Biomedical Engineering Reference
In-Depth Information
that more aggressive pouring would eventually result in the threshold being reached but only very slowly.
It may also be possible to pour water in only for some short period of time. If this is the case, then the rate
at which you pour and the duration of your pour will determine if the water will reach the threshold. You
could in fact create a strength-duration plot for this cup-water system. Furthermore, if you assume that
the cup already has water in it, you may ask how long it will take for the cup to drain.The two parameters
of interest will be the size of the cup (capacity) and the size of the hole (resistance). The combination of
the two, as in the circuit analogy, can be used to define the time constant of the filling or draining of the
cup.
2.4 THEMEMBRANE AT REST
A careful examination of Fig. 2.4 will reveal that
V
res
m
must be 0
mV
, which biologically is not true. In
this section we will examine how a cell can maintain a nonzero resting potential.
2.4.1 The Forces Driving IonMovement
Consider Fig. 2.7 where circles and dots represent two types of positively charged ions but the membrane
will only allow dots to pass through. The special property of the membrane to easily pass some ions but
not others is called
selective permeability
and results in a nonzero resting potential.
F
c
F
Figure 2.7:
Concentrations and electrical potentials in a cell.
There are two forces driving the motion of a ion. The electric force,
F
φ
, is due to any difference
in potential (
φ
) between the inside and outside of the cell. Remember that potential differences arise
because there are different amounts of charge on either side of the membrane. The potential is therefore
due to
all
of the charges, whether they are able to cross the membrane or not. The chemical force,
F
C
,is
due differences in
specific
ionic concentrations (
C
) across the membrane and will act only on a single
type of ion (e.g., dot or circle in Fig. 2.7). It is because
F
φ
is a function of all charges and
F
C
is a function
of only a specific ion that the membrane can support a nonzero rest potential.
2.4.2 AHeliumBalloon Analogy
An alternative way to think of the balance of two forces is using an analogy to a Helium balloon. There
are always two forces acting on the balloon: gravity pulling the balloon downward and, because Helium
gas is less dense than air, an upward buoyant force. When the balloon is first bought it is full of Helium
gas that will not easily pass through the balloon and the buoyant force is much stronger than the pull of
gravity. Therefore, the balloon will tend to sail into the air. As the balloon sails higher, however, the air
