Biomedical Engineering Reference
In-Depth Information
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P
,
P
,
P
,
P
,
P
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Figure 8.1:
Summation of dipoles in calculating an extracellular potential.
8.2
EXTRACELLULAR POTENTIAL RECORDINGS
8.2.1 Extracellular Potentials Generated by an Active Cable
In our derivation of propagation in a cable, we assumed that the cable was very thin. If we also assume
that the cable is surrounded by a large bath and an electrode far from the cable, the current sources,
I
m
,
will appear to be point sources. Furthermore, if we align the cable with the x-axis, then the infinitesimal
volume in Eq. (8.1) because an infinitesimal length,
dx
:
I
m
(x,y,z)
r
1
4
πσ
e
φ
e
(x
,y
,z
)
=
dx
(8.11)
where
I
m
at each point in the cable may be computed in one of two ways.
I
m
=
C
m
dV
m
dt
−
I
ion
(8.12)
or
πr
2
R
i
d
2
V
m
dx
2
I
m
=
.
(8.13)
Note that in the second formulation
φ
e
can be computed at a particular moment in time by knowing only
the spatial variation in
V
m
along the cable.
