Biomedical Engineering Reference
In-Depth Information
and ensures that at the first and last node, Eqs. (4.36) and (4.37) are satisfied.
Combining Eq. (4.34) and the sealed-end, we can write the equation for node 1 as
V
gleft
2
V
m
+
V
m
dt
c
m
−
V
m
r
m
m
dV
m
=
−
(4.40)
r
e
)dx
2
(r
i
−
2
V
m
−
.
2
V
m
dt
c
m
V
m
r
m
dV
m
=
r
e
)dx
2
−
(4.41)
(r
i
−
/HIW(QGRI&DEOH
F
L
U
L
U
L
F
P
U
P
U
H
U
H
F
H
J
Figure 4.8:
Sealed-end boundary condition.
Other possible boundary conditions for the end of the cable are to allow current to leave (
leaky end
)orto
clamp the voltage (
clamped end
).
4.5 NUMERICALMETHODS: TEMPLATE FORCABLE PROP-
AGATION
In Sec. 2.5, a way of numerically solving a differential equation was outlines. In the active membrane
models, we need to keep track of several differential equations as well as compute rate constants, steady-
state values and currents. Below is a template for how to write a program to solve the active equations.
Define constants (e.g.,
R
i
,R
e
,a,C
m
,
other membrane variables)
Compute initial
α
s and
β
s
Compute initial conditions for state variables
(e.g.,
V
rest
,m,h,n
)
m
for (time=0 to time=end in increments of
dt
)
for (i=1 to i=Last Node in increments of (1)
