Biomedical Engineering Reference
In-Depth Information
EXAMPLE 3.5
If a cell membrane has a capacitance of 0.95 mF/cm
2
, how many K
+
ions need to cross the
membrane to obtain a potential of 100 mV?
From (3.16),
2
QC
0.95 * 0.1
0.095
C
/cm
=ΔΦ=
=
μ
ch
m
From (3.17),
Q
0.095
10
−
6
(
C
/cm )
2
×
2
n
ch
5,930 ions per m of membrane
==
=
μ
96, 484
zF
(1)*
C
/ions
+
23
6.023
10
×
Capacitors oppose changes in voltage by drawing or supplying current as they
charge or discharge to the new voltage level. In other words, capacitors conduct
current (rate of change of charge) in proportion to the rate of voltage change. The
current that flows across a capacitor is
t
dQ
d
ΔΦ
1
0
I
=
ch
=
C
m
or
ΔΦ=
i dt
(3.18)
C
m
m
c
dt
dt
C
m
Ionic current described by (3.12) is different than capacitative current. In a
circuit containing a capacitor with a battery of
ΔΦ
rest
[Figure 3.3(a)], the capacitor
charges linearly until the voltage reaches a new steady state voltage,
ΔΦ
SS
[Figure
3.3(b)]. After reaching the new voltage, the driving force is lost. Since the volt-
age does not change, there is no capacitative current flow. The capacitance of the
membrane per unit length determines the amount of charge required to achieve a
certain potential and affects the time needed to reach the threshold. In other words,
slop of the line in Figure 3.3(b) is affected by capacitance. When the conductance
is increased by two, steady state voltage is reduced. However, the slope of the line
is much higher.
Capacitive reactance (
R
C
) (generally referred to as reactance and expressed in
ohms,
) is the opposition to the instantaneous flow of electric current caused by
capacitance. Reactances pass more current for faster-changing voltages (as they
Ω
Figure 3.3
(a, b) Circuit with a capacitor.
