,,
+
Pt
OPG
rep OBA
,
OPG
OPG d
,
OPG
(8.5)
(
)
(
)
PTH
β⋅
OBA
⋅Π +
F
Iftw
OPG
rep OBA
,
OPG
+
D
OPG
OPG
max
where
F
OPG
(
I, f, t, w
) is the influence of PEMF on OPG secretion character-
ized by its intensity, frequency, time, and waveform. Further, PEMF inhib-
its RANKL expression in OBP and PTH upregulates the RANKL “effective
carrying capacity” of OBP [39]. Using the formulation presented in Pivonka
et al., [25], the concentration of RANKL can be obtained:
PTH
ROBP
K
⋅
⋅Π
RL
actOBP
,
RL
=
1
+
⋅
PG
+
K
⋅
K
ARL
1,
A
2,
RL
(8.6)
(
)
()
β⋅
OBPF
⋅
Iftw
,,,
+
Pt
RL
RL
RL d
,
⋅
(
)
PTH
β⋅
OBPF
⋅
Iftw
,,,
+
DROBP
⋅
⋅
⋅Π
RL
RL
RL
RL
actOBP
,
where
F
FR
(
I, f, t, w
) is the effect of PEMF on RANKL production characterized
by its intensity, frequency, time, and waveform. Then, the activation func-
tion of RANKL on differentiation of osteoclast precursor cells OCP can be
obtained using Equations (7.3) and (8.6) and is the same as Equation (7.30),
except that
RL
is calculated from Equation (8.6). All the model parameters
and their values can be found in Tables 6.1 and 7.1.
8.3 Numerical Investigation of the Model
Bone remodeling is an important biological system when it comes to bone
fracture healing, nonunion fracture, and bone diseases such as osteoporosis.
It is executed by coordinated activities of osteoclastic cells and osteoblastic
cells in BMUs. The coupling between osteoclastic cells and osteoblastic cells
