Biomedical Engineering Reference
In-Depth Information
Compute Currents at node i
Compute
α
s and
β
s at node i
if (i=1)
Update Differential Equations at left boundary
else if (i=last node)
Update Differential Equations at right boundary
else
Update Differential Equations at all middle nodes
end
Save values of interest into an array (e.g.,
V
m
(i)
)
end
end
Store values of interest to a file
Homework Problems
(1) Work out the units for Eqs. (4.13)-(4.16).
(2) Show the steps between Eq. (4.22) and Eq. (4.23).
(3) Show how Eq. (4.24) becomes Eq. (4.23) as
t
→∞
.
(4) Using Eq. (4.24), show that at
x
=
λ
, the time constant,
τ
m
, can be found as 63% of the steady-state
value. Show that at
x
=
0,
τ
m
can be found as 84% of the steady-state value.
=
(5) A passive nerve of radius 50
μm
is stimulated with a current pulse of 10
nA
in the middle (
x
0
.
0
cm
) of and cable. Using the plots below to answer the questions:
a) Find
τ
in
msec
.
b) Find
λ
in
cm
. Start with the full solution to the cable equation.
c) What is the
R
m
in
cm
2
?
(6) In Fig. 4.6:
a) What is the propagation velocity in
cm/s
?
b) Explain what would happen to the spatial distribution if the propagation velocity was slower.
c) Explain what would happen to the spatial distribution be is the propagation direction was
reversed?
d) Explain what would happen to the spatial distribution if the propagation was saltatory.
(7) In Fig. 4.6, assume
a
=
10
μm
, and predict the propagation velocity if
a
is changed to
a
=
13
μm
.
