Biomedical Engineering Reference
In-Depth Information
Differences in specific ion concentrations between the intracellular and ex-
tracellular fluids;
Differences in the membrane permeabilities for different ions, which is re-
lated to the number of open ion channels.
At rest, separation of charges and ionic concentrations across the membrane
must be maintained for the resting potential to remain constant. At times, mem-
brane potential changes in response to a change in the permeability of the mem-
brane. This change in permeability occurs due to a stimulus, which may be in
the form of a foreign chemical in the environment, a mechanical stimulus such as
shear stress, or electrical pulses. For example, when the axon is stimulated by an
electrical current, the Na
+
ion channels at that node open and allow the diffusion
of Na
+
ions into the cell (Figure 3.1). This free diffusion of Na
+
ions is driven by
the greater concentration of Na
+
ion outside the cell than inside [Figure 2.2(b)].
Initially, diffusion is aided by the electric potential difference across the membrane.
As the Na
+
ion concentration inside the cell increases, the intracellular potential
rises from -70 mV towards zero. A cell is said to be depolarized when the inside
becomes more positive and it is said to be hyperpolarized when the inside becomes
more negative. At the depolarized state, the Na
+
ion diffusion is driven only by the
concentration gradient, and continues despite the opposing electric potential dif-
ference. When the potential reaches a threshold level (
35 mV), the K
+
ion chan-
nels open and permit the free diffusion of K
+
ions out of the cell, thereby lowering
and ultimately reversing the net charge inside the cell. When the K
+
ion diffusion
brings the intracellular potential back to its original value of resting potential (-70
mV), the diffusion channels close and the Na
+
and K
+
ion pumps turn on. Na
+
/
K
+
ion pumps are used to pump back Na
+
and K
+
ions in the opposite direction
of their gradients to maintain the balance at the expense of energy. The Na
+
ion
pump transports Na
+
ions
out of the cell against the concentration gradient and
the K pump transports K
+
ions into the cell, also against the concentration gradi-
ent. When the original K
+
ion and Na
+
ion imbalances are restored the pumps stop
transporting the ions. This entire process is similar in all excitable cells with the
variation in the threshold levels.
+
3.2.1 Nernst Equation
The movement of ions across the cell wall affects the membrane potential. To un-
derstand the changes in membrane potential, relating it to the ionic concentration
change is necessary. Consider the movement of molecules across the membrane,
which is driven by two factors: the concentration gradient and the electrical gradi-
ent (Figure 3.1). Analogous to the concentration flux discussed in Chapter 2, (2.8),
electrical flux (
J
electric
) across a membrane with a potential gradient (
d
ΔΦ
), in the
x
-dimension (
dx
) is written as
z
d
z
ΔΦ
J
=−
u
(3.1)
electric
