Biomedical Engineering Reference
In-Depth Information
Once the strains, electrical field, and magnetic field are obtained, the
differential equations (5.2) and (5.23) can be rewritten as
dp
dt
=
ftpab
(, ,,),
1
da
dt
(5.26)
=
ftpab
(, ,,),
2
db
dt
=
ftpab
(, ,,)
3
where
i
ftpabQNQN
(, ,,)
=
−
1
RR
FF
(5.27)
f
2
(
t
,
p
,
a
,
b
) = −
k
e
(
N
F
− N
0
)
(5.28)
f
3
(
t
,
p
,
a
,
b
) = −
k
p
(
N
F
− N
0
)
(5.29)
The following fourth-order Runge-Kutta integrating process can be used
to obtain the numerical solution:
Step 1:
p
t
t
t
Kf
=
(,
tp ab
,
,
)
1
1
a
t
t
t
(5.30)
Kf
=
(,
tp ab
,
,
)
1
2
b
t
t
t
Kf
=
(,
tp ab
,
,
)
1
3
Step 2:
+
∆
t
+
∆
t
Ka
+
∆
t
Kb
+
∆
t
K
p
p
t
t
a
t
b
Kf
=
t
,
p
,
,
2
1
1
1
1
2
2
2
2
+
∆
t
+
∆
t
Ka
+
∆
t
Kb
+
∆
t
K
p
a
t
t
a
t
b
Kf
=
t
,
p
,
,
2
2
1
1
1
2
2
2
2
+
∆
t
+
∆
t
Ka
+
∆
t
Kb
+
∆
t
K
p
b
t
t
a
t
b
Kf
=
t
,
p
,
,
2
3
1
1
1
2
2
2
2
