Biomedical Engineering Reference
In-Depth Information
satisfy the system of equations
(2
NAQu QR U
++ℵ++ℵ =
)
(
)
0,
r
r
ℵ+ℵ+
∂
Qu RU
C
∂
−=
(
uU
)
0
(2.88)
r
r
r
r
t
with homogeneous boundary conditions at
r
=
a
and
r
=
b
:
=
++
∂
∂
++ ++
∂
u
r
AQ
u
r
U
r
U
r
r
r
r
r
(2
NAQ
)
(
)
(
QR
)
+
0
(2.89)
∂
and at
S:
(
AQbu
+
)((,)
bt
−
au
(,))
at
++
(
RQbU
)(
( ,)
bt
−
aU
(,))
at
=
0
(2.90)
r
r
r
r
The system of Equation (2.88) can be rewritten as
u
u
0
QC t RCt
NAQQR
ℵ+ ∂∂ ℵ− ∂∂
++ℵ+ ℵ
/
/
r
r
D
=
=
(2.91)
(2
)
(
)
0
U
U
r
r
Introducing a function
h
such that det(
D
)
h
= 0 [30], Papathanasopoulou
et al. obtained
∂
∂
∂
∂
−++ −
(
QRQC
t
+ +
)
(2
NAQR C
)
ℵ=
h
0
(2.92)
t
Assuming that
h
=
h
1
+
h
2
, Equation (2.92) leads to
ℵ
h
1
= 0
and
ℵ
h
2
+
k
∂
h
2
/∂
t
= 0
(2.93)
where
CN QRA
Q
(2
+++
−
2
)
k
=
(2.94)
2
2
RAR
−
The solution of Equation (2.93)
1
is obviously
At
r
()
4
hrt
(,)
=
Atr
( )
+
(2.95)
1
3