Biomedical Engineering Reference
In-Depth Information
Substituting Equations (3.61) and (3.62) into Equation (3.63) and then solving
Equation (3.63) for
p
1
(
t
), we obtain
2
1
δ
−
b
ba
H
1
1
pt
()
=−
H
+
ba
H
+
(3.65)
1
1
2
3
b
a
2
2
2
2
Ha
−
−
ln
where
2
µ+λ
µλ+µ
−
2
(3
c
Fc
1
b
ba
33
3
H
=
2
+
(3.66)
∗
2
2
2)
−
c
−
11
12
2
c
c
−
c
Fc
1
β+
13
33
∗
H
=
c
λ −λ
T
2
+
Tpt
()
(3.67)
1
13
1
3
0
20
∗
∗
F
−
c
3
11
3
11
12
2
cPt
( )
13
(3.68)
H
=
2
∗
F
π
3
cc
λ
T
2
c
c
λ −
λ
−
λ
T
33
12
10
13
3
10
H
=
−
cT
(3.69)
3
1
13
0
∗
∗
Fc
F
2
c
311
3
11
11
Equation (3.65) is the solution of the internal surface pressure induced by an
inserting medullar pin.
3.6 Numerical Examples
As numerical illustration of the analytical and semianalytical solutions
described before, a femur with
a
= 25 mm and
b
= 35 mm is considered. The
material properties assumed for the bone are
c
11
= 15(1 +
e
)GPa,
c
12
=
c
13
= 6.6(1 +
e
)GPa,
c
33
= 12(1 +
e
)GPa,
c
44
= 4.4(1 +
e
)GPa, λ
1
= 0.621(1 +
e
) × 10
5
NK
−1
m
−2
,
λ
3
= 0.551(1 +
e
) × 10
5
NK
−1
m
−2
, χ
3
= 0.0133(1 +
e
)CK
−1
m
−2
e
31
= −0.435(1 +
e
)C/m
2
,
e
33
= 1.75(1+
e
)C/m
2
,
(3.70)
e
15
= 1.14(1 +
e
)C/m
2
, κ
1
= 111.5(1 +
e
)κ
0
,
3
= 126(1 +
e
)κ
0
, κ
0
= 8.85 × 10
−12
C
2
/Nm
2
= permittivity of free space
The remodeling rate coefficients are assumed to be
C
0
= 3.09 × 10
−9
sec
−1
, C
1
= 2 × 10
−7
sec
−1
, C
2
= 10
−6
sec
−1
