Biomedical Engineering Reference
In-Depth Information
where
t
is the time at which
N
R
is calculated and
N
0
represents the number
of BMUs that are required to resorb the naturally timeworn osteocytes
and those that have been destroyed by microdamage. As proposed [2], the
resorption of osteocytes is activated by the microdamage. So the BMU acti-
vation frequency,
f
a
(BMUs/volume/time), is assumed to be a function of the
existing state of damage
k
Φ
f
=
f
(1
−
e
)
(5.13)
R
a
a
(max)
where
f
a
(max)
= 0.8 BMU/mm
3
/day [2], and
k
R
= −1.6 defines the shape of the
curve. Φ is defined here as an environmental stimulus:
q
(
)
e
(5.14)
Φ= ε+ +
CR CE
GB
f
ij
ij
L
i
i
i
i
Here,
C
ij
,
C
i
,
and
G
i
are the damage rate coefficients. ε
ij
, E
i
,
and
H
i
are strains,
electrical field, and magnetic field, respectively. The value for the exponent
q
is set at a nominal 2/3. The mechanical loading rate,
R
L
, is assumed to be
3,000 cpd, and
f
e
is the frequency of the electromagnetic field.
The population
N
F
in Equation (5.2) is found by multiplying the quantities
of resorbed osteocyte by
k
F
:
N
F
= k
F
N
R
(5.15)
where
k
F
is the correlation coefficient of the refilling BMUs, indicating the
relation between the refilling and the resorbing process.
k
F
is defined as a
piecewise function of Φ and
p
[2]:
c
Φ≤Φ≤Φ
0
L
U
(5.16)
k
=
c
Φ<Φ
F
1
U
n
p
p
(
)
cc
−
+ Φ<Φ
c
0
2
2
L
0
Considering that the quantity of growth factors retained in osteo-
cytes changes along with the environmental loads, as mentioned before,
Φ
L
and Φ
U
can be considered as
MESr
and
MESm,
respectively. When
Φ
L
≤ Φ ≤ Φ
U
,
the growth factors remain unchanged (
k
F
= c
0
) and the bone
tissue is in the remodeling state. When Φ < Φ
U
,
more growth factors
(
k
F
= c
1
>
c
0
) are generated, which results in bone modeling. When Φ
L
< Φ
fewer growth factors (
k
F
=
(
c
1
>
c
0
)(
p
/
p
0
)
n
+
c
2
<
c
0
) result in a disuse mode of
bone tissue.
