Biomedical Engineering Reference
In-Depth Information
on the temperature—the higher the temperature, the greater the speed of the molecules.
The motion of a molecule is completely random and equally likely to move in any direction.
If the motion is restricted to one axis, the probability of the molecule moving left or right is
equal—that is,
As the molecule
is moving, it collides with other molecules or the compartment wall, and then changes
direction. The collision of one molecule into another molecule involves a transfer of kinetic
energy. Sometimes collisions between molecules cause chemical reactions to occur, as will
be described in a later chapter.
Consider a tube with a thin permeable membrane separating molecules from the right
and left side at
p
¼
0.5. This motion is often referred to as a
random walk.
0, as illustrated in Figure 7.2. As shown, the number of molecules on
the left side is greater than the right side at
t
¼
0. After a period of time, half the molecules
on the left side move to the right and half of those on the right side move to the left. Thus,
there is a net movement of molecules from the left to the right side, since there are more
molecules on the left at
t
¼
.
We call this process simple diffusion. The rate of simple diffusion is impacted by the velocity
of the molecules (temperature) and the number of channels in the membrane. A second
type of diffusion is called facilitated diffusion or carrier-mediated diffusion. This requires the
binding of carrier proteins to the molecule to move through the membrane and may involve
the movement of molecules at rates greater than predicted by simple diffusion.
One typically works with concentrations rather than the number or quantity of molecules
or ions, since measurements are made in concentration rather than quantity. The following
relationship is used in moving between quantity and concentration:
t
¼
0. The number of molecules on each side are equal at
t
¼1
Quantity
Volume
The flow of particles due to diffusion is along the concentration gradient, with particles
moving from high concentration areas to low ones. Physiological compartments are sur-
rounded by membranes. Membranes provide structure, filter molecules and ions entering
and leaving the cell, and control the cell volume. A cell membrane readily allows water,
oxygen, and carbon dioxide to move across it, but prohibits other molecules and ions from
passing through, except through protein channels. For example, a neuron's cell membrane
consists of a lipid bilayer made of phospholipids, cholesterol, and proteins, which separates
ions from the inside and outside of the cell, as shown in Figure 7.3. Cell membranes are
selective, allowing some ions to pass through and not others. Figure 7.3 illustrates the use
of a passive channel that allows only a particular ion to pass through by diffusion and
Concentration
¼
Δ
x
FIGURE 7.2
A tube filled with molecules and separated into two compartments by a thin membrane of width
D
x
0. The membrane has a number of channels that allow the molecules to pass through it. Assume that the
left and right sides of the compartments are of equal volume.
at
t
¼
