Biomedical Engineering Reference
In-Depth Information
Solution
By conservation of mass,
K
½
i
þ
K
½
o
¼
500
Cl
½
i
þ
Cl
½
o
¼
1000
and space charge neutrality,
K
½
i
þ
¼
Cl
½
i
500
K
½
o
¼
Cl
½
o
From the Donnan equilibrium,
½
K
þ
o
½
K
þ
i
¼
½
Cl
i
½
Cl
o
K
½
o
Cl
½
o
Substituting for
and
from the conservation of mass equations into the Donnan
equilibrium equation gives
500
½
K
þ
i
½
K
þ
i
½
Cl
i
1000
¼
½
Cl
i
Cl
½
i
and eliminating
by using the space charge neutrality equations gives
500
½
K
þ
i
½
K
þ
i
½
K
þ
i
þ
500
500
¼
½
K
þ
i
þ
500
¼
½
K
þ
i
½
K
þ
i
1000
500
K
½
i
¼
Solving the preceding equation yields
167 mM at steady-state. Using the conservation of
mass equations and space charge neutrality equation gives
K
½
o
¼
Cl
½
i
¼
333 mM,
667 mM,
Cl
½
o
¼
and
333 mM at steady-state. At steady-state and at room temperature, the Nernst
potential for either ion is 18 mV, as shown for
K
½
:
26 ln
333
E
K
¼
v
i
v
o
¼
167
¼
18
mV
Summarizing, at steady-state
