Biomedical Engineering Reference
In-Depth Information
All currents are represented by a unique parallel pathway through which current may cross the membrane.
In the literature, this circuit is therefore known as the
parallel conductance model
. By conservation of current,
the total membrane current,
I
m
, must sum to zero, so
0
=
I
cm
+
I
ion
+
I
syn
−
I
stim
.
(2.3)
I
stim
i
I
syn
I
cm
I
ion
e
Figure 2.3:
Parallel conductance model.
Substituting the know the relationship between voltage and current for a capacitor,
=
C
m
dV
m
dt
0
+
I
ion
+
I
syn
−
I
stim
(2.4)
C
m
−
I
stim
.
dV
m
dt
1
=
I
ion
−
I
syn
+
(2.5)
Equation (2.5) is a differential equation that describes how
V
m
evolves over time based upon the currents
that flow across the cell membrane.
2.1.4 The Membrane Capacitance
The value of the membrane capacitance can be directly computed by
k
0
d
C
m
=
(2.6)
10
−
9
/
36
πF/m
2
),
where
k
is the dielectric constant of the insulator,
0
is the permittivity of free space (1
×
and
d
is the membrane thickness. Using
k
=
3 (value for oil) and
d
=
3
nm
:
10
−
9
3
×
0
.
009
F
m
2
0
.
9
μF
cm
2
C
m
=
10
−
9
)
=
=
.
(2.7)
36
π(
3
×
For simplicity, 1
μF /cm
2
is often used as an approximation for
C
m
. As our estimate for
C
m
is measured
per unit area, it is independent of the size of the cell.
