Biomedical Engineering Reference
In-Depth Information
where
01
V
þ
10
a
n
¼
0
:
V
þ
10
10
e
1
80
b
n
¼
0
:
125
e
V
¼
V
rp
V
m
V
rp
is the membrane potential at rest without any membrane stimulation. Note that
V
is
the displacement from resting potential and should be negative. Clearly,
is a time-
dependent variable, since it depends on Eq. (12.43), and a voltage-dependent variable, since
n
G
K
depends on voltage because of a
n
and b
.
n
Sodium
The sodium conductance waveform in Figure 12.26 is described by a rise to a peak and a
subsequent decline. These aspects are included in a model of
as the product of two func-
tions, one describing the rising phase and the other describing the falling phase, and modeled as
G
NA
¼
G
Na
m
G
Na
3
h
ð
12
:
44
Þ
where
G
Na
Na
þ
conductance, and
are thought of as rate constants and
given as the solutions to the following differential equations:
is maximum
m
and
h
dm
dt
¼
a
m
1
ð
m
Þ
b
m
m
ð
12
:
45
Þ
where
1
V
þ
25
a
m
¼
0
:
V
þ
25
10
e
1
18
b
m
¼
4
e
and
dh
dt
¼
a
h
ð Þ
1
b
h
h
ð
12
:
46
Þ
where
20
a
h
¼
0
:
07
e
1
b
h
¼
V
þ
30
10
e
þ
1
Note that
m
describes the rising phase and
h
describes the falling phase of
G
Na
. The units for
the a
i
0
s
0
in Eqs. (12.43), (12.45), and (12.46) are ms
-1
, while
and b
s
n, m,
and
h
are dimension-
i
less and range in value from 0 to 1.
