Biomedical Engineering Reference
In-Depth Information
8.4.1 Diffusion and Biochemical Reactions
Consider the movement of a substrate
A
into a cell by diffusion, which then reacts with
B
to form product
P,
as shown in Figure 8.15
.
Product
P
then leaves the cell by diffusion.
Assume that the quantity of
B
i
is regulated by another system. Let subscript
i
denote inside
the cell, and let
o
denote outside the cell. The chemical reaction is
q
A
i
¼
K
q
A
i
q
B
i
þ
K
1
q
P
i
1
ð
8
:
68
Þ
q
P
i
¼
K
q
A
i
q
B
i
K
1
q
P
i
1
where
K
1
and
K
1
are the reaction rates,
q
A
o
and
q
A
i
are the quantities of substrate
A
,
q
B
i
is
the quantity of substrate
B
i
, and
q
P
o
and
q
P
i
are the quantities of product
P
. Diffusion across
the membrane is given by
q
A
i
¼
C
oi
q
Ao
C
io
q
A
i
q
P
i
¼
D
oi
q
P
o
D
io
q
P
i
ð
8
:
69
Þ
where
are the diffusion transfer rates that depend on the volume, as
described in Example Problem 7.5. The equations describing the complete system (biochem-
ical reaction and diffusion) are
C
oi
,C
,
D
oi
,and
D
io
io
q
A
o
¼
C
oi
q
A
o
þ
C
io
q
A
i
q
A
i
¼
K
q
A
i
q
B
i
þ
K
1
q
P
i
þ
C
oi
q
A
o
C
io
q
A
i
1
ð
8
:
70
Þ
q
P
o
¼
D
oi
q
P
o
þ
D
io
q
P
i
q
P
i
¼
K
q
A
i
q
B
i
K
1
q
P
i
þ
D
oi
q
P
o
D
io
q
P
i
1
Transport of Oxygen into a Slow Muscle Fiber
Consider the delivery of oxygen into a slow muscle fiber. Let's begin at the lung where
oxygen first diffuses through the alveoli membrane into the capillaries and from the capil-
laries into the red blood cell, as shown in Figure 8.16. Let
q
O
A
be the quantity of
O
2
in the
P
o
A
o
Outside
C
oi
C
io
D
oi
D
io
Inside
B
i
P
i
A
i
K
1
K
-1
®
A
i
+
B
i
P
i
FIGURE 8.15
Diffusion and a biochemical reaction.
