Biomedical Engineering Reference
In-Depth Information
B
out
= 0
J
i
G
Fig. 3.29.
A current dipole oriented parallel to the radius
Therefore,
4
π
Q
×
1
r
·
r
0
U
(
r
)=
−
,
(3.78)
F
where
F
=
a
(
ra
+
r
r
0
. As a result, we obtain an equation
for the magnetic field outside the spherical conductor
G
as follows:
−
r
0
·
r
)
,
a
=
r
−
μ
0
4
πF
2
(
F
B
(
r
)=
Q
×
r
0
−
Q
×
r
0
·
r
∇
F
)
,
(3.79)
where,
F
=(
r
−
1
a
2
+
a
−
1
(
(
a
+2
r
+
a
−
1
(
∇
a
·
r
)+2
a
+2
r
)
r
−
a
·
r
))
r
0
.
(3.80)
From (3.78) or (3.79) we find that if the dipole is parallel to the radial direc-
tion, the magnetic field does not appear outside
G
.Furthermore,themagnetic
field outside
G
does not depend on the value of the conductivity
σ
.
Examples of Field Patterns.
We demonstrate typical field patterns ge-
nerated by the spherical conductor model (see Fig. 3.30). Figures 3.31, 3.32,
and 3.33 show the contour maps of the
x
,
y
,and
z
components of the ma-
gnetic field, respectively. For comparison, we show the contour maps due to
a current dipole only in Figs. 3.34, 3.35, and 3.36. From these figures, we
can show that the tangential components are easily affected by the volume
currents in the conductor.
3.3.2 The Inverse Problem
The Equivalent Current Dipole.
The MEG inverse problem consists in
estimating the neuromagnetic source characteristics from the observed ma-
