Biomedical Engineering Reference
In-Depth Information
Step 3:
+
∆
t
+
∆
t
Ka
+
∆
t
Kb
+
∆
t
K
p
t
p
t
a
t
b
Kf
=
t
,
p
,
,
1
2
2
3
2
2
2
2
2
+
∆
t
+
∆
t
Ka
+
∆
t
Kb
+
∆
t
K
a
t
p
t
a
t
b
Kf
=
t
,
p
,
,
3
2
2
2
2
2
2
2
2
+
∆
t
+
∆
t
Ka
+
∆
t
Kb
+
∆
t
K
b
t
p
t
a
t
b
Kf
=
t
,
p
,
,
3
3
2
2
2
2
2
2
2
Step 4:
+
∆
t
Kb
+
∆
t
K
p
t
p
t
a
t
b
Kf
=
t
+∆ ∆
t ptKa
,
,
,
1
3
3
4
3
2
2
+
∆
t
Kb
+
∆
t
K
a
t
p
t
a
t
b
Kf
=
t
+∆ ∆
t ptKa
,
,
,
4
2
3
3
3
2
2
+
∆
t
Kb
+
∆
t
K
b
t
p
t
a
t
b
Kf
=
t
+∆ ∆
t ptKa
,
,
,
4
3
3
3
3
2
2
Then, the variables at
t
+ Δ
t
are calculated by
=+
∆
+++
t
(
)
p
p
p
p
tt
+∆
t
p
p
KKKK
2
2
1
2
3
4
6
=+
∆
+++
t
(
)
tt
+∆
t
a
a
a
a
a
a
KKKK
2
2
1
2
3
4
6
=+
∆
+++
t
(
)
tt
+∆
t
b
b
b
b
b
b
KKKK
2
2
1
2
3
4
6
The algorithm described here is used in the next section.
5.5.2 Bone Remodeling Simulation
For simplicity, He et al. [3] considered a section of hollow cylindrical bone
that is subjected to axial compressive pressure
P,
transverse pressure
p
t
,
and
pulse electromagnetic loads. We also assume that the strain ε
ij
,
the electric
ield
E
i
,
and the magnetic field
H
i
all return to zero at the end of each load
cycle, so their ranges and peaks are the same. The model is given an initial
porosity of 8%. The state variables and constants are shown in Table 5.2.
As a numerical illustration of the bone surface remodeling process, He
et al. [3] considered a femur with
a
= 25 mm and
b
= 35 mm. The elastic moduli
