Biomedical Engineering Reference
In-Depth Information
Fig. A.1
The three
orthogonal directions
(
z
e
r
used to express
the source vector when the
spherically-symmetric
conductor model is used for
the forward calculation
e
r
,
e
ˆ
,
e
ʸ
)
e
ʸ
˕
e
ʸ
˕
x
y
terms on the left-hand side of Eq. (
A.59
) contain the vector product
Q
×
r
0
, which
is equal to zero when
Q
and
r
0
are parallel.
Therefore, when using the spherically-homogeneous conductor model, instead
of the
x
,
y
,
z
directions, we usually use the three orthogonal directions
ʸ
)
to express the source vector. These directions are illustrated in Fig.
A.1
. Because
the
e
r
component of a source never creates a measurable magnetic field outside the
spherical conductor, we can disregard this component and only deal with the
e
(
e
r
,
e
ˆ
,
e
and
ˆ
e
components of the source vector.
ʸ
References
1. R. Plonsey,
Bioelectric phenomena
. Wiley Online Library, 1969.
2. H. Tuckwell, “Introduction to Theoretical Neurobiology vols. 1 and 2, 1988,”
Cambridge University Press, Cambridge, Longtin A., Bulsara A., Moss F., Phys.
Rev. Lett
, vol. 65, p. 656, 1991.
3. B. Hille,
Ion channels of excitable membranes
, vol. 507. Sinauer Sunderland,
MA, 2001.
4. R. M. Gulrajani,
Bioelectricity and biomagnetism
. John Wiley and Sons, 1998.
5. D. B. Geselowitz, “On the magnetic field generated outside an inhomogeneous
volume conductor by internal current sources,”
IEEE Trans. Biomed. Eng.
,vol.2,
pp. 346-347, 1970.
6. J. Sarvas, “Basic mathematical and electromagnetic concepts of the biomagnetic
inverse problem,”
Phys. Med. Biol.
, vol. 32, pp. 11-22, 1987.
