Biomedical Engineering Reference
In-Depth Information
V
1
V n
Gkbar*u^4
1
Gkbar*n^4
n
GK
Output Potassium Conductance to MATLAB Workspace
V m
Gnabar*u^3
m
2
Gnabar*m^3*h
Product
V h
GNa
h
Output Sodium Conductance to MATLAB Workspace
FIGURE 12.31
SIMULINK program for the
K
þ
and
Na
þ
conductance channels.
10
6
F. Figure 12.23 is a SIMULINK simulation of an action potential. The
blocks Gl*(El-u), Ek-u, and Ena-u are function blocks that were used to represent the terms
G
l
(
and
C
m
¼
1
in Eq. (12.48), respectively.
The stimulus pulse current was created by using the SIMULINK step function as shown
in Figure 12.30. The first step function starts at
E
l
V
m
Þ
,(
V
m
Þ
,and(
V
m
Þ
E
E
K
Na
t
¼
0
with magnitude
K
, and the other one
starts at
t
¼
t
0
with magnitude
K
. The current pulse should be sufficient to quickly bring
V
m
above threshold.
Figure 12.31 illustrates the SIMULINK program for the conductance channels for
Na
þ
and
G
K
n
4
,
G
Na
m
3
,
K
þ
. Function blocks Gkbar*u
^
4, Gnabar*u
^
3, and Gnabar*m
^
3*h represent
and
G
Na
m
3
h
, respectively. The subsystems
n
,
m,
and
h
are described in Figure 12.32 and
are based on six algebraic equations for
a
i
's and
b
i
's in Eqs. (12.43), (12.45),and(12.46).
12.7 MODEL OF A WHOLE NEURON
This section brings together the entire neuron, combing the dendrite, soma, axon, and
presynaptic terminal. Dendrites and axons can be modeled as a series of cylindrical compart-
ments, each connected together with an axial resistance, as described in Section 12.5.3.Both
the axon and dendrites are connected to the soma. Of course, real neurons have many different
arrangements, such as the dendrite connected to the axon, which then connects to the soma. The
basic neuron consists of many dendrites, one axon, and one soma. Note that the dendrite and
axon do not have to have constant diameter cylinders but may narrow toward the periphery.
As described previously, Figure 12.17 illustrates a generic electrical dendrite compart-
ment model with passive channels, and Figure 12.28 illustrates the axon compartment with
active channels at the axon hillock and the node of Ranvier. To model the myelinated por-
tion of the axon, a set of passive compartments, like the dendrite compartment, can be used
with capacitance, passive ion channels, and axial resistance. Shown in Figure 12.33 is a por-
tion of the axon with myelin sheath, with three passive channels, and an active component
