Biomedical Engineering Reference
In-Depth Information
where
G
is the conductance (siemens, S
is the mem-
brane potential (i.e., the voltage between inside and outside of the cell membrane).
Equation (3.12) is called
Ohm's law
. The reciprocal of conductance is called resis-
tance and a widely used form of Ohm's law in electrical engineering is:
=
A/V) of the circuit and
ΔΦ
ΔΦ
I
=
(3.13)
where
R
is the resistance. All substances have resistance to the flow of an electric
current. For example, metal conductors such as copper have low resistance whereas
insulators have very high resistances. Pure electrical resistance is the same when ap-
plying direct current and alternating current at any frequency. In the body, highly
conductive (or low resistance electrical pathway) lean tissues contain large amounts
of water and conducting electrolytes. Fat and bone, on the other hand, are poor
conductors with low amounts of fluid and conducting electrolytes. These changes
form the basis of measuring the body composition in a person.
When the cell membrane is “at rest,” it is in the state of dynamic equilibrium
where a current leak from the outside to inside is balanced by the current provided
by pumps and ion channels so that the net current is zero. In this dynamic equilib-
rium state, ionic current flowing through an ion channel is written as
IG
=ΔΦ −Δ
,
(
( )
t
φ
)
(3.14)
i
m
rest i
Δφ
rest,i
is the equilibrium potential for the
i
th species, and
Δφ
m
(
t
)
− Δφ
rest,i
is
the net driving force.
EXAMPLE 3.4
If a muscle membrane has a single Na
+
ion channel conductance of 20 pS, find the cur-
rent flowing through the channel when the membrane potential is
−
30 mV. The Nernst
potential for the membrane is
+
100 mV.
Solution:
(
)
( )
I
g
t
=ΔΦ
−ΔΦ
m
rest
(
)
(
) (
) (
)
12
3
3
12
20
10
−
S
30
10
−
V
100
10
−
V
2.6
10
−
A
2.6 pA
=×
−×
− ×
=−×
=−
3.3.2 Cell Membrane as a Capacitor
Intracellular and extracellular fluids are conducting electrolytes, but the lipid bi-
layer is electrically nonconductive. Thus the nonconductive layer is sandwiched be-
tween two conductive compartments. It can be treated as a
capacitor
consisting of
two conducting plates separated by an insulator or nonconductive material known
as a dielectric. Hence, the cell membrane is modeled as a capacitor, charged by the
