Biomedical Engineering Reference
In-Depth Information
charge and discharge to the same voltage peaks in less time), and less current for
slower-changing voltages. In other words, reactance for any capacitor is inverse-
ly proportional to the frequency of the alternating current. In alternating current
(AC) circuit, reactance is expressed by
1
R
=
(3.19)
C
2
π
fC
m
where
f
is the frequency of the alternating current in hertz. Equation (3.19) suggests
that reactance is the reciprocal of frequency (i.e., reactance decreases as frequency
increases). At very low frequencies reactance is nearly infinite. However, capaci-
tance is independent of frequency and indirectly defines cell membrane volume.
Ideally reactance is expressed in capacitance at a given frequency. Large capacitance
values mean a slower rate of ion transfer.
3.3.3 Resistance-Capacitance Circuit
Based on the above discussion, the cell membrane has both resistive and capacita-
tive properties. Then, a cell membrane can be represented by an equivalent circuit
of a single resistor and capacitor in parallel (Figure 3.4) with a resting potential
calculated using the Nernst equation for an individual ionic species. When mul-
tiple ionic species are involved in causing changes in electrical activity, resistance of
each species is considered separately. It is conceived that cells and their supporting
mechanisms are not a series of extracellular and intracellular components but reside
in parallel with a small series effect from the nucleolus of the cells. Simplification
of circuits with resistors in series or parallel by replacing them with equivalent
resistors is possible using the
Kirchoff's laws
in electrical circuits. Two resistors in
series are replaced by one whose resistance equals the sum of the original two resis-
tances, since voltage and resistance are proportional. Reciprocals of resistances of
two resistors in parallel are added to obtain the equivalent resistance since current
and resistance are inversely proportional. Conversely, capacitor values are added
normally when connected in parallel, but are added in reciprocal when connected
in series, exactly the opposite of resistors.
Extracellular fluid
Plasma membrane
capacitance
C
m
R
I
inj
ΔΦ
rest
Ion channel
(conductance)
Cytosol
(a)
(b)
Figure 3.4
(a, b) Equivalent circuit of a cell wall.
