Biomedical Engineering Reference
In-Depth Information
for the node of Ranvier. The structure in Figure 12.33 can be modified for any number of
compartments as appropriate. The soma can be modeled as an active or passive compart-
ment depending on the type of neuron.
To model the neuron in Figure 12.33, Kirchhoff's current law is applied for each compart-
ment (i.e., each line in Eq. (12.49) is for a compartment), giving
0
...þ
C
m
dV
m
(
V
m
V
TH
Þ
R
TH
(
V
m
V
m
Þ
dt
þ
þ
R
a
0
0
0
00
þ
C
m
dV
(
V
m
V
TH
Þ
R
TH
(
V
m
V
m
Þ
m
dt
þ
þ
R
a
ð
12
:
49
Þ
00
00
00
000
m
Þ
þ
C
m
dV
(
V
m
V
TH
Þ
R
TH
(
V
m
V
m
dt
þ
þ
R
a
000
m
E
l
þ
G
Na
V
þ
V
000
m
þ
C
m
dV
000
m
E
K
000
m
E
Na
þ
G
K
V
dt
þ...
R
l
Because neurons usually have other channels in addition to the three of the squid giant axon,
a model of the neuron should have the capability of including other channels, such as a fast
sodium channel, delayed potassium conductance, high threshold calcium conductance, and
so forth. Additional ion channels can be added for each compartment in Eq. (12.49) by adding
X
n
1
G
i
V
m
E
i
ð
Þ
i
¼
for each compartment for channels
i
¼
1,
n
. The values of
C
m
,
R
TH
,
R
a
, and
G
i
are depen-
dent on the size of the compartment and the type of neuron modeled.
A complete model of the neuron can be constructed by including as many dendritic
branches as needed, each described using Figure 12.17 and each modeled by
0
0
0
0
00
...þ
C
m
dV
m
(
V
m
V
TH
Þ
R
TH
(
V
m
V
m
Þ
þ
C
m
dV
(
V
m
V
TH
Þ
R
TH
(
V
m
V
m
Þ
m
dt
þ
dt
þ
þ
þ
þ ...
R
a
R
a
ð
12
:
50
Þ
a soma with passive or active properties using either
0
C
m
dV
m
(
V
m
V
TH
Þ
R
TH
(
V
m
V
m
Þ
dt
þ
þ
ð
12
:
51
Þ
R
a
or
000
000
þ
V
m
E
l
þ
C
m
dV
m
000
000
G
K
V
m
E
K
þ
G
Na
V
m
E
Na
ð
12
:
52
Þ
R
l
dt
and an axon using Eq. (12.49) as described in Rodriguez and Enderle [3]. Except for the ter-
minal compartment, two inputs are needed for the dendrite compartment: the input
defined by the previous compartment's membrane potential and the next compartment's
