Biomedical Engineering Reference
In-Depth Information
Outside
R
TH
I
m
C
m
V
m
-
V
TH
+
Inside
Outside
R
Na
R
K
R
Cl
V
m
I
m
C
m
-
-
-
E
Na
E
K
E
Cl
+
+
+
Inside
FIGURE 12.28
Na
þ
are
represented using the variable voltage-time conductances given in Eqs. (12.42) and (12.44). The passive gates for
Na
þ
,
K
þ
and
Circuit model of an unmyelinated section of squid giant axon. The channels for
K
þ
, and
Cl
are given by a leakage channel with resistance,
R
l
, and Nernst potential,
E
l
. The
Na-K
pump is
not drawn for ease in analysis, since it does not contribute any current to the rest of the circuit.
during an action potential, four differential equations (Eqs. (12.43), (12.45),
(12.46),and(12.47)) and six algebraic equations (a
i
0
s
To find
V
m
0
in Eqs. (12.43), (12.45),
and (12.46)) need to be solved. Since the system of equations is nonlinear due to the
n
and b
s
i
4
and
3
conductance terms, an analytic solution is not possible. To solve for
,itis
therefore necessary to simulate the solution. There are many computer tools that allow
a simulation solution of nonlinear systems. SIMULINK, a general purpose toolbox in
MATLAB that simulates solutions for linear and nonlinear, continuous, and discrete
dynamic systems, is used in this textbook. SIMULINK is a popular and widely used sim-
ulation program with a user-friendly interface that is fully integrated within MATLAB.
SIMULINK is interactive and works on most computer platforms. Analogous to an
analog computer, programs for SIMULINK are developed based on a block diagram of
the system.
m
V
m
