Biomedical Engineering Reference
In-Depth Information
The complete solution is
¼
C
2
Kt
V
1
e
10
2
þ
1
c
1
for
t
0. Note that the concentration in compartment 2 is found using Eq. (7.8) as
c
2
¼
V
C
V
c
¼
C
2
Kt
V
1
e
1
10
1
1
10
2
1
V
2
If
V
1
6¼
V
2
, then
V
2
e
K
V
1
þ
V
2
ð
Þ
C
10
t
c
1
¼
þ
V
1
u
ð
t
Þ
V
1
V
2
ð
V
þ
V
Þ
1
2
and
e
K
V
1
þ
V
2
ð
Þ
V
1
C
10
V
t
c
¼
1
V
1
V
2
u
ð
t
Þ
2
ð
þ
V
Þ
1
2
At steady state, the concentrations on either side of the membrane are equal. In fact, if the
volumes of the compartments are not equal, the concentrations at steady state are still
equal. This should also be clear using Eq. (7.6); setting the derivative term equal to zero
gives
). Note, however, that the number of moles of solute will be greater
in the larger compartment.
c
1
(
1
)
¼
c
2
(
1
7.3.3 Osmosis
Solutes and fluids must be maintained within a rigid tolerance in the body, both inside
and outside the cell. Of all substances that move through the cell membrane, the most
plentiful is water. Each second, the amount of water moving in and out of a cell is about
100 times the volume of the cell, with no net movement of water. Osmosis is the process
that drives water across the membrane to maintain a zero water concentration gradient
across the membrane. If the concentration gradient of water is not zero, then osmosis occurs
to force it to zero. Obviously, any net movement of water through a cell membrane causes
the cell to swell or shrink.
The distribution of water and solutes among the body's compartments is regulated by
chemical and physical forces. The chemical potential is a function of concentration, pressure,
and temperature. With regard to water concentration, pure water has a higher concentration
than water mixed with a solute. Consider two compartments that are initially filled with
water and different solute concentrations on either side of the membrane. Further assume
that the membrane is not permeable to the solute. Osmosis causes a net movement of water
along the concentration gradient, from the high concentration side to the low concentration
side until the gradient is zero.
Pressure, defined as a force per unit area, is observed throughout the body for gases and
liquids. The term
used to describe the
force per unit area for solids. When discussing pressure, we talk about a pressure difference
pressure
is reserved for gases and liquids, with
stress
