Biomedical Engineering Reference
In-Depth Information
TABLE 5.2
Model S
tate Variables and Constants
State variables
Number of resorbing BMUs due to microdamage
N
1
Number of refilling BMUs in surface bone remodeling
N
s
Number of refilling BMUs in internal bone remodeling
N
i
N
0
Maximum of refilling BMUs consumed by internal remodeling strains
Constant values used in He et al. [3]
Maximum BMUs that can be generated by the body
0.8
1
N
R
(max)
k
f
Correlation coefficient of the refilling and resorbing
process
1.8
k
s
Proportional coefficient
0.6
k
e
Inner surface bone remodeling rate coefficient
0.25
k
p
Outer surface bone remodeling rate coefficient
0.4
f
e
Frequency of the electromagnetic field
2
Upper threshold of bone remodeling
0.0048
Φ
U
N
0
Number of naturally timeworn osteocytes
0.4
c
1
Value of
k
f
during the remodeling process
3.6 × 10
2
0
n
0
n
,
and
α=α−
p
0
(1
)
n
were calculated as
=− =−
,
where
c
i
0
,
e
i
0
and
α
i
0
are constants that are related to the properties of materials
and
n
= 3 [48]. The reference values of material properties are assumed as
follows:
cc
(1
pe e
),
(1
p
)
ij
ij
ij
ij
ij
ij
0
0
0
0
c
=
15GPa,
c
=
c
=
6.6GPa,
c
=
12GPa,
0
0
2
c
=
4.4GPa,
e
=
1.14C/m,
11
12
13
33
44
15
0
α=550N/Am.
15
Bone is usually subjected to pressure, and greater pressure can strengthen
it. It has been reported that osteoclasts migrate to the positive electrode in
an electric field, whereas osteoblasts migrate to the negative electrode [65].
Therefore, all the remodeling rate coefficients are negative. They can be
shown as
C
rr
= −0.06 m/day,
C
θθ
= −0.03 m/day,
C
zz
= −0.04 m/day
C
zr
= −0.01 m/day,
C
r
= 3 × 10
−7
V
−1
m
2
/day, and
G
r
= 4 × 10
−8
A
−1
m
2
/d a y
The initial inner and outer radii are again assumed to be
a
0
= 25 mm,
b
0
= 35 mm.
